A NEW
SCHOOL METHOD

(Complete),

For Pupil Teachers and Students.

JOS. H. COWHAM.

WESTMINSTER SCHOOL BOOK DEPOT, tsa, RORBBFBRHY »0&D, %M,%

Aleo from BIMFKIH, MARSHALL, HAKILTOK, KBMT ft CO., Ltd., STATIOKS^S*

HALL COURT, H.C.

THE LIBRARY

THE UNIVERSITY

OF CALIFORNIA

LOS ANGELES

FIFTH EDITION.

A NEW

SCHOOL METHOD

{.COMPLETE).

Containing in Onk Volume—

Part l.-HOW TO TEACH READING, WRITING, SPELLING AND DRAWING.

Part II.— HOW TO TEACH ARITHMETIC.

Part III.— HOW TO TEACH GEOGRAPHY, GRAMMAR, HISTORY, AND
ELEMENTARY SCIENCE.

Bv JOSEPH H. COWHAM,

Lecturer on Education, Westminstek Traimxg Coi.legr, S.W.,
Author of 'The Princhlrs oj- Oral Teaching •& Mental Thaining,

'School Organization,'

'Graihic Lessons in Physical Cieogratiiv,'

"The .School Joiknev,' &c.

LONnON: WESTMINSTER SCHOOL BOOK

DEPOT, 128, Horseferrv Road, S.W. ; and al.so

FROM SIMPKIN, MARSHALL, HAMH.TON.

KENT & CO. Lii.nTKD, and all Booksellers.

i9«>5. [all rights rfsrkvkp.

Cowham's New School Method.

PUBLISHED IN PARTS.

Part i. How to teach Reading, Spelling, Writing

and Drawing ... Price 1/6

,, ii. How to teach Arithmetic , 1/6

,, iii. How to teach Geography, Grammar,

History and Elementary Science ... ,, 1/6

OPINIONS OF EMINENT EDUCATIONALISTS AND OF THE PRESS.

The Reu. T. W. Sharpe, M.A., C.B., writes: — 'Its lucid style, the
great use made of simple illustrations, and tlic clearness of its pr.ictical
suggestions, are admiiable features.'

A Sub-Inspector of Schools writes : — 'I know of no manual cover-
ing the same ground that is so thorough and practical. I am struck
with its comprehensive scope and its great clearness of style. The book
ought to be of the greatest service to all young teachers, and in fact, to
teachers of any age.'

The Schoolmaster Reviewer says: — 'The author's name is a sure
guarantee of the efficiency of this new book on "school method."
Publishing in three separate parts is a very convenient arr.ingement for
pupil teai hers, in that Part I. supi)lies the needs of the first and second
years; Part II. of the third year; and P.irt III. nf the fourth year.
All whose training in the science ;ind .art of teaching h.is been neglected,
should slmiy this hook preparatory to the Scholarship E.xaiiiinatio>i.'

The. Journal of Education writes /—Mr. Cowh.im, Lecturer on
p]dii(Mtion .at Westminster 1 raining College, sets forth his principles
clearly and with sulVicient fulness, .and applies them carefully and with
adequ.'ite t.xplan.ition to the subjects with which he has to deal, ll^e
tertainly like the book.'

PREFACE.

I ^HE advance in educational science and the expansion of
-^ the school curriculum have created a demand for
corresponding expansion and advance in school methods.

The ' new education ' asks for training as well as instruction,
and it demands, in future, that training shall be the chief
aim of all teaching.

The object of 'A A'cw School Method'' is to show how
the teacher may combine the highest training with the best
instruction.

The work is the result of nearly 20 years' experience
jn the professional tuition of the student teachers of the
Westminster Training College. It is now presented to the
wider community of pupil teachers and students in the hope
that its lessons may serve to enlighten school work, and may
tend to make school methods more scientific and successful.

The introduction of numerous illustrations throughout the
various sections of the book will, it is hoped, help to
elucidate the text, and at the same time serve to present
a method of instruction which needs development.

The work has been divided into three complete sections, each
of which is published separately. This arrangement is intended
to facilitate the use of each book as a class manual.
A volume is also published embracing the entire work.

JOSEPH H. COWHAM,

Westminster Trainimu

"8§4^49

CONTENTS OF PART I.

PAGE

READING 1-63

Aims and Difficulties of Reading i — 9
First Lessons in Reading ...9—28

The Alphabet

The Alphabetical Method
The Phonic Method

The Phonetic Method 16

The Look and Say Method ... 17

The Combined Method at

Word building 23 — 25

Good Reading— Junior Stage 28—36
Pronunci.ition ... ... ... 29

Fluency and Ease... .. ... 33

Simultaneous Re.iding ... ... 35

Draft and Silent Reading ... 36

Reading in the Upper Classes 37—48

Development of Intelligence ... 37

Emphasis and Pause ... ... 39

Expression and Feeling ... .. 42

Explan.-ition of New Words ... 45
Contrast between Lower and

Higher Stage <if Readini; ... 48

Reading Books 49

Home Reading and School
Libraries ... 51

The Practice of Reading 52—56

Specimen Notes of a Reading
Lesson 57

Questions for Examination ... 61

Additional Notes on Reading ... «>;

SPELLING 65-75

Objects of Teaching 65

Difficulties of Tc.iching 65

A .Memory Exercise .. ... 66

When should be MasterctI ... 67

Methods of Teaching

Dictation

Spelling Reform

Rules of the Department

WRITING

V.alues of Teaching
Method of Teaching

(n) Locke

(/') Mulhauser
Criticism of Methods

Capital Letters

Class 7'. Individual Teach
Writing Appliances
Class Man.'igement
Notes of Lesson ...

DRAWING

Aims at Teaching...
Kensington Course

Standards I. and II.

Criticism and Suggestions
Standard III

Tlu- 1 >rawing of Curves ..
Writing .mil Drawing

Standards IV. and V. ..
Lesson — Dr.iuing to .Seal
Model Dr.iwing ...
The Gl.ass Pl.ine ...

Standards VI. and VII.

.Solid (iionietry ...
Notes of Lessons ..
Opinion of Experts

Modelling

Questions

Additional Notes

!•.^^.K

... 68

... 70

•• 75

76 — 96
76
77
77

83
86

87
90

9'
94

97-

-124

97
98

lo.^

104

105

109

109
1 10
1 12

'13
"•5
120

122
124

ii6

COiNTENTS OF PART II.

Introductory-
Code Requirements
Practical Course ...
Twofold Aim

Notation and Numeration

Place Values

Notation Groups

Simple Addition

Simple Subtraction ..

By Decomposition
By Equal Additions
Proving Sums

Simple Multiplication

Tables

Stages in order

Simple Division

Place of Long Division .,

Mental Arithmetic ..

The ' Alternative Course '
Art versus Science ...

129
131
133

Numbers— Concrete & Abstract 135

137

139
140

141

146

147
149

153

154

155
156

159
165
166

i6v

171

Compound Rules —

Addition ...

.Subtraction

Multiplication

Division

Reduction— Money

Weiglitb and Measures ...
Decimal and Metric Systems
Practice

I'AGK

. 174

. 178

. 180

. 184

. 186

. 191

Rule of Three -

Unitary Method

... 203

Proportion ...

... 20s

Measures and Multiples ...

... 211

Vulgar Fractions

... 214

Decimal Fractions

... 226

Advanced Rules

— 233

General Rules of Teaching

... 240

Class Management

... 242

Questions

... 245

Additional Notes

•• 247

CONTENTS OF PART III.

PAGE

GEOGRAPHY 249—302

First Lessons — Home Geo-
graphy 250—263

The Starting Point 250

Plans 251

Mariner's Compass 25"

Relief Model and Sketch Map... 258
Suitable Occupations ... 257 & 260
Geography of Hills and

Rivers 263—270

A Suitable Course 263

Method of Teaching 264

Case of Special Difficulty ... 267

Suggested Order of Teaching ... 268

Geographical Terms ... 270—273

Method of Teaching 27°

Criticism of Method 271

Model and Map— Both Helpful 272
Geography of England and

Wales 273—287

Text-book Order Faulty ... 273

The New Method of Teaching 276
Suggested Course of Lessons ... 277
General Build of Country ... 278

Raised Model 279 & 281

Drainage Areas 280

Natural Sections 282

Climate and Soil 283

Mining and Manufactures ... 283
Commercial Geography ... 284

Political Geography 285

Geography— Starting Point of

History . ... 287

Geography and other School

Studies 28S

Shape, Size, and Motions of the

Earth 29°

Excursions and Museums ... 296

Mental Training 298

Notes of Lesson 301

THE TEACHING OF

ENGLISH 303—338

Language an Inheritance, &c. 303
Position of Grammar in a

School Course 305—307

Nature of the Study 305

.Suited to Upper Classes 306

Should follow Geography ... 307

Speech — How Acquired and

Developed ... . 308—312

Oral Composition 309

Statement to accompany

Acquisition ... ... ... 3'°

.More Advanced Exercises in
Oral Statement 3"

PAGE

The Parts of Speech 312

Method of Teaching by Con-
trast and Comparison ... 315

Inductive Teaching 317

Parsing 319—322

Method of Conducting Lesson... 320

The Deductive Method ... ... 321

Value of Lesson ... ... ... 322

Need of Careful Preparation ... 322

Analysis 322—326

Parsing and Analysis Related ... 323
Analysis Necessary in Parsing... 324

Scheme for Combinin^

and .\nalysis
The Method of Contrast

Parsinij

325
325
326

329

Notes of Lesson

Composition and Paraphrasing

THE TEACHING OF
HISTORY
History and Geography

The Starting Point

Aims of Teaching

Simple Stories

Lives of Remarkable Men
Value of a Selected Period ...

Learning of Dates

Hints on the Higher Teaching

OBJECT LESSONS & ELE-
MENTARY SCIENCE 351-376

Lower Class Work needs

Brightening 351

Aims of the Object Lesson 353— 360

Tr.iiTiing the Observation
.Aw.ikening Interest
The Scholar's .Activity ...
Judgment

339—350

•■• 339
... 340
... 341
••• 343
••• 345
347
349
350

and

353
354

355

Kxerci.se
Reason

Increase of Knowledge ...

Increase in use of Language

Moral Training ...
Courses of Lessons

Their Preparation

How 10 begin the Lesson

Selection and Arrangement of
.Matter

Kaulty .Arrangement

Krom Known to Unknown

Krom .Abstract to Concrete

Nature Study 370—374

Instruction of Infants 375

355
357
358
359
360—369
362
363

363
365
.367
367

HOW TO TEACH READING.

1. Introductory.

' The value of good reading has never been recognised,' says
Mr. Thring. ' Good reading is the first training of the beginner,
the last crowning excellence of the finished master. All skill
of heart, of head, of lips, is summed up in the charmed sound
of noble utterance falling with thrilling melody on the souls of
those over whom a great reader casts his spell.' These words,
written by an experienced teacher, set forth the true nature of
good reading ; they also reveal the complexity and difficulty of
the eff"ort ; and to some extent they explain the reason why
a really effective reading lesson is but rarely heard. It is
assumed too readily that because any one can read fairly w^ell
himself, he is therefore competent to teach reading to
others, and to teach, moreover, with very little or no prepara-
tion. The need, however, for the thorough preparation of a
reading lesson, and for the development of considerable
teaching skill on the part of the teacher, becomes evident
immediately the complex nature of the reading efibrt is realized.
It may be of service to any one who is beginning to teach if we
state at the outset the chief objects of the reading lesson,
together with a brief summary of the methods by which the
skilled teacher strives to secure these objects. In this way we
may best be able to set forth the difficulties which beset the
reading lesson for the scholar, and the need of complete
preparation of the lesson by the teacher.

2. Chief aims of the reading lesson.

These aims may be summed up in the concise phrase ' Good
reading.' Now good reading demands amongst other features
the following, viz. : — (i) the immediate recognition of words as
they occur in written language ; (2) the association of spoken

How to Teach Reading.

sounds with the word-forms, and the correct and distinct utter-
ance of these sounds by the organs of speech ; and (3) the
abihty to take in at a glance the meaning uf a sentence, or a
group of sentences, and, by skilful modulation of the voice, to
interpret and to give expression to that meaning. The
above features of good reading demand full consideration.
Their complete discussion will be found upon subsequent
pages. At present a brief review of each must suffice:—

{a) The immediate recognition of words as they occur in written
language. This recognition includes that of the accurate spelling as well
as that of the general appearance of each word. In the higher branches
of reading it involves furthermore the power both to see and to retain a
considerable number ot words in advance of the voice utterance. This
recognition is vastly aided by good eyesight, by sufficient though not
powerful light, by the adjustment of the book as to distance from the eye
and the angle at which it is held, by clear type, and above all by the
concentrated attention of the reader.

(/') The association of spoken sounds with the word forms, and
the correct and distinct utterance of these sounds by the organs of
speech. The use of the organs of speech in the full and accurate utterance
of spoken words is only acquired after considerable practice. This practice,
in order to be successful, must be made under the following conditions, viz.: —
(i) The imitation of good patterns ; (2) The early exercise of the vocal
organs in the imitation of these patterns ; and (3) The cultivation of a
sense of hearing sufficiently acute to enable the learner to judge when the
sounds are correct.

The above conditions of good reading are exercises for the most part
of a very simple form of memory. It is, however, most important that
these memory exercises should be almost perfectly performed. For, if
the reading effort is to be characterized by ease and fluency, there
must be no hesitation either in the recognition of the words as they
successively occur or in the connection of the proper sounds with the
word-forms.

(c) The ability to take in at a glance the meaning of a sentence
or a group of sentences, and, by skilful modulation of the voice, to
interpret and to give expression to that meaning. This third aim
may be held to be successfully attained when the reader and those who
listen are awakened to the thoughts and are stirred by the feelings which
were originally in the mind of the author. Such a result as this cannot,
however, be realised without considerable activity of mind on the part of
both reader and listener.

Brief Revietu of Methods.

These considerations make it evident that the effort of
reading with inteUigence and ease is one which is both com-
plex and difficult. It involves a highly developed power of
sight in order to secure a rapid survey of words and sentence ;
it demands furthermore a fully developed power of hearing
whereby the reader judges whether the proper modulation of
voice for effective expression is made ; and, finally, it requires
the possession of considerable knowledge, of intellectual bright-
ness, and of a cultivated taste.

3. Brief review of the methods by which a skilful
teacher secures the objects aimed at.

If we watch a skilfully conducted reading lesson we shall
recognise the following as being amongst the most important
conditions of successful effort, viz. : —

(a) A good pattern carefully prepared and well delivered
by the teacher.

This pattern will be the result of a thorough rehearsal of
the matter of the lesson on the part of the teacher. Such a
rehearsal is necessary if the teacher is to possess a complete
familiarity with the words and the thought of the narrative,
and if his pattern reading is to be characterised by ease of
expression. Whilst the teacher's pattern should not be too
highly declamatory, it will be well if it slightly exaggerate both
emphasis and expression. There is but little danger of a pupil
intensifying the teacher's expression ; he is far more likely to
fall far short of it.

The pattern reading of the teacher should not only fulfil the
above conditions, it should also form a very prominent feature
in every reading lesson.

(^) The example of reading by the brighter members of
the class.

Whilst the teacher is careful to make his own pattern reading
a very prominent feature in every lesson, and whilst he must
depend mainly upon it for stimulus to improved effort on the pari,
of his pupils, he must not be unmindful of the great advantage

How to Teach Reading.

which children derive from hearing good reading on the
part of their schoolfellows. Children are great imitators of one
another. Next to the teacher's pattern a few good readers in
a class are the most eflective help in the reading lesson. Good
and indifferent readers should be intermixed in such a way
that the good reading of the brighter scholars becomes a direct
stimulus to the duller pupils, care being taken that the latter
are not discouraged and that the former are not unduly elated
during the competitive exercise.

(f) Imitatiue efiort by the scholars.

This is secured by allowing a succession ot two or three
scholars to read immediately upon the conclusion of the
teacher's pattern. A reading lesson should provide abundance
of actual practice in reading by the pupils themselves. Each
scholar moreover should be animated by the desire to attain
the high standard of his teacher's pattern. The teacher mean-
while must, by means of a thorough preparation of his lesson,
be able to follow the scholar's reading effort so that at its close
he is immediately ready to present, for discussion and comment,
the errors made by his pupil.

A thorough preparation will frequently enable the teacher to
anticipate the more probable errors. It will certainly give him
freedom to look away from his book, and to follow more closely
the reading of his pupils, and will, at the same time, leave him
free to concentrate his attention upon the mistakes they make
and upon the most effective methods of correcting them.

(J) The correction of errors in reading.

In no part of the reading lesson does the teacher need
to be more active than in the ready detection of mistakes,
and in the careful selection of those which will most profitably
bear correction. The practice of allowing scholars to criticise
one another generally results in the enumeration of trivial
mistakes, and often diverts the attention both of the reader
and of the class from more important errors. Immediately
after each scholar has finished reading, the skilful teacher
reproduces one or two of the most important mistakes ; he
follows this exposure of error by a correct reading of his
own, and then, after a little encouragement, prepares the
reader for a fresh endeavour. If a lengthy criticism be given

Reading Lessons must vary in Method.

in which many faults are stated, the scholar is in danger ol
becoming lost in his attempt to follow the teacher, and, as a
consequence, he tries again under the consciousness of his own
weakness and frequently produces a less satisfactory result than
before. Should the reading by the scholar be satisfactory in
all respects, another pupil known to be somewhat weak may
be asked to try to read as well as his fellow pupil.

{e) Additional conditions of successful teaching.

Besides setting a good pattern of reading, and besides
making use of the stimulus afforded by the reading of his
brighter scholars, and, further, besides allowing no really impor-
tant error to pass unnoticed, the teacher must be prepared to
question his class upon the meaning of the difficult passages ;
to call attention to words where spelling is likely to occasion
difficulty, and throughout the entire effort to adopt devices
which practice and skill in teaching suggest for securing and
maintaining the complete attention of every pupil.

/4. Reading lessons must vary in method with the
class under instruction.

Sufficient has now been stated to show the great importance
of reading as a branch of school instruction, as well as to
indicate the difficulties which accompany the attempt to give a
really stimulating and successful lesson. It will be the purpose
of succeeding pages to set out the best methods which experi-
ence has devised for obtaining successful reading throughout
the various stages of school life. The character of the teaching
necessarily changes with the development of the pupil's know-
ledge. At first, effort will be expended mainly upon mastering
the letter- and the word-forms ; the ultimate aim, however, will
be to develop the power of interpreting correctly and expressing
clearly the thoughts and feelings of another. The transition
from the early and almost purely mechanical stage to the later
and highly intellectual effort is a gradual one. The change,
however, must be recognised, and a corresponding change
must be adopted in our methods of teaching.

At the outset it may be well to repeat in a somewhat different form
the truth that reading lessons must not be conducted on any rigid and
fixed plan throughout the entire school course. The nature of tho

How to Teach Reading.

exercise will be found to vary with almost every class, e.g., in the
infant classes the effort is mainly that of connecting verbal forms with
the vocal sounds which have been already acquired, and any serious
attempt at voluntary expression at first will be found entirely out of
place, although the effort to read naturally after the teacher's pattern
should be encouraged as much and as early as possible. In the upper
classes, on the other hand, there ought to be nothing to learn so
far as the sounds requ'red for the correct formation of each word
are concerned. The entire thought and effort of the reader ought in
consequence to be available for the expressive rendering of the
author's meaning. Evidently, therefore, the nature of the exercise
changes with the intellectual condition of the reader, and it is equally
plain that our methods of teaching must be subject to a corresponding
change. One change of method, out of many, may be noted as an
example. Simultaneous reading will be found of great assistance
during the earlier stages of reading, but will not be of much service in
the later ones. This may be made clear by reference to the effort
which children should be encouraged to make to develop an expressive
style of reading. The interpretations of passages read (upon which
the expression must mainly depend) will not be the same for the
entire class. There will, therefore, be considerable variety of expres-
sion. These differences of expression indicate self-effort on the part
of individual readers, and should be encouraged as much as possible.
Anything like simultaneous expression in the upper classes must tend
to discourage the individual's own efforts towards expression, and
must in consequence lead to the development of a niechanical and
monotonous style of reading.

The chief difficulties of reading— whence they arise.

A knowledge of the sources whence the difficulties of
teaching to read arise will prove of great service in any enquiry
into the best methods of overcoming them. These difficulties
are two in number, and may be stated and illustrated in the
following manner : —

I Jhe first difficulty arises from a deficiency of letters
to represent the difi'erent sounds.

in our spoken language there are not less than forty-three
distinct sounds with only twenty-six letters to represent them.
Nor is this all, for it will be found on examination that four of
the existing letters are redundant, e.g. : —

The Chief Difficulties of Reading.

1. The letter C may be represented by either K or S, as in Cat, City.

2. The letter Q, in (2uire, may be represented by KW.

3. The letter W, in ^Fire, may be represented by 00.

4. The letter X, in exile, Exeter, &c., may be represented by either GS or KS-

There are left, therefore, only iwenty-two effective letters
for the forty-three sounds, and as a result of this deficiency it
becomes necessary to make some of the letters stand for more
than one sound.

Examples of letters standing for more sounds than one.

r- I. The letter a has the four following sounds, viz. :
Examples short as in fat, optit as in father.

of s long as in fate, broad as in fall.

Vowels ~ The letter e has the two following sounds, viz. :

^ short as in met, long as in mete.

r I. The letter c has the two following sounds, viz. :
^ I soft as in cite, hard as in command.

I 2. The letter s has the following three sounds, viz. :

Consonants

{a) as in sing, (/') as in sure, (r) as in raise.

The above are only a few examples out of very many which the
student should collect for himself or herself.

2. The second difficulty arises from the same sound being
frequently represented by different letters.

The difficulties arising from the second cause are more
numerous and perplexing than are those which arise from the
first named cause. It is not necessary to enumerate more than
two typical examples of this second cause of difficulty, viz. : —

((?) Vowel example : — The long sound of a, used in the word fate, is
represented by the following letters or letter combinations —

ay in the word ray | ea in the word pear

ey ,, ,, they I ai ,, ,, pair

ei ,, ,, their 1 au ,, ,, gauge

e ,, ,, there j eigh „ ,, neigh

(/') Consonant examples : — The sound of s in ' .-^ing ' is represented by
C in citizen, and the sound of j in the word ' rejoice ' is represented by g in
the words regent and gaol.

The reader may easily multiply examples of inconsistency in the
manner in which both vowel and consonant sounds are represented.

How to Teach Reading.

How the irregularities between the alphabetic sym-
bols and the spoken sounds affect the exercise
of reading.

If a symbol has more than one sound it is evident that as
soon as the learner becomes aware of the fact he will be at a
loss to know which of the various sounds he ought to give the
symbol in any new letter combination. He has learned, for
example, the sound of o in the word go and in the word
on. How is he to pronounce the letter in the word to ? If
he adopt either of the sounds of o previously learned, he will
make a mistake. He must evidently master this new sound as
he mastered the sounds of o in the words go and on, viz., as
a new word-sound. In future he will not read the letter o as a
separate and distinct sound in any of the words quoted above.
The less he thinks about the letter o and its distinct sounds
the better. He will read go, on, and to as distinct and entire
word combinations, and will do his best neither to think about
the letters composing the words nor the different sounds which
these letters possess.

In teaching words of irregular notation like those enumerated
above, it will be best to help the learner in his endeavour to forget
the different sounds of the separate letters and assist him to remember
the sound of the word as a whole. This we shall do if we refrain from
spelling all such words before they are read and if we merely sound
the word as a whole.

Several methods of teaching an English boy or girl to read
have been devised. They are fairly distinct one from the
other. Each method will now be briefly stated and illustrated.
At this stage it will be sufficient simply to enumerate them.
They are : —

1. The Alphabetic Method.

2. The Phonic and Phonetic Methods. /

3. The Look and Say Method.

4. The Combined Method.

The Alphabet.

FIRST LESSONS IN READING.

(A.) The Alphabet

Very little progress is made in any of the methods above
mentioned without gaining at the same time a knowledge of the
alphabet, more or less complete. In the alphabetic and phonic
methods the letters (associated with the names in the former and
the sound in the latter case) are the first consideration. Pro-
gress in both systems is from letters to word combinations. For
this reason both are termed ' Synthetic' The ' Look and Say '
method, on the other hand, deals first with words ; the letters
become known through the practice of reading entire words.
FoT this reason the 'Look and Say' is termed an ' Analytic '
method. Seeing that the alphabet must be learned no matter
what system of teaching is adopted, it will be well at this stage
to consider how it may best be taught.

Formerly the letters were taught by wearisome repetition. In contrast
with the old-fashioned method a much more interesting and effective mode
of teaching may be observed in very many infant schools ot the present
day. Instead of attempting at first to learn the complete alphabet, a few
letters only are mastered. The letters are then combined to form simple
words, and these again are made into easy sentences. The letters of the
alphabet furthermore, are carefully arranged, and are learned by means
of a variety of exercises which tend to render their acquisition easy and
attractive.

The following plan is frequently adopted in teaching the
alphabet : —

1. The form of each letter is printed on the black-board.

2. The scholars make the same fonn by means of sticks or pieces of

cardboard.

3. The letter is then drawn by the scholars on their slates.

lo How to Teach Reading.

4. At each stage the scholar gives either the name or the sound of the
letter.

By these means the form of each letter becomes completely asso-
ciated with either its name or its sound. There is no wearisome and
listless repetition. The making of each letter by a variety of efforts
impresses the shape on the memory. Children, furthermore, like to
affix a name to anything they make, and in this way an interest is
created in the purely arbitrary name of each letter. Lastly, the
exercises of reading, writing, and drawing are so combined that whilst
all are made more interesting, each exercise is more thoroughly
mastered.

The value of the black-board for impressing form, and of a distinct
voice for impressing sound.

The use of the black-board for the purpose of marking each letter in
simple outline is advised at this stage for the following reasons. Young
children watch with great interest anything that the teacher does. This
interest is of the utmost value wherever very young childien have to be
taught. They attempt to write letters or words made on the board in
their presence much more readily than they attempt to copy letters from the
printed page. Along with the form, it is equally important that the teacher
impress the sound of each letter. The effort of distinct utterance may
develop a slightly exaggerated style of enunciation on the part of the
teacher, and this style may sometimes approach what is termed ' pedantry.'
It should be remembered, however, that the teaching of most subjects (and
in none more than the teaching of reading) demands special aptitudes.
For the teacher, therefore, to be slightly pedantic in the eyes of those who
have not to teach need occasion no misgivings.

The old-fashioned associations of the letter A with a picture of an
archer, of B with that of a butcher, &c., are helpful, inasmuch as they
arouse interest. This method, furthermore, associates the form of the
letter with its name, and also its power in a word, but neither the
picture of an archer nor that of a butcher suggests the shape of the
respective letters. The letter O, associated with the picture of an
orange, is a much better combination, because the letter-shape and
that of the object arc nearly the same. There are, however, no
associations so helpful as those which accompany and arouse
the self-activity of the scholars themselves. Hence the value
of allowing children to make the letters with sticks and card-
board, and to draw them on their slates, at the same time that
they utter the sounds.

The Alphabetic Method. Ji

Classification of letters.

The capital letters may be grouped according to their shape. This
grouping is of service where children are encouraged to make the letters by
means of straight and curved strips of cardboard. The following classifi-
cation according to shape may be adopted.

1st class. I L T H F E = straight lines.

2nd ,, A N M W V = straight lines, some oblique.

3rd ,, O C G D Q = curved lines.

4th ,, P B R K = curved and straight lines.

5th ,, U Y S X Z = miscellaneous.

The small letters do not lend themselves so readily to a classification
based upon their form as do the capital letters. It is not at all necessary,
however, that they should be thus taught. Similarity either in the sounds or
in the organ producing them may be used as a basis of arrangement with
good effect. Any form of classification will be better than none. The
following may be adopted as a serviceable grouping : —

1st class, a e i o u. The vowel sounds.

The lip sounds (labials).
The teeth sounds (dentals).
The palate sounds (palatals).
The throat rounds (gutturals).
The hissing sounds (sibilants).*

2nd ,,

b p m V w

3rd „

d t n th.

4th ,,

j ch y r sh.

5th „

g k q h ng-.

6th ,,

c (soft) s z 1.

(B.) The Alphabetic Method.

The chief characteristics of this method are : (i) the thorough
mastery of the names of all the letters of the alphabet, and (2)
the reading of syllables and of short words by first pronouncing
in succession the letters composing them. This method has
become almost utterly discredited, and is worthy of mention
chiefly because of the historic interest which gathers round it.
The following are the chief features in the method : —

I. After the alphabet has been thoroughly mastered the vowel sounds
are in turn associated with each consonant. Such combinations
as the following are formed, viz., ab, eb, ib.

'Arrangement taken chiefly from Prof. Meik'.ejolin's Grammar.

12 How to Teach Reading.

2. The lessons are extended by affixing a consonant either before or

after each of the above combinations, as, e.g., bad, bed, bid,&c.

3. The short vowel sounds are lengthened by the addition of e after

the final consonant, as, e.g., bade, bide, &c.

4. By multiplying such combinations as the above, and by regularly

repeating the letters forming each word before sounding it as a
whole, it is expected that the scholar will in time learn (<?) to
pronounce the words without spelling them, and (/') apply
the knowledge already gained to the mastery of entirely
new^ words.

Criticism of the method.

The following are the advantages (?) claimed for, and the disadvantages
urged against, the Alphabetic method.

Advantages claimed (?). , Disadvantages urgep.

The name-sounds of the
letters composing each word
(when uttered in succession)
sometimes suggest the sound of
the entire word.

The advantages claimed are
almost entirely in favour of spelling
and not of reading. They are
printed in the foot-note.* There is
no reason why advantages of spel-
ling should be placed to the account
of readinsj.

The name-sounds of the letters
when combined do not often
yield the sound of the entire
word.

In many irregular words the
spelling is a positive hindrance
to the scholar's acquiring the
word sound.

The introduction of awkward and
useless combinations of letters
is a waste of time.

The repetition of letter-names
and word-sounds becomes a
very wearying and irksome
task.

(C.) The Phonic System.

This system ignores the names of the letters. It first
separates the sound or the power whicli each letter has in a
word combination, and then unites these into the required
word sound. When using this method the teacher is expected
to spHt up a word into its several sounds. He then presents
each sound along with its symbol or letter, and after the
successive sounds have been repeated separately they are united
into the word-sound. Take the word cat for illustration.
Instead of say'mgsee-a-iee cat, as in the alphabetic method, the

♦ The scholar's attention is constantly being directed to the letters forming each
word. In this way good spelling is secured.

The Phonic System, 13

teacher attempts to isolate each letter sound. He first tries to
sound c as though it were the consonant k sounded very quickly ;
then the letter a is sounded like ah short, and lastly the letter t
is sounded as though the double e were cut off the end of the
sound. Then the three sounds, Ke-a-te, are combined into
the complete word cat.

Mr. Robinson's is the best known phonic method. It attempts to
remove the difficulties arising from the deficiency and uncertainty of the
English alphabet by the following expedients : —

1. Diacritical signs are added to letters having more than one sound

in order to indicate the particular sound used in any given words
For example, the four sounds of the letter a are printed as
follows : —

a as in fat has no mark.

a ,, fare becomes SL.

a ,, far ,, a.

a ,, fall ,, a.

N.B. — •• A are the diacritical marks used in the above instances.

2. Digraphs are introduced wherever more than one letter is used for

a single sound. For example, the word soap is printed s oa p.
The term ' digraph ' is applied to the close arrangement of the
two letters oa having one vowel sound.

3. Silent letters are indicated by italic type. Thus the words trait

and though are respectively printed traiV and thoii^/i.

4. Whispered consonants are printed in light type, whilst the

vocalised consonants are in black type. The whispered s is
simply a Jtiss, as in the word song, whilst the vocalised s is a
buzz, as in the word as. They are both formed by the same
arrangement of lips, teeth, &c., but in the former letter there is
only the hissing of the breath through the teeth, whereas in the
latter there is a voice-sound accompanying the hiss.

Robinson's Phonic Symbols.

In the following table there are sixty-five symbols. Of these thirty-two
are vowel and thirty-three are consonant symbols. The light type conso-
nant letters indicate whispered sounds, and the accompanying black letters
indicate vocalised sounds. The digraphs are all inserted. Bracketed
letters have the same sound.

Holu to Teach Reading.

■tJ

4->

•0

3
0)

■

•v4

-4-> ■

:>>

H-

buO

•^>

J3
u
C

'en

4J
01

<
o

(/]

,„

■ o

(/I •

. -_^

<OT

;Z!-

,r;

" V

> V

V '

a
a.

•0

rt
S

bo
c

►

•«

4->

•0

—

bfl

(hfl

s:
o

G
3

•a

-s:

■+-1

•<^

•■

-c

•"

>»

*
1

— \r

-4->

■3

-4^

■(5

3
rt

rt
01

3
u

soon

first

;

t z

<to

>•

•

V '

(«

irt

;nl

.rt

•a

.b>

-u

-i->

tjO

•♦o

ctj

• -4

•

:3
V '

The Phonic System. 15

A phonic reading lesson in the early stages of teaching
tc read proceeds somewhat on the following plan : —

1. A simple word of two sounds like d ay is written on the board. The

teacher at the same time gives separately the sound of d and of ay.

2. The children simultaneously imitate the teacher, and after a successful

effort to make the two sounds separately, the teacher and children
combine them into the entire word sound, viz., day.

3. The work is now reversed. For example, the entire word is sounded,

and the children are required to make the two component sounds.

4. Finally the teacher exercises the children in silent spelling. This is

done by the teacher placing her mouth in the positions necessary for
sounding successively d and ay, but without making any sound
whatever. She then asks the children to name each sound and also
to say the entire word.

5. Other words follow, like b ay, d ay, g ay, ai m, ai 1, &c. In all

these words the same vowel sound is used.

During first lessons there is always a drilling in the phonic alphabet.
This is followed by exercises in the vocabulary lessons, beginning with
carefully arranged words of two sounds and proceeding to words of three
and four sounds. The vocabularies are arranged so that the teaching of
one word is helpful to learning the next. Thus the words d ie, 1 ie, and
t ie, are taken together. Similarly with words of three sounds. Such
words as pig, big, and wig are taught at the same time, as are also
words like the following, viz., silk, milk ; sti ng, and sli iig. The
learning of these vocabularies is accompanied by exercises n reading
simple narratives in which the sounds already learned are chiefly
employed.

Phonic Reading Books.

The ordinary primer may be made to approach a phonic reading book
by adding the diacritical marks and by putting the pencil through all
silent letters. The digraphs would not appear, nor would the distinction
between whispered and vocalized consonants be shown. The following is
a sample paragraph taken from a phonic reader : —

1. Life is real ! life is earnest ! and the grave is not the goal; dust thou

art, to dust returnest, was not spoken of the so«l.

2. Art is loiig, and time is fleeting, and our h(?arts, though stout and

brave,... still, like muftl^d drums, arc beating, funeral marches to the
grave

How to Teach Reading.

Advantages Claimed for the Phonic Method.

Against the Method.

That it is almost impossible to
isolate the consonant sounds, and the
attempt sometimes leads to stam-
mering.

That it does not meet the difficulty
of those sounds which have many
different symbols to represent them.

That when the vocabulary exer-
cises are prolonged the method
becomes tedious to young children.

That as children are already
acquainted with words in speech,
the early reading lessons should str' rt
with those words which have a mean
ing in the eyes of the learner, and
not with parts of words which
po«:sess no meaning.

Advantages Claimed for the
Method.

That the adoption of the enlarged
alphabet extends the words of regu-
lar notation to 75 P^"" cent., and
leaves only 25 per cent, to be dealt
with by the * Look and Say '
method.

That it effects this without des-
troying the ordinary spelling.

That it is strictly synthetic — the
whole word resulting from sounding
each part in quick succession.

That it secures a good articulation
and enunciation, and does this by
exercising the various vocal organs
in the production of correct letter-
and word-sounds. It does this fur-
thermore at the time when the organs
are growing and are in consequence
better able to be trained.

That, as it directs the attention
of the learner to the parts (letters")
making up each word, it assists
spelling.

That, whilst memory is exercised in
the association of the sounds of the
letters in word combination, there
is the higher power of apjjlying the
knowledge gained to fresh cases.

That in the case of the phonic
method this application of know-
ledge takes place earlier than in other
methods.

That lessons must be carefully ar-
ranged and graduated, and teachers
must be thorouglily trained.

(D.) The Phonetic Method.

This method bears a close resemblance to the phonic. The
sounds or powers of the letters are used and not their names.
A separate letter is, however, jjrovided for each of the sounds
in the language. It diflers, therefore, from the phonic system
mainly in having several totally new letters, e.g. —

1. The .symbol for a in ;;/(/;/ is

2. The symbol for a in tall is

3. The symbol for a in rate is

4. The symbol for a in father is

CAPITAL.

()

r
n

SMALL

o
f.

* The entire Phonetic Alphabet may be studied in Pitman's Primer.

The ^ Look and Say* Method. "^17'

The method of teaching by this method is like that of the
phonic system, and the same arguments, both for and against
the method, may be urged with the following additions, viz. :—

(a) That the new letters give an altered appearance to the printed
matter, so that it looks like a new language to an untrained eye.

{b) That the origin of many words wouki cease to be indicated by the
spelling.

(c) That should the pupil afterwards be taught the ordinary spelling of
words, he must continue to be hampered with the tendency to spell
phonetically. Some shorthand writers make mistakes in ordinary spelling
from this cause.

Specimen of Phonetic Reading Lesson.*

Phonetic Type.

KIURITJ A BLEIND

ELEFANT.

An elefant belogig tu an

Indian ofiser had a di9J_z ov de

ciz, and had bjn bleind for ^rj,

dez. Its erner askt a fizi-

Jan if hj kud dn, enilig for

(le rel^f ov de animal. 3e

doktor sed dat hj woz wilig

tu trei, on wsn ov de eiz, de

efekt ov kostik, a remedi kom-

onli yi^zd for disjzez ov de

liiuraan ei.

Ordinary Type.
CURING A BLIND
ELEPHANT.
An elephant belonging to an
Indian officer had a disease of the
eyes, and had been blind for three
days. Its owner asked a physi-
cian if he could do anything for
the relief of the animal. The
doctor said that he was willing
to try, on one of the eyes, the
eftect of caustic, a remedy com-
monly used for diseases of the
human eye.

(E.) The 'Look and Say' Method.

Each of the methods of ' teaching to read ' already examined
attempts to build up entire word-sounds by a combination of
the different letters composing them. The anomalous and
irregular character of English spelling is the prime obstacle
to the establishment of a purely synthetic method. The
Alphabetic is undoubtedly the least, and the Phonic the most
acceptable of the systems already mentioned. The difficulties
which beset the attempt to reduce many words (and those
frequently the common words such as is, are, one, were,
&c.) to system are, however, so great that neither the use of the
diacritical marks of the phonic method nor the introduction of
the extended alphabet of the phonetic system enables the teacher
to readily surmount them. Fortunately, where the teacher
sees so much difficulty the youthful learner finds but little.

* This specimen is taken from pp. 4 and 5 of Pitman's Phonetic Reading (Transition)
Ejok by special permission.

How to Teach Reading.

The child does not stop to question why the two words one
and were (both of which begin with the same sound) begin
with entirely different letters. The scholar is not troubled with
scruples about the way he should pronounce each word.
Instead of stopping to argue, he accepts the teacher's word.
He sees the group of letters in each case, and associates with
the group its sound.

So long as the exercises in reading are kept to the use of words with
which the child is already familiar in speech, the learner's interest is
sufficient to enable him quickly to associate the most arbitrary word-forms
with the familiar sounds. Taking advantage of the facility which nearly
every child exhibits to rapidly learn the words whose sound and meaning
are already familiar in speech, some teachers have discarded the old-
fashioned alphabetic method entirely, and have not troubled to understand
the new-fashioned phonic systems. They have adopted what has been
termed the 'Look and Say' or 'Chinese' method. Briefly described
this method introduces the child to simple words and sentences
already familiar both in sound and meaning, and by frequently
associating the sound with the word enables the child to recognise
the word, and to give its appropriate sound.

SPECIMEN OF FIRST LESSONS IN READING ON THE
'LOOK AND SAY' PLAN.*

Part I.

Intr educing the five short vcnvels.
These vcnvels are first learned in
'wards. The letters are learned after
the -words and not before.

A cat!

A cat !

Arat !

The rat

is on the

mat.

The rat ran to the hat.
Run, rat ! Run, cat !

The rat is ofT !

Part II.

Introducing short and long voivels
■with double consonants, together with
nnomaloits words. N'o attempt is made
to explain such 'words as 'caught ' he-
cause no explanation suited to a young
child is possible.

The boy has

a bail.

The man sits

on the wall.

Dick had a bad fall.

• •••••

A bird sits on

the rail.

Rain ! rain !

Go away.

The bird is in

the rain.

N.B. — On opposite pages to the printed matter are attractive picture.-
of every object named in the text.

• This specimen is t.ikcn from The New Readers' in Prof. Meiklejohn's series.
I he 'readers' are designed to make the first efforts of reading as attractive and
as easy as possible.

The ^ Look and Say' Method. 19

Criticism of the ' Loof< and Say ' metfiod.

The child is delighted with the quick acquisition of the power to
read an easy book, and apparently makes rapid progress in the art of
reading. It is a general experience that the child learns to read a particular
book by this method much more quickly than by any other. It may not
acquire the power to deal with a new book, or to spell the words of the
old one so readily as by the phonic method. The scholar does, however,
in time no doubt learn to recognise the letters making up the entire word,
although this is not done perfectly at first. The general appearance of the
word is sufficient for reading purposes. And it is after the attention has been
frequently directed to words as w.holes in reading, and to the letters
composing them in transcription and m other spelling exercises, that the
child becomes proficient in spelling. The scholar taught by this system
sometimes confounds words which resemble each other, as, e.g., though
with through, their with there, and of with /^r and //vw.

In reply to the charge that the power of dealing with new words
is of slower growth under the ' Look and Say ' method than under
the Phonic, it may be stated that the ' Look and Say ' method does
in the long run enable the reader to deal with new words. This is
especially the case when the first reading lessons are systematically
arranged. There is no reason why lessons on the ' Look and Say '
method should not be arranged with such a classification of similar
letter combinations as would assist the learner in the attempt to apply
his knowledge to new words. If the first lesson sheet in Prof. Meikle-
john's readers be examined it will be seen that the repeti:ion of the
sound at in cat, rat, mat, and hat prepares the child for dealing
with such words as sat, bat, &c. The danger to be avoided in
preparing such lessons as these is that of presenting a long string of
words of regular and recurring sounds without ? sufficient embodiment
of the new words in simple sentences. When, however, new words
are systematically introduced after the manner described above, and
when the words, as they are learned, are associated with others to make
simple and interesting sentences, the learner gradually and naturally
acquires a knowledge of the powers of letters both singly and in
groups, and finally gains ability to apply his knowledge to new cases.*
For the purpose of strengthening the spelling there is no better
exercise than that of transcription. With reference to the weakness
in enunciation which the Chinese or 'Look and Say' method is said to
develop, it may be stated that the correct enunciation of each part of
the word is dependent almost entirely on the teacher's pattern reading
and the careful imitation of it by the children.

* It should be remembered that the words used in the reading lesson are for the
most part familiar as 'whole .vord-s' in speech. It is natural, therefore, for the child to
leazn the entire word-form which rep-esents the sound it knows already.

How to Teach Reading.

SUMMARY OF ADVANTAGES AND DISADVANTAGES OF
THE 'LOOK AND SAY' METHOD.

Advantages claimed.

1. The method follows the natural

mode of speech. Words are first
spoken and read as wholes.

2. It enables a child to make most use

of its already acquired know-
ledge of words in speech.

3. The child is more interested in

recognising the words it knows
than in uttering sounds of let-
ters which have no meaning.

4. The power to read a particular

book is gained more rapidly by
this method than by any other.

5. There arevery many words which

can be learned by no other
method. These words, more-
over, are largely those of the
child's speech.

Remarks.

Disadvantages urged.

Whilst ability to read a particular
book is rapidly gained, the
power to apply the knowledge
of reading to t/ie new words
of any book is not so rapidly
developed as by the Phonic
method.

Spelling is likely to suffer if the
method be not supplemented
by transcription.

Words of similar form are some-
times confounded.

The method does not specially
lend itself to the acquisition of
a careful and distinct enuncia-
tion.

There is no doubt that the eye in reading is satisfied by a very rapid
glance at the general appearance of the words, and that ultimately we
come to read almost entirely by the ' Look and .Say ' me'-hc^l. It is there-
fore a useful preparation for the final effort of reading that the meiiiod
we use at last should be that which we use all through the course.
Perhaps the strongest plea in favour of the method is lliat it is the most
interesting so far as the child is concerned. Whatever system can claim
the aroused activity and interest of the learner will always be in favour.
The child's power of retention at this particular stage is the intellectual
condition which renders the ' Look and Say ' a very suitable exercise,
.^s for the disadvantages urged against it, the power to master a new
book, or, to put the case in other words, the ability to apply the
knowledge gained to new words, is greatly assisted, if, as has been
stated already, the lesions be properly arranged. The few words
likely to be confounded are very well known, and this danger is easily

The Combined Method. 21

avoided by printing all such words side by side for comparison. The
spelling objection vanishes when transcription accompanies the exercise
of reading, and when it is remembered that the final appeal (so far as
spelling is concerned) is the appearance of the word as a whole. The
difficulty of articulation and enunciation remains and perhaps is the
strongest plea that can be urged against the method. It should be
remembered, however, that children speak distinctly by imitation
mainly of good patterns. No method supplies so great and varied an
exercise in the pattern reading of entire words as does the ' Look and
Say ' method.

(F.) The Combined Method.

It has been shown that each of the methods of teaching
already noticed has advantages which can be urged in its
favour. In consequence, however, of the irregularities in the
sound of the letters and in the mode in which each sound is
represented, it is almost impossible to make use exclusively
of any one system. It is a wise practice therefore for teachers
to select from each method the portions which they approve,

1. To take advantage of the classification of words and syllables of
similar sounds which the phonic and other systems have devised.

2. To make the series of lessons approximate to the phonic method in
maintaining as far as possible one sound for the same letter, and to
repeat that sound in various combinations until it is quite familiar.

3. When difficulties of articulation and enunciation arise, to direct
attention to the position of lips, tongue, and teeth {the Phonic
method).

4. To use the ' Look and Say ' method exclusively in teaching irregular
words such as is, was, were, which, &c.

5. To correct errors in spelling by inspecting the arrangement of the
letters in the word misspelled, and to frequently write the word on
the blackboard for class inspection {the alphabetic method).

The use of the blackboard in teaching to read
words and sentences.

We have come to look upon books and printed sheets as
almost indispensable for the purpose of teaching children to
read. They are undoubtedly of service, especially when they

22 How to Teach Reading.

have been carefully arranged. It should be remembered,
however, that the black-board provides the most effective
method of teaching. The most successful infant teachers use
the board throughout all their earliest lessons— reading primers
and sheets being merely supplementary to black-board work.
The new regulations of the Department make it possible for
teachers of infant schools to follow their own plans in the
methods they devise for the initial stages of reading -the
book being required only when children reach the First
Standard. The following are some of the uses to which
the black-board may be put with advantage whilst teaching
to read, viz.: —

1. Words may be used which are already familiar, both in speech and

meaning. These words may be names of objects either of the school
or of the home, or they may be names of things taught in the object
lessons. These words may further be united into sentences suited to
the knowledge of the class. In this way an immediate connection
between the words read and the ideas they express may be made.
The interest so necessary for success in all infant school work will be
aroused by this method of teaching to a far greater extent than when
lessons (which have little or no connection with the actual life of the
school) are read from a book. This connection of language
lessons one with the other is a most valuable feature in modern
school practice. The exclusive use of a reading book in the
lower classes does not allow the connection to be made either
so readily or so frequently as when the black-board is used in
the way suggested above.

2. The attention of the children may be concentrated upon the letters

forming each word. They see the word grow as it were, letter by
letter, before them. This concentration of mind upon the details ot
each word will prove of high value in both the spelling exercises and
the complete and accurate pronunciation of every part of the new
word.

3. The children may be encouraged to attempt for themselves the writing of

the new words and sentences, after they have seen their teacher pro-
duce them. This imitative activity will be found of the highest value
for securing accurate and full knowledge of the words. Children
learn a word most thoroughly when they construct it, their attention

Word-building. 2 3

being completely concentrated upon the word as a whole and upon
each letter composing it. In this way writing may be taught
simultaneously with reading.

4. The exercise of word-building, suited to the adopted system (phonic

or otherwise), may be regulated to the progress of the pupil.
If, for example, we suppose the word pet to have been taught. It
may be analysed into p-et, and then followed by the word n-et.
The two words may then be combined into the sentence : ' my pet
is in the net.'

5. Lastly, simple diagrams for purposes of illustration may be constructed

to accompany the new words. These will arouse interest and suggest
meaning. If drawing be taught after the reading, the lesson on the
black-board will connect reading with spelling, with writing, and with
drawing. ,

Directions for the construction of a series of first
lessons in reading and word building by means
of black-board and spelling frame.

The freedom to devise a system of exercises in reading,
independently of reading primers and sheets, will undoubtedly
encourage on the part of teachers the greater use of the black-
board in teaching reading and writing. A few hints may
appropriately be given at this stage on the general arrange-
ment which all such lessons should follow. The same hints
apply to the construction of primers and reading sheets, and
where these are used the suggestions will guide the young
teacher in making a selection of them. The general directions
which follow are embodied in a few of the primers and reading
sheets already published. Those by Mr. Langler (for many
years before the public), and the new primers of Professor
Meiklejohn, appear to carry out the directions most completely.
The latter have the addition of abundant illustrations, whereby
every object and every action named is accompanied by an
attractive and suggestive picture.

24 How to Teach Reading.

Directions,

1. Introduce short uoivel sounds joined to such consonants as s, t,

n, &c. Words like it, is, in, as, at, and an will thus be formed.

It is a sound principle in teaching to proceed with one diffi-
culty at a time. There is within the English language a
considerable number of words in which the sounds are fairly
regular. The short vowel sounds are the most regular of all,
and for this reason they should be used first. They furthermore
enter largely into the structure of the short and familiar words.

2. Malie up simple sentences containing the words as soon as

their sounds and meanings are learned, e.g.,

As soon as such words as at, cat, sat, and mat are known,
they should be combined into a simple sentence like the
following : 'the cat sat on the mat.'

J-

Irregular but necessary words lilie the, are, was, and on
should be gradually introduced.

These words are best taught entirely by the ' Look and Say '
method. They are very common words, and hence very
familiar in speech. The frequent repetition of them will lead
to their early recognition.

4. Introduce new consonants as far as possible according to the
organ producing them— labials, dentals, &c.

The classification of the small letters on the basis of the
organ producing them has been given on a preceding page.
This arrangement will assist the learner in clearly distinguishing
sounds like p and b, t and d, &c. All such comparisons will
prove helpful in obtaining correct and clear articulation.

5 Double consonants lilie 11, ck, sh, Ac, may now be introduced
at the beginning and at the end of simple words.

Do not make long lists of words at this stage. Allow the
children to learn a few new words at a time, such as, for
example, ball, fall, wall, &c., and use each word when
learned in a simple sentence, e.t;. : I am on the wall ; there
is my ball ; do not let it fall.

6. Vowels may now be lengthened by the following methods
uiz. : —

(a) By the addition of final e, as fat, fate ; mat, mate.
(,b) By doubling the vowel, as met, meet : bet, beet.

met, meat ; bet, beat.

The Spelling Frame.

Incentive to self-activity.

Along with the examples supplied by the teacher (as in the
above lesson) for imitation there should be frequent appeals
to the children to supply similar word-examples of their own.
At first very little will be obtained from the class. They
naturally shrink from anything like original effort. The
success of one child in an attempt to follow the teacher's
pattern and to produce an original example will be quickly
followed by others. This self-activity must be patiently
encouraged. It is the most fruitful of all school effort.

a ma

Substitute for the black-board. The spelling frame and
how to use it.

Spelling frames are of service where difficulty in using the black-board
is experienced. They lack that vitality of teaching effort which is the
especial accompaniment of all black-board work. A simple form of
spelling frame may be obtained, consisting of a box with twenty-four
compartments.* Two or
three specimens of each
letter, boldly printed
on strong card-board
or on wooden tablets,
should be placed in
their own compartment.
The frame may be used
in the following way : —
The letters making to-
gether the word cat, for
example, may be placed
on a shelf fixed on the
the hd of the box. These
letters may be first placed

apart on the upper ledge, and another set may afterwards be made into
the complete word on the lower ledge. The spelling and the complete
word are thus shown together. After this first word has been sufficiently
taught, the letters b, f, m, p, &c., may be placed in turn before the letter
group -at. In this way an interesting lesson in word-building may be
given. Children should sometimes be asked to suggest a new initial con-
sonant, and be permitted frequently to construct the words themselves.

Spelling frame for word-building

The letter z may be placed with x.

Hoiv to Teach Reading.

Lesson in Word-building for Infant Classes.

PLAN OF LESSON.

1. Preliminary.

It is assumed that such words as 'at' and
'an' have been taught either by the ' Look
and Say ' or the ' Phonic ' method. The
present lesson is designed to extend the
pupil's knowledge by making additions to
these familiar words. A knowledge of
the names of the letters of the alphabet is
also assumed.

2. Ho'w to teach the words —

m -at, c -at, and s -at.

1. Show a picture of a mat. Ask the class
to state its name. Then require one child
to say the word.

2. Now write the word m- at on the board
and ask the class to point out the new
letter.

3. Try to isolate the sound of m, and ask
the children to notice the position of the
lips when making the sound.

4. Deal similarly with the word c-at. Also
with the word s-at.

3. Introduction of simple sentences.

1. Make a sketch of the 'cat on the mat,'
and write on the board the following sen-
tence : The c-at sat on the m-at.

2. Try to obtain from the class the portion
of the three words cat, sat and mat
which is repeated. Thus lead them to
recognise the fact that the first letter i>
the only one which is changed.

4. Other words suggested by the class.

1. As snon as the class recognizes that
words can be made by changing the first
letter they should be encouraged to try
to make other words. They will, perhaps,
suggest h-at, b-at, &c.

2. Make these words interesting by a sketch
drawing, and, if possible, work these up
into sentences, as I have a bat and a
hat.

5. Further use made of the words.

Besides writing the words on the board
and associating the words with pictures
of the things for which they stand and the
sound of each word both isolated and in a
sentence, the children should be permitted
to write each word a few times on a ruled
slate.

Black-board Writing
AND Illustrations.

Separate, at first, the
portion -at from the letters
m, c and s as shown in
the text ; afterwards, write
in the ordinary way.

Fig. 3

Besides writing the
words the scholars might
attempt a drawing of the
bat.

The difficulties should be mastered early. 27

The difficulties of 'learning to read' should be
overcome as early as possible.

If we watch a class of young children learning to read
we find that the effort is mainly one of observation and of
memory. A quick sight sense to take in the word-forms, a
ready ear to distinguish the appropriate word-sounds, and a
retentive memory to keep firmly the association between the
words and their correct sounds, these are the efforts required
for success in first reading lessons. Happily for both teacher
and scholar the power of memory is developed very early,
and during the period when a child is ' learning to read '
the memory is at its best. It should be noticed that owing
to the irregularities of English spelling it is necessary to
learn a very large proportion of our words quite apart from
their resemblances to other words. We teach the word ' city,'
for example, but cannot make use of the knowledge thus
acquired to teach the word ' cite.' Each group of letters must,
for the most part, be learned as a word distinct from other
words, hence the exercises of observation and of memory are
the only forms of effort available at this stage.

It will not be advisable to delay the exercise of reading to too late
a period. The forms which familiar statements assume in books
should be acquired as early as possible for the reasons already stated
and here again briefly reviewed. Observation in the form of sight
and hearing, together with the memory, are very active during
infant and junior school life, and advantage should be taken of
this activity for the purpose of overcoming the difficulties of the
first reading lessons.

The gradual change from the language exercises of the infant school
to the expressive reading in the school for older scholars will be fully
considered in future chapters. It will be sufficient for the present to
indicate briefly the nature of the effort so far as the infant school is
concerned. In the lower divisions of this school, language should be
mainly associated with the observation of objects, with the change
which these material substances may be made to assume, and with the
various ' occupations ' introduced to engage and satisfy the child's
instinctive love of activity. These exercises in simple statements may
be used to develop the power of clear and correct utterance. They
should be mainly conversational in their character, the children being
encouraged to state what they observe whilst the teacher assists by

How to Teach Reading.

shaping their imperfect statements into forms more perfect. The
introduction of nursery rhymes and simple stories will be found helpful
to correct speech at this stage.

GOOD READING:-JUNIOR STAGE.

WHAT IT IS, AND HOW TO TEACH IT.

Introduction.

In previous pages we have dealt with that part of our subject
which may be termed ' learning to read,' so far as the phrase
includes (i) a knowledge of the letters of the alphabet, and
(2) a knowledge of the spelling and pronunciation of simple
words. Our subject changes at this point, not only in the efforts
it demands, but in the processes it requires, and the ends it
secures. In this introductory statement it will be sufficient to
mention the ends aimed at, leaving the efforts and the pro-
cesses required to secure these ends to be gradually unfolded.
The ends in view, in the reading of scholars in our upper
classes, are (i) the full, clear, and accurate utterance of every
word, (2) the interpretation of the meaning of the passage as a
whole so that the thoughts of the author are conveyed by the
voice of the reader, and (3) the fluent and expressive rendering
of the passage read. The first of these features of good reading
is generally summed up in the term ' pronunciation,' the second
is marked out by the term ' reading with intelligence,' and
the last feature properly belongs to the subject of ' rhetoric'

A more detailed analysis of the chief features of good read-
ing is shown in the following tabular statement : —

(a) Pronunciation.

1. Articulation, i.e., the use of the

vocal organs in the production
of the required sounds.

2. Enunciation, i.e., the power of

uttering clearly and distinctly
the different parts of each word
and syllable.

3. Accent, i.e., the differences of

stress placed upon the syllables
of a word.

(/') Intelligence and Expression.

1. Fluency, i.e., the power to re-

cognise words and to convey
their correct pronunciation and
meaning without either haste
or hesitation.

2. Emphasis, i.e., the different

stresses placed upon the words
in a sentence in order to convey
meaning.

3. Expression, i.e., the changes of

tone and rate by which feeling
is conveyed by the voice.

Pronunciation. 29

The terms articulation and enunciation are frequently used in the
same meaning. In the following chapters no distinction will be made
between them. The above tabular statement brings out the fact that
pronunciation is concerned with associating letters and words with
their sounds, and is dependent mainly upon a good memory and a
delicate observation by the senses of sight and hearing. Intelligent
and expressive reading on the other hand deals with entire sentences
and demands the exercise of well-developed powers of intelligence and
feeling. The latter truth will be worked out more fully in future
chapters.

I. Pronunciation*

The correctness of the pronunciation of words depends upon
clear and accurate enunciation, upon the purity of the vowel
sounds, the proper use of the aspirate, and upon the right
placing of the accent.

{a) Enunciation.

A clear enunciation is a marked feature of good reading.
Some children, owing to their early training and to an
inherited ability, acquire very rapidly a good style of
enunciation. There are, however, very many scholars who
come to school remarkably defective in this power of clear,
distinct, and accurate en^inciation. Many of them have formed
habits of slovenly utterance, and considerable patience and
repeated effort are required in order to correct these habits.
Tlie teacher will best correct them by the frequent presentation
of an excellent pattern, and by the correction of mistakes
whenever they are made. It will not be necessary to dwell
further upon the value of the teacher's pattern. A few of the
common mistakes which children make, and which are charac-
teristic of slovenly pronunciation, may prove of service.

(a) The omission of certain letters and the substitution of others.

and is sounded like an
skating ,, ,, skatin

amendments ,, ,, amenments

Picture is sounded like pitcher
insects ,, ,, insex

finds ,, ,, fines

When the same sound is found at the end and beginning respectively of
adjacent words, the effect of omitting one of the sounds is at times very
ridiculous, e.g., ' Take this start ' is sounded like ' Take this tart.'

3o How to Teach Rcadbur.

(l>) The omission and insertion of syllables.

Omission.

separate = sep-rate
generally = gen-rally
regularly — reg-larly

Insertion,
aerated = arcated

minster = minister

mischievous = mischievzjus

These mistakes are best corrected by the teacher writing the entire word
in syllables on the blackboard, and by the children pronouncing each
syllable distinctly after the teacher's pattern until the word is firmly asso-
ciated with its correct sound.

Indistinct utterance is a very common fault amongst country
children. Such children should be encouraged to stand erect, to
expand the chest, to open the mouth, to raise the voice, and, above
all, to read and speak with confidence. Stammering and lisping are
serious faults. The stammerer should always be treated with forbear-
ance. If allowed to read simultaneously with another child, the
stammer will sometimes entirely disappear. Two boys in the same
class who stammered hopelessly when each read separately were
recently allowed to read together. They then read with the utmost
fluency. Lisping may be improved by the construction of a few
sentences in which the ridiculous nature of the error is made to strike
the reader. The boy who persists in saying ' thing ' for ' sing ' will
try not to say ' thing a thong of thixthpenth.' In all these cases a
little private help will prove more effective than frequent correction
before an entire class. The pupil will appreciate the help thus
afforded and will strive to overcome the defect.

(^) Correct vowel sounds— prouincialisms.

The complete and correct mastery of all the vowel sounds is
not an easy task. It has been already shown that each of the
five vowels in the alphabet stands for more than one sound.
The letter a, for example, is dilTerently sounded in each of the
words fate, fat, father, and UA\ ; and the letter o in the state-
ment 'I go on to do my duty' represents several quite distinct
vowel sounds. In this way the number of recognised vowel
sounds may be shown to be largely in excess of the vowel
symbols, and the task of learning all of them correctly is
correspondingly increased. When it is furthermore considered
that by far the larger number of provincialisms (such as, for
example, dye in London, and da-ah in Lincolnshire, for the
sound of the word day) are produced by the incorrect use of
the vowels, the necessity for looking very carefully after the
vowels becomes apparent.

Pronunciation — Accent. 31

(<:) The right use of the aspirate.

The chief difficulty in the use of the aspirate with children
whose speech has been neglected is at first to get them to use it
at all. When this initial difficulty has been overcome it is fol-
lowed by that of preventing them from using it far too frequently.
Th only effective remedy is to make every reading lesson a
special training in the correct use of this much abused letter.
When this practice is followed during a series of years, the
children thus constantly exercised come (notwithstanding the
influence of unfavourable surroundings) to use the aspirate
with creditable correctness and effect.

The few words in which the aspirate is not sounded should be
placed in a prominent position in each class-room. The constant
reference which the public display of this list secures will prove the
most effective method of teaching.

(d) Accent

Every syllable in a word is not pronounced with the same
amount of force. Some syllables are selected for special stress,
whilst others are passed over with the slightest sound effort.
Mr. Sweet, in his Handbook of Phonetics, says ' the variations
of stress are infinite, and in a single sound-group (word or
sentence)* every syllable may have a different degree of stress.
Thus, such a word as " impenetrability " has, roughly speaking,
two stresses, one strong one on the fifth, and a medium one on
the second. But if we pronounce " bility " by itself we shall
find that all three syllables have a different stress, the third
being stronger than the second, and yet, of course, weaker than
the first. In " penetra " there is the. same relation, but all the
syllables are a shade weaker than the corresponding ones in
"bility." The order of the syllables in stress is therefore as
follows, I being the highest : —

327 5164'
im - pe - ne - tra - bi - li - ty.

If the several syllables making up the word be whispered it will at
once be noticed that the syllables are not all taken at the same rate.
Accent may thus be shown to be a variation in pitch, rate, and
intensity of sound. When the complexity of the effort of accent

* Mr. Sweet includes emphasis in ilie ' sentence ' stress.

32 Hmv to Teach Reading.

becomes fully evident, the wonder is that children learn to read with
fairly accurate accent as quickly as they do. The difficulty is increased
when it is remembered that accent frequently changes, e.g., the word
formid 'able is now read for'midable, obliga'tory is now read oblig'atory,
and the word crys'talline is now frequently read crystal'line.

These words are chosen to impress the fact that it is the fashion to
change the accent of words. Some of the above words have but very
recently changed, and others are still in dispute.

\/alue of a well trained ear and voice for securing good
accent.

It has been shown that accent demands the use of a great
variety of sounds. The child hears this variety in the accent of
others. He then strives to reproduce the same variety himself.
Now, whether the effort be that of listening or that of produc-
ing, it is necessarily an effort demanding the activity of the
hearing sense.

An early training of the voice in the reproduction of the
variations of accent is of the greatest value. It is quite as
important that the vocal organs should be exercised in the
production of the varied sounds as that the ear should be
trained to distinguish them. The teacher of a class of young
children must have been frequently struck with the differences
of ability which his scholars manifest in this respect. Both the
vocal organs and the ear are capable of improvement, and the
aim of every class teacher should be to develop the powers
which the children possess to the utmost. The following hints
upon the best methods of cultivating a pleasing and correct
accent should be followed : —

Hints upon the cultivation of a proper accent.

1. Prepare every reading lesson carefully, so that the words likely to

present difficulty in accent receive special attention in the pattern
reading.

2. Provide a slightly exaggerated accent in the pattern reading wherever

difficulty is anticipated.

3. Watch carefully the imitative reading of the scholar, and do not rest

content with the mutual corrections of the children.

4. Require each scholar to listen to the faulty accent in his own reading,

and then to comiiare it willi tlu' cdi rcct accent of the teacher's jmttern.
Children often fail to notice their own slight faults of accent. The
errors need to he exaggerated somewhat by the teacher and to be
placed iu immediate contact with the correct sounds.

Fluency and Ease in Readifig. 33

5. Write the words mis-pronounced on the board with accent marks placed

so as to show both the error and its correction. For example, the
error 'uncultiva'ted should be shown alongside the correction
'uncult'ivated.'

6. At the close of each lesson let a list of all words presenting difficulties

appear with proper accent marks on the blackboard. These should
be preserved by the teacher and at intervals be revised by the
scholars.

2. Fluency and ease in reading.

Fluency is the power to utter freely and correctly the sounds
of a series of words following one another on either the printed
or written page. Any hesitation arising either from failure to
recognise readily a more or less familiar word, or from inability
to apply the knowledge already in possession to the pronuncia-
tion of a new word, is destructive of a fluent style. Fluency
depends upon (a) clearly printed matter, good light and
eyesight ; (/-') a good verbal memory ; {c) a logically arranged
text ; (d) an ability to understand the matter read, and
(e) upon a plentiful exercise of reading. Each of the above
conditions for securing fluent reading demands more detailed
consideration.

{a) Clear print, good light, and eyesight.

The value of new and clearly cut type cannot be over-estimated wherever
the reading of young children is concerned. The effort of reading is so
complex that it becomes necessary that the type should be such as to afford
the utmost assistance. Large type is of less importance than perfectly
haped letters and words correctly distanced. The meaning is often suffi-
cient to suggest the succession of words to an adult, but children do not
anticipate words from the context to the same extent as their elders, hence
the need that the words should stand out clearly on the printed page. A
good light is also of importance during the reading exercise. It is bettei
that the light should not come from the front of the reader, for then the
direct reflection of light from the page becomes wearisome to the eye.
The page should be well illuminated by a side and rather high light.

If the book be held near the eyes on account of insufficient light two
evils arise, viz., (i) there is a strain upon the lenses of the eye in order
to secure a proper focussing of the image of each word upon the retina,
and (2) the eye cannot take in an entire line of the printed page at one
and the same time. The above evils follow also from defective eye-
sight on the part of the pupil.

Ho7v to Teach Reading.

{b) A good verbal memory.

Tlie eye of a fluent reader travels considerably in advance of the voice.
The words thus rapidly noticed by the visual sense are retained in the
memory and reproduced in the order in which they occur. The memory
for words (verbal memory) differs with each reader. Proficiency in any case
can only be obtained by practice. With some, however, a fluent style is
obtained much more readily than with others. The latter will, in most
cases, be found to observe both by eye and ear less acutely, and to retain
by memory less completely, than the former. The slower children should
be provided with as much practice in reading as possible so that both
Ihe observation and the mem Dry of words may be quickened.

{c) The value of a logically arranged text

The same thought may be expressed in a variety of ways. Some authors
are very difficult to read because their thoughts are expressed either in
awkwardly constructed or in long and involved sentences. Simplicity in
the structure of the sentences will prove helpful to the fluency of th^
youthful reader. Great care should be exercised in the selection of a child's
reading book, and wherever the literary style is defective the book should be
avoided even when its other features are attractive.

d) The ability to understand the matter read.

Fluency cannot be expected when the reading is not ' with the under-
standing.' This condition of fluent reading will be fully dealt with under
the heading of 'expressive reading.' It will be sufficient here to state,
that whenever an unfamiliar word looms in the distance the energy of the
pupil becomes concentrated upon this unknown word. Effort which
should be available for the fluent rendering of the passage becomes used up
in the attempt to clear away the difficulty — as a result, hesitancy and a
stumbling manner at once manifest themselves.

If the reading book has been composed with sufficient thought there
should be but few words on any given page beyond the knowledge ot
the reader ; and if the lesson has been carefully prepared by the
teacher all unfamiliar words will be presented to the scholar and all
difficulty will be removed before he attempts to read the passage in
which the unfamiliar words occur.

(e) The plentiful exercise of reading.

This is an all important condition for securing fluency. The practice
of reading aloud so that the vocal organs and the hearing sense maybe
conjointly exercised is the condition best fitted to produce ease and
fluency in reading. How to secure the retjui^ite amount of exercise is a
problem wlrich must be carefully considered. Class instruction, especially

Shmiltaneoiis Reading. 05

where the groups are large, tends to prevent the frequent reading aloud by
individuals. In order to aflbrd sufficient practice some teachers depend
largely upon siimiltancoits reading ; others prefer draft reading, whilst
others again adopt a mixture of individual, simultaneous, and draft reading.
Added to the above modes is that of reading silently. Each of these
methods will be now considered in fuller detail.

Simultaneous reading.

So long as the children are mainly imitators of the pattern
reading of their teacher, simultaneous reading may with advan-
tage be used ; but when there are ability and desire on the part
of the learner to cultivate independent expression, the use of
simultaneous reading must be considerably lessened and the
exercise of individual reading correspondingly increased. The
lower half of the school may with advantage often read simulta-
neously. By this means the scholars obtain more practice
in reading aloud than by any other method. Independent
expressive reading cannot be developed to any considerable
extent at this stage, because the knowledge and thought
necessary for its exercise have not, as yet, been sufficiently
developed. It is well, therefore, to take advantage of the
imitative powers of children at this early period, and to afford
ample oi)portunity for their exercise. This is best done by a
plentiful supply of pattern reading by the teacher, and the
simultaneous imitation of it by the scholars.

The teacher's pattern reading may be imitated by a large class
simultaneously as well as, or even better than by an individual scholar.
Children who hesitate to read with expression when reading alone are
encouraged to make the attempt when they are supported by the
efforts of their fellow scholars and the pattern of their teacher. As
soon, however, as children are clever enough to express in their own
way and by themselves the meaning of an author the simultaneous
reading exercise must largely give place to individual effort. Simul-
taneous reading can never be so conducive to the individual scholar's
expression as it is helpful to his imitation of the expression of the
teacher. It follows, therefore, (i) that simultaneous reading should
be plentiiully introduced into the reading of the junior classes, (2) that
its use should be gradually lessened in the higher classes, and (3) that
it should be rarely heard in the highest division. The best method
of conducting the simultaneous reading ol a large class will be
considered in the chapter on ' Methods of conducting a reading
lesson.'

36 How to Teach Rcaditig.

Draft reading.

This is a device by which many children are exercised in
reading at the same time. In the lower classes draft reading
should follow the simultaneous reading. The children have
had the advantage of the teacher's pattern; they have furthermore
attempted, along with the entire class, to copy that pattern, and
now they have the opportunity of reproducing the same
independently of the teacher.

The following are the weak features of the draft reading, viz., (i) the
monitors who hear the reading are incapable of stimulating their fellow
scholars to make the best of their opportunity, (2) the noise of many voices
encourages a loud and loose style of reading, and (3) the mistakes which
arise are, more frequently than not, allowed to pass uncorrected.

Silent reading.

In the upper classes of a school, where simultaneous and
draft reading are not suitable, the exercise of individual reading
may be extended by allowing the pupils to read silently. This
form of reading calls forth all the intellectual exercises of vocal
reading. The words are seen and therefore their spelling is
strengthened; the thoughts and ideas of the author are realised
in the same way as when the voice accompanies the thought ;
the imagination of the scholar is therefore awakened and his
knowledge is increased. Silent reading is thus seen to be a
valuable school exercise and should be encouraged. It cannot
alone produce fluency, and in this aspect it is not so valuable
as reading aloud.

As silent reading is entirely dependent upon the scholars' self-effort, it
should be introduced into those parts of the school where self-effort is
available. Evidently the upper classes are the most suitable for its
exercise, and in these classes it will be further serviceable in developing a
greater degree of self-effort. Finally, it should be remembered that silent
reading is the form which reading must mainly assume when the scholar
leaves school, and the practice of it in school will prepare for its continuance
in future years.

The Development of the Intelligence. 37

READING LESSONS IN THE UPPER

CLASSES.

INTELLIGENCE AND EXPRESSION,

Introduction.

The qualities of good reading hitherto mentioned are shared
to a greater or less extent by both the junior and the senior
classes. Clear enunciation, correct pronunciation, and a fair
amount of fluency may be expected from young children.
The highest qualities of good reading, however, must not be
expected at a very early age. Reading with intelligence
accompanies the general development of the child's mind.
This highest style of reading demands (i) the development of
the general intelligence in order that there may be the ability to
understand the meaning of what is read ; (2) the possession of
those feelings or emotions which the passage awakens, and (3)
the power to give interpretation to that meaning (emphasis)
and utterance to those feelings (expression) Dy means of the
skilful modulation of the voice.

I. The development of the intelligence.

The first of the demands mentioned above is best satisfied
by the general growth of knowledge and the association of
language in harmony with the knowledge acquired. To this
end object lessons, lessons in geography and elementary
science, together with the observation of things and events as
these occur in daily life, will prove of service. Reading lessons
in geography, history, and elementary science will prove of
especial value because the exercise of language is maintained
in these lessons side by side with the acquisition of knowledge.
The development of the intelligence is not only dependent
upon this growth of knowledge, it is dependent also upon the
gradual unfolding of the higher powers of the mind. In the
early stages of reading it was shown that for the child to read
with fluency it needed a well-trained eye to observe the words
in rapid succession, and an immediate and almost automatic
association of the form of the word with its sound, such asso-
ciation affording for the most part an exercise of the memory.
In the advanced stage of reading, now under consideration, a

^8 How to Teach Reading.

higher kind of intellectual effort becomes needful. This will
be evident if we take the example of a boy reading a passage
from a book of adventure like Rob'mson Crusoe : —

The shipwreck and the landing on the lonely strand are matters which do
not come within the range of the reader's experience. Observation and
memory therefore cannot directly and immediately supply these notions.
We want, however, the scholar to 'read as though the shipwreck and
landing of Crusoe were actual experiences. How does the reader advance
to this required condition of intelligence? Evidently by making use of the
knowledge which he already has. The words ' shipwreck,' ' landing,'
'lonely,' and 'shore' are all more or less familiar. The reader may have
visited the sea-side; if so, the words 'shore' and 'landing' will call up
images in accord with actual experiences. He knows in all probability
what it is to be alone, and he may have seen a picture of a wreck. Out
of these isolated items of observed knowledge the scholar elaborates a
purely mental combination — a new idea, viz., that of the ship-wrecked
Crusoe first stepping on the shore of his solitary abode. The formation of
this new idea has called forth the exercise of something more than
observation and memory. These intellectual powers have undoubtedly
supplied the reader with the material out of which the new idea must be
formed, but the power by which the material supplied by memory is re-
arranged is that of imagination. Here, then, we have a simple example of
the exercise of one of those higher intellectual powers which reading with
intelligence both demands and exercises. Good reading cannot exist apart
from a considerable development of the powers of imagination. To sum
up this part of our subject, it should be plain that in order to read with
intelligence there must first be a broad basis of observed and readily
remembered knowledge ; there must also be the association of this know-
ledge with appropriate language, and there must finally be the ability on
the part of the reader to re-arrange the items of knowledge which the
words suggest, by the exercise of an active imagination. It should now be
evident that the wider the range of observed and remembered knowledge
available for vivid and immediate reproduction, the more completely will
the imagination be able to formulate the ideas which the effort of intelligent
reading demands. A well informed and intelligfent condition of mind
is therefore a necessary preparation for the effort of the higher
style of reading.

The reading lesson is thus seen not only to demand an effort
of the intelligence but also to lend itself to the acquisition of new know-
ledge. Knowledge accpiiied by reading will he found to constitute
a very considerable proportiuii of the stock in the possession of a well
informed pujiil. If we ask ourselves, whenever we are dealing with
any branch of knowledge, how much of this knowledge has come first-
hand and direct, and how much is the result of reading, we shall at

Meanifig of * Emphasis ' a)id ' Pause.* 39

once see that we are very largely indebted to reading. In history, for
example, dealing as the subject does with the facts and events of the
past, or in geography, dealing as this subject does with the range of
facts and events over a wide area of space, how very little is it possible
for us to become acquainted with except through the medium ol
reading and through the exercise of the imagination. In
school work it will be found that the reading lesson supplies the
material by which imagination assists us to acquiie the knowledge
which in both history and geography is far beyond the range of actual
experience. What is true of history and geography may similarly be
shown to be true of other branches of knowledge.

2. Meaning conveyed by the use of * emphasis ' and
* pause.'

In dealing with the pronunciation of words it was seen that
some of the syllables in a word were stibject to greater stress
than the rest, and it was then stated that this variation in stress
gives rise to what is termed ' accent.' There was also seen
to be a considerable variation in the rate in which the different
syllables followed one another. If attention be now directed
from the word to the sentence, it will be found that the meaning
of the latter depends largely upon the way in which stress
(emphasis) is laid upon certain words in the sentence. Fur-
thermore, the meanmg thus conveyed is frequently rendered
more distinct by the use of the ' pause.' The relation in which
emphasis and pause stand to good reading now claims attention.

{a) Emphasis.

When such words as 'to-day,' * I,' 'church,' 'in,' and 'sing
are seen or heard alone, i.e., apart from any context, each word
serves to recall a certain definite notion. When, however, these
words are found in a sentence, such as ' I sing in the church
to-day,' the full meaning given to the sentence as a whole
depends not only on the meaning of each separate word but
also upon the word or words which are selected for special
stress or emphasis, e.g. : — ■
I sing in the church to-day.

Is an intitiiatio)t also tJiat some one else does not,
I sing in the church to-day.

~ Indicates also that sometimes I do other service.

I sing in the church to-day.

Conveys also the notion that sometimes I sing in other place<i
I sing in the church to-day.

Implies also that another day I may sing somewhere else.

40 How to Teach Reading.

It is clear from the above examples that emphasis is closely connected
with the meanings which it is intended to give to the sentence. There are
in fact two meanings conveyed in each of the above expressions. One
common to all four, viz., 'that of singing in the church to-day,' the other
implied and changing with the variation in emphasis. (This second
and implied meaning is printed in italic type beneath each sentence.) It is
also evident that the sentence as a whole must be known, and the particular
meaning to be given to it must be determined before any attempt be made
to apportion the emphasis. In fact, the sentences '_! sing in church to-day,
but you do not ' must be in the mind, and their "elations to one another
determined, before the voice begins to utter the initial and emphatic
word I.

The value of good eyesight, of clear type, of logically arranged
matter, and a well-informed and bright intellect, is abundantly
established when the sum of efforts involved in reading with intelli-
gence and correct emphasis is clearly distinguished. The futility of
attempting to secure simultaneous emphasis on the part ot a large
class of scholars becomes also evident. It would be impossible for
agreement to exist between many readers as to the emphasis to be
put upon all the words in a somewhat long and complex sentence.
The attempt to secure voluntary emphasis amongst a large number
of readers at the same time, must lead at first to confusion, and, if
persisted in, will result in the pupils relinquishing all emphasis which
depends upon thought and in their substituting for it either a
rythmic sing-song or a monotonous chant.

Rules of emphasis.

1. In ordinary narrative the greatest stress is laid upon the object of the

verb. For example, in the sentence

'The boy wrote a letter '
the object 'letter' is the most emphatic word ; the predicate 'wrote'
stands next in order of stress, whilst the subject 'boy' stands third.
The word 'the' and the particle 'a' arc passed over with the least
emphasis.

2. Words and phrases when used to introduce a new idea are thereby

rendered emphatic. For cxami)le, in the sentence (juoted above, viz.,

'The boy wrote a letter, '

if, instead of the word 'letter,' the word 'boy' be made the most
emphatic word, thus: —

'The boy wrote a letter,'

it is evident that the word 'boy' implies more than is stated, viz.,
that in the mind of the speaker there is the further fact thai 'the
girl' or 'the man' did not write a letter.

Aleaning of ' Emphasis ' a7id ' Pause.^ 41

In the following passages the words underlined introduce new ideas,
and hence are emphatic : —

'We'll hear him, we'll follow him, we'll die with him.'

'The third day comes a frost, a killing frost.'
3. Words expressing contrast must be emphasized.

'And this man
Is now become a God ; and Cas^ius is

A wretched creature.'

'Corruption wins not more than honesty. '

ijj) The pause is a most effective device for the display of
intelligence in reading. By its judicious use the reader secures
sufficient time to make out the meaning of a passage in
advance. It serves also to intensify the emphasis and to
conserve the reader's breath. The pause furthermore marks
off the subordinate clauses and adjuncts in each complex sen-
tence. The value ol a knowledge of the logical analysis of a
sentence for the purposes of good reading is now apparent.
The correct use of the pause in fact mainly depends upon the
ability of the reader to review rapidly a group of allied
sentences and their adjuncts, and to classify these into
sentences which are respectively principal and subordinate.
The stops which are ordinarily inserted in the text are no
doubt helpful, but some of the most effective pauses are those
which are inserted where no stop is found. The following
paragraph is marked by spaces to show where pauses may be
inserted with good effect : —

' While I lay musing on my pillow, I heard the sound of little

feet pattering outside the door, and a whispering consultation.

Presently a choir of small voices chanted forth an old

Christmas carol. I rose softly, slipped on my clothes,

opened the door suddenly, and beheld one of the most beautiful little fairy
groups that a painter could imagine. It consisted of a boy and two

girls — the eldest not more than six and lovely as seraphs.'

IVashington Imiiig.

Good phrasing, i.e., the expressive use of the pause, follows the

imitation of good patterns, and the thorough knowledge of the

relationship between the different parts of a sentence — the latter

product being mainly dependent upon practice in analysis. During

42 Hotv to Teach Reading.

first phrasing efforts, it will be well to read lessons already familiar.
The highest form of independent phrasing will however be developed
only by much individual practice upon entirely new matter.

3. Expression and feeling.

Any feeling which moves in the mind may be made to reveal
Itself through the medium of speech. The little child knows
by the tones of its father's voice whether he is angry or pleased,
and learns whilst playing with its companions to express its
feelings in similar tones. There are some feelings which are
more natural than others to the child. The feelings which
belong to child-life are easily expressed in child-speech. The
readmg-lesson should be adapted to the condition of the
reader's mind. If, on the one hand, the reading-lesson be a
simple narration of child experience, it will readily appeal
to the feelings of the child, and we may expect the reader to
adopt the tone of voice suited to the feeling aroused. On the
other hand, if the reading-lesson consist of matter entirely
outside the range of child experience and deal with incidents
and conditions which find no response in child knowledge and
life, the reader cannot be expected to adopt the tone of voice
suited to the required feeling.

{a) Growth of the power of feeling in a child, arid
corresponding change in his reading lessons.

This subject belongs to mental science. A knowledge of it,
however, forms the only safe guide both for the compilation of
a child's reader and for its selection. If the chapters in his
reading book frequently appeal to a feeling of ambition —
involving as this does the apprehension of the effect of remote
influences ; or if they appeal to the feeling of patriotism —
involving a knowledge of history and a love of country, such
chapters are only suited to the capacity of the senior scholars ;
they are entirely unsuited to the minds of little children. But
lessons which appeal to a child's love of the different forms of
animal activity, especially the activity of its home pets ; or which
awaken its social instincts — love of parents and interest in the
affairs of the home ; or which satisfy its rich j^lay of fancy and
love of adventure — all such lessons stir the emotions character-
istic of childhood. These emotions are wonder, curiosity, joy,
sorrow, jiity, &c. Lessons which appeal mainly to these and
allied feelings are suited to the youngest minds.

Expression and Feeling. 43

Prof. Sully, speaking of the exercise of the imagination by means of
reading, says : — 'Descriptions and narrations should increase in length and
intricacy by gradual steps. The first exercises of the imagination should
be by means of short telling narrations of interesting incidents in animal
and cliiid life. Such stories deal in experiences which are thoroughly
intelligible and interesting to the child. The best of the traditional stories,
as that of Cinderella, are well fitted by their simplicity as well as by their
romantic and adventurous character to please and engross the imagination.
And fables in which the moral element is not made too strong and
depressing, and in which the child's characteristic feelings, e.g., his love of
fun, are allowed a certain scope, will commonly be reckoned among his
favourites. As the feeling of curiosity unfolds and the imaginative faculty
gains strength by exercise, more elaborate and less exciting stories may be
introduced.'

John Locke, in ' Some thoughts concerning Education," criticising
the custom of using the Bible as a common reading book, says : —
'For what pleasure or encouragement can it be to a child to exercise
himself in reading those parts of a book wherein he understands
nothing? And how little are the law of Moses, the prophecies in the
Old, and the Epistles and Apocalypse in the New Testament suited to
a child's capacity. And though the history of the Evangelists and the
Acts have something easier, yet, taken altogether, it is very dispropf)r-
tionable to the understanding of childhood. Give me leave,' Locke
continues, ' to say that there are some parts of the Scripture which
may be proper to put into the hands of a child* to engage him to
read ; such as are the story of Joseph and his brethren, of David and
Goliah, of David and Jonathan, &c.'

The remarks of Locke apply to any selections which may be
made for reading lessons in history. Simple stories, like those
of Canute and the flowing tide, the hiding of King Charles in
the oak, King Alfred and the cakes, &c., are suited to the
youngest readers. Biographies of notable men simply related
are suited to the next stage of readers. But the full and com-
plex conditions of national life as these are stated in a complete
historical record should be read only by scholars in the highest
classes. The same principles apply to reading lessons
in natural history and elementary science. First lessons
should consist of striking facts simply related. Advance should
be in the direction of longer lessons, in which the facts admit

* Locke is referring to a child who has mastered a primer and is beginning to read a
book.

44 Hmv to Teach Reading.

of organization and arrangement, until finally the truths, prin-
ciples, and definitions of a particular brancli of scientific reading
should be formulated and stated in connection with the facts
which illustrate them.

{b) Reading with intelligence and expression by means
of the skilful modulation of the voice.

The vocal organs and the organ of hearing are capable of
development. The general conditions of all forms of training
should be observed in any attempt to develop the organs of
speech. They should, for example, be suitably exercised
whilst in the growing stage, and any faulty modes of speech
should be corrected before habits of erroneous utterance have
become established. Teachers of young children and their
parents possess a unique position as voice-trainers. Unfor-
tunately the home and school are not always in accord, and a
mischievous result ensues. So far as the school is concerned,
the following are general directions which experience has
proved of service : —

1. Exercise in the simpler forms of expressive reading should begin as soon

as the first difficulties of reading are overcome.* In order to secure
this exercise, children should be allowed to read passages which
appeal to their own experience. The early reading books should
supply stories and narratives which awaken and satisfy the child's
wonderful play of fancy.

2. I'he teacher's pattern reading will prove helpful both as a stimulus and

a guide. It should be noted, however, that this pattern is imposed
from ivithoiit the child, whereas true expression should be the outcome
of that which is stirring ivithin the child. We must aim at expression
by the child in harmony with its own feelings. This alone will prove
of highest value for training.

3. Assistance in training the voice will be gained by requiring scholars to

speak with expression whenever they answer a question or prefer a
request. The training of the voice by means of singing will also prove
helpful.

4. The pleasure which accompanies the gradual acquisition of the power

to express the various feelings by means of voice modulations will
prove a most helpful stimulus to expressive reading, especially in
the upper classes of the school. This pleasure will increase with
increase ot power. A child is often unconscious of the power it

'Expression in imitation of the teacher's pattern may begin with infant recitations.

Explanation of New and Unknown Words. 45

possesses. The teacher must make it known. He must furthermore
seize the earliest opportunity for its exercise or much valuable time
may be lost. When this pleasurable accompaniment of expressive
reading is experienced it becomes at once a stimulus to self-improve-
ment, and this self-activity (in reading as well as in any other direction
in which it is manifested) immediately becomes the most fruitful of all
educational forces.

In many schools ' a reading ' by the teacher on the Friday aftern®on
to a group of classes or to the entire school is followed by good results.
This exercise by the teacher may be alternated by allowing some of the
scholars to volunteer a reading or a recitation. By these means a
considerable development in power of expression may be rapidly gained,
so that by the time the scholar leaves school he shall have acquired
ability to read with pleasure to himself and with profit to others.

4. Explanation of new and unknown words.

Training to read with intelligence requires the explanation of
all unknown words. It has been stated that the reading-lesson
has a two-fold aim, viz., the extension of knowledge and the
development of intelligence. These aims are not incompatible
one with the other. A clear distinction should be drawn
between a book specially prepared for the exercise of reading
with intelligence and expression, and a text-book designed
chiefly for the extension of knowledge. The same distinction
must be drawn between a ' reading lesson ' and a ' lesson of
information.' A reading lesson is one in which at least {Jths of
the time is devoted to the exercise of reading. If much time
is devoted to explanations, spellings, &c., the lesson becomes
largely one of information. A reading book designed to
develop the art of reading with intelligence should consist of a
series of lessons so graduated that the new words occurring in
any given chapter are few. If the text abound in strange
words the reading must suffer. Valuable additions to the
scholar's knowledge may be acquired and his intelligence may
be exercised without an extensive enlargement of his stock of
words. New words, however, should not be entirely excluded,
and whenever they occur they should be recognised and be
dealt with by the teacher. The following are hints on the
explanation of new words : —

I. If the context suggest an explanation sufficient for intelligent reading,
the fuller explanation may be left until after the lesson. If the word
be entirely outside the reader's range of ideas and if the context afford

46 Ho^v to Teach Reading.

little or no clue to the meaning (a contingency which rarely occurs
in a properly selected book), it is necessary to explain the passage
. before calling upon a pupil to read.

2. New words are sometimes introduced into the pupil's vocabulary to

take the place of other words used in ordinary discourse. Thus the
word 'discourse' may be associated with the well-known word
' speech.' The words seem at first to cover nearly the same area; the
meaning, however, ofthe latter word may readily be shown to cover
much more than the word discourse. In the explanations which
follow, the exact limit of all such new words must be carefully defined.
The ability to set out clearly, by the aid of apt examples, the meaning
of words which are almost synonymous will be a great help at this
stage of the reading lesson.

3. When asked to state the meaning, of a word, children generally answei

by suggesting another word. A teacher lacking in resource will often
refuse the word suggested by a scholar unless it be exactly correct.
He contents himself with simply saying ' No,' and passes to another
scholar for a more correct reply. Instead of this treatment of the
difficulty it would be better to accept the answer in so far as it is
correct, and, by the supply of examples, lead the scholar to the right
meaning.

4. The teacher who acts the part of a dictionary will not greatly benefit his

scholars. He must strive to bring the new word into organic con-
nection with the knowledge already possessed. A question is
frequently sufficient to do this. If, for example, a scholar suggest the
word 'speech 'in place of the word 'discourse,' and the class be told that
' speech ' is used in conversation, in reading, and in continuous oral
statement, whilst the word discourse can only be used in one of them.
For which of these efforts is the word discourse used ? In this way the
chiklren are led to see that a discourse is only one form of speech.

5. A conversation on the matter read.

Besides the extension ofthe reader's knowledge of particular
words, the explanation should supply a review of the whole of
the matter read. By means of a few questions the scholars
may be taken mentally over the imjwrtant features of the
lesson. In this way the teacher will find out whether the new
ideas have been acquired. Such a review will tend to fasten
the new knowledge on the memory so that it becomes an
available basis upon which to found the matter of future
lessons.

It may be well at this point to raise a warning against using a set
of prepared questions on the matter of the lesson. Books arc compiled

Rules for Cultivating Expressive Reading. 47

which supply a series of questions of this kind. The use of all such
questions must wealcen the teacher in the eyes of his class. They
prevent him exercising that intellectual activity which is of the highest
value in any attempt to stimulate activity on the part of his class.
They further hinder the teacher in his efforts to deal with the answers
of his pupils. In order to secure the most fruitful conversational
exercise upon the matter of the reading lesson, the teacher must
possess a vivid picture of the entire scene as it is depicted by the
words of the narrative. Language will then come readily enough
for the purpose of supplying explanatory statements and of formulating
questions.

6. Rules to be observed in cultivating expressive
reading.

It is not necessary nor indeed advisable to laden the exercise
of expressive reading with many rules. An abundance of
practice is much more valuable for the end we have in view
than a multitude of precepts. The following rules, however,
are important, and should be insisted upon : —

I. The rising and falling inflexion {Tone).

So long as the idea conveyed by the words is incomplete the pitch of the
voice should be kept up. When, however, the sense is completed, the
voice should be lowered. Questions are usually finished with a rising
inflexion. Answers, on the other hand, are finished with a faUing inflexion.
The following example will further illustrate what is meant : —

' Paul had never risen from his little bed {falling injlexioii). He lay
there {voice kept up) listening to the noises in the street {Toiie rising)
quite tranquilly {falling inflexion), and not caring much how the
time went {falling inflexion), but watching it {I'oice kept up) and
watching everything about him with observing eyes ' (falling
inflexion).

2. Change of rate is an effective device or conveying variety of
expression. A quick rate is suggestive of an excited condition of mind ; a
slow rate on the other hand accompanies a mournful and depressed state
of feeling. The follo\ving selections from Lord Macaulay's Ivry, a song of
the Huguenots, illustrate both rates of reading : —
(a) The king is come to maashal us, all in his armour dres't,

And he has bound a snow white plume upon his gallant crest.

{ordinary rate)
{l>) He looked upon his people, and a tear was in his eye ;

{slower rate)

How to

Teach Reading.

((■) He looked upon the traitor, and his glance was stern and high.

{faster rate)

((/) Now by the lips of those ye love, fair gentlemen of France,
Charge for the golden lilies— ui'ion them with the lance.
A thousand spurs are striking deep, a thousand spears in rest,
A thousand knights are pressing close behind the snow white crest ;
And in they burst, and on they rushed, while like a guiding star
Amidst the thickest carnage blazed the helmet of Navarre.

{fast rate)

(<■) Ho ! maidens of Venice ! Ho ; matrons of Lucerne,

Weep, weep, and rend your hair for those who never shall return.

{slow rate)

Contrast between the reading lesson of the lower
stage and that of the higher stage.

LOWER STAGE.

1 . The matter of the reading lesson

consists of words— their pro-
nunciation, spelling and mean-
ing.

2. The aim of the lesson is the

correct and full enunciation of
each letter sound, together with
the pure pronunciation of each
syllable and of every word-
emphasis and expression being
obtained mainly by imitation
of the teacher's pattern.

3. The method of conducting the

lesson is by simultaneous imita-
tion of the pattern, together
with plenty of indivilual and
draft reading.

4. The explanations are those of

the new words as these occur
in their several sentences, com-
bined with a general review of
the passage read.

5. The mental efforts arc those ol

observation in readily recog-
ni.Mng the form and spelling of
entire words, and memory in
associating the re<iuired sound
with its word symbol, together
with a concentrated effort oi
attention.

HIGHER STAGE.

The matter of the lesson consists
of sentences and groups of
sentences, whose relationships
have to be clearly expressed.

The aim of the lesson is to
interpret the meaning of the
author by means of voice modu-
lation — reading, that is, with
inteUigence and expression.

r/;enje^/iO(/ of teaching is mainly
that of individual practice aided
and stimulated by thw teacher's
exam])le.

Explanations arc not so much
directed towards fixing the
meaning of individual words as
towards accjuiring the meaning
of entire sentences and phrases,
followed by an exercise in simple
paraphrasing.

The mental effort (in addition
to those of the lower stage)
demands (l) the exercise of an
active imagination in order to
realize the meaning, and (2) the
voluntary expression of feel-
ing ill harmi'iiy with the
Ihnuglit and emotion of the
author.

Reading-books and the Development of Taste. 49

Gradual progress in the aims and methods of reading.

The above comparative statement shows at a glance the
contrast between the aims, the methods, and the intellectual
efforts of the two stages of readmg respectively. The change from
the conditions of the lower to those of the higher stage should
be a gradual one. It follows the gradual development of the
scholar's knowledge and mental power. Begmning with simple
narratives calling forthe exercise chieflyof observation of memory
and of childish fancy, the lessons proceed to descriptions
which utilize the gradually unfolding powers of imagination ; and
finally advance to forms of literature which recognize and
demand the highest conditions of knowledge and of feeling. It
should furthermore be noted that this latest stage cannot be
attained unless there has been the right use of the earlier
stages. If the correct spelling, the exact enunciation and
pronunciation, and the correct meaning of the words be
neglected in the early stage, the loss entailed can never be
thoroughly recovered in the later stage.

Along with the changes in the effort of the scholar there should be
corresponding changes in the methods of the teacher. If the
methods of teaching suited to the early period be continued through-
out, the effect will be to fix a mechanical and stunted style of reading.
Whilst the reading exercises throughout the school require adjustments
suited to the children's knowledge and intelligence, there is one con
dition which remains constant throughout. That condition is the
supply of a plentiful amount of pattern reading by the teacher. So
long as the teacher's pattern is in advance of the reading of his class
that pattern will be the best stimulus to their successful effort. A
word of caution may with advantage be given at this stage. There is
some danger of the reading lesson degenerating into an oral examina-
tion of the meaning and spelling of particular words. If much ot
this is needed either the children are wrongly classified or the reading
book is not wisely chosen. The reading lesson should always be
made primarily an exercise in the practice of reading.

Reading-books, and the development of a taste for
reading.

The code requires two or more sets of readers for each class.
The kind of readers chosen for use in the various classes is of
more importance than the number used. Evidently, if we are to
use the reader primarily to develop the art of reading, and not so
much for the purpose of gaining knowledge, the choice of the

50 Hoiu to Teach Reading.

reading book becomes a matter of prime importance. Two kinds
of readers are clearly required, each determined by the age and
attainments of the scholars. These are (i) those used in the
lower classes where the mechanical difficulties found in the
shorter words of irregular notation are systematically intro-
duced, and (2) those which are specially prepared to cultivate
the art of reading with fluency and intelligence, and to foster a
love of reading for the pleasure the exercise affords and for the
knowledge it provides. Another question should be settled
before finally determining upon a reading book in the higher
classes. The ordinary readers (leaving out of account those
which relate to history, geography, or elementary science) con-
sist for the most part of selections from a variety of standard
prose authors, with ballads and other poetical compositions
interspersed. These selections are especially valuable, both
for the information they supply and the points of literary
excellence they present ; at the same time, the supply of discon-
nected reading material which they contain appears to have
developed a remarkable taste for literary fragments. These
fragments, whilst they occupy the thought, and to some extent
satisfy the desire for reading which the school has aroused,
supply no solid mental food, and develop very little intellectual
power. Reading-books are, however, being provided of another
kind, viz., those containing one or more continuous narratives.
It will be necessary to decide between the relative merits of
these two kinds of reading-books, and in order to do this it
may be well to indicate the special value which the latter form
of reading-book possesses.

Tlic advantages of the continuous narrative arise from the fact that new
matter is introduced in a gradual and natural order, and thus the knowledge
gained in a previous lesson becomes available as a basis of instruction in
the new lesson ; moreover, by continued contact with the characters of the
narrative — their experiences and actions — the pupil's interest is maintained
from lesson to lesson, and thus the feeling necessary for intelligent expres-
sion is. readily awakened ; furthermore, the power to sustain the reading
efibrt over a lengthened period, anil to grasp the relations existing between
an extended scries of associations, is strengthened ; and finally, a more or less
thorough preparation for reading with pleasure and success a complete and
serious work is gained. It may be that the best books will in future aim at
uniting the good features of both readers, leaving the school library and home
reading to stimulate still further the exercise of reading a complete work.*

' Cowham's 'School Organization, '.'ist Edition, 1S91.

Home Reading and School Libraries. 51

The code of 1893 has carried the views expressed in the above
paragraph into practical effect by the following authoritative state-
ment : — ' The chief requisites of a good school reading book are that it
should be written in good Enghsh, that its style and contents should
be calculated to stimulate thought, to be attractive to scholars, and to
establish in their minds pleasant associations with the art of reading.
Though the subjects may be properly varied it is desirable that some
of the lessons should be in a series, and should afford, especially in the
higher classes, means of sustaining the serious interest of the scholars.'

Home Reading". — The ability to read with the under-
standing gives a new power to its possessor. Like other
powers of the body and mind, the abihty to read will be used.
It rests somewhat, though not entirely, with the school to
determine how this almost universally acquired power shall be
exercised. The reading books used in the school (and
especially those which awaken a sustained interest in their
continuous narratives) supply, almost without exception,
reading matter which is both healthy and stimulating. These
books do not now belong to the scholar so much as formerly.
They are the property of the school and as such are kept in
the school. Thus it comes to pass that the reading material
is diminished at a time when the readers are being vastly
multiplied. The scholar is frequently left very much to his
own guidance in the choice of reading matter, and it must not
be surprising if his choice be not always of the best. School
committees and others may do very much to remedy the
threatened evil, by allowing the boys and girls in their schools
to take their readers home with them after the manner of
years gone by, and may still further guide the reading of their
scholars by the establishment of school libraries.

School Libraries should be universal, and the books in
them should be selected so as to provide attractive and
healthy reading. Picture stories and simple fairy tales are the
delight of the little ones. Books like ' Robinson Crusoe ' and
selections of the best tales of Fenimore Cooper, Henty,
and Ballantyne, together with biographies of such worthies as
Faraday, Wellington, Edwards, Lincoln, &:c., are suitable for
older scholars. The encouragement of scholars to take and
read a ' school periodical ' will be accompanied by good
results. The habit of reading thus formed will undoubtedlv
prove a civilising influence of no mean dimensions in the ^
course of a generation.

52 How to Teach Reading.

THE PRACTICE OF READING.
How to Conduct a Reading Lesson.

The general conditions for securing progress in reading have
been explained in previous chapters. It remains for us to consider
the chief divisions of a reading lesson, and the best methods for
the successful teaching of each stage of the lesson. The following
are the prominent divisions of a reading lesson, viz. : — (i) A brief
introduction. (2) Pattern reading by the teacher. (3) Imitation of
the teacher's pattern by the children. (4) The correction of faulty
reading. (5) An explanation of the matter read, together with a
conversation on the general scope of the subject of the lesson.

It will at once be seen that some of the above divisions have already
been disposed of. In all such cases it will be sufficient to refer the
reader to the pages on which the necessary m.ittcr occurs. In a few
cases a certain amount of repetition will be unavoidable.

1. The introduction to a reading lesson.

The .ntroduction should either connect the matter of the lesson
with previous knowledge or should bring a few of the leiding ideas
of the new matter vividly before the minds of the scholars. In the
first case a few questions will generally suffice to bring under
review the knowledge in possession, and in the latter case a brief
statement by the teacher should serve to awaken a desire on the
part of the class to become accpiaintcd with the new matter. When
this desire is aroused the scholars are placed in the best condition
for starting the actual reading of the lesson. The introduction
should in all cases be short, and in order that this short introduc-
tion may be eftective it must be carefully prepared.

The teacher is warned against spending much lime in writing a long
list of words on the board before beginning to read. All new or more
or less unfamiliar words arc best learned in connection with the
reading of the sentences in which they occur. The spelling of hard
words forms a useful exercise after the reading lesson, and all words
presenting difficulties of either spelling or meaning should appear od
the black-board at its close.

2. Pattern reading.

The pattern reading should supply a model of pronunciation, 01
emphasis, and of expression. The amount to be read for imitation
depends entirely upon the efficiency of the class. With children of
ages from six to seven years it will be sufficient to read three or

Imitaiioti by the Children. 53

four words only, but with children of nine or ten a complete
sentence extending over a couple of lines may be attempted ; whilst
with scholars in the upper classes an extended sentence or a short
paragraph may be read. One of the problems calling for tact on
the part of the teacher is to gauge carefully the amount of
matter which it is safe for him to require his class to imitate. This
amount should be sufficient to demand the continuous attention of
the scholars, and at the same time it should not be extended so far
that the children fail to follow and to reproduce the teacher's
pattern.

The teachers who best stimulate effort on the part of the children
exaggerate at times both accent and emphasis, especially when they
have reason to suspect that the scholars will fall short of this necessary
effort. All such exaggeration is open to the charge of pedantry. That
charge teachers can well afford to ignore. It will generally be found
that children hesitate to adopt a free style of expression, and they can
be lured to the attempt only by the slightly exaggerated style of their
teacher. Next to the style of the teacher's pattern is its amount. The
truth that the pattern will do more to give style and finish to the
reading of the class than any other teaching device, cannot be too
deeply impressed. Practice in reading the children must have or they
will not read at all ; a good pattern ought to be supplied if they are to
read well. Hence the necessity for the teacher continuing frequently
to read before his class.

3. Imitation by the children.

{a) In the junior classes— simultaneous reading.

It has already been argued that so long as children are in the
main imitators merely, they may with economy be practised in the
simultaneous imitation of the teacher's pattern. If this portion of
the lesson is to be conducted with best effect the teacher must see
to it that the scholars do imitate. The noise of many voices may
be accompanied by veiy little reading. The best simultaneous
reading is not the loudest. More frequently it is found when the
entire class reads together in a low tone. After the children have
read a few sentences simultaneously, the same sentences may be
read over again without the assistance of the teacher. The prime
condition of success in this part of the reading lesson consists in
obtaining the combined effort of every pupil. The following are
some of the devices which may be adopted in order to secure this
condition of successful effort. The method of conducting the
individual reading will be considered in succeeding paragraphs.

Devices fot securing the simultaneous reading of the entire class.

1. Cause the children to move simultaneously through a few simple
physical exercises, and finish these with that of causing the children
to stand in reading position and to hold their books after the

54 Hoiv to Teach Reading.

teacher's model. It should be observed that the attitude of attention
secured by the above devices may fairly be expected to continue
during the reading effort. On no account should the class begin to
read before the attention of every scholar has been secured.

2. After a time, allow that portion of the class which appears to be
most attentive to resume their seats, and then conduct the simulta-
neous reading in two sections — one reading whilst the other section
listens. In this way a degree of legitimate emulation may be
stimulated. When the standing section satisfies the teacher's require-
ments, the scholars in it may also be allowed to resume their seats.

3. Should the above incentives be without effect the few scholars unaffected
should be challenged at uncertain intervals to read individually. All
such scholars will be well known to an active class teacher. The
knowledge that they must be prepared to read individually unless
they join their companions will, in most cases, prove an effective
stimulus to effort.

{b) In the senior classes — indiuiciual reading.

In these classes the imitation of the teacher's reading should
mainly be by means of individual effort. The reasons for this
are given on pp. 6 and 40. The most difficult problem before
the class teacher during the individual reading is the following,
viz., how to conduct the lesson so that whilst one scholar only
is reading sioud all the other pupils are accompanying by
silent reading. The successful solution of this problem presents,
to view one of the triumphs of the class teachci-'s art. Different
teachers adopt different methods, and the same teacher frequently
changes liis methods. The following are a few of the devices
by which all may be stimulated to join in the reading exercise : —

Devices for securing ttic combined effort of tlie entire class during
individual reading.

1. By the teacher knowing the passage sufficiently well to allow him to
keep a watchful eye over the entire class.

2. By the certainty with which the teacher detects the scholars who
prove inattentive, and by such scholars being summoned to take up
the reading at any point.

3. By not putting too great a strain upon the attention of the good
readers by reason of calling upon a succession of slow and hesitating
readers. Good and faulty readers should be intermixed. The atten-
tion of a class nearly always (lags under the influence of a succcssior
of poor readers.

4. By allowing a limited amount of mutual correction. This device ts
of real service only so far as it serves to maintain the attention of the
class. The criticisms themselves arc frecjucntly worthless ; lliey
should be kept within carefully defmed limits.

The Correction of Faults. 55

5. By sometimes permitting a few good readers to present a model in
place of the teacher.

6. By comparing the reading of portions of the class with other portions,
but not individuals with other individuals. One effort of a scholar
may be compared with another effort of the same scholar, and any
amendment due to the scholar's own effort should be acknowledged.

-"a^

7. By selecting readers from all parts of the class.

4. The correction of faults made by individual
readers.

(a) The teacher's corrections.

These demand the highest effort on the part of the teacher.
Inspectors and others who hear reading lessons know that this
portion of the lesson affords the best opportunity for gauging the
power and skill of the teacher. The pattern reading and the
explanations of words may be prepared so thoroughly that the
teacher knows beforehand all that is required of him. In the
correction of faults, however, there are difficulties which are sprung
suddenly upon him — difficulties of pronunciation, emphasis, and
expression, which he must recognise and correct. In his cor-
rections, furthermore, he needs to be ready to present each fault
side by side with its correction, and during the entire effort he needs
so to present faults and corrections that the scholars recognise the
one whilst they successfully endeavour to make the other.

The need for the ' higher criticism ' of the scholars' reading is one
of the demands of the present day. Trifling errors of pronunciation
are exposed, whilst grave faults of emphasis and expression are left
unnoticed. There should not be an attempt to correct every slip as it
occurs. Only two or three of the more glaring faults should be
corrected at one time. If errors be numerous and much time
be occupied in their correction, the class becomes weary and the
reader discouraged. After correction, it will generally be well to allow
the scholar to read the passage again ; sometimes, however, another
pupil may be called upon to read and to avoid the errors indicated.
It is not well to stop a reader frequently in the middle of his effort,
unless very gross mistakes are made ; and scholars should on no
account be allowed to interrupt a reader by thrusting out their hands
before the teacher requests them to do so.

(d) Mutual corrections.

After the reader has completed the passage, the members of the
class may sometimes be asked to state any mistakes they have
noticed. This form of correction is mainly of value for the
stimulus it gives to the attention of the class. As a rule the

Hoiv to Teach Heading.

criticisms of tlie scliolars are not inucli value, and the teacher
must not depend much upon them. Unfortunately where mutual
correction is encouraged, there is a tendency to rest satisfied with
these criticisms, and thus the 'higher criticism' of the teacher is
not sufficiently exercised.

5. Explanations and general review of the matter of
the reading lesson.

The method of conducting this branch of the reading lesson has
been fully treated on pj). 45-46. With the exception of rare and
totally unfamiliar words, the reading should proceed without
interruptions for the purpose of explanation. There is a tendency
to make too much of the explanation and too little of the
practice of reading. The explanations of the reading sometimes
take the form of an oral lesson on the meanings of words, and at
the close the impression left on the minds of those who have heard
the lesson is that reading by the scholars has been less in amount
than the oral statement by the teacher. After a paragraph has
been read a few questions may be put upon the meaning of words
in the passages, and at the close of the lesson a general review of
the entire narrative may be made. The explanations of the reading
matter will necessarily change with the condition of the class. The
following statement sets out a few of the differences which a teacher
should note in preparing the explanations for a lesson in the Junior
and Senior classes respectively.

FoK Junior Classes.

Provide meanings of chosen
words taken in connection with
the sentences in which they occur.

Introduce examples of the use
of words in a variety of sentences
so that the scholars may be led
to a fuller knowledge of their
meanings.

Prepare illustrations — verba',
pictorial and objective, of new
words.

When words of similar meaning
are suggested, show wherein the
similar words arc alike and
wherein they are dilTcrent in
meaning from the c.riginal word.

Praw attention to the spelling
and pronunciation of unfamiliar
words.

For Senior Classes.

In addition to the methods sug-
gested for junior classes : —

1. Draw attention to the construc-
tion of complex and involved
sentences.

2. Exjilain poetical and figurative
expressions.

J. Criticise the style of composition
and provide simple exercises in
paraphrasing.

4 Appeal to the derivation of words.

5. Make use of the knowledge the
pupils possess of the analysis of
sentences, and arrange poetkal
statements in prose order.

Reading Lesson for Junior Pupils. 57

SPECIMEN NOTES OF READING LESSONS.*

(I.) Notes of a Reading Lesson for Junior Pupils.

Subject matter of lesson :—

THE COAT AND BUTTONS.

f Edward had one day • been reading a fairy tale, * in which * not only

beasts and birds, • but inanimate things, — • flowers in the garden, • and

I teacups on tlie table, • were made to speak • and give an account • of

themselves. • ' I think it would be very funny • to hear my coat speak,' •

said Edward ; • and a moment afterwards • a soft voice * issued from the

bosom • of his coat, " and spoke as follows : — •

/ ' I recollect once growing • on the back of a sheep.' • Edward could

\ not help • starting back with surprise; • however, ' he interrupted him, •

saying, • ' I am afraid, Mr. Coat, • you do not know • what you are

talking about, • for coats do not grow, • nor do sheep wear coats.' • ' I

was only wool • when I grew on the sheep,' * replied the voice, * ' and

\ a very pleasant hfe * we led together, * spending all the day • in the

\ green fields, • and resting at night on the grass.' •
"^^ —

PLAN OF LESSON. HINTS UPON HOW THE PLAN

_, ^. IS TO BE CARRIED OUT.

1. Preparation.

f,j\ TVip mnttpr of tViP Ipsdnn ns ^"^ The teacher's book should be marked

W ine matter ot ine lesson, as lightly with lead pencil to show the por-

tO words likely to be mispro- tions to be read for the scholars' imita-

nounced, and others whose lion. Doublelinesindicatespecialletters

meaning may need explana- forclear pronunciation. Single lines in-

o J r dicate either words to be explained or

nation. words needing special emphasis.

(J>) The class — its arrangement (^) Arrange the class in symmetrical posi-
and supply of material. ''°"' ^"^ see that every boy has a book.

2. Introduction.

Refer to knowledge con-
veyed through the telling of an Contrast the two methods of conveying
interesting story. The matter knowledge. Ask class which method
of the story is true, but the thevprefer,viz.(i) the teacher to state

,_ ti, 4„<-„Uf„;^; tl,„ r^^ffo- the facts, or(2) the coat to be supposed

method of obtaining the matter j^ speak for itself.

is imagined.

* Nofcs of a lesson for the infant stage are printed on an earlier page.

How to Teach Reading.

3. Pattern reading of teacher and

simultaneous imitation by

the class.
Read portions marked off by
dots with clear pronunciation,
and distinct emphasis. The
children to listen in order to
reproduce the teacher's pattern
simultaneously. After the para-
graph has been read in
portions, it should be road
through, for the simultaneous
imitation by the class.

4. Expected difficulties in the

scholar's imitation. (Sam-
ples only.)

{a) The fmal ng in reading
' growing,' &c.

(/;) The final ts in 'beasts.'

\c) The en in ' garden.'

id) Keeping up the voice at the
word.s ' beast,' ' things,"garden,'
& ' table,' in the first paragraph.

\^c) Reading in a slow, subdued
tone ' a soft voice issued from
the bosom of his coat,' chang-
ing to a bright cheerful tone
in the sentence beginning ' I
recollect once,' <S:c.

5. Words and meanings.

((z) Fairy tale... a story related by
an imnginary being.

(l>) Inanimate things ... things
without life.

(() An account of themselues...
telling their own his-
tory; how they be-
came what they arc.
( 77ic akn'c are satnpL-s only taken
from the first parai^raph. )

6. Individual reading and its

correction.

(.;) I Jitlerent scholars to be called
upon to read short portions.

(/') FauUs of pronunciation,
accent, emphasis, and expres-
sion to be pointed out along
with their correction.

(a) When the portions .ire short each

scholar might be required to point to

the place.
(/') Durin;; '.he second lime of reading;, it

would be well to discourage point irig.
((■) If hesitation occur, or if indistinct

utterance, or if false accent or emphasis

be detected, require the .scholars to read

a second time.
(</) Create emulation by permitting' the

left half of the class to read ; then

follow by requiring the right half to

read.
(e) The class should read in a low pitch of

voice.

(a). (/'), (c). Exaggerate the sounds 01 the
final consonants .at first, so .as to catch
t\>e attention of the scholars. If
the class fail to sound these satisfiic-
torilv, repeat until correct. Allow a
scholar, upon whom dependence can be
placed, to read these words. His cor-
rect reading will be more stimulating
than that of the teacher.

(i) .'Xdopt a hif,'hly surprised tone of voice
and expect the class to copy it.

Method of explanation.

(a) -Some tales are true, others .are not. In
this story there arc both the true and
the false. Question .as to what is true
(ihc history of llu- coat) and what is
not true. Ask children if they know the
name given to imagin.ary beings who
are made to tell stories.

(/') Contrast teacups with beasts ; bring
out, by reference to the schol.irs' know-
ledge, th.at teacups .are made .and have
I oleelinp, whilst beasts live .and grow.
.\.I5. — Klowers arc wrongly classfd.

(c) Ask schol.irs to use another word for
'.account.' If imable to do so at once,
.ask a boy to give an account of himself
since he .arose in the morning=history
Contrast with tradesman's account.

1. Mix stfiolars, go d with weak readers.

2. A strong contrast will generally enable
the schol.ir to recognize a fault. Per-
severe until correct, but do not repeat
so often that the clxss becomes weary
of waiting.

Notes of a Portion of a Lesson to Standard VI. 59

{c) The same scholar generally to
attempt to read correctly after
faults have been pointed out.
(Sometimes another may read.)

{d) Mutual correction to be al-
lowed, but kept within narrow
limits. The teacher's own cor-
rections to be considered of
most value.

. Conclusion.

matter read.

4. Allow a scholar to suggest a correction
Do not ask for show of hands until the
scholar has finished reading. Be pre-
pared to make a few corrections but
not many.

The lesson to be completed by a general review of the

2. Notes of a Portion of a Lesson to Standard VI.

•.,A.^-^>V-

SCENERY OF THE TROSACHS.— A> W. Scott.

Subject matter (specimen) ;—

' The western waves of ebbing day
Rolled o'er the glen their level way ;
Each purple peak, each flinty spire, .
Was bathed in floods of living fire.
But not a setting beam could glow
Within the dark ravines below,
Where twined the path, in shadow hid,
Round many a rocky pyramid,
Shooting abruptly from the dell ; - - -

Its thunder-splintered pinnacle.'

Plan of teaching, with hints upon method.

1. Introduction.

Show on the map of Scotland the position of Loch Katrine and exhibit
(if possible) a picture of the lake with its mountainous surroundings. The
class might also be told that the favourite route for tourists is through the
Trosachs. Associate Scott, the Scotch poet, with Scotch lake and border
scenery ; also Wordsworth with Enghsh lake scenery.

2. Pattern Reading-.

(a) Read the first two lines with deliberation.

(d) Emphasise equally the words ' peak and spire,' and contrast with

'the dark ravines below' by reading the latter in a lower and more

subdued tone of voice.
(c) The description of the twining path should be read slowly, and the

last two lines, from 'shooting' to 'pinnacle,' should be re^d more

xJ-«--"

quickly.

6o How to Teach Reading.

3. Imitation of pattern and correction of faults.

{a) Each reader should attempt the whole of the above passajre.

(/') As there is no word of special difficulty, so far as pronunciation is

concerned, the emphasis and expression must be watched carefully,
(r) If the first boy read well, call on a weaker reader to try to read

as well.
((/) Errors of expression (on the lines suggested under pattern reading)

must be watched for. If made, each error should be reproduced along

with its correction.
{/) Mutual correction may be permitted to a limited extent.

4. Explanation.

Phrase for explanation. Method of explanation.

(a) Ebbing day. (") Refer to tide going down. The day

clo>-ing. {Liitt^iinge /igurathe.)
{/') Western waves of. <''') Light travels in w.Tives. Why called

western? The setting sun.
((■) Rolled level way. C*^) Comr.ist with the direction of light at

mid-day, .Thiiost vertical.
((/) Purple peak flinty spire. (</; Tlie tops of the mountains have a

purple hue when seen from a distance.

In some cases the colour i!> due to the

flowering heather.

(e) Bathed living fire. W Compare with clouds, gold-tipped by

° the setting sun. The hill-tops similarly

immersed in a golden light,
(y) The dark ravine below. (/) Kvening light could not enter the

ravine. Why ?

5 Revision.

(i) Allow two or three scholars to read the passage again, and expect

more life and feeling.
(2) Question afterwards upon meaning of phrases.

6. Continuation and end of Lesson.

Continue the lesson in the same fashion throughout the following stanza.

Remaining Hints upon the management of the
lesson.

1. The teacher .should always lake up a commanding position in front of
his cla.ss. He should stand sufficiently far from tlie front row of
scholars to be able to sec distinctly the children at cither end of the
row.

2. He should be sufficiently acquainted with the reading matter to be
able frequently to look away from his book and to survey the entire
class.

3. The class should always be symmetrically arranged before the com-
nicnccnicnl of the lesson, and no ihiid should afterwards be allowed to
remove from the place occuuicH nt the commencement. Sometimes

Questions for Examination. 6i

the teacher should require the entire class to stand, and should allow

portions to sit whenever they give evidence of satisfactory effort.

Individual readers should always stand during the reading exercise.

Each scholar should be provided with his or her own book. * Looking

over ' is a fruitful source of disorder.

In order to secure and keep the attention of the entire class during

either the simultaneous or the individual reading, the following

methods may be adopted, viz. : —

{a) Pointing, so long only as children read short portions and so
long as they are expected only to imitate the teacher. As soon
as children are able to attempt expression on their own account
'pointing' must be discouraged. Reading, with expression,
requires the eye to travel some distance ahead of the voice and
' pointing ' would hinder a child in this respect.

(/■') If a scholar be suspected of indifference, he should at once be
called upon to read. During simultaneous reading the class
should be suddenly stopped and the inattentive .scholar should
be required to take up the reading at the point where the class
has stopped.

(r) Introduce emulation between two portions of the class, allowing
one half to read whilst the other half listens ; and after a remark
upon the reading of the first half encourage the second half to
read the passage so as to avoid the mistakes of their fellows.

QUESTIONS FOR EXAMINATION.

(these questions are reproduced in order to show the
nature of the examination in school method.)

a) Taken from Government Examination Papers for Pupil-Teachers.

What is the best way ot arranging a class for a reading lesson so as to
secure (a) distinctness of utterance, and {d) readiness on the part of the
scholars to observe and correct mistakes ? ^"^

It is said that some children know their reading books almost by heart,
and that when examined they are only reciting, not reading. How could
you detect this fault, and by what means could you guard against it ?

What is the use of 'pattern reading' in teaching a class to read?
Mention any common faults which a good teacher should avoid in giving
such lessons. X/t""^^

What is meant by 'simultaneous' rgading? How should it be con-
" it ? \x^^

ducted, and what is the use of it

62 How to Teach Reading.

What is meant by tone, accent, emphasis, and expression in reading ?
Say why they rji^ed special attention, and how you can best deal
with them. K^

What is meant by distinct articulation in reading ? Name any words
that present special difficulty to learners, and mention any^ form of
exercise that is most useful in correcting faulty articulation. V- '

Explain what is the best use to make of a box of movable letters in an
infant class.

Describe a plan followed in your school in beginning to teach the
youngest children to read. S-""^^

Point out the silent letters in 'light,' 'height,' 'which,' 'colour,' and
'tremble.' v/^

(6) Taken from recent Scholarship papers.

What are the commonest faults which you have fpund in the reading ot
children ? How would you correct these faults ? t/

It is sometimes complained that children do not read well, because their
reading lessons are constantly interrupted by the oral spelling of the more
difficult words. Do you consider such interruption necessary, and if not,
how may good spelling be attained without it ? V"^

In teaching reading to very young children, some teachers begin with
the alphabet, and others teach little words first, and afterwards call
attention to the names oL«eparate letters. Which of these methods do
you prefer, and why ? V^

Give some rules which you intend to follow for spring (i) distinct
articulation ; (2) intelligent expression in reading. V^

Detail some of the advantages and disadvantages ot teaching reading
by the 'alphabet method.'

Point out some of the advantages to be gained by ' simultaneous ' class
reading, and deduce from those considerations for which classes of a.
school this method is best adapted, and the dangers to be avoided ? ^x"^

In the following sentence explain the peculiar difficulties presented by
the words printed in italics in the early stage of reading : He 7cioii/t/ take
no />.iiiis to (t-(ic/i any h^ who could not at least utritc what boys of eight
years old can wrXc.^r

What especial care would you bestow upon the less advanced readers in
your class before, during, or after the reding lesson? How can home
lessons be utilised forTeaching reading ?V^

What should be the next ste])s in reading after a child has mastered the
fi.rnis of letters and powers of the vowels? Give examples ot a few
such lessons. |><^ _

Additio7ial Notes on Reading' d^^

64 Additional Notes on Readitig.

The Object aimed at. 65

HOW TO TEACH SPELLING.

The object aimed at.

Briefly stated, the result we strive to attain is the correct
spelling of all words in the language likely to be required by
the scholar in written exercises. In other words, it is the
existence in the memory of a perfectly correct image of the
succession of letters making up the words used in writing.

The inability to spell is regarded as evidence ol a neglected educa-
tion, and so long as this opinion prevails the teaching of spelling must
have a prominent place in the school curriculum. In succeeding
paragraphs the nature of the exercise will be explained. It will
then be seen that the power to spell correctly is not necessarily
evidence of either marked ability or superior training on the part of its
possessor. There is scarcely any subject in the entire range of school
study which presents so little material for orderly arrangement, for
classification, and for the establishment and application of rules as
the subject of spelling. When these facts become clearly recognized
it will be evident that the subject cannot present much opportunity for
the exercise and development of the higher mental powers.

The difficulties of English spelling.

A careful enquiry into the difficulties of both reading and
spelling shows that they are the same in kind, and, furthermore,
that they arise from the same causes. These causes may be
summarized as follows, viz., (i) the deficiency in the letters
of the alphabet ; (2) the use of the same letter for more than
one sound, and (3) the representation of the same sound by
different letters or different letter combinations.

These three sources of difficulty are equally operative in both
reading and spelling. In reading the exercise is one of associating the
proper sound with the printed or written word. In spelling the
exercise is one of associating the correct form of word with the sound.
It is clearly evident, therefore, that the difficulties of both exercises are
closely related. That this is so is further evidenced by the fact that most
good readers can spell well, whereas a defective reader is frequently
weak in spelling.

66 Hmv to Teach Spelling.

The pupil in relation to the above spelling difficulties.

We have seen whence the difficulties of speUing mainly arise
so far as the language is concerned. The next enquiry deals
with the learner. What ability does he possess for overcoming
the difficulties, and how may this ability be turned to best
account ? It has been already stated that the reasoning powers
of the child find very little opportunity for exercise on account
of the absence from spelling of material for either classification
or for the formation and application of rules. There is still less
room for the exercise of the imagination. We do not want a
child to imagine a word is spelled so and so. The child must
know how each individual word he requires is spelled,
and unless he has this knowledge no amount of imagination
nor power of reasoning will yield it. Having thus briefly shown
the intellectual efforts which are not available in spelling,
there are left for consideration those which are of service.
These are seeing, hearing, and remembering.

I think it will be found that the intellectual effort of spelling may be
resolved into one mainly of memory. A word is repeatedly seen, its form
is then retained, and, when the word is again heard, the form is recalled.
In all spelling exercises the memory should act automatically. Any
hesitation over the spelling of a word is as likely to result in error as
hesitation in the use of the multiplication table.

The nature of the memory exercise in spelling.

Memory exhibits different forms of activity. If we can dis-
tinguish these, and then determine which form of activity is
available for spelling, we shall approach the best position for
solving the difficulties of spellmg so far as the pupil is con-
cerned. The following illustrations will enable us to distinguish
the different conditions of memory activity: —

1. Repetition. A scholar is asked what 5 times 5 are equal to. He

immediately replies, 25. The answer appears to be ready without
a moment's thought. If asked how he came by this ability the
scholar would say, ' I have said the same thing so often before.'
Memory in this case is due to repetition.

2. Concentration and interest. In strong contrast with the above

example, suppose that during a scholar's first visit to the sea-side a
gale springs up, and a ship is unfortunately dashed on the beach.
Throughout the whole of life tlie slightest reference to a shipwreck will
be sufficient to bring to the observer's memory the impression made
ujjon that first visit to the sea. In this example, the memory acts as
automatically as in the case above. But there has been no repetition

spelling a Memory Exercise. 67

in the latter case, and it is natural to ask what has taken its place.
Evidently a highly awakened 171 teres t and a concentrated state of mind.
3. Association, The remembrance of the wreck brings with it those
of the place, the appearance of the sea, and the means taken to save
the captain and crew of the ship. This train of events is recalled by
association. Any one of the above events is sufficient to suggest all
the others. This power of recalling by suggestion or association is
the highest form of memory activity. We use it whenever we
classify or group together facts or events, because of some relation
found to exist between the members of each class or group.

Which of the above conditions of memory may be
used with best results in the spelling lesson ?

We shall have no hesitation in stating, in reply, that in all
exercises of spelling the child manifests but little interest. We
cannot, therefore, make much use of this condition. The
arrangement of words in groups, on account of a similar element
recurring throughout the group — in other words, the classifica-
tion of words of similar structure, and the formation of rules
of spelling, cannot be profitably undertaken, because of the
many exceptions to every rule. Hence, spelling by association
(of the highest kind) cannot be adopted. Repetition remains,
and this is the condition of memory activity, which, so far as
spelling is concerned, is of chief service. The problem of
spelling is thus reduced to one of extreme simplicity. The
school exercises which repeatedly bring words under the notice
of the scholar (especially under the eye) are of greatest service
for securing good spelling.

The period of school life best fitted for mastering
the difficulties of spelling.

The conclusions arrived at in the preceding paragraphs aiford
an indication of the age when the spelhng of our most irregular,
i.e.., our most common English words may be acquired with
the least expenditure of effort. In the junior classes, up to the
age say of ten years, the memory is wonderfully active, and
vast stores of unorganised matter are readily accumulated with
very little manifest effort. Up to this age there is very little
attempt spontaneously to arrange and classify knowledge.
Forms, tables, words — their sounds and spelling — are accepted
and remembered without either hesitation or enquiry. This is
evidently the period when the irrational spelling of our common
words should be mastered. If we delay to do this until the time
when reasons and rules are demanded (/.«., until the senior

68 Hmv to Teach Spelling.

school age of from 12 to 15), a great amount of trouble and
vexation, with but indiflerent success, will follow.

It is not to be expected that a child of ten years of age should be
able to spell all the words it uses. It is, however, very desirable
that most of the common and irregular words should be mastered
at that age. The learning of spelling must go on so long as new
words are added to our list. But delay in mastering the spelling of
common and irregular words appears to be dangerous, and so long as
absolutely correct spelling is demanded of our scholars (whatever else
may be neglected during the junior school period) correct spelling
cannot with safety be either neglected or delayed.

Methods of teaching spelling.

I. The reading lesson. Tiiis lesson provides for the fre-
quent repetition of words by sight. This repetition is secured
without feelings of monotony or weariness on the part of the
learner. The reader is thinking about the subject whilst his
eyes fall upon the words. The recognition of the words of a
narrative is a preliminary to the understanding of the matter. At
the same time this frequent recognition of the words provides
the most favourable condition for mastering their spelling.

There is at times weakness in spelling even amongst good readers.
Some children of bright intellect readily acquire the power of reading the
meaning of the i)iece rather than the words of w^hich it is composed. They
know what should come next, and a rapid glance at the word is sufficient
for reading purposes. Such children need to have their attention specially
directed to difficult words. This may be done by selecting some of the
methods described below. Transcription is especially valuable in these
cases.

In infant classes words may be built up by means of reading or

spelling frames. The exercise should be made to resemble the reading

effort as much as possible. Short sentences like ' The boy reads '

should be taken rather than detached words like 'boy' or 'reads.'

Any word which the teacher wishes to impress upon the class durin"

an oral lesson might be taken separately on either the black-board or

the spelling frame. In the upper classes the blackboard may be used

to show the s])elling of new words in much the same way as the

spelling frame is used for infant classes.

2. Transcription. Transcription is, after reading, the best

form of spelling exercise, and should be suppletiientarv to

reading. Transcription derives its value from the fart that the

effort of writing a word secures a sustained attention upon its

form as a whole and upon the several letters composing it. It

Method of Teaching Spelling. 69

should, however, be remembered that transcription is a slow
exercise, and does noi secure the repetition of words to the
same extent that reading does.

There is one serious danger associated with the transcription exer-
cise. It arises when the lesson is not carefully examined. There is no
excuse for error, and if the work is to have its desired effect there must
be no errors. The fact that transcription fixes the attention upon the
words more completely than any other spelling exercise is the strongest
reason for the words being correctly written. Let a child copy words
wrongly, and the error is very likely to be reproduced. Next to the
folly of showing a word incorrectly spelled on the blackboard is that
of carelessly passing over errors of transcription. Children should
never, if possible, see a mistake in spelling, nor should probable
mistakes be ever suggested to them.

3. Oral spelling may be used with advantage after a lesson
has been carefully prepared. It affords a rapid means of
testing a class. Its value as a teaching device is doubtful.
This arises from the fact that nearly all words whose spelling
needs to be taught are words not spelled according to the
sound of the word as a whole, e.g., write, right, rite, and
7vright. The necessity of placing the word to be spelled in a
sentence is also evident from the examples just quoted. The
sound of the isolated word does not enable the scholar to
determine which of the four words is meant. For two reasons,
therefore, the exercise of oral spelling is faulty, viz., (i) because
the sound of the word as a whole does not often suggest all the
letter sounds in the word, and (2) because when a word with
more than one form is sounded we are in doubt as to which
form is required.

Oral spelling may oliow, with best effect, a reading lesson, a home
lesson in which the chapter from whence the spelling is taken has
been prepared, and after the correction of words misspelled during a
dictation lesson.

4. Rules of spelling.

There are certain rules of spelling in use which may be briefly noticed.
If, for example, we take the words ' rat,' ' mat,' ' pin,' (S:c., the short vowel
becomes lengthened by the addition of final e. The exceptions are note-
worthy as being amongst the commonest words, e.g., ' have,' 'give,' 'live,'
'bade,' 'were,'«S:c. Again, the rule 'that when final e silent is preceded
by a double consonant the first vowel does not take the long sound,' as
'dance,' 'fence,' 'mince,' &.c. The exceptions to this rule include such

7© IIo70 to Teach Spelling.

words as 'scarce,' 'force,' ' clothe,' &c. The difficulty of dealing with
the diphthongs ei and ie is met by the rule ' that ei follows the c sound,
whilst ie follows any other consonant sound,' and the examples ' receive,'
' believe,' <S:c., are quoted. The words ' siege,' ' weird,' ' neither,'
'leisure,' &c., are notable exceptions. The following additional examples
of spelling rules, with a few exceptions under each, may be quoted, but
their value for teaching purj)oses is doubtful : — •

i. Change final y into i when a syllable is adaed, as beauty,
beautiful. Be careful how the scholar spells the word beauteous, if
too much stress is placed on this rule.
ii. Drop the final e before the addition of a syllable beginning
with a consonant, as judge, judgment ; sense, sensible, <S:c.

ExcnpriONS. — The word 'serviceable,' and most words ending in
ge and ce, retain the final e.
iii. When the final consonant is not accented, it is not doubled
by the addition of a syllable, as, f.g., analyst, pugilist, &t.
E.XCEPTioxs. — Crystalline, travelling, &c.

If there were not so many exceptions to nearly every spelling rule,
and if these exceptions were not for the most part the conmionest
words, we might be encouraged to lessen the work of spelling by
grouping words into classes, and by applying spelling rules. There
are, however, so many exceptions to every rule that the attempt
to spell by them becomes dangerous.

5. Word-building.

The practice of teaching to spell byword-building depends for success upon
the consistent use of certain letters and combinations of letters to represent
the same or similar sounds. For example, a first lesson would include an
exercise like the following —

man. ..mane

can... cane

rat ...rate

mad... made

ban. ..bane

far ...fare

not ...note

bit ...bite

hop... hope

n examination of tho>

• word.-i must lead to t

he establishment of the

r>ll<>wing rule, vi/., that the long vowel sound requires the letter e to
follo^w the final consonant. This rule would be helpful so long as cases
were supplied which fi)lk)wcd the rule. Suppo.sc a child, who has this rule
in mint!, is asked to spell the following common words, done, gi<r. Sec,
in which the .short vowel sound is followed V>y the final e, or to spell the
common words, /ai/, soap, coat, tear (clothes), &c., in which the vowel
SDund is made long without the final e, how wouM it proceed ? ICvidently
the rule would not assist in tlie.sc latter rases. They must be learned
quite aj art from the rule. The safer plan would be to place all common
an<l exceptional words in sentences and not in iisl-i, and, in this way, to

A Dictation Lesson. 71

lead the learner to associate the form of each individual word with its
meaning and use.

Word-building by derivations. WTien the pupil begins the study of
words through their derivations, the recognition of a common root
will undoubtedly assist the spelling of a group of allied words.
The knowledge that the words 'precede,' 'concede,' 'secede,' 'recede,'
'intercede,' &c., are derived from the same Latin root, cidcre, must
give steadiness to the spelling. There would, futhermore, be little
danger of such a pupil failing to spell the word ' supersede,' derived
from the Latin scdere. Entire dependence upon derivation, howe\er,
would sometimes lead to error, for the words which fail to follow the
spelling of the allied group are fre(]uently both many and important.
For example, the words 'proceed,' 'exceed,' 'succeed,' &c., are derived
also from the Latin root cedere and unless these were specially treated
the rule formed by the examination of the first group of words
(precede, &c.), would lead to error.
It is evident from the above that spelling by word-building needs all
the precautions urged when dealing with spelling by means of ' rules,'

DICTATION.

Dictation is helpful to spelling only so far as it is an exercise
in repeating in writing the words which are already correctly
known. So far as it results in writing words incorrectly it is a
hindrance to correct spelling. Dictation is a ready test, and
like oral spelling should only be used after very careful and
complete preparation. Remembering the truth that the sight
of a mis-spelled word is a positive evil, we ought to take every
precaution against children either making mistakes themselves
or seeing the mistakes of others. There are three important
conditions of a sound dictation exercise which follow from the
above introductory statement, viz., (i) that every dictation
lesson should be preceded by thorough preparation ; (2) that,
should a child make a mistake, notwithstanding all precautions
to the contrary, the correction should be written out a sufficient
number of times to obliterate the original error from the mind ;
and (3) that children should see only their own errors.

It is evidently a faulty method to select the most difficult passages
in a reader, and to attempt by this means to secure as large a number of
errors as possible. It is still more faulty to distribute books with
numerous errors in them over the various members of the class. Perhaps
the greatest fault of all in connection with a dictation lesson is that of
showing the mistakes made by a few of the weakest scholars to the
entire class on the black-board.

72 Hmv to Teach Spelling.

Suggestions for conducting a Dictation Lesson.
(A.) Preparation.

(i) The Teacher —

(a) To select a suitable paragraph, and a few difficult words from

other paragraphs in the chapter prepared by the class.
(/') To provide material — paper, pens, &c.
(c) To write beforehand a model dictation sheet, for exhibition to the

scholars of the required style of writing.

(2) The Class—

(rt) To prepare the spelling of the entire chapter from which the
dictated paragraph is taken. This preparation may be secured
by reading the passage, by reviewing the spelling at home, or by
allowing tinid for becoming familiar with the words before the
lesson commences.*

(J>) Each scholar to be seated in writing places, the distance between
each scholar to be sufficient to prevent anyone overlooking his
neighbours' work.

(B.) Stage I. — The Writing Exercise.

(I) Style of Writing—

(a) The teacher to write the heading on the black-board as a model

of good style.
(^) The children to be shown (i) where to begin, (2) the proper
margin, (3) to be told to ])uncluate, and (4) to be questioned
on the right use of capital letters.
{2) Dictation of Piece —

(a) The entire piece to be read through whilst the class listens. Some
words cannot be spelled correctly until their connection in the
sentence has been determined.
(/') The paragraph to be dictated once only in suitable portions.

(C.) Management of class during the writing exercise.

(a) The teacher must take up a position well in liont ot the class, and

must maintain this position.
(Ji) Any movement of a scholar to the right or left should be seen and

corrected. A teacher who moves amongst his pupils cannot see

all of them when so doing.
(<•) By means of this alertness on the teacher's part no copying ought to

be possible.
{</) Start the writing by the same code of signals as those used in the

writing lesson.

• This part of the prcpar.tlion exercise must be very ihoroiigh. It is far better 10
prevent mistakes than to correct them. Lessen the chances of error in spelling as
much as possible.

Additional Sjiggestions for Dietitian Lesson.

(D.) Marking mistakes.

{a) By the Teacher —
This is the most satisfactory method. With a large class it is not
often possible. A teacher accustomed to detect mistakes can
review the slates of a class very quickly.

(/O By the Scholars—

Mutual marking is a favourite device on account of the saving of time
which it effects. It is accompanied by loss on account of the
presentation of erroneous spelling to the children who mark the
mistakes. Children should never see the mis-spelled words
of other scholars. The difficulty here mentioned is overcome
when children can be trusted to mark their own mistakes. They
should be encouraged to do this as early as possible.

[c) Mode of Marking Errors —
Thi? may be done by passing the pen or pencil lightly through the
wrong letters, and by placing the correct letters above or below
each error.

(E.) Correction of errors made.

{a) Write the corrected spelling at least three times, in order to fix the

proper form of each word.
\b) Cause each scholar to keep a list of these corrected words, and at

intervals to submit to a test of his or her ability to spell them. Then

lessen the list of errors by the number of words they spell correctly.
(c) Whilst their neighbours are correcting their errors, set a pleasant

exercise to those scholars who have either very few or no mistakes.

Additional suggestions for conducting a Dictation
Lesson.

Whilst following, in the main, the plan just sketched, there
are certain variations and modifications of the dictation lesson
which, at times, may be introduced with advantage. The
writing should be on paper as soon as the pupil has acquired
moderate facility in the use of the pen. Dictation when neatly
written is a very serviceable penmanship effort. The paper
exercise furthermore demands the scholars' thought before they
commit themselves to the spelling of a difficult word. On the
other hand the facility with which alterations may be made on
a slate tends to render the pupil somewhat careless of the
spelling. These alterations can be readily detected in the
paper exercise. They show uncertainty in the mind of the
pupil, and hence, whether they result in correct or erroneous
spelling, they should be regarded as evidence of spelling
weakness and should therefore be treated as mistakes.

74 Hcnv to Teach Spelling.

All mistakes do not arise from the same cause. There are spelling
errors which are the result of ignorance ; these need to be repeatedly
written until the words become familiar. When a mis-spelled word is the
result of nervousness or over-anxiety on the part of a child, a word or two
of caution accompanied by encouragement will suffice so far as the learner
is concerned. The teacher should consider, on his part, whether or no his
discipline, in all such cases, should not be somewhat relaxed. Many
children call up wrong impressions when under a feeling of fear and anxiety,
and nearly all children fail to do their best when over-excited. Mistakes
arising from carelessness cause most difficulty. The habit of carelessness
must be weakened, and that of thoughtfulness strengthened. When the
careless boy, who is frequently at the same time a lazy fellow, finds that by
thoughtless spelling he brings upon himself an increase of work, he will in time
select the short course, and do his best to spell correctly at the lirst attempt.

The words most commonly mis-spelled sliould be written correctly and
clearly on either a black-board reserved for the purpose or on a sheet of card-
board. These difficult words should remain in a conspicuous position for some
time, and at intervals should be made the subject of a special spelling test.

Spelling Reform. — There have been various attempts
made to reform the irregularities of English speUing. Amongst
those who have worked in this field of enquiry the names of
Messrs. Ellis, Pitman, and Jones may be mentioned. The
adoption of the signs in the phonic system, and the creation of
new letters in the phonetic system (both of which have been
illustrated on previous pages), are methods of spelling reform.
There is a third method, which, whilst it retains the letters of
the alphabet, entirely changes the si)elling of all irregular
words. The following five rules are given by Sir Isaac Pitman
as a first step toward reform. The rules are printed in the new
style. The chief objections to any such reform are (i) that it
would tend to obliterate the history which many words j^resent
in their spelling, (2) that it would soon diminish the value of
our store of literature, and (3) that as yet there is no new style of
spelling which has gained the general acceptance of literarymen.

Spelling Reform Rules —

Rule I. — Evcri konsonant iz auiwayz rcprc7.cnted bci the same leter.

Rule 2. — The siks short vouelz ar riten az in prtl, p<t, p/t, pot, b//t and p//t.

Rule 3. — The long vouelz ar reprezcntcd thus :— father, atimz ; (avor,
piir(\, par; me, meei. ; au\ (all), ]ti7t> ; so, s<'(jp ; iood, trwth. Aul
uthcr s[)elingz ov long voutiz shud be redii'ist tu order.

Rule 4. — Diflnongz ar riten b^i the tii (two) Icterz :— trtm, out, ni/i,
di (yes), hoi.

Recent Instructions on the Teaching of Spelling. 75

Rule 5 — When the deigrafs ' th, sh, zh, ng,' reprezent tu leterz, insert a
heifen, thus, short-hand, mis-hap, hogz-hed, en-grave. When the tu
leterz that reprezent a long vouel hav separate valiuz, puta heifen
after a prefiks ; az, re-engaje, re-instate, ko-alesent, ko-inseid,
ko-operate ; and a deieresis in uther kasez ; az, being, deifei, mozaik.

Recent instructions from the Education Depart-
ment on the teaching of spelling.

* Correct spelling is, of course, an essential part of
elementary instruction, and often demands considerable
labour from the teachers. But this labour might be greatly
abridged by the adoption of more skilful methods than are
commonly in use. The practice of oral spelling is not only
wearisome and uninteresting to children, but it often wholly fails
to effect its intended purpose. No child ever learns to spell
well merely by reciting aloud the names of the tetters which
compose a word. It is by judicious exercises in word-building
and in grouping together on the black-board words of similar
structure ; and above all, by more frequent exercises in writing
and transcription from books, that the difficulties of our
anomalous spelling can be most effectually overcome in early
childhood. It is to the eye rather than to the verbal memory
that all spelling lessons should be addressed, and it is by
written, not oral, tests that the results of such lessons should
be measured. When words are sounded alike, but differently
spelled, the best way of dealing with them is to require the
scholars to put them into short sentences of their own writing ;
and by this means to make the spellmg exercise helpful as
elementary training in composition.'

' These general principles will serve as a guide to the best method of
forming an equitable judgment on the success with which this difficult
subject has been taught, whether the spellintj be tested by a dictation
exercise, or by an examination in word-building according to a scheme
prepared by the teacher. In the Second and Third Standards it will
not be reasonable to expect more than the power to write correctly
common words of comparatively regular notation, and some of the
anomalous words which occur frequently in conversation, or in easy
reading books. And even in the higher standards, when proper names,
the technical terms of a science not studied in the class, foreign words,
or words of rare or exceptional character, occur in the dictation lesson, it
is right to omit such words from your estimate when you are reporting on
the results of the instruction in spelling. The services of the teacher in
giving out the passage for dictation may often be used with advantage.'

76 How to Teach Writ ins;.

HOW TO TEACH WRITING.

I. Introductory.

Writing is one of the three essential subjects of school
instruction. Its value is twofold, viz., {(i) for practical pur-
poses, and {U) for mental training.

{a) Practical value.

Writing is necessary in nearly all the affairs of life. In
school work the value of writing is seen in the power of exact
statement which it yields. Oral statements are often accepted
which are mere approximations to full and exact knowledge.
The written exercise, on the other hand, is a means of stating
with definiteness the knowledge acquired. In business affairs
the value of writing, both in correspondence and in the keeping
of records, is so obvious that it needs only to be briefly
mentioned.

{b) Value of writing for mental discipline and training.

The disciplinary \alues of writing are neither so great nor so
evident as are those of reading and of arithmetic. To become
a good writer requires, nevertheless, the exercise of consider-
able mental j^ower. A copy must be closely observed before it
can be successfully imitated. The sense of sight is especially
awake during the writing effort, and the steady control of
the hand in wielding the pen is a most valuable training in
dexterity. The comparison of the scholars' writing with
their copies, and tlie discovery of faults as a result of this
comparison, are exercises of Judi:;ificnt. The retention of
typical letter forms, with which the i)upil mentally compares
his own (when no cojjy is present for imitation), is an exercise
of the mciiiorx. No one who watches a young child in an
early effort of writing can fail lo note how conccntrateil is its
attention. I'inally, the scholar who produces a neat copybook

Good Writing — Locke's Method. 77-

with improvement manifest on every page, supplies proof of
having acquired habits of perseverance, of neatness, and of
careful njess.

2. Good writing invariably manifests the following charac-
teristics, viz., {a) Legibility ; (/>) Symmetry, and hence beauty
of style ; and (r) Ease and rapidity of production.

{a) Legibility is obtained when the writing is sufficiently large to be
easily read ; when it is free from irregular strokes and unmeaning
flourishes ; and when the shape of each letter and the form of the entire
word are distinctly and readily recognized.

(d) Symmetry and beauty depend upon parallelism of strokes ; upon
regularly formed and somewhat oval curves ; upon the evenness of
height and of joinings ; and upon the uniform spacing of each letter
and word.

(r) Ease and rapidity of writing should not be attempted until (a) and (/')
have been acquired. Rapid, and at the same time legible and beautiful
writing is an accomplishment which can only be obtained after much
practice. The way should be prepared for the acquisition of a rapid
style by accustoming the scholars to the joining of all the letters com-
posing each word, but on no account should this style be hastily
enforced.

3. Methods in use for obtaining: good writing.

There are three fairly distinguishable methods at present
used for obtaining a good style of penmanship. These are
(i) Locke's, or the analytic method; (2) Mulhauser's, or
the synthetic method ; (3) the Mixed method, which, as its
name indicates, combines some features of both the analytic
and the synthetic methods ; and (4) Vertical Writing.
Each of these methods will now be briefly described.

(i) Locke's method.

The method of teaching which Locke advises in his work
entitled ' Some Thoughts on Education ' may be stated m the
following way : —

a) An engraved copy of letters and words to be prepared.
(^) The copy to be in red ink and the pupil to write over the copy with

black ink. ( Tracing. )
(r) The copy to be 'a pretty deal bigger than he (the pupil) should

ordinarily write,' and gradually to become smaller.

7 8 How to Teach Writing,

{d) The teacher to direct the scholar as follows, viz. : — (i) where to begin,
/ (2) how to form each letter, (3) as to the mode of holding the pen,
^ and (4) how to place the paper.

{e) WTien progress has been made on the traced paper the pupil to write
on ' fair ' or untraced sheets, and thus ' be brought to write the hand
you desire.'

Many of the above features have been adopted in modern copy-
books. Those issued by Darnell, and used in schools for the past
thirty-five years, very nearly approach the system which Locke
recommends. Recent issues of copybooks adopt the system so far as
presenting copies for tracing in the early numbers and advancing from
large to small hand. At the same time they generally follow the
synthetic method of proceeding from the elements of which letters are
composed to the construction of letters, words, and sentences.

Criticism of the analytic method.

This method possesses the following advantages. It is in-
teresting from the first lesson onwards. The learner's ambition
to be able to write words is satisfied. The method, further-
more, proceeds on the plan by which much of our knowledge
is acquired, as, for example, in learning to read, i.e., from the
whole to its parts. Against the method it may be urged that the
writing of letters and words, as entire forms, does not readily
enable the learner to make use of the knowledge and power
already acquired. Many forms are repeated in different letters
{e.g., the hook in nine letters). When this fact is pointed out
the new letters containing the hook are easily made. The
analytic method ignores this help. Those who support the
synthetic method hold that the bungling results which learners
make at first in imitation of entire letters and words are either
discouraging to the pupil, or, if not, that the incorrect forms
tend to become set and habitual. The analytic method,
furthermore, violates the principle in teaching which holds
generally when anything has to be done, viz., that progress
should be from the simple to the complex.

(2) Mulhauser's system of writing.

In the year 1829 M. Mulhauscr was appointed Inspector of
Writing by the Primary Schools Commission of Geneva. He
found writing taught in the schools under his supervision,

Mulhauser's System oj Writing. 79

without any approach to method. Copies were distributed for
imitation in haphazard fashion. Children with remarkable
imitative powers made satisfactory progress ; but the majority
made but slow advance. The art of correct writing was acquired
only after a laborious and long-continued effort. Mulhauser at
once determined to place the teaching of writing in the schools
under his control upon a rational basis. His method of proce-
dure was as follows : —

I. Analysis of script letters into four elements. After careful analysis
of all the small script characters, Mulhauser reduced them to the
following four elementary forms : —

i. The right line ^ / ii. The curve down f \

and up / / and up ^ ^

down and up

iii. The lo-
down and up

iii. The loop yf J^ iy_ The crotchet W /^
iwn and up (^ ' '

2. Classification of letters according to the elements composing them.
The twenty-six small letters were next arranged in seven classes, each
class having one or more of the above fundamental forms as its distinc-
tive feature.

i. i U t I

ii. n 7n p 7l

iii. C e

iv. a d q

V. w V r i

^'■- J 9 y f

vii. To S X Z

Exercise of writing in rhomboids. Besides classifying the letters
according to similarity of form, Mulhauser devised rhomboids by
which the parallelism of stroke, the oval curve, the regular height and
distance of each letter, together with the position of the joining, could
be determined with the strictest accuracy. These rhomboids with letters
in them arranged in classes, with names to the different portions of
each letter and with hints upon their use in writing lessons, will now
be illustrated and considered. '

How to Teach Writing.

CLASS I.

Letters

ARKAN'GEl) IN

RlIOMIiOIUS.

Names of the
Elements oe
EACH Letter.

right
link.

right line, h'nk ;
right line, link.

Remarks and Teaching

Hints.

Class L — The letters in this
class consist of the right line
with the addition of a curve at
the bottom called a link. The
link is a part of nineteen out o
the twenty-six letters, and is
exactly the same shape in all.
When once it is thoroughly
mastered the correct shape of
the lower portion of each of the
nineteen letters is secured.

Notice the use of the terms
height, ^ height, and tivo heights.

right line, 2
link.

heights

right line, i\

heights ;
link, bar.

Teaching Hints —

The above letters may be
combined into words as it, ill,
till, tilt. The following errors
must be expected, viz., ((7)
strokes made thickest in the
middle, {i') pointed tops, (e) strokes with one edge ragged due to the pen
being pressed unevenly upon its two points, (d) painted strokes, (e) faulty
link, the curve beginning too soon and hence producing a pointed curve at the
bottom, (/) the joining up-stroke entering the following stroke too abruptly
as though it would cut through it. These errors will be general in a class
beginning to write. They should be corrected by the teacher writinL' them in
a somewhat exaggerated form on the black-board. The scholars should be
asked to point out the error, and be required to avoid it in future attempts.

CLASS IL

Class IL introduces the /w^/",
a curve in the opposite direction
to that of the link. The hook
is an upper part of nine letters.

Teaching Hints —

Do not begin the hook in the
angle made by the middle hori-
zontal and the oblique lines.
Begin to the right of the above
jioint by the thickness of the
riglit line. The hook and link
will then be exactly the same in
shape.

The double curve, forming
the last portion of the letters n,
m, p, and h, is a very difficult
stroke. The hook is generally
made larger than the link, and

hook.

right 1

line ;

hook.

right ;

line ;

link.

hook,

right 1

line ;

hook,

right 1

line ;

hook.

right 1

line ;

link.

right

line, 2

hei

ghts ;

hook,

right

line.

link.

right line, 2

heights,

I height down ;

hook.

right

line.

link.

Miilhatiser' s System of Writing.

the down stroke instead of being straight in the middle is made to curve
throughout. The best method of detecting the error is to examine
the writing upside down. The following words may now be introduced,
viz., nut, mint, pint, pulp, &c.

CLASS III.

curve,
link.

double curve,
half crotchet.

loop,

link.

curve.

Class III. — The new feature
is the curve. The upper portion
of the curve is the same shape
in each letter, with the exception
of the starting points. The
lower curve of both c and e is
an extended link occupying a
space and a half; that of the
letter £> is a link.

Teaching Hints —

The dot of the letter c requires especial care. Place it one-third the
distance between the top and middle lines, and not quite as far forward as
the oblique line in front. Complete the dot and then bring the pen with a
sweep round the bottom and along the front of the dot. The lower portion
of o is exactly like the link in the letter i. The following words may now
be written : coin, ounce, clump, choice, &c.

CLASS IV.

double curve ;
right line, link.

double curve ;
right line, 2

heights ;
link.

double curve ;
right line, 2

heights down ;
half crotchet.

Class IV. — No new stroke is
introduced in this set of letters.
In the letter a, if the o portion
be first correctly formed, and
then the right line and link be
written on the right-hand side of
the oblique line, it will be in
contact with the o only at and
above the middle line. The
letter ^ is correctly written in
the engraving, the letter a is not.

Teaching Hints —

Children often make the right line either to cut through the o, or to
touch it just at the middle line. Both errors must be corrected. The o in
each of the three letters a, d and q should not be altered in shape by
contact with the right line. Practise the following words : add, cloud,
addition, queen, quoit, &c.

How to Teach Writing.

CLASS V.

right line, 2

heights down
loop ;

\ link.

double curve ;
as for/.

hook, right line,
link ;
as for/.

Class V. — Consists of looped
letters. The letter/ is the only
new feature. Learn this shape
thoroughly ; it is repeated in
both g and y.

There are three parts of the
letter j which need careful
watching, viz. : —

1. The lower end should extend
exactly midway between the
the lowest horizontal line and
the one above it.

2. The intersection of the loop
must be made in the place
shown in the engraving.

3. The end of the loop must
slope gradually into the
angle.

Teaching Hints —

If the class can be induced to avoid the three errors against which they
are warned above, there will be little need of further direction in making
these looped letters. Write the following words : judge, juicy, gagging.

CLASS VL

right line, 2

heights ;
link ;
crotchet.

Idop, I height

above ;
right line, 3

heights ;
crotchet.

hook, right line ;
crotchet.

hook, right line,
link, crotchet.

riL;lit litie, link ;
right line, Imk ;
irnt( hct.

Class VL— These are ootchet
letters. The crotchet is a curved
stroke throughout ; it takes two
shapes, that of the letter /
being different from that in the
other four letters of the group.
The letter /■ is an ui)ward loop
slightly longer than the letter
y, but otherwise it is seen,
when inverted, to resemble the
latter letter.

These crotchet letters are
brought together into one class.
Some authorities urge the intro-
duction of the letters r, v, and
•w at an earlier stage, because
being short letters they are more
easily made than the long letters
j, 1, or d.

Criticism of the Synthetic Method.

Teaching Hints —

A child who has learned to make the letter 1 should recognize that b is
the letter 1 with the crotchet added to it. Similarly each of the letters r,
V and w should be associated with letters m, n and u respectively. In
this way the teaching of former lessons is made to assist in the present.
f is the longest letter ; it should be made by a single movement of the pen.
Words for practice are brown, fibre, wharf, beautiful, &c.

CLASS VII.

right line, 2

heights ;
hook, i- curve ;
5-curve, link.

link, to the

height ;
2 half- curves.

hook, 2 opposite

curves ;
link.

crotchet, right

line, hook ;
curve, I height

down ;
loop, i-link.

Class VII. — Consists of the
complex letters which do not
fall readily into any of the
preceding classes. The let-
ters forming this group have
very little in common, hence
each must be practised un-
til its particular shape is
familiar.

Teacning Hints —

The letter k should be contrasted with the letter h. The letter s occupies
a space and a half. When s follows either c or e the two together occupy
two spaces. The upper portion of letter z is the only thin down stroke in
the series. Words for practice are knapsack, zig-zag, exists, &c.

Tracing is helpful when a child is first learning to write. Holding and
guiding the pen are difficult exercises for a little hand. The tracing
enables the learner to concentrate less attention upon these necessary
preliminaries to writing. As soon as sufficient skill in the management
of the pen has been gained, effort on the part of the child will be
available for observing the shape of the letters, and as this eftbrt of
observation increases there should be less tracing supplied. If tracing
be continued beyond the first few books the child's self-effort of
observation will not be sufficiently exercised.

Criticism of the synthetic method.

This method begins with simple forms well within the power
of the child to construct. Hence the learner is free from the
discouragement which failure to produce a more complex form
might produce. Whilst the system provides for the mastery in

84 Hoiv to Teach Writing.

turn of each form of stroke, it seeks to make full use of the
knowledge already acquired. For example, in the first lessons
the straight line / leads naturally to the straight line connected
with the link, viz., the letter I ; and this second form repeated
yields the letter ^ / a simple lengthening of the stroke already
mastered makes the letter ^, and by a still further lengthenmg
of the stroke the letter / is formed. An apparently valid objec-
tion is raised against the system to the eflVct that it keeps the
learner too long engaged in writing unmeaning strokes, hnks,
hooks, &c. In reply it maybe pointed out that in the four exercises
forming the introductory stage, viz., the exercises /, /, Vb, t, I,
the first stroke only can be termed in any sense unmeaning. It
is immediately followed by the letters i, u, t, 1, and these are
afterwards combined into words like it, tilt, till, &c. The
method is valuable in that it saves the teacher's time and the
scholar's effort. For example, when once it is clearly seen that
the link portion of the letter i is repeated in the lower portions
of the letters u, t, 1, as well as in no less than fifteen other
letters, it is a great gain to master this stroke once for all. We
thus secure that the portion of the nineteen letters into which
the link enters shall be correctly made. The rhomboids are
objected to on the ground that they are confusing. This is,
perhaps, the most serious and real difiiculty. The difficulty,
however, is not so great as it appears, and with a little practice
it is overcome. Some ridicule has been heai)ed on the method
on account of the introduction of the special terms /loo/:, link,
\ heig/it, ike. In reply it may be stated that at most these
terms are only twelve in number, and that they are readily
learned when used in connection with the forms for which
they stand.

(3) The Mixed method of teaching writing-.

In most of the copybooks recently comj>ile(l the valuable features of the
two methods already described have been adopted, and an attcm])t, more
or less successful, has been made to avoid their defects. The following
features which the copybooks of to-day display may readily be placed to
the account of one or other of the above systems.

I. The elementary forms arc attempted in the early lessons. {Sytifhetic
system. )

2 Tracing is introduced into these first copies. {Aitalvtic sysUm.)

The Mixed Method oj Teaching Writing. 85

3. Letter and word forms are soon reached, {Synthetic and Analytic
systems. )

4. Half-text is taught first, leading gradually to large-hand and to small-
hand. {Modification of both systems.)

5. Horizontal lines are adopted for guidance in fixing the joinings and
relative heights of different letters. [Synthetic system.)

Systematic instruction without the use of copybooks.

Copybooks with printed head-lines became common with
the employment of pupil teachers. Before that event plain ruled
books were chiefly used, the copies being set by the teacher.
It frequently happened that the teacher was a highly-skilled
penman, and as a result the writing was excellent ; many
schools, in fact, gained a high reputation for their penmanship.
During the past few years there has been a tendency to return
to the use of plainly ruled books, accompanied by a regular
system of class teaching from blackboard or cardboard copies.

Criticism of the method.

Advantages.
I. The simultaneous effort of an entire class upon the same copy, by which

a considerable amount of emulation amongst the pupils is secured.
ii. The arrangement of a series of lessons on a definite plan, and the

careful preparation of each lesson in the series by the teacher,
iii. The substitution of regular class instruction for somewhat desultory

individual direction,
iv. The imitation by the scholars of the teacher's copy. This copy, when
well written, has a more stimulating effect upon the class than the
engraved heading. Children regard the printed headline as something
far beyond their power to imitate successfully, whereas all may fairly
aim at imitating the teacher's copy.

Disadvantages.
i. That unless the same teacher continues to move upward in the school

with the scholars, the changes in the style of writing in the different

classes must tend, for a time, to confusion,
ii. That teachers are not always excellent writers,
iii. That children do not progress uniformly, and that to keep all the

scholars constantly at the same class of exercise might weary the

bright or discourage the slow.

86 Hoiu to Teach Writing.

(4) Sloping and vertical hand-writing.

The writing practised in schools is generally sloping in its
character. The slope in Mulhauser's system amounts to 60"
with the horizontal. In Civil Service hand-writing the slope is
not so great. The vertical style which has recently been intro-
duced, and for which copybooks with vertical head-lines have
been constructed, is recommended by its supporters for the
following reasons, viz, : —

4. Strokes being shorter the writing
is more rapid.

5. Occupies less space.

6. Easy to learn and to teach.

7. Good for discipline, the writers
being more easily kept in their
proper places, and the tendency
to talk more readily discovered
and prevented.

Prevents bodily distortion. The
two arms being placed equally
in front, the shoulders are both
held at the same height. There
is no twisting of the back.
The eyes being equidistant from
the writing, their adjustment for
clear vision is rendered more easy
and natural.

The writing is in the same
direction as ordinary type and
therefore legible.

It should be observed that with perfectly vertical downstrokcs and
with upstrokes joining /lU W\) at the top and bottom (as in the
examples given) the upstrokes must be sloping. Hence the term
vertical only applies to one half of the strokes. Then again the
remarkable uniformity which appears when a copy of a head-line is
examined (the long letters making a perfectly straight and vertical
line) is not so m.anifest when a paragraph of ordinarily printed matter
is copied. There have always been persons who, by preference, have
written vertical characters. The length of the fingers and the general
shape of hand are ' personal factors ' to be taken into account. The
strongest claim in favour of vertical writing is the hygienic one. The
spread of type-writing is helpful to the growth of a more upright style,
and fashion (which is ever ready to adopt a change) may give addi-
tional stimulus. In one school where the system was recently adopted,
it was reluctantly abandoned because of opposition from different firms
to the introduction of the vertical style into their ledgers, &c.

The Capital Letters.

Mulhauser did not analyse and classify the capital letters.
The following grouping of these letters is presented as one
which has been found serviceable in teaching. The value of
the classification becomes ajjparent when it is seen that the

The Capital Letters.

same lines are repeated, with slight modifications, throughout
every letter in each class. When letters are thus arranged in
groups, the knowledge and skill acquired in learning one
letter become of service in mastering the subsequent letters
of the same group. Hence the classification of the capital
letters results in each letter being more easily made, as well as
more fully known. Along with the representation of each
class of capital letter are a few hints for teaching it.

CLASS I.

Directions for teaching. — The first stroke is
repeated in each of the letters of this class. It is
also found in each of the letters of the succeeding
group. It forms in fact an important part of no
less than ten capital letters. When its shape has
become thoroughly known, and when the scholars can produce it with
ease and accuracy, the additions required to form the letters S, L, I, T
and F respectively, should be introduced one by one. The scholars
should be encouraged to distinguish the portion of the letter which is new
from that which is old. It will be seen that a slight modification is
sufficient to yield the shape of each letter in turn. New letters should not
be introduced until power to make the previous letters has been acquired.
The letters should furthermore be written in connection with a word.
Some teachers prefer a more upright style. In that case the oblique lines
(rhomboids) may approach more nearly the perpendicular. The figures
I 2 3 on the diagram are intended to indicate equal spaces between
the strokes.

CLASS II.

How to Teach Writing.

Directions for teaching. — The long down stroke is the same as that in
Class I. Encourage the class to indicate tlie new feature in each letter.
Practise the upper curved portion of the letter P until it is known. This
knowledge will enable the scholar very readily to form the two following
letters, viz., B and R. The letters H and K introduce considerable
modifications and additions, and must, in consequence, be allowed more
time for practice.

CLASS III.

Directions for teaching. — The chief new eature here is the first
up-stroke of each of the letters A, M, and N. These letters should
follow one another. The letters V and W have common forms and
should be taught together. Draw attention to the equal distances between
the strokes indicated by the figures, and to the similarity in the curve of
the downstrokes of the last four letters. After each letter is mastered, it
should be written as the initial letter of a word. The length of the
letters which are not capitals should extend from the fourth to the sixth
horizontal line, counting from the top of the diagram.

CLASS IV.

Directions for teaching. — The down curve of the letter C is repro-
duced in each of the following letters. In the letter E it is modified near
the middle, and in the letter X a reverse curve is added. The chief
variations arc found in the terminations of each letter in the group.
Encourage the class to indicate the new feature before attempting to write
it. It is well sometimes to examine the letters upside down. The
irregularities in shape are often best shown in this way. Children are in
danger of becoming accustomed to a mis-shapen letter, and of accepting
this for the correct form.

Class Teaching.

CLASS V.

Directions for teaching. — The upper curves
•of each of the first five letters in this group
are exactly alike in shape. The letters Q to
Y are furthermore begun in exactly the same
way. U and Y are nearly the same in shape
throughout. These resemblances should be
recognised by the class. The recognition will
prove helpful in writing. The letters D and
Z are peculiar forms and must receive more
attention than the other letters of the group.

Class teaching and individual instruction of writing.

The conditions under which class teaching of writing becomes
possible have already been discussed. When copybooks are
used, an obstacle presents itself in the way of systematic
class instruction, inasmuch as the children throughout the class
can but rarely be kept at the same copy. When different
copies are written by the several scholars, the class teaching
must be very general, and can scarcely be termed systematic.
When, however, ruled books without head-lines are used it
becomes possible, in every lesson, to introduce class instruction
of a systematic kind. The prime condition of success, whichever
method may be selected, is the presence and active co-operation
of a skilled teacher, capable of arranging a series of writing
lessons according to one or other of the systems already de-
scribed, and able, at the same time, to present to the class a
good style of writing for their imitation. Under these conditions
the production of uniformly good writing may be expected.

A black-board, with ruled lines to correspond with the books, is a
necessary appliance in class teaching. Such a board enables the
teacher to exhibit the errors* made by the scholars. It also enables
him to show models of correct writing for his pupils to copy. There

* This is contrarj' to the advice given for the correction ot spelling. No errors in
mis-spelling should ever be shown. Errors in writing, however, may not only be shown
but they may be exaggerated with good effect.

9^ How to Teach Writing.

will still be need for individual instruction ; but, where class teaching
is conducted under the conditions just enumerated, there will be less
need for individual direction than when the class is at work at a variety
of copies. When children of one class are occupied upon a variety of
copies the teaching must be mainly individual.

Writing appliances.

{a) Desks. The dual desk affords excellent means of access to each scholar.
For individual correction and instruction, therefore, they are most
serviceable. Whether dual or long desks are used, the front edge of
the seat should be nearly in a straight line (vertically) with the front
edge of the desk, and children should not be permitted, under any
circumstances, to bend in awkward positions over their copybooks.
The slope of the desk for writing purposes should be about 20° from
the horizontal. A foot-rest placed at right angles to the direction of the
leg is a source of great comfort.

{b Ink. Good writing is impossible with inferior ink, or with inkwells in a
dirty condition. The porcelain inkwell, having a hole for the insertion
of the pen, appears to work well. It prevents the accumulation of dust
and it delays evaporation. The difficulty of washing thoroughly clean
is its only drawback.

[c] Pen-wipers. If pens are collected without being dried they soon
corrode. Children should learn to be tidy in their habits. The writing
lessons afford a good opportunity for cultivating neatness, and the use
of pen-wipers and blotting paper may be made conducive to this end.

((/) Cabinets for storing copybooks should be pro-
vided for each writing division. The number
of compartments in the cabinet depends upon
the number of desks. If the class be seated
in dual desks five rows in depth, then a cabinet
with five compartments should be provided.
The books of all the scholars in the front desk
should be collected in the order in which the
children sit. The writing monitor, at the close
of the lesson, should place these copybooks in

order in compartment No. i. The books in the second set of desks
should be placed in compartment No. 2 ; and so on throughout the
class.

(<•) Copy-slips. These have almost passed out of use. They have the
advantage of providing the copy best suited to each individual scholar;
the copy can also be repeated as often as the teacher wishes. Disad-
vantages arise (i) from their distribution, (2) from being no scholar's

Class Management during the Writing Lesson. ■ 91

direct property they are not sufficiently cared for and hence are apt to
become untidy, and (3) from the copy-slip being placed on one side as
soon as the first line is written so that the scholar is left to imitate his
own writing.

A best boob is used in some schools with good effect. In this book a
copy which has reached the standard of writing required by the teacher
is written once by the scholar. When completed, this book exhibits
the best efforts of the pupil, hence its name.

Class management during the writing lesson.

The writing lesson is one in which activity may be combined
with almost complete quiet. There are some lessons in which
a little noisy activity is a good feature. Draft reading, the
mutual recitation class, mental arithmetic in the form of rapidly
put question and answer, are examples. Restlessness or noise
of any kind, however, during the writing lesson is fatal to steady
effort. The state of the copybooks is a fair indication of the
discipline which prevails in any class. If writing lessons
are to be followed by the disciplinary effects mentioned on p.
76, the scholars must be under skilful control. The following
details of class management may be of service.

I. Arrangement of class. Place the children an equal number in each
desk, and in regular rows from front to back. Keep them whilst
writing in the same position throughout the lesson. This arrangement
will help to prevent restlessness. In order, however, to carry out such
a plan and not to weary the children there should be a comfortable desk
provided, with foot-rest, &c., as already described. Children should on
no account be forced to reach beyond their own position for an ink
supply. During a lesson of 45 minutes it will be necessary to allow the
children a little physical exercise. Pause, once or twice, for a cheerful
song.

2. Distribution of material. The copybooks should be taken from the
cabinets by a writing monitor, and placed at the end of each row of
desks in the order in which the scholars are arranged. At the word
' books ' the first boy prepares to pass the books, and at the word
' passed ' they should be passed quietly along the desk, one at a time.
Similarly with the pens and pen-wipers. Pens are usually passed in a
vertical position with points directed upwards. The passing of pens
provides an opportunity for a mischievous boy displaying himself, and
the teacher should be on the alert to detect the first signs of irregularity.

92 Holu to Teach IVritifig.

3. Signals for starting to write. The complete control of the entire
class is a most important condition of successful effort. Steady control
is best secured at this stage of the lesson by a few simultaneous move-
ments in obedience to well-known signals. These may be the numbers
'one,' 'two,' &c., taps on a bell, or the sounds of a whistle.
With the signal ' one.' Copybooks to be opened and placed in position.

,, ,, 'two.' .Scholars to take writing positions.

,, ,, 'three.' Pens to be held forward. The method of holding
the pen to be noted and any faults corrected.

,, ,, 'four.' Pens to be dipped and the scholars to commence

writing either one, two, or three lines, accor-
ding to their proficiency.
The whole of the above signals need not be taken every time the
scholars begin to write. It is best not to work any code of signals so
frequently that they lose all stimulating effect. Children like to act with
precision and with simultaneous movement. The novelty of the signal
movements, however, is worn off when they are frequently introduced
during the same lesson. At times, the signal ' four' will be sufficient to
start the class ; at other times, it should be understood that the dying
away of the last notes of a school song becomes the signal for quiet
resumption of writing. A good effect is sometimes produced by the
teacher taking his seat at his desk, and from that position performing
the above operations in front of the scholars— the class meanwhile
silently imitating each movement.

Value of these drill mouements.

The habit of obedience is perfect when there is no hesitation in following
the command, i.e., when there is no manifestation of the smallest trace of
opposition. The action thus becomes mechanical. As tending to accelerate
the formation of the perfect habit of obedience, signals and drill movements
are of great service. The following are some of the advantages following
their use, viz. : —

1. Signals, such as the sound of a whistle, the tnp on a bell, the words
'one,' 'two,'&c., are short, and the association between the signal
and the action may be made instantaneous and complete.

2. There is no room for hesitation in interpreting the command. When
a mechanical association is sought to be formed, hesitation or delay
arising from any cause tends both to weaken and postpone the
association.

3. The tendency to imitate the action of others which all childien
possess is fully utilised.

4. The f)ersonaI cltmcnt, so far as the teacher is concerned, is removed.
The signal is obeyed ; the teacher's urd«r is not thought of.

Sripervision of the Writing of the Class. 93

Supervision of the writing of the class.

Whilst the scholars are quietly occupied with writing, the
teacher should move quickly round the class, making general
comments, at the same time, upon the quality of the writing.
He should stimulate his pupils to make their present effort
better than anything they have done before. He may also
with advantage express satisfaction at the general improvement
apparent in the writing. It will not be well to award frequent
praise to the writing of any particular scholar ; at the same
time an excellent copy, or a book, which exhibits marked
improvement throughout may be placed in some position of
honour as a stimulus to the entire class.

There will be cases in which the writing of individuals will need
correction. The best correction in all such cases is to point out the
mistake and to write the letter or word again for the scholar's
benefit. Any general error may be mentioned to the entire class, and
this may be done without necessarily stopping the writing of the
scholars. The exercise of writing is not so absorbing as to prevent the
class noticing the teacher's remarks whilst they continue to write. A
teacher must not be content with passing round his class and whis-
pering mdividual corrections into the ears of his pupils. On the other
hand, the teacher must avoid the objectionable practice of frequently
stopping the entire class in the midst of either a line or a word in order
to publicly correct the writing of one or two scholars.

To prevent the pupil copying his own mistakes it will be necessary to
provide more than one copy on each page. The teacher, during super-
vision, must carefully correct every repetition of an error, and during class
instruction he must frequently impress upon his scholars the necessity of
imitating the copy. Only by these means can his demand ' to have each
new line an improvement upon the last ' be obeyed.

Holding the Pe/?.— Children at first grip the pen too tightly between the
forefinger and thumb, and as a consequence both are bent far too much.

The following directions are slightly modified from those issued under
the sanction of the Committee of Council on Education, and published by
J. W. Parker, West Strand.

1. The pen is held between the first two fingers above, and the thumb

beneath.

2. The fingers should be slightly bent, but not too much doubled up. The

thumb is most bent.

94 Hozv to Teach Writing.

3. The hand supports itself upon the fourth and fifth fingers, and upon

these the hand glides along the paper from left to right.

4. The fingers holding the pen must not pass below the open portion of it.

5. In writing, the pen must point towards the shoulder. It ought to be

pressed very lightly and make little or no noise.

9. Press both sides of the pen nib equally on the paper.

10. The fingers holding the pen should alone move, and the hand should
not be sujiported by the wrist but by the arm a little below the elbow.

Close of the lesson.

AVhen the time for the writing lesson has expired copybooks
should be shown. The rapid review of the teacher should be
accompanied by a few words of criticism — comparing, here
and there, a pupil's effort with that previously made by him,
rather than comparing one scholar's work with that of his
neighbour. If marks are given, the same principle should
guide their allotment, otherwise the most painstaking effort of
a dull scholar may fail to be recognised.

The wiping of pens, blotting of the writing, the orderly arrangement
of books, their disposal into the cabinets, and the collection of pens,
should follow the directions already stated.

fiotes of a Penmanship Lesson.
SUBJECT: A BUSINESS LETTER.

Standard VI. Time 30 minutes.

(i) Preparation:

(a) Specimen letter written as a model on the black-board.

{i>) Specimen letters on paper — one a model of good, the other of bad

style and writing for purposes of contrast.
(c) Materials — pens, good ink supply, and a sheet of note paper.
(it) The class arranged in writing places. N'o movement from these

jilaces to be alluwed.

(2) Introduction:

(«) Refer to the advantage in after life ol being able to write a good

business letter.
(i) Read over the letter of a supposed customer, asking for a supj)ly of

goods.

Notes of a Penmanship LessoJi.

(f) Nature of the reply. ' None of the required goods in stock ; will

order immediately, and forward without delay.'
[d) The above curt statements of the principal of the firm to be taken

by a youth and turned into a proper business letter.

(3) Features of the letter :

Style of writing —

{a) Legible, because useless without, and likely to irritate, to waste

time, and to lose custom.
(1^) Neat, thus manifesting thought and care.

Style of Composition —

(a) Exact and unmistakable, in order to prevent error.

(/') Concise, so as to save time.

(4) Specimen letter.

''rospect House,

Stockport.
Aug. i8th, i8g .
Dear Sir,

Your esteemed order of the
lyth inst. is to hand and is receiv-
ing our prompt attention. We have
not the goods you require in stock,
but have comnunticated luith the
i7iam4facturers, and will forward
them to you ifnmediately jipon their
arrival.

Trusting this will suit your con-
venience.

We are. Sir,
Vour obedient servants,
WILLIAMS &- CO.
per J. Wilson.

To y. Richards, Esq. ,

Commercial House,
Lincoln.

Remarks and teaching
hints.

1. Re-write the letter so that each

part may be made a subject
for question and discussion.

2. The arrangement of the address

will perhaps be familiar. If
not, special attention must be
drawn to it.

3. Contrast uses of such terms as

Sir, Dear Sir, Gentlemen,
Madam, &c.

4. Notice the effect of a straight

margin on appearance of let-
ter. Show an irregular margin
for purposes of contrast.

5. Explain the contraction inst.,

and contrast with ' ?///.' and
'prox:

6. Draw special attention to the

arrangement of lines and
names at the bottom of the
letter.

96 Hmv to Teach Writing.

(5) Exercise and conclusion.

{a) After the board exercise, each scholar should be told to write

a model letter on the paper provided.
{b') The teacher, during this silent exercise, to pass quickly round the

class, making observations to individual scholars in a voice

sufficiently loud to be heard by the class,
(c) At the close of the writing exercise, half a dozen copies should be

taken from various parts of the class — some excellent, others

faulty. These should be criticised without mentioning the names

of their writers.

The Aims of Teaching Drawing. 97

DRAWING AS A MEANS OF GENERAL

EDUCATION.

The aims of teaching drawing.

The drawing exercise is often looked upon as merely a device
■for enabling children to imitate with more or less success a
drawing copy. One of the aims of teaching drawing is, no
doubt, to develop skill in the imitation of outline drawings.
This aim, however, is by no means either the only or the most
important one. Skill in using the pencil may be considered
one of the lower effects of the drawing exercise. A much
higher one is that of the cultivation of the eye to observe
accurately. Drawing is one of the most valuable means of
directing and of concentrating the eifort of accurate observa-
tion. Besides training the eye to accurate observation and
the hand to skilful representation, the drawing of symmetrical
figures and of natural objects results in a cultivation of the
pupil's taste for what is beautiful in outline, shade, and colour.
Lastly, but not least, drawing is a means of increasing and of
presenting knowledge. Our knowledge of any object becomes
much more full and real when we take pains to outline it in a
drawing, and our power of presenting knowledge becomes
much more effective when we accompany our statement with
either an outline sketch or a more finished drawing.

The four aims of drawing just stated should be constantly kept
before us in teaching the subject. They furnish a guide both in the
selection of the drawing exercises best suited to the class and to the
methods most likely to yield success in teaching. This is not the
place to enter upon a discussion of the various courses of instruction
which different authorities have laid down. When the importance of
training children to observe carefully and to know accurately, as well
as to draw correctly, becomes more clearly recognized, certain modifi-
cations of the drawing syllabus may be expected. It will be sufficient
here to insist that our methods of instruction (no matter what the
scheme of examination may be) should keep in vie'.7 not one only but

Draiving as a Means of General Education.

all the aims of drawing already set forth. The ' drawing course '
which most completely enables us to secure the group of aims herein
demanded is the one we should now follow, and the one which must
ultimately prevail.

Drawing course of the Science and Art Department
The Science and Art Department has issued an illustrated
syllabus of the samples of the work required of each standard
in an elementary school. The syllabus indicates the nature and
extent of the examination in drawing, but leaves the method of
tuition to the teacher. Many of the following sketches arc
taken (with permission of the Controller of Her Majesty's
Stationery Oiiice) from the illustrated syllabus mentioned above.

Standards I. and II.

Draxi-in^ fruhund ami unth ruler lives, ai^^^fs, parallels, and the simplest
iight-lined formsy such as some of those in Dyees Drawui: Book. Slau-
dard T. to dra-.o on slates. Standard II. on paper— drawing the figures
frrchatui and aftcrn'ards with the ruler.

Suggestions on the Teaching of Drmving. 99

The syllabus states, in a footnote, that ' in order to interest the children
it is advisable to teach them to draw as early as possible from actual
objects, such as the doors and windows, furniture and apparatus of the
schoolroom. It will also be found quite possible and very desirable to go
beyond the foregoing standards in teaching. Thus, drawing of bold
curves may be introduced in Standards I. and II., and exercises may be
advantageously given, in all standards, in drawing from memory.

Children in the first three standards should draw their figures 6 or 7
inches in length. In higher standards enlarging and reducing their free-
hand examples must be practised. They should generally draw on a larger
scale than children in the lower standards.'

Suggestions on the teaching of drawing in Stan-
dards I. and II.

When it is remembered that the boys of the infant school
have been practising the drawing of Hnes — vertical, horizontal,
and oblique — for two or three years, and that nearly the same
course is continued for two more years, i.e., in Standards I. and
II., it is evident that there is danger of the drawing exeicise
at the outset becoming a somewhat dreary and monotonous
task. These early lessons in drawing must be brightened in
some way or other. The footnote jxiragraphs just quoted
indicate the direction in which the monotony of the exercise may
be relieved. Children take much more delight in attempting to
draw a common object than in imitating a drawing copy. If,
by submitting objects of simple outline for the drawing exer-
cise, we are able to arouse the learner's interest, increase his
knowledge, develop his powers of observation, and at the same
time make him proficient in drawing the various lines and
figures required by the Department, we shall have done much
to solve the drawing problem, so far as Standards I. and II.
are concerned. Having laid down the general principles which
should guide us in teaching these standards, the following
details of method may prove of service : —

I. Straight lines— vertical, oblique, and parallel. Objects such as
sticks and laths should be placed in these different positions. The
parallel bars of the ball-frame, or of a gridiron, may be shown in hori-
zontal, vertical, and inclined positions. An attempt to draw some of
these may afterwards be made. At first the efforts will be very crude.
The correction of errors ; the gradual recognition of these errors, under
the guidance of the teacher ; and the efforts made by the children

loo Drawing as a Means of General Education.

themselves to improve their first attempts, are exercises which will
prove of the highest educational value. By this method drawing may
appear to make slow progress, but it should be remembered that
observation, knowledge, and interest are being maintained and
developed.

2. Straight lines conuerging so as to enclose angles of various kinds.
Here again the method of proceeding from the observation of objects to
their drawing may be followed. Sticks or laths may be arranged
by the pupils in imitation of the teacher's model. A carpenter's foot-
rule or an open book may be made to represent the angles at first
made by means of the laths. A door may be opened at the same angles.
Roman type capital letters cut out of card-board make very good
drawing copies. If the scholars be allowed to cut out the letters before
drawing their shapes, the exercise becomes still more interesting and
valuable. The names n\i;-/i( angle, acute angle, &c., may be given,
after each has been recognized in connection with a concrete presenta-
tion of it. A drawing of the edge of the carpenter's foot-rule opened
at these angles may be then attempted.

3. Simple right-lined forms. The method of treating these forms may
be shown by a first lesson upon drawing a square.

Sketch of a first lesson on drawing a square.

{a) Show a cube, and ask the class which

face they would like to draw. The t\

similarity existing between all the
faces will at once be recognized.

{!)) Place the face chosen by the scholars
in front of the class. It will be best
(if possible) to arrange two cubes of
the same size in front of the scholars
so as to prevent the sides of the cube
coming too distinctly into view, liuth
cubes should be placed at the same B

height and about level with the eye.

(c) Ask any scholar to draw on the board the direction of the edge
marked A. The teacher should perfect the attempt of the scholar,
and determine the length of the line. If the cube be one foot long in
side, make the line one foot long. Allow a scholar to nvjasure, by
means of the foot-rule, both the edge of the cube and the line repre-
senting it on the black-board.

Exercises on the Square.

lOI

{d) Take now the edge D, and ask any scholar (who thinks he can show
the direction of this edge) to draw it on the black-board. The teacher
to perfect the drawing as before.

{e) A comparison and contrast should now be made in the following
way : — Exercise the pupils in trying to settle the length of the line D.
This exercise will practise the class in estimating lengths by the eye.
Afterwards allow another scholar to measure the lengths of A and D.
Then make the lines A and D the same in length, viz., i foot. Now
point to the direction of the two lines. The contrast being estab-
lished the names horizontal and vertical may be introduced. Other
lines bearing the same relative direction should be indicated, as, e.g.,
the side and the top of the door, the side and sill of the window.
The corner enclosed by the two lines should also be named. The
term ' right angle ' is familiar, and may, therefore, be used in this
connection.

(/) Complete the figure by the same method of teaching. Introduce the
term ' parallel' when A and C, or when D and B are compared.

(g) After completing the figure on the black-board, allow the class to
draw the face of the cube smaller in size on paper. At first the
drawing on the board might remain alongside the object. When the
class has drawn a few such figures the black-board drawing may be
\vithdrawn, and the drawing made directly from the objeci. The
name ' square ' may now be applied to the completed figure.

[h) With increase of skill in drawing, the figures which have been taught,
after the above method, may be drawn by the scholars without refer-
ence either to the object or the blackboard drawing of it. Simply
tell the class to draw from memory a square with sides 5 inches in
length.

Exercises on the square.

Fig. I.

Fig.

J-

Fig. 4.

When a knowledge of the square has been gained, the chil-
dren may be required to develop other figures from it. They
might, for example, be asked to divide the square into two as
nearly equal parts as possible, and by as many ways as they

I02 Drawing as a Means of General Education.

are able. A little time would be occupied in finding out the
different figures. If a square made of paper or card-board be
supplied, it might be folded by each child so as to be divided
in several different ways. The exercise would partake of
the nature of a puzzle and as such would interest the children
Some would divide the square as in figure i ; others would
divide it as in figure 3 ; others again as in figure 4 ; and a few
might be found able to divide the square by all four methods.
In each case the eye should be trained to divide carefully into
equal parts or halves.

The new figures A, B, C, and D introduce the form of the oblong. The
face of a soHd oblong, a skeleton wire oblong, a picture frame, or a door
frame, should then be shown, and a comparison and contrast L; instituted
between the sides of the square and those of the oblong. A lesson on the
oblong should be followed by exercises similar to those on the square. It
will not be necessary here to work through the entire course of figures
required in Standards I. and II. The plan suggested in the above outline
should be followed throughout the course. The main features in the plan
are the following : —

1. Show the outline you intend to teach by means of an object.

2. Draw on the black-board the outline representation of the object. In
this exercise obtain, as far as possible, the active assistance of the
scholars.

3. Allow the children to make an outline drawing for themselves, {a) from
both object and black-board, [l>) from object alone, (<) from memory.

4. Supply names to lines and figures after the notion of each has
become familiar through the examination and drawing of objects
containing them.

5. Develop a scries of exercises in drawing common objects related to
the square, the oblong, and their divisions ; and encourage the
children to discover others. For example, a window pane, the
black-board, or a picture frai are objects allied in form to cither
the square or the oblong.

6. Frequently practise the class in judging the lengths of lines, and
after each effort test its success by ruler measurements.

7. Bear in mind that drawing has only recently been introduced as a
subject of universal school work, and that it will, therefore, be
necessary to prepare for fresh developments.

8. Remember, finally, that the first aim throughout every drawing
lesson is to develop and train the powers of the child through the
exercise, rather than to make the scholar pass an examination in
drawing.

The Drawing of Curves,

103

Standard III.

Freehand Drawing of regular forms and curved figures from the £at.

The drawing- of curves.

The drawing of curves may be approached from two direc-
tions. We may begin by using guiding hnes as shown
in Figs. I, 2, 3, and 4.

# #' "tf'

-0 c-

-Jn

Copy.

Fi?. I.

Fig. 2. Fig. 3.

Fig. 4.

The figures on the drawings indicate the order in which each curve is to be dra'wn.

I04 Drawing as a Means of General Education.

Or, we may proceed by drawing some familiar thing, such as a
kite, or a natural object, such as a leaf, without the aid of right-
line figures. We must be guided, in our selection of methods,
by the principles already set forth.

2 3

Simple objects for drawing copies.

Remarks upon the two methods.

The first method will undoubtedly enable the scholar, with least effort,
to produce a pair of well-balanced and symmetrical curves ; it will,
furthermore, result in an exercise of the eye in recognizing two equal and
opposite curves in a more or less mechanical manner.

The second method will result, at first, in a very imperfect drawing of
the object. That imperfect attempt, however, is a reflex of the scholar's
mind, and reveals the imperfect nature of its observations. This is most
important knowledge for the teacher to gain respecting the mind of his
pupil. It affords him the opportunity of directing the attention of his
scholar to what is faulty, or, better still, by a hint, of leading him to detect
what is faulty. This detection of fault, made by the pupil, and afterwards
corrected by himself, is of far higher value for intellectual ends than the
almost perfect drawing of the curves, by placing them in squares or
measuring lines (method l). So far, therefore, as the development of i/ie
p<nvcrs of perception and the training of the mind to accurate observation
are concerned the second method is in advance of the former.

Again, knaivledge is increased by the second or more natural method of
teaching. The scholar is exercised in representing an object as he sees it.
His observation at first may be imperfect and his knowledge in consequence
must be imperfect also. By the teaching to which he is subject, however,
he is led to recognize that the outlines of the leaf and the kite are made
up of a series of symmetrical curves. Afterwards, when the learner proceeds
to make a kite or to describe a leaf he will embody this knowledge in both
construction and statement. He will also look for symmetrical structures

Drawing and Writing.

105

amongst other natural objects, and wheie they do not occur, the contrast
between the bodies of irregular and symmetrical shapes will provide a
means by which the former objects will in time come to be recognized.

If the interest accompanying the effort be accepted as a measure of the
success of any method, there can be no hesitation about the right course
to follow. A pupil will take infinitely more delight in drawing objects
than he will in producing meaningless curves in square or oblong frames.
If a child be provided with drawing materials, he will at once set about
pleasing himself by drawing familiar objects. A course which succeeds in
arousing this self-effort on the part of the learner is one which we should
not hesitate to follow. Thus, it may be shown that the second
method is superior to the first in the amount of observation it
arouses, in the knowledge it provides, and in the interest it
awakens.

Why should not these curves be taught along
with Writing ?

In their report, the Royal Commissioners on Technical
Instruction state, that ' they are of opinion that some
instruction in the rudiments of drawing should be incorpo-
rated with writing in all primary schools, both for boys and
girls.' There is without doubt much that is common between
the two exercises, and they ought to be more closely related in
school work than they are at present. Take, for example, the
following simple exercise, in illustration of the association
between drawing and writing referred to.

Fig. showing connection between writing and drawing.

lo6 Drajvhig as a Means of General Education.

The most casual inspection of the sketches reveals the following
facts, viz. : —

1. That the lines on the sketches have very much in them that is
common.

2. That the scholar who can construct the letter P by means of a
couple of curved strokes, would not find much difficulty in making
the allied strokes in the subsequent sketches.

3. That drawing taught in this way would develop the power of
making bold continuous strokes instead of the scratchy tentatives
which we too often see in the drawing of to-day.

4. That both drawing and writing, by this connection, would be
mutually improved— the writing becoming more bold, symmetrical,
and beautiful, the drawing less scratchy and mechanical.

5. That the drawing lesson would, in this way, become a much more
interesting exercise than when unmeaning curves are copied from
a design.

6. That opportunity would be afforded the pupil for the exercise of
original drawing.*

Value and place of blocking out lines.

The question arises as to whether guiding lines should have
any place in drawing curved figures. At first, our drawing
subjects should be selected on account of their extremely
simple outline. After the child has made its first attempt, and
when the teacher is snowmg wherein the drawing is fault\-, a
series of straight lines, or a square, or an oblong, may, with
advantage, be placed upon the figure. By this means the
errors can be made evident. After a few failures and correc-
tions the learner may be expected to make a careful inspection
of his object before beginning to draw, and will, himself, devise
methods for securing his drawing from error. This thorough
inspection of the object, preliminary to the exercise of drawing
it, is the effort which, of all others, should be most carefully
developed. If before drawing a flat outline copy we place it
in a framework of straight lines, the result must be an

Whilst passine the proofs of this work through the press, a book entitled
nrawini; and Design.' by K. Tavlor, of the Rirmiogham School of Art. lias been
piit.lish.H bv Me'.>rs. M.icinillan & C.-). Ii bases the effort of dc^iKning upon the
acquired power of writing. ^

Curved Outline Object Copies. 107

outline drawn by a series of detached efforts, and thus the exercise
of observing the figure as a whole must become consider-
ably weakened. For the drawing of simple outline curves at
this stage, therefore, we should recommend a very sparing
use of lines for blocking out the drawing, and these should
be of the child's own choice. At the same time, the utmost
encouragement should be given to the learner to mentally
compare the various parts of the object before attempting to
make a drawing of it.

Curved outline object copies and the method of using
them.

Before proceeding to draw the regular forms and curved
figures from the flat copies shown in the syllabus, it has been
advised, in previous paragraphs, to begin with the drawing cf
the outlines of curved objects. These at first must be of the
simplest shape. Most gardens will provide leaves of simple
form, such as those of the rhododendron, bay-tree, laurel, apple,
and pear. From these the learner should proceed to more
difficult outline forms, such as the ivy-leaf, grasses with stems,
and to branches with leaves.* Ornamental forms, like those
of the syllabus, may be interspersed with these object forms
whenever a natural figure approaches and suggests them.
There are a few regular outline forms of common objects
which the scholars will take pleasure in drawing, such as, e.g.,
a pair of eye-glasses, a gas pendant, a simple two branched
chandelier, a horse-shoe, a cart-wheel, &c.

How to use the object copies.

1. Whenever possible allow each scholar to have an example of the leaf
or other natural object he is expected to draw.

2. Sometimes, as a special privilege and when a copy is well done, a
scholar may be encouraged to colour the drawing.

3. Before beginning to draw, the object must be closely examined and its
shape contrasted with that of any other object previously examined and
drawn.

4. When examining the scholar's drawing, the teacher may place measuring
lines upon it to enable the learner better to recognize his errors.

*Leaves should be mounted on card-board so as to make their outlines very distinct.
When a number of leaves are mounted on the same sheet they may easily be arranged
so as to make an effective design.

io8 Drawing as a Means of General Education.

5. Draw the copy in fine lines first ; afterwards in dark and steady outline.
Encourage real free-hand, rather than drawing by means of a series of
detached scratches.

6. When any form has been carefully studied and frequently drawn,
practise the class in drawing the same form ' from memory.'

Standard III.

Simple outline figures to be drawn freehand and also with rulers.

Hints upon the method of teaching these figures.

1. 'i he figures of regular form, such as the equilateral triangle, rhombus,
hexagon, octagon, and pentagon, should be constructed by means of
strips of thin brass wire, three or four inches in length. The bundles
of thin rounded sticks of the kindergarten will do nearly as well for
this purpose.

2. When constructed each figure should become the subject of a little
lesson. The characteristics of the structure should be pointed out by
the class, and when these arc known the name of the figure should be
given.

3. .Accompanying each construction there should be a freehand drawng
of it, the same in size. The two should be compared and tlie errors
in the freehand drawing discovered and corrected.

4. Ruler drawing of most of the regular figures may be aided by the
use of set squares. The pentagon is a difficult figure to draw with ruler
and set square. Its angle is 108", i.e., 90°, and 18° (or i^ of a right
angle).

Scale Drawing.

109

Standard IV.

The drawing of Standard IV. introduces simple scales and
drawing to scale. A simple notion of a ' drawing to scale '
will have been acquired in the geography lessons of the earlier
Standards. The subject is an interesting one for children,
and the knowledge gained is of practical value. The following
sketch of a lesson shows the character of the more advanced
exercise, and the mode of treating it : —

Suggestions for Teaching a
LESSON IN SCALE DRAWING.

1. The exercise.

It is proposed to draw the adjoining figure
upon the scale of i" to i'. Place the complete
copy, with its measurements, before the class,
and allow one scholar to state the length of
A B, another the length of C D, and a third
the length of A E.

This drawing might be shown full size on
a blackboard. The necessity for a smaller
drawing on paper would then be evident.

2. The scale.

At first it would be well to allow the
scholars to make the scale on their papers
before using it. Afterwards, they may calcu-
late the length of the various lines and draw
them the lengths determined by these calcula-
tions.

The scale on this paper is
less than the one required.
It has been reduced by half.
When teaching from a black- "^'^^ 9 e 3
board, it will be necessary to ' ' '

enlarge the scale, otherwise
the class will scarcely be able
to see the drawing.

2 FT.

The Scale.

no Drawing as a Means of General Education.

Drawing the uerticai and horizontal lines,
{a) The horizontal line is drawn first in

order to secure the Jrawing a central

position on the paper.
{b) A few questions like the following

should be worked mentally —

What length on my paper repies ts

1 foot? Ans. i".
What length on my \ aper represents

2 feet ? Ans. 2".
What length represents 6 inches?

Ans. i".
What length represents 9 inches?
Ans. f".

{c) Now measure off {a) A B equal to
2' 9", viz., 2|" ; {b) A E equal to i ',
viz., l".

{tf) Place the ruler and set-square as shown
in the diagram, gradually moving the
set-square up to E, and draw E D
equal to half i' 6", viz., 9", i.e., f"

long. Complete E C in the same line

and the same length as E D.
, Drawing the oblique lines.

{a) Place the pencil point on D, and the
ruler against it, and gradually elevate
the ruler to point A, as shown in the
figure. Then draw the line DA.

{!>) Draw similarly the three remaining
oblique lines and the figure required
is completed.

Standard V.

How to use set-square and
ruler.

How to draw a line be-
tween two points.

The nrawirif]; of this Standard introduces the scholar to the
outlines of simple rectangular and circular models. The
followi.ig are samples of the objects to be drawn : —

Model Drmving. 1 1 1

Mr. Herbert Spencer, in his work on ' Education,' recom-
mends a simple contrivance for giving the scholars the elemen-
tary notions of perspective required for the correct drawing of
such objects as the above. He says : — -

' A plate of glass so framed as to stand vertically on the table, being
placed before the pupil, and a book or like simple object laid on the
other s-ida of it, he is requested, while keeping the eye in one position,
to make ink-dots on the glass, so that they may coincide with or
hide the corners of this object. He is next told to join these dots by
lines ; on doing which he perceives that the lines he makes hide or
coincide with the outlines of the object. And then, by putting, a
sheet of paper on the other side of the glass, it is made manifest to
him that the lines he has thus drawn represent the object as he saw
it. They not only look like it, but he perceives that they must be
like it, because he made them agree with its outlines, and by
removing the paper he can convince himself that they do agree with
its outlines. The fact is new and striking, and serves him as an
experimental demonstration that lines of certain lengths, placed in
certain directions on a plane, can represent lines of other lengths and
having other directions in space. By gradually changing the position
of the object, he may be led to observe how some lines shorten and
disappear, while others come into sight and lengthen. The con-
vergence of parallel lines, and, indeed, all the leading facts ot
perspective, may, from time to time, be similarly illustrated to him.
If he has been duly accustomed to self-help, he will gladly, when it
is suggested, attempt to draw one of these outlines on paper by the
eyes only ; and it may soon be made an exciting aim to produce,
unassisted, a representation as like as he can to one subsequently
sketched on a glass. Thus, without the unintelligent, mechanical
practice of copying others' drawings, but by a method at once simple
and attractive — rational, yet not abstract — a familiarity with the
hneal appearances of things, and a faculty of rendering them, may
be, step by step, acquired. To which advantages add these :— That
even thus early the pupil learns, almost unconsciously, the true theory
of a picture (namely, that it is a delineation of objects as they appear
when projected on a plane placed between them and the eye) ; and
that when he reaches a fit age for commencing scientific perspective,
he is already thoroughly acquainted with the facts which form its
logical basis.' An illustration of this Glass Plane is supplied on the
following page.

112

Dratcfing as a Means of General Education.

:.'Y

//lustration of the
Glass-Plane. — The drawing
of the cube on th glass-plane
represents the appearance ot
cube on that plane as seen
from the jiosition of the eye.

Horizontal curved surfaces are difficult to draw in
outline. When, for example, a child attempts to outline a
drinking glass resting on a table, it is in danger of drawing
wliat it kno7vs rather than what it sees. The table is known to
be a flat surface, hence the scholar represents the lower curve
of the glass by a horizontal line. This line can be correct
only when the bottom of the glass
is level with the eye. When the
glass is below the eye-level (and
this is the position in which it is
generally placed), the lower curve
is more rounded than the upper
one. In order to make this feature
of curved outlines clear to the
class, a simple contrivance, repre-
sented by the adjoining figure,
may be introduced. The scholars
will readily see that the ring placed
at eye-level looks like a straight
edge, whilst those above and below
are elliptical in appearance and
gradually become more round as
they are raised or lowered.

Ring - Stand showing
change in appearance of
rings placed at different
levels.

Solid Geometrv.

Standards VI. and VII.

The solid geometry required in Standards VI. and VII. is
best taught by means of two blackboards arranged at right
angles to each other, one for the representation of the
horizontal plane, and the other for that of the vertica, plane.
When the representation of each plane has been drawn, the
horizontal portion of the board is lowered. The two portions
of the blackboard then exhibit the ordinary method of drawing
the two planes on a sheet of paper. The following sketch
explains the use of the board for teaching the two planes,
and shows the appearance of the drawing when made on a
single sheet of paper : —

Double-Plane Black-board for illustrating ' plan ' and ' elevation.

Assistance in solid geometry from card-board
models.

The diflikulty of giving first notions ot 'plan' and
'elevation,' and also of 'sections' — vertical, horizontal, and
oblique, may be met by allowing scholars to construct

I.I4 Drawing as a Means of General Education.

card-board models of some of the simpler figures. The
following drawings show the figures and the mode of their
construction : —

,^^^

/v\

Specimens of drawingf and cardboard exercises.

A square is described on the line AB in the uppermost fipure.

•^i'T>'''ir sqiLires .ire described on each of the sides AH, RD. CD, and AC : the square

MLNP is described on ML. Cut the cardbo.ird along the unbroken lines and fold

over along the dotted lines to form a cube similar to X .

On AB and on DC, in the middle figure, hexagons are drawn by the rules of

geometr>': the lines AB and CD ire xtended as shown in the figure, and two

portions equal to All .ire marked off on the line aliove A. and three portions equal to

AB on the line below M. Rectangular figures similar to those in thesketih arc then

drawn. After the cardlward has been rit along the unbroken lines, and folded along

rhc dotted lines, the hexagonal prism V. is formed.

Similarly draw and fold the triangular prism G.

A Lesson in Solid Geometry.

Specimen Lessons in Solid Geometry.*

The teaching of soHd geometry presents special difficulties.
For this reason it has received more attention here than either
freehand or plane geometry. The following notes of lessons
exhibit in detail the method of arranging, illustrating, and
presenting the matter to be taught.

Hints for Teaching a

FIRST LESSON ON SECTIONS.
(Solid Geometry.)

STAGE I.— First notions of 'plan' and 'elevation' of
a cube.

1. Place a cube in
position on a double-
plane blackboard, as
shown in the above
diagram. Allow a
scholar to mark out
both plan and eleva-
tion on the boards.

2. Deal similarly
with a cube on edge,
making equal angles
with the H P (hori-
zontal plane).

Appearance of ' plan '
and ' elevation ' on the
board when opened
out. The scholars
should be questioned
as to their ability to
identify the edges on
the model which each
line drawn on the
board represents.

Representation of the
drawing of both ' plan '
and ' elevation ' to be
made by each scholar
on paper.

The drawing of ' pla n '
and ' elevation ' of other
cubes of larger dimen-
sions should be required
as a test.

* The subject of shading would take us beyond the purpose of this book. It is
admirably treated in a work by Professor Cusack, of the City of London Day Training
College.

ii6 Drawing as a Means of General Education.

STAGE II.— Plan and elevation of a cube resting on one
edge {making equal angles with HP) and of
section A B.

Make a cardboard
cube and cut a section
along A B. A square
of soap may be more
quickly prepared iu the
same manner.

1. The ' elevation '
is seen to differ from
that of the cube in
Stage I. Allow a
scholar to look at
the front of the cube,
and to indicate how
this difference may
be shown (see the
drawing on the board
opened out, and di-
rect attention to the
position of A B).

2. The 'plan'
should be determined
by a scholar viewing
the cube from above,
and stating to the
class where each line
should l)e drawn on
the horizontal i)lane.

In this drawing are
shown the lines indica-
ting both ' elevation '
and * plan ' on the
double-plane board
opened out.

The ' projectors '
(dotted lines) are in-
serted so as to prepare
for the drawing on the
' right.'

Appearance of the
drawing, on paper, of
both ' plan ' and ' ele-
vation,' together with
projector lines.

Each scholar should
make the drawing on
a sheet of paper after
following the explana-
tion already given.

Make the drawing
on paper on a much
larger scale than this
small diagram.

Questions for the revision of Stage 11.

1. State what the line A B in the elevation
represents.

2. What does the shaded portion of the plan
represent ?

3. Point out the projector lines which fix the
limits of the plan of the section A B.

4. Wlicrc must the eye be placed so as to view
the plan of the cube ?

Solid Geometry.

117

STAGE III. — Plan and eleuatlon of a cube resting on
one end {with one side inclined 30° with the
vertical plane), and section along A B.

1. Proceed again as
above. A scholar
should be encouraged
to mark out the ' plan '
of the entire cube and
also of the section
along the line A B.

2. The ' elevation '
will need more careful
examination. Allow a
scholar to look straight
in front of the cube,
and then to indicate
where the boundary
lines of both cube and
section would appear
on the vertical board,
also to show how the
positions of these lines
could be obtained from
the ' plan ' by means of

V a i

5 a

This drawing indi-
cates both ' plan ' and
' elevation ' on the
board when opened
out. It also exhibits
the use of projector
lines for determining
the ' elevation ' from
the ' plan.'

Appearance of the
drawing of both ' plan '
and ' elevation.' Each
scholar to make this
drawing on paper. In
order to test the know-
ledge gained, drawings
of ' plan ' and ' eleva-
tion ' of a cube, with
side inclined 45° with
the vertical plane,
should be required.

Questions for the revision of Stage III.

1. From A and B on the cube draw the two
projector lines which fix the limits of the elevation
of the section A B.

2. Point out the position of the two projector

the dotted projector lines on the plan

lines shown on the ,,„ , , , 1

, J , f C - 3- " here must the eye be placed so as to view

_. P *• ' the position of the projector lines on the plan ?
nex/ Fig.).

Hints for a Lesson on the
SOLID GEOMETRY OF THE SPHERE

and Simple Sections.
Introductory.

The fact ' that the plan and elevation of a sphere in any
position is a circle ' should be taught previously, and be
sirnply revised as an introduction to this lesson.

ii8 Drawing as a Afeans oj General Education.

STAGE I. — To draw the plan and elevation of a sphere
and to show the elevation of the vertical section A B.

1. Place the sphere in Posi-
tion I, and point out the vertical
section A B on the sphere.

2. By viewing the sphere in
front, the scholars may be led
to see and to state —

Position I. Fig i.

Drawing of elevation o
section A B. Fig. 2.

(a) That the elevation of the section A B is a circle.
(i) That this circle is less than that representing the sphere.
{c) That both the circles, representing- the elevation of the
sphere and its section, have a common centre.

3. To draw the elevation of the sphere and the section A B. Fig. 2. After
drawing the plan (a circle) of the entire sphere, a scholar should be asked
to place his eye above the sphere (Fig. l), and by looking down upon it to
indicate upon the horizontal plane the position of the line A B (Fig. 2). Then,
in order to draw the elevation required, first lower the horizontal plane of the
board, and draw a circle vertically above xy to represent the elevation
of the entire sphere. Draw the lines CD and cd, diameters to both
circles respectively. As A B represents the diameter of the circular
section, if vertical lines (projectors) be drawn from A and B to a and d
respectively on the elevation, then the line a d is the diameter of the
circle representing the elevation of section A B.

STAGE II. — To draw the plan and elevation of a sphere
and to show the plan of the horizontal section A B.

I. Direct the attention of the
class to the horizontal section
A B. If a scholar be allowed
to look down upon the section
he will observe —

(a) That the plan of the

section is a circle.
{b) That it is less than the circle representing the plan of

the sphere.

{c) That the plans of both section and sphere are concentric
circles.

Solid Geometry. 119

2. Draw the plan and elevation of entire sphere as before Then from
observing the section of the sphere on the double-plane board, a scholar
should be led to fix the position of the line A B on the circle representing
tlie elevation of the sphere. A B represents the diameter of the circular
section whose plaa is to be drawn. Draw the diameters C D and c d, and
drop perpendiculars (projectors) from AB to ab. Then ab xi, the
diameter of the section. Construct the carcle on this diameter, and shade
it by parallel lines to represent the required plan of section A B.

STAGE It I.— To draw the plan and eleuatlon of a sphere
and to show the plan of the oblique section A B.

1. The elevation. Direct ^ ^
the attention of the class to the
oblique section A B, and after
drawing a circle to represent
the elevation of the complete
sphere, allow a scholar to look,
from the front of the sphere,
along the oblique section. The
line A B on the elevation will

thus be determined. The following facts may now be shown, viz. : —

{a) The section A B is bounded by a circle. Simple inspection

of the section will show this.
{b) The line A B is the diameter of this circle.
(<r) A semi-circle A C B drawn on A B as diameter represents

the true shape of half of the circular section.
((/) In order to determine the position of the points D and E,

the semi-circle A C B is enveloped in the rectilineal

figure.

2. The plan. The scholars will find a diiT!iculty in determining the
true shape of the plan of the section by simple inspection. The following
directions must be supplied, viz. : —

(a) Draw a circle vertically below the elevation circle. Join centres,
and draw the diameter through a 6 on the plan.

(1^) Then a 6 is the plan representation of the diameter A B.

{c) The points f, k, I on ab represent the plan of F, K, and L
respectively on the elevation.

{(T) In order to determine the curve representing one-half of the
section, draw I e, kc, and fd equal in length to the corre-
sponding lines on the elevation, and through the three points
thus determined draw the curve adcb, and repeat on he
other side of a 6 to complete the section in plan.

120 Drawing as a Means of General Education.

Summary of opinions of educational experts on
drawing as a means of training-.

Drawing has recently assumed a position of great importance
in general school work. Instead of being an optional subject
taken by a few schools, it has become, by a recent enactment,
compulsory in all schools for older boys. Hitherto, the subject
has been viewed mainly from its practical and artistic aspects.
Now that it takes its place amongst the ordinary subjects
of school instruction, and is made to rank with those
which are termed obligatory, it becomes necessary to look at it
as a means of mental discipline, as well as a means of
developing artistic skill. The power to represent the outlines
of familiar objects by a drawing is possessed by all children.
This is evident whenever a pencil and paper are placed in
their hands. These first eflforts are very crude, it is true, but
crude as they are, the attempts to draw the outlines of
surrounding objects give great pleasure to the child who
makes them, and when encouraged and directed the pupil
makes good progress. With drawing, as with arithmetic, the
question of first importance is not so much how to obtain a
certain amount of skill as how to develop the powers of the
child in the way most interesting and most natural to it. The
lesson in drawing is of value jirimarily in the following direc-
tions, viz., ( I ) as an exercise of the eye in observmg exact shape ,
and (2) as an effort of the hand in guiding the pen or pencil so
as to reproduce the observed shape. These iwc primary efTects
are followed by others, viz., (3) increased knowledge of the
objects drawn, (4) power to reproduce that knowledge, and (5) a
sense of the harmonious in form and colour. These intellectual
effects are the most important for the teacher to aim at, and any
permanent curriculum of drawing must lend itself in the first
place towards securing them. The course at present laid down
for the little children up to the end of Standard II. is not so fully
adapted to the ends in view as could be desired. There has
been an attempt in the above pages to suggest directions in
which the course might with advantage be either altered or
extended. Before a final judgment is formed, it may be well
for the reader to become accjuainted with what has been said
about drawing by educationists whose advice has been followed
in most of the recent modifications in other branches of
school work.

opinions of Educationl Experts. \2X

' Provide children with occupation for mind and hand. Drawing is to
be practised by all. It matters not whether the objects be correctly
drawn or otherwise, provided that they afford delight to the mind.' —
CoMENius, quoted by Rev. R. H. Quick.

' Children, who are great imitators, all try to draw. I should wish my
child to cultivate this art, not exactly for the art itself, but to make his
eye correct and his hand supple. My intention is not so much that he
should get to imitate objects, as to get to know them.' — -Rousseau.

' A person who is in the habit of drawing, especially from nature, will
easily perceive many circumstances which are commonly overlooked,
and will form a much more correct impression even of such objects as
he does not stop to examine minutely than one who has never been
taught to look upon what he sees with an intention of reproducing a
likeness of it. The attention to the exact shape of the whole and the
proportion of its parts which is requisite for the taking of an adequate
sketch, is converted into a habit, and becomes productive both of
instruction and amusement.' — Pestalozzi.

'The spreading recognition of drawing as an element of education
is one among many signs of the more rational views on mental culture
now beginning to prevail. . . . Once more it may be remarked that
teachers are at length adopting the course which nature has perpetually
been pressing on their notice. The spontaneous attempts made by
children to represent the men, houses, trees, and animals around them,
are familiar to all. Had teachers been guided by nature's hints, not
only in making drawing a part of education, but in choosing modes of
teaching it, they would have done still better than they have done.
No matter how grotesque the shapes produced; no matter how daubed
and glaring the colours. The question is not, whether the child is
producing good drawings. The question is, whether it is developing
its faculties.'

' From what has been said, it may be readily mferred that we condemn
the practice of drawing from copies ; and still more so, that formal
discipline in making straight lines and curved lines and compound lines
with which it is the fashion of some teachers to begin. It has been well
said concerning the custom of prefacing the art of speaking any
tongue by a drilling in the parts of speech and their functions, that it
is about as reasonable as prefacing the art of walking by a course of
lessons on the bones, muscles, and nerves of the legs ; and much the
same thing may be said of the proposal to preface the art of represen-
ting objects by a nomenclature and definitions of the lines which they
yield on analysis. Just as the child incidentally gathers the meaning of
ordinary words from the conversations going on around it, without the
help of dictionaries, so, from the remarks on objects, pictures, and its
own drawings, will it presently acquire, not only without support, but
even pleasurably, those same scientific terms which, when taught at
first, are a mystery and a weariness.' — H. Spencer.

The following statement on the different values of drawing is taken
from a work on ' Industrial Training ' by Sir Philip Magnus. He says : —
' Drawing is the most important of all means suggested for the training
of the hand and eye ; its practical uses in industrial life are universally

122 Modelling as a Means of Intellectual Training.

recognised and, as mental discipline, its value is attested by the stimulus
it affords to the accurate observation of things. As a universal lan-
guage it ought to be taught to ail. By writing we are understood by
those only who know the language in which we write ; but drawing
affords a means of expression which all who run may read. To the
artisan, drawing is essential that he may be able to receive or to give
instructions and to properly understand his own work. To be taught
to draw is as essential to a child who is to be employed in any one of
the mechanical arts as to be taught to speak and to write. It is one of
the three modes of expression which every one should have the oppor-
tunity of learning.

' The recognition of the importance of cultivating the hand, not only
as an instrument of artistic skill, but also as an organ for acquiring
knowledge, is a distinguishing feature of the "New Education." The
hand, properly cultivated, helps to convey to the mind accurate infor-
mation of the external world, and is the instrument by which mental
images of form and beauty are impressed upon the crude and shapeless
matter. It is a channel through which the mind is enabled to perceive
the properties of things and the implement by which it impresses upon
things its own ideas. The artisan who fixes in clay, in wood, in ivory,
or in silver, the forms of beauty projected from his mind, is a true poet.'

Modelling in Clay.— A means of intellectual training.

In many infant schools, and in some upper schools, oppor-
tunity is afforded for operations in clay modelhng. This
exercise is designed especially to train the sense of sight and of
touch — eye and hand. In drawing we represent objects by
lines on a flat surface ; the sphere, for example, is represented
by a circle, with shading to give the appearance of solidity; the
drawing, therefore, is an expression only of what the eye
recognises in the sphere, i.e., outline and distribution of light
and shade ; the model, however, is a complete reproduction of
all the features of exact size and solid shape which the sphere
possesses, and is, therefore, a much more real and concrete form
of representation. At the same time that these fuller and more
perfect notions of spherical form are being developed by the
fingers and the hand, the eye is bemg exercised in taking in the
appearances of light and shade which indicate that form. In
fact, the movement of the hand in moulding the clay into the
spherical shape is directed by the appearance the clay object
presents to the eye, and when the eye is satisfied with the shape
produced by the hands the modeller ceases to work. Intel-
lectually the exercise is of high value for — (i) cultivating the
powers of observation ; (2) developing an appreciation of form ;
(3) fostering habits of neatness and order; (4) forming a

Modelling in Clay. , 123

habit of attention with the least expenditure of energy; and (5)
developing manual dexterity.

The modelling of the sphere is largely aided by rolling on a board ;
when, however, the sphere has been satisfactorily modelled, it may be
modified by the hands and fingers into a variety of shapes, as e.g. an
apple, an orange, a pear, a bird's nest, a cup, &c.

In the same way a series of exercises may be developed having the
cyHnder as their basis, the allied objects being a candle, a ruler, an
gg, inkivell, drinking glass, &c.

Unless these exercises be made means of exact observation, the
educational value of the lesson will be but slight. At first the child
makes a very rough attempt. The teacher's copy, worked out in the
presence of the class, suggests further effort and stimulates to more
successful work. When, however, the pupil has become satisfied with
his result, the teacher will be able to indicate error in shape which had
escaped the child's notice. Fresh effort is aroused ; closer and more
exact observation is awakened and a finer discrimination of shape is
secured. The intellectual advantages of the lesson in clay modelling
will be due largely to the skill with which the teacher leads the pupil
to the recognition of unobserved defects, and to the tact with which
he stimulates the modeller to renewed and successful effort.

Practical value of modelling. — Besides the intellec-
tual effects enumerated above, there should be placed to the
credit of the exercise, a gradual growth of finger and hand power.
This power needs early development, and unless practice is
afforded whilst the fingers and hands are in a pliant condition,
i.e., before the ages of twelve to fourteen, the higher kind of
manipulation is but rarely attained. When this power is
developed it becomes of great service to the possessor when
he takes his place in the workshop or factory.

The Royal Commissioners on Technical Instruction state in their report,
that they ' are of opinion that more attention than has hitherto been
devoted to it should be directed to the subject of modelling in the elemen-
tary school. Modelling is an exercise of great imj^ortance to the future
workman, and its rudiments can well be taken up, as in Continental
schools, at the earliest age.' One of the Commissioners (Sir P. Magnus)
has also written in his work on Industrial Education to the following
effect : —

' Modelling may be regarded as the complement of drawing. In its
earlier states it is an easier, and is generally found to be a more
interesting exercise. The first efforts of the pupil should be directed
to the production in clay of a fac-simile of some simple solid object,
such as an orange or a pear. The resemblance between the object

124 Questions /or Examination.

and the clay model will be more easily recognized by the child than
the likeness of the object to its outline on paper. In the production
of the solid model there is a gratification of the sense of power, which
affords the child more satisfaction and pleasure than in making a
representation of the object on a flat surface. The training of the
eye in appreciating form and size is very valuable, as is also the
exercise of the hand in translating into the concrete the visual im-
pressions. Any one who has witnessed the concentration of thought
shown by children engaged in modelling, and their successive efforts
to make their model similar in shape and size to the object before
them, will realize the value of such lessons as sense exercises. Lessons
in modelling may be easily graduated, and as the pupil advances he
may be taught to model from ordinary drawings, producing in relief
what he sees in the flat. The relation between an object and its
picture will be best understood when a child can correctly depict the
object on a flat surface, and can conversely pioduce a solid object
from its pictorial representation. The skill acquired by modelling is
of great practical use in the plastic arts, bui as a subject of elementary
education, its value is greatest as an educational discipline.

Modelling requires very simple and inexpensive appliances, and it
can be taught with equal advantages to boys and girls.'

QUESTIONS FOR EXAMINATION.

Taken from the Pupil Teachers' Examinations.

What points would you chiefly keep in view in giving a dictation lesson?

Take the following words, and give a list of others which might be
grouped with them for a spelling lesson — rough, should, which, many,
taught.

Name eight words in the spelling of which young children often make
mistakes, and explain by what sort of exercises such mistakes may be
corrected or avoided.

Write as a large-hand copy the words ' Geometrical Drawing,' and point
out which of the letters is likely to present special difficulties to a young
scholar, and what rules should be observed in forming snch letters.

Arrange the letters of the alphabet in the order of their difficulty for
the teaching of writing, and show how you would group together the
gasiest of them for lessons to young beginners.

Describe the best way of ruling slates so as to help young scholars to
understand the forms and proportions of letters. Give an example.

Describe the way of teaching the children to hold their pencils properly.
What are the common mistakes to be guarded ngainst ?

In writing in copy-books there is a great tendency to repeat the same
mistake down a whole page. What is the best method of correcting this ?

Qi4estio7n for Examination. 125

_ Arrange in groups the capital letters, putting together those which are
similarly formed. Show in what order you would teach them, beginning
with the easiest group, and proceeding to the most difficult.

What is the use of tracing in the earlier copy-book exercises, and what
are the objections, if any, to the practice ?

Write the word 'striding' in small letters, and point out the mistakes in
it which you would watch for ?

What use could you make of a threefold ruling of the lines on a child's
slate and on the teacher's black-board, in order to show more clearly the
forms and proportions of letters, and the mode of joining them— Supply
an example, after making three parallel lines for the copy ?

Say how you could, either by paper folding, or by simple drawing,
make the properties of a square visible to young children, and explain
what are the uses of such a lesson.

Taking a square of paper, what simple ideas of form can you impress
on a class by folding a paper so as to make a single crease in it ?

Taken from Scholarship Examinations.

Mention twelve words of special difficulty, and show how you would
help your scholars to spell them correctly.

Give specimens of any six capital letters, carefully written, so as to
illustrate their proportions, and the rules for their formation.

flow should the mistakes be corrected in a dictation lesson to
Standard III. ?

What preparatory observations as to difficulties of spelling should be
made before proceeding to write the following from dictation ? : —

The watery dykes display luxuriant verdure ; bulrushes and water-
flags have attained their freshness; willows nre rich with foliage in
sylvan nooks, agreeably hidden in a leafy arbour.

126 Alternative Syllabus of Instruction in Drawing.

Alternative Syllabus of Instruction in Drawing in
Elementary Schools.

In pages 99-102 it has been suggested that the drawing in the lower classes
should be made much more varied and interesting. The value of drawing
outlines of natural objects instead of drawing from flat copies has been also
urged, and the necessity for changes in the old drawing Syllabus has been
indicated. The Department has recently published "An Alternative Syllabus
of Instruction in Drawing," from which the following "Introductory Notes"
and Sample Copies are taken. The complete Syllabus can be obtained at a
charge of 4id.

INTRODUCTORY NOTES.

"This Syllabus is framed on somewhat different lines from the Syllabus
hitherto in use and is not intended to supersede the latter, but merely to provide
an alternative course of instruction for such Schools as choose to adopt it.

The principles on which this Alternative Syllabus is founded are a develop-
ment adapted to the needs of older'scholars, of methods with which teachers
are already familiar in the infant school.*

A leading feature in this Syllabus is the introduction of drawing at arm's
length. Where there are facilities as regards room, etc., this will be best done
by scholars standing in front of their slates or boards, which should be fi.xed in
a nearly upright position. In schools where this cannot be arranged the
scholars should sit as far back as possible, leaning against the desk behind,
with slate or board propped nearly upright on the desk and at arm's length
from the scholar, who should work freely from the shoulder, never touching the
slate or board with the wrist or more of the hand than the top joint of the little
finger. The slate or board must not be turned, aljout nor the position of the
body shifted in order to draw curves or lines in various directions. These
remarks do not, however, apply to brush-work or drawing with instruments.

The possible close connection of the present course of drawing with other
modes of teaching in the school should not be lost sight of. Kor example, at
many points a good teacher may find it possible to use this course as a basis for
hand and eye training in other suitable material, while the introduction of each
new form, e.t^., the egg-form, V\g. 7, .Standards I. and II., may be suitably con-
nected with object lessons or stories on familiar objects which suggest that form.

The forms produced and their combinations will naturally suggest decorative
and natural shapes, and it should_be the object of the teacher to develop this
as.sociation of ideas.

The materials required will be (i) slates, with chalks, white or coloured, or
soft composition slate pencil; or, where this is practicable, small black-boards or
pieces of blackened millboard with chalksTand a damp sponge or rag ; (2) cart-
ridge-paper and pencils ; (3) camel's hair brush, and one or more water colours.

Nothing in this .Syllabus must be taken to imply that importance is not to be
attached to accuracy and care in the^e.xecution of the work herein suggested."

• The followintj passages in''a CircuI,ir[.on the' sulijcct* (Education Department Circular 322, 6th
I-"ebruary, 1893I may Xtc noted ; —
Two leading principles should be regarded as a sound basis for tlic education of early childhood.
^1) I'he recognition of the child's spontaneous activity, and the stimulation of this activity in certain

wcll-dcfined tlirections by the teachers,
a) The liarnionious and complete development of the whole of a child's faculties. The teacher
should pay (especial regard to the love of tnovement. which can alone secure healthy physical
conditions ; to the observant use of the organs of sense, especi.dly those of sight and touch ; and
10 that eager desire of (|uestioning which intelligent children exhibit. All these should be
encouraged under due limitations, and should be ueveloi>ed simultaneously, so that each stage
of development may be complete in itself.

• ••••••

You should direct the attention of teachers to the chief consideration which underlies true methods
of infant teaching, viz., the association of imc lesson with another through some one leading
idea or ideas.

The development of the above principles in the lower standards of schools for older scholars is
dealt with in Circular 333 (Educational Department, 6th lanuary, 1894).

Alternative Syllabus of Instruction in Dratving. 127

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H(nv to Teach Arithmetic. 129

HOW TO TEACH ARITHMETIC.

Introduction.

The subject of arithmetic is one. of primary importance in
every school curriculum. Whether we consider its value for
purposes of every day life, for progress in other branches of
instruction, or for mental discipline, the importance of a know-
ledge of arithmetic becomes immediately apparent. We shall
be best able to set out the relations existing between the
various values of arithmetic after a full consideration of the
objects aimed at in teaching the subject and the methods
best suited for the attainment of them.

Code requirements.

The Code sets out the order in which the different branches
of this subject are to be taken. The order therein stated is
well known and need not be repeated. It may, however, be
noted that after the simple rules have been taught there is
no necessity, arising from the nature of the subject, for the
compound rules, and those of practice and proportion to follow
immediately. It is certainly a more scientific plan to take
fractions immediately after the simple rules, and afterwards to
apply the knowledge gained of both integers and fractions to
the consideration of the compound rules, of practice and of
proportion.

A knowledge of fractions is very helpful to a full understanding of some of
the processes required in working the compound rules, as, for example, the
fractional parts of a penny. These become unmanageable in compound
division without a knowledge of fractions, and where remainders are
repeated in succession only an approximate answer is possible. The same
difficulty is felt in the successive divisions of a sum in practice. Aliquot
parts again involve a knowledge of fractions, and the theory of
proportion cannot be completely grasped without this knowledge.
For these, amongst other reasons, it is held by many that a simple
course in fractions should be taken before attempting the compound rules.
On the other hand, it is urged that the effort to master fractions before
the more useful compound rules involves too long a delay of the latter.

t30 Ho7v to Teach Arithmetic,

These latter rules are of great service in almost every occupation, and it is
held that their practical utility is sufficient just'fication for the prior position
in which they are ordinarily placed.

// the curriculum arranged in tlie code be examined it will be
se3n that a middle course is therein adopted. For example, along
with practice and single rule of three by the rule of unity, there is a
prescribed course in the addition and subtraction of proper fractions
with denominators not exceeding 12. In Standard VI. both vulgar
and decimal fractions are taken before proportion and interest. This
compromise does not claar all the difficulties out of the way. For
example, the remainders in the farthings of compound division have
still to be neglected, and for the full working of the successive
remainders in a practice sum a knowledge of both multiplication and
division of fractions is necessary. So long' as our complex system
of compound rules holds, and so long as children leave school
before passing through the entire curriculum of the Standards,
it will be necessary to accept the compromise and to disregard
a completely scientific order in the sequence of the rules of
arithmetic.

Recent additions to the arithmetic course.

A significant addition to the arithmetic curriculum appeared
for the first time in the Code of 1890. The paragraph reads as
follows : — ' The Inspector should satisfy himself that the prin-
ciples of arithmetic are properly taught in the school.' In the
Instructiofis to Jnspectors this paragraph is referred to in the
I'ollowing terms : — ' A footnote to Schedule I. requires you to
satisfy yourself that the reasons of arithmetical processes have
been properly explained and understood. This is a depart-
ment of school work which has been much overlooked. There
is in an elementary school course scarcely any more effective
discipline in thinking than is to be obtained from an investiga-
tion of the principles which underlie the rules of arithmetic.
It is, therefore, desirable that you should very frequently ask
the teacher of tlie class to give a demonstrative lesson on the
subject, and he should so work out an example on the black-
board as to make the reason for every step of the process
intelligible and interesting to the scholars. When children
obtain answers to sums and problems by mere mechanical
routine, without knowing why they use the rule, they cannot
be said to be well instructed in arithmetic'

In the departmental circular on the instruction of pupil -teachers

it is stated that 'The papers prepared by the pupil-teachers at the
periodical examination show that the teaching of arithmetic leaves
much to be desired. The arithmetical e:<?rcises have been too cfteo

Need of Practical Application of Arithmetic. T31

limited to the woikiag out of sums, and have failed to exercise the
reason of the learners in connexion with the meaning and the theorv
of the rules employed. More attention will now be needed to this
important part of the teacher's training.'

The above paragraphs sufficiently indicate the growing im-
portance attached to the teaching of the principles of arithmetic.
In the following pages guidance will be offered sufficient to
suggest the direction in which the teaching of arithmetic should
proceed in order that the above requirements may be fulfilled.
An exhaustive treatment of the subject will not be attempted.
The teacher's best methods of instruction in the principles of
arithmetic will generally be those which his own ingenuity
devises, and modification of the methods suggested in these
pages may with advantage be made in accordance with the
material at the disposal of the teacher and in harmony with
the condition of the knowledge of the pupil.*

Need for a more practical application of the processes
of arithmetic to the circumstances of every-day
life, and to the facts of History, Geography, and
Science.

The introduction of problems has necessitated the association
of the rules of arithmetic with the experiences of the field, the
market, and the counting house. There seems to be no reason
why these associations should not be considerably extended, nor
why arithmetic should not become a means of communicating
and fixing very much useful knowledge in connection with
history, geography, and science. The persistent and continued
isolation of arithmetical exercises from all connection with the
other school studies must result in a waste of effort. The
mind of the pupil might, whilst working sums, be economically
concentrated upon distances, dates, measurements, &c., the
acquisition and retention of which would prove of service in other
branches of learning. The associations suggested below would
result in the scholar being ready to make more use of his
knowledge in ordinary affairs, and would tend to weaken the
habit of always connecting arithmetical operations with par-
ticular rules.

The class-subject course of ' Experimental Arithmetic,
Physics, and Chemistry ' and ' The Alternative Courses of

* Other additions to the curriculum, including ' tots,' the metric system, and the new
alternative scheme for teaching the simple rules, will be dealt with in the chapters of
which each topic naturally belongs.

132 How to Teach Arithmetic.

Arithmetic in Schedule I.' are steps in the direction indicated.
This matter is treated very fully in Prof. Bain's ' Education as a
Science.' The following extracts afford excellent suggestions for
the construction of a rational course of arithmetical studv, and
they indicate, furthermore, the reason why such a course is
likely to be followed by valuable intellectual results.

' There is an important principle of economy in Education that applies to
Arithmetic, but not to it alone, that is, the utilizing of the questions or
exercises by making them the medium ©f useful information. Instead of
giving unmeaning numbers to add, subtract, multiply, and so on, we might,
after the more preliminary instances, make every question contain some
important numerical data relating to the facts of nature, or the conventional
usages of life ; anticipating as far as may be the future exigencies of the
pupils in their station of life. Not that they should be asked to commit
these data to memory, or be twitted for not having attended to them, but
that in those moments when attention is not engrossed with the difficulties
of the purely arithmetical work, it may chance to fix upon the numbers given
in the question, and thereby impress these on the memory ; for example —

' The leading dates In chronology might be embodied in a \tiriety of
questions. Such simple examples in subtraction as how many years have
elapsed since the Conquest, since the death of Charles I., since the nnion
of England and Scotland, the dates being either given in the question,
or assumed to have been otherwis'e given, would help to impress these
on the memory.

'In a similar way, important geographical numbers could be
stamped on the recollection by being manijiulated in a variety of
questions. The dimensions, area, and population of the three kingdoms;
the proportion of cultivated and uncultivated land ; the population of
the largest cities ; the productions, trade, taxation of the country — all
which become the subject of reference and the groundwork of reasoning
in politics — could receive an increased hold on the mind by their iteration
in the arithmetical sums.

' The common weights and measures should be familiar to everyone,
and these might be so wrapped up in exercises that the pupil could not
avoid taking note of them. A most valuable datum in the ordinary con-
tingencies of life is the relation of weight to bulk, given through the
medium of water. A cubic foot of water weighs 62^ lbs., and a gallon
weighs 10 lbs. ; these are data that no mind should be without. If a few
leading specific gravities — cork, wood (of some of the commoner kind),
building stone, iron, lead, gold — were added, there would be the means
of readily arriving at many interesting facts.

' Frequent reference might be made to foreign moneys and scales of
weights and measures, as of almost universal interest ; and especially to
the decimal system of foreign countries.

Twofold Aim and Result of Teachmg Arithmetic. 133

' Such is the so-called perversity of human nature that the
mind would often take a delight in dwelling upon these casual
figures, because to remember them was not a part of the task.
And further, by a general law of the mind, if a question for
some reason or other has engaged the attention in an unusual
degree, the memory will receive the indelible stamp of all its
parts and accompaniments.'

The twofold aim and result of teaching arithmetic.

From what has been stated it becomes evident that our aim
in teaching arithmetic must be twofold. We must aim at
securing ability to work sums correctly, and we must provide that
mental discipline which a thorough knowledge of the reasons of
the rules of arithmetic is capable of yielding. Corresponding to
each of the above aims are the following results. There are
those which may be termed practical, and there are others
which may be termed theoretical and scientifc. The first may be
summed up in the ability a pupil manifests to use the rules of
arithmetic with certainty, accuracy, and rapidity. To be able
to grasp the nature of a problem, to apply the right rule or
rules to its solution, and to work through the several stages of
the exercise with accuracy and rapidity, are evidences of a
practical knowledge of arithmetic. The learner is acquainted
with the 'art of arithmetic' When, however, the scholar is
able to explain each stage in the working of a sum ; to show
why the process he uses brings about the desired result ; when
he is able to state the means by which any given rule has been
established, and is able, furthermore, to show that the sum
to be worked is a particular example of the rule in question,
then his knowledge of arithmetic becomes scientific. The
pupil is acquainted with ' arithmetic as a science.'

Whilst recognising the great importance of a thorough grounding
in the principles of arithmetic (an operation which perhaps more than
any other in the entire round of school work affords opportunities for
exact statement and reasoning) we must be on our guard against
asserting that the so-called ' mechanical practice of arithmetic ' is of
no value whatever for intellectual exercise and result. There are
efforts of memory, of concentrated attention, of orderly arrangement,
and of accuracy which accompany the study of arithmetic for practical
purposes not to be despised in any estimate of the intellectual value of
this school subject.

134 How to Teach Arithmetic.

An example in illustration of arithmetic taught («) as an
art, {b) as a science.

If a \mY>\\ be required to work the following sum in subtraction, viz., to
take 17 from 85, he is told, it may be, to arrange the sum thus, viz., 5i

and to proceed by borrowing ten so as to make the 5 in the units place equal
to 15 ; he is further told that 7 from 15 = 8, and that this figure is to be
placed in the units column of the answer. The pupil is then desired to
proceed to the tens column and told that ha\ing borrowed ten in order to
make the five in the units column 15, he must pay back i to the next figure
to the left in the subtrahend. The operation is completed by subtracting
the 2 (obtained by paying back i) from the 8, making in this way the
figure 6 to be inserted in the tens place of the answer. Thus the answer
68 is obtained. The pupil has arrived at the correct result, and for
ordinary purposes this is sufficient. A practical result has been obtained
by a mechanical method. The scholar may in this way acquire ability
to work any example in subtraction and be unable to explain a single
step in the process.

If, now, instead of proceeding as above, the pupil is taken over a
series of examples like the following, viz. : —

6-2 = 4, 9-5=4, 8-4 = 4, 11-7 = 4,
he will soon recognise that the answer is 4 in all the cases, and with a
little guidance he may further be led to see that in each example the
same number is added to both minuend and subtrahend. The general
truth, viz.. 'that the ansv/er remains unaltered when the
same number is added to both minuend and subtrahend," should
now be recognised and stated. If the scholar be encouraged to aj^iply
the truth formulated above to the example in subtraction just worked,
he may be expected to state that lO has been added to the units
figure 5 in the minuend in order to make it 15, and he may then be
asked (after the process of subtracting 7 from 15 has been completed)
to state what number must be added to the subtrahend in order that
the answer may remain unaltered. The pupil (applying the principle
or rule established above) will answer 10, and now instead of using
the misleading expression ' pay back one,' the scholar is prepared to
state that i ten must be added to the subtrahend because lO has been
already added to the minuend. The reason for making the i ten
in the subtrahend 2 tens is recognised ; the pupil is in fact
applying the principle of equal additions previously established. There
is nothing mysterious in the operation, nothing is accepted on trust from
the teacher. The scholar is trained by a simple form of reasoning and
by his own efl'ort both to formulate a truth and to apply it to a
particular ixampli', A practical result has been obtained as
before, but it has been obtained by a scientific method.

The twofold result of teaching arithmetic exemplified above will be
kept in view in the succeeding chatters, and it will sron become
evident that both aims may be simultaneously secured. 'Ihe work of
both teacher and pu])il will be considerably increased during the early

Each Stage to he taken In Logi^ 137

stages of arithmetic, and somewhat slower pr\ \ " -■^11(5^

rules may consequently be expected. When, ho' \ „

the higher branches of arithmetic he will be "^ \

much more rapid progress than would be possii r*

results were aimed at in the simple rules.

Each successive stage to be taken in lo,

and no use to be made of mere ..^^eii

devices.

Let this be accepted as the golden rule throughout the entire,
range of our arithmetical exercises. Let there be no use of
mysterious contrivances to obtain equally mysterious answers.
In the division of fractions, for example, let the class know
why we invert the divisor ; in multiplication by 35, let the
scholars be in a position to state why we place the first figure
of the result when multiplying by 3 {i.e., 30) one place to the
left ; in division by two factors, let them know why, in order to
find the true remainder, we multiply the first divisor by the
second remainder and add the first remainder to the result ; in
proportion, let the reason for placing the term of the same name
as the answer in the third place be made quite clear. Let
all similar difficulties be explained as they arise, and let there
be, furthermore, a logical arrangement of the successive stages
in each rule, so that the connections between a present process
and those which immediately precede and follow become
evident. If in this way, from the simple effort of adding one
and one onward, we let no stage pass without a thorough
explanation of the processes used, we shall have done much to
secure the twofold aim we have in view.

Numbers— concrete and abstract.

{a) First notions of number are concrete.

For example, the number ' one ' is at first associated in the
child's mind with one house, one doll, one horse, one dog, and
so on. Afterwards one doll and one doll are termed ' two
dolls,' one dog and one dog are termed ' two dogs,' and so on
for horses, houses, &c. So^long as the child uses number in
association with objects, the number so used is said to be
concrete. Uncivilized races continue to use number in the
concrete throughout life much in the same way as the child
does. For example, the number three is associated with thre^
stones, or with three notches in a stick.

136 Hoto to Teach Arithmetic.

The Kindergarten exercises of the infant school afford many ojiera-
lions in counting, in adding, subtracting, multiplying, and in dividing
by concrete numbers. First notions of the equal parts into which whole
numbers may be divided, i.e., of fractions, may be given in the concrete
by means of the divided cubes of Frnebel's gifts. In the early stages
of arithmetic number is necessarily concrete. In the more advanced
exercises purely concrete notions of number are mainly introduced for
purposes of illustration.

(^) Progress to the abstract.

After several exercises in the addition of concrete numbers,
as, for example, two sticks and two sticks to make four sticks ;
two marbles and two marbles to make fojir marbles, &c., the
notions of two and four tend to become separated from their
connection with sticks and marbles or other objects. Instead
of objects of any kind we associate these numbers with the
more or less arbitrary symbols, 2 and 4. We then proceed to
the addition of 2 and 2 to make 4, or we multiply 2 by 3 and
make 6. The numbers in each of these latter cases are entirely
separated from association with objects such as sticks and
marbles. Whenever we thus deal with numbers (either in
counting, or adding, or multiplying, &c.), without reference to
objects of any kind, we use number in the abstract.

Only small calculations can be dealt with by means of concrete
numbers. It would be an extremely cumbersome exercise to attempt
a long sum in addition or in multiplication by means of concrete
numbers. Children sometimes make extended calculations in multipli-
cation and division by means of strokes on their slates. In this case
they are using number in the concrete, and hence they make very slow
advance. To make rapid progress it becomes necessary to be able to
use abstract number. As, therefore, advance is from concrete to
abstract, it becomes important in teaching to determine how the tran-
sition can most readily be effected

The ability to use and understand abstract number is one
of the first signs of real progress in arithmetic. The child
prefers to associate number with objects ; it will count the
beads on the ball-frame, and will add and divide the cubes of
Gift III. ; it will state the number of its sticks or its corks,
with very little apparent effort. If, however, instead of adding
together two cubes and two cubes to make four cubes, we
])lare the figures 2 and 2 together in the form of addition, the
child hesitates, there is less interest awakened in the

Numeration and Notation. 137

operation ; the teacher must assist and stimulate the child.
The following are two important directions in which assistance
may be rendered : —

I. By working exercises by means of objects side by side witt} abstract
symbols.

For example, the addition of four cubes and four cubes to
make eight cubes may be shown as in the diagram. At the B^ BS
same time the figures 4 and 4 may be placed in the form of ^ -*

simple addition and the sum 8 (obtained first in the concrete) jwg^
may afterwards be placed in the answer Many exercises of
this mixed character must be worked before the transition
from the concrete to the abstract is made.

eOL

4
4

2. By associating tlie number witli a variety of objects.

Suppose the number five is only known in the concrete, and we wish the
abstract number to take its place. The number in question must be first
considered in connection with difi'erent objects, such as five balls, five slates,
five sticks, five desks, &c. Amidst the varying aspects of the different
groups of objects — some square, others round, some made of stone, whilst
others are made of wood — the pupil learns to identify a similarity in the
number of objects in each group. This common condition of the different
groups is in time withdrawn by an effort of abstraction from connection
with any of the objects themselves, and is finally associated with a purely
arbitrary sign, viz., the figure 5. Afterwards when the child says
5 + 5 = 10, or 5 X 5 = 25, it does not associate objects at all with
these numbers. It has been led to use number in the abstract, and in
doing this it has been materially assisted by the teacher presenting the same
number associated with many different things.

NUMERATION AND NOTATION.

We may express our notions of number in two ways: —
{a) We may say or write the word ten, for example, and
thus express number in words. This is termed mimeration.
(t>) We may express the same number by means of certain
accepted characters or symbols, as, e.g., 10 or X. The latter
mode of expressing numbers is termed notation.

The two modes of expression should be simultaneously
acquired by young children. The word nine, for example, may
be associated at first with nine cubes, sticks, &c. Afterwards
both the name and the symbol (9) should be thus associated.

138

How to Teach Arithmetic.

Finally, the figure 9 alone should be used to denote the
number. When advance is made to higher numbers it will be
well to have sums in addition, subtraction, &c., set in both
words and figures.

There are two well-known methods of notation which our scholars need
to learn, viz. : —

{a) The Arabic o i 2 3 4 5 6 7 8 9, &c.

{b) The Roman I. II. III. I\'. V. VI. VII. VIII. IX. X., &c.

The Roman notation is not used in ordinary arithmetic, but it may be
made the subject of an interesting lesson if its connection with concrete
objects (the fingers and the hands) be explained. A little after the Norman
Conquest of England the present mode of notation (Arabic) was introduced
into Europe. It is supposed to have come originally from India. The
great advantnge which the Arabic notation possesses over the Roman is
at once seen if we attempt to write down the number one thousand eight
hundred and ninety eight in both notations. In the Roman notation the
number is represented thus, ]\IDCCCXCVIII. ; in the Arabic thus, 189S.
Besides being a short method of writing down a large number the Arabic
is much more certain than the Rnman. The number eight, for example,
in the Roman is represented in two ways to show that in the one case it is
eight miits, and in the other case it is eight hundreds. In the Arabic the
same symbol stands for units and hundreds, the position being sufficient to
distinguish between them.

In actual school work it will be of service to construct a
comparative table of numbers up to nine on a sheet of card-
board in some such form as the following. The sheet should
be placed in the room where scholars are learning their first
notions of number.

Number \n ^ Arabic Roman

the Concrete. "'""^- Sijmbol. Symbol.

one

• •
• • •

•

six

VI.

• •

two

II.

• • •

•

seven

VII.

• ••

three

III.

• •

four

IV.

• « •

• • •

eight

VIII.

•

• •

nine

IX.

• e •

hve

• • •

•

Number in „,„„,„ Arabic Roman
the Concrete. """^^- Symbol. Symbol.

How to leach the value of figures according: to their
position place value.— One of the earliest didicuUies in
teaching arithmetic is that of giving young children a clear

Sketch of a First Lesson on Place Value.

139

notion of ' place value.' The following is a sketch of a lesson
designed to assist them over this difficulty: —

OUTLINE SKETCH OF A FIRST LESSON ON
' PLACE VALUE.'

Plan and Matter of Lesson.

Illustrations.

1. Concrete examples— preliminary.

Distribute sticks or cubes, &c., to the number
of 30 or 40 to each child. Exercise the class in
placing together various groups of sticks, from
one to nine in each group.

This will be familiar work, and need occupy very
little time. Care must be taken to associate each
bundle with the figure representing it in the abstract.

(a) Bundles of single sticks.

2. First notions of tens.

Place ten single sticks side by side; count them,
and then tie into a single bundle. Call this o/w
ten.

Allow the children to make similar bundles, and
group these into two, three, or four tens. Deal
similarly with peas, marbles, &c.

(/') One ten. Ten single
sticks.

3. Combinations of tens and units.

Proceed to combine a tens bundle with one or
more of the single sticks. These latter should
now be termed inii/s to distinguish them from the
bundles (tens).

For e.vample, let one ten be combined with two units,
as in fig. c. The name twelve may now be supplied ;
the scholars at the same time should decompose the
number into one ten and two units. Combination ot
one ten and three units, one ten and four units, &c.,
should follow. The names twelve, fourteen. Sic,
should be associated with the concrete number as soon (c) One ten. Two units,
as each is represented by means of sticks.

4. Graphic figures.

The mode of representing by ordinary figures
may now be approached, but not by a single step.
The figures representing tens and units are
usually made the same in size, whereas they
stand for very different values.

Do not risk confusion by writing the ordinarj- symbol
for twelve too soon. It would be better to make *
graphic representation of the relative values of the two

figures as shown in fig. cl. Deal similarly with the {d) One ten nnd two
figures fourteen, fifteen, &c. units — twelve.

1 2 = 12

140

How to Teach Arithmetic.

Ordinary figures.

T. U.
I I

T. U.

The final stage in the lesson is that of repre-
senting the numbers eleven, twelve, &c., by the II 12
ordinary figures, distinguishing the units figure by
placing the letter U over it, and the tens figure
by placing over it the letter T. T. U.

Deal similarly with numbers 12, 13 and 14. The
children should frequently practise the decomposition ^ 3
of each of the above numbers into units and tens.

Future lessons ivoiild deal 7vi(k nitmbers up to 19. Aftenoards, numbers
beyond 19, siich as 20, 25, 34, 58, ^'c., may be introduced and taught by the
method Just sketched.

Place value up to hundreds.

The method adopted in the preceding sketch may be con-
tinued in order to teach place value up to hundreds. The
apparatus for showing tens and hundreds in the concrete is
shown below.

Hundreds. Tens. Units.

H. I T.

= 113

U.
9

When numbers have been put together in this systematic way and
the relationships between the units, tens, and hundreds have become
clearly understood, the converse process of decomposition may be
attempted. For example, three tens and nine units maybe decomposed
into 39 units ; one ten and nine unit.; into 19 units; one hundred and
thirty-nine into 13 tens and 9 units, &c.

Notation groups of numbers.

'I'he following groups of figures should be taught in their respective
classes, viz. : —

{<i) Numbers one to nine.

{b) Numbers ten to nineteen. These numbers introduce an entirely
new feature, viz., that of re[)eatiiig the number one along with eacfi
of the digits in a, thus, lo 11 12 13, &c., and giving the one thus
repeated the place value of 10.

((■) Numbers twenty to ninety-nine. When group {/>) has been
lliurouglily mastered, the successive numbers two, three, four, &c. ,
are made to stand for two tens, three tens, four tens, &c., or 20, 30,
and 40 respectively.

Simple Addition. 141

{d) Numbers one hundred to nine hundred and ninety-nine. This

group introduces the digits one to nine into the third place on the left
of the units. Each figure thus introduced becomes one hundred
times its original value.

There are in reality only three distinct stages in the above groups,
viz. — Group I, including the units up to nine inclusive. Each of
these when standing alone is said to represent ' unity of the first
degree.' Group 2, in which the same figures are nitroduced in
conjunction with those of group I to represent numbers from ten to
ninety-nine. The figures on the left side of the units figure are called
tens and are said to represent 'unity of the second degree.' Group 3.
The same digits, when used in the third place on the left of the units,
are termed hundreds, and are said to represent ' unity of the third
degree.' *

SIMPLE ADDITION.
I. Addition and subtraction of numbers up to nine.

Exercises in addition must begin with counting by ones ;
thus one and one are two. two and one are three, &c. With the
advance to addition by twos, we must show first the connec-
tion of this with the previous stage by adding one -f one and
one ; two + one and one, &c., before adding by two direct.
Again, when adding by threes, we must take one -f two and
one, two + two and one, &c., and finally proceed to adding
by three direct.

At first these easy sums should be worked both in
the concrete and abstract. The abacus or ball
frame with small black-board attacherl is a most useful
appliance for exhibiting the two methods at the same
time.

Combination of simple exercises in addition and
subtraction,
A saving of effort is made, and a clearer Insight into
the early exercises is secured, by adopting the 'New
Code alternative scheme of arithmetic' For example,
when the numbers 3 and 4 have been added together to

* Terms. — The terms 'unity of the first degree,' &c., need not be introduced in
actual teaching at this stage. They are used here to assist in distinguishing each
group of numbers. ' Device of place ' is sometimes used to signify the different vahies
given to the digits according to their position. As the o (nought) means nothing
and is only used to occupy- a ' place'- not required by the other digits, the other digits
are distinguished from the ' nought' by being termed ' significant digits.'

142 Ho%v to Teach Arithmetic.

make 7, at that moment there is present to the mind of the child the fact that
7 is made up of the numbers 3 and 4. To take 4 from 7 is at once seen to
yield 3, and to take 3 from 7 is as readily seen to leave 4. The several
processes are evidently mutually helpful. If addition be continued alone
for several weeks without the reverse operation of subtraction, it will be
found that subtraction is made a continuation of addition. The number 7,
in the above example, would not be decomposed into 4 and 3, but if 4 be
required to be subtracted from 7 the child would say ' four and three make
seven,' i.e., it would add three to the number four in order to make 7, and
would not subtract 4 from 7 to make the difference 3. When equal numbers
are added together (as, e.g., 4 and 4 to make eight), there is opportunity
for extending the operations of addition and subtraction to those of multi-
plication and division. Twice four are seen at once to make 8 ; and 8 is
furthermore seen to contain 4 two times. It may be well to limit exercises
at first to addition and subtraction. If we vary the operations too much
at the beginning there is some danger of the weaker children becoming
confused.

The early stages of adding and subtracting by one, by two, or by
any higher number, may be illustrated by means of cubes, marbles, &c;
Do not use fingers or strokes on the slate. Concrete examples musC
be considered as essentially a stepping stone to the use of number in
the abstract. The use of fingers and strokes cannot readily be
abandoned, and consequently children are in danger of using them
too long.

Simple Mental Arithmetic— a valuable exercise at this
stage.

The value of mental arithmetic in the early exercises of arithmetic arises
from the following facts, viz., (i) the numbers available for adding and
subtracting are small, and can, therefore, be readily kept in mind ; (2)
mental arithmetic provides a rapid mode of dealing with these small numbers,
and hence many sums may be worked in a short time ; (3) it makes provi-
sion for dealing with small numbers in the abstract ; and (4) it develops
a mental acutencss and agility in dealing with arithmetical processes. A
succession of simple mental exercises may be arranged on the following
plan, viz. : —

((?) Ptace a line of figures on the blackboard, and require the class
to read them ofl, \i/.. : —

354652719

(/') Add one, two, three, &c., in turn, to each number in the line of
figures. The cliildren .should be allowed to announce the answer
only. Whenever hesitation in stating the result is noticed, the
addition is difficult at that point. The difficulty should first be
explained, and the exercise afterwards be repeated until all
hesitation disappears.

Simple Addition.

143

((-) Subtract one, two, dc, in turn, from each figure, and wherever

hesitation is apparent, explain and repeat as for addition.
((/) Count by twos, threes, dc, by addition and subtraction, ^'.^..•—

(i) Addition 2468; i 3 5 7
(2) Subtraction 8642:9753

(i') Follow with miscellaneous exercises such as, for example : —

1. How many twos in four?

2. What number must be added to 5 to make 8 ?

3. What three figures added together make 7, 9, 5, &c. ?

2. Addition of numbers containing both units and tens.

(a) Without carrying.

We cannot add together such numbers as 35 and 54 at one
step. It is necessary to make use of the principle upon which
the additions of all large numbers are based, viz., to split up
each large number into parts and add together these parts.
Thus in the above example we perform the addition by adding
30 + 5 to 50 -]- 4. Instead, however, of adding 30 and 50 we
call these tens and add 5 tens to 3 tens.

In order to give children an insight into the

principle of addition a few sums should be

worked as shown in the adjoining example.

Afterwards, the examples should be worked by

the contracted method in order to accustom

children to add units to units and tens to tens.

{/>) With carrying.

When the notion of adding tens to tens is understood an
example in which carrying to the tens is re-
quired may be introduced. In the annexed
example the 12 units (obtained by adding 5
units to 7 units) are decomposed into i ten

and 2 units. The units figure 2 is then

placed under the units and the i ten is

added to the tens figures in order to make 6 tens.

3
5

5
4

Parts of

each No.

= 30+5

= 50+4

= 80+9

The process of carrying may be illus-
trated by actually changing 12 sticks into
I bundle of ten and 2 single sticks to
represent units. A few examples worked
in the concrete will be helpful at this
stage.

UNITS.
12

12 sticks = I ten + 2 units.

144

Hmv to Teach Arithmetic.

3. Addition introducing hundreds with carrying.

There is no new principle to explain here,
working may be afforded by the numerical box.

Assistance in

/ >^ / 7-/^/

Suppose the numbers 165, 46,
and 152 are to be added together.
They would ordinarily be ar-
ranged as follows : —

H. T.

I 6

I 5

3 6

The numerical box.

In using the apparatus, sticks
to the number of 5, 6, and 2
would be placed in the respec-
tive compartments under the
letter U. These, when added together, would make one ten bundle, and
leave three single sticks to represent the units in the lowest or answer
compartment. The next step would be to add together the 6, 4, and 5
bundles of tens already arranged in the compartments, under the letter T.
These, together with the one bundle carried from the units column, make
16 bundles of ten each. Ten of these make a large hundred bundle,
leaving 6 of the bundles of tens to be placed in the answer compartment
below the tens. The operation is completed by putting together the three
large bundles to represent the hundreds. At the end of the above opera-
tion all the sticks will be in the lowest or answer set of compartments, and
the actual numbers added together will, unfortunately, have disappeared.
This difficulty might be obviated by retaining the numbers, in figures, on
an adjoining blackboard. The retention, furthermore, would lead to
the use of numbers in the abstract, which is the result aimed at. As soon
as this is secured it will be wl-11 to throw all concrete expedients aside.

The addition of higher numbers introduces no new difficulties and
requires therefore no special reference.

4. Further hints on the teaching of addition.

{a) Concrete numbers. The use of concrete numbers may be abandoned
at this stage. Concrete examples should not be continued beyond the
stage when they can be of real service. Their use beyond that stage
(except in cases where their introduction is of service in explaining a

Simple Addition.

new rule) may be regarded as a cumbersome operation, taking up much
time and delaying the advance of the scholar to the use of number in
the abstract.

{b) The use of the letters h. t. u., to distinguish the hundred's, ten's, and
unit's column respectively, may be continued throughout addition and
subtraction with advantage.

{c) The use of periods. When larger numbers than hundreds are intro-
duced a period should be placed between the millions and the hundreds
of thousands, and between the thousands and the hundreds. The pupils
thus become accustomed to the arrangement of these large numbers in
groups of threes, as for example : —

Millions. Thousands. Units.
241, 358, 579.

(</) Decomposition of different groups of figures will be found a most valuable
exercise at this stage. For example, the above group of thousands may
be termed 35 ten thousands and 8 thousands; or 3 hundred and
58 thousands; or 3 hundred, 5 ten, and 8 thousands. In this way the
thousands' group, made up as it is of units of thousands, tens cf
thousands, and hundreds of thousands, becomes clearly distinguished
from the hundreds, tens, and single numbers in the group of units.

{c) Abundant practice in the mental decomposition of simple numbers
will yield excellent results in future arithmetical processes, and will, at
the same time, help to explain a present rule. The operations of
subtraction, multiplication, and division, as well as that of addition,
require the rapid decomposition of numbers in the following manner,
viz. : —

{a) Splitting up {decomposition) of
nu7nbers mentally : —

15 = I ten

and 5 units

84 = 8 tens

>, 4 ,,

84 = 80 units

M 4 ,,

146 = 14 tens

M 6 ,,

146 = I hundred

,, 46 ,,

&c., &c..

&c.

ip)

Combination of parts

making up

a mimber

3 tens and 5 units

= 35-

2 tens ,, 15 ,,

= 35-

I ten „ 25 „

= 35-

7 tens ,, 2 ,,

= 72.

70 units ,, 2 ,,

= 72.

&c., &c.,

&c.

In all such mental arithmetic exercises as the above, it will be well to
encourage individual scholars to find out as many methods of splitting
up and combining numbers as they can. Original eflbrt should in all
cases be encouraged.

(/) Full working. When addition sums are too large for illustration by
means of concrete example the process of carrying should sometimes be
shown by placing the full working on the blackboard, e.g. —

146

How to Teach Arithmetic.

{a)
TH. H. T. U.

3. 5 78
1.846

4. 2 o 8

f*)

Kc)

9-63

2 —

TH.

22 units =

1 1 tens =

15 hundreds =

8 thousands —

TH.

The ability to set out examples in addition in full form, as
above, may be considered satisfactory evidence of the pupil's
complete knowledge of the operation of addition. The reason
for each stage in the working has become known ; the process of
carrying has been explained ; there has been no mystery involved in
the effort, and the scholar has, furthermore, been taught to look
for similarly complete explanations in the future.

{g) The addition table should be often repeated throughout all the stages
of addition. Children make fewer mistakes in multiplication than in
addition, because they learn the multiplication table perfectly, whilst
the addition table is frequently neglected.

SIMPLE SUBTRACTION.

1. Connection of Addition with Subtraction (numbers

below 20).

It has already been stated that there is no reason why the
early processes of addition and subtraction should not be taken
together. When a pupil has put together 2 sticks and 3 sticks,
to make 5 sticks {synthesis), the splitting up of the 5 sticks into
2 sticks and 3 sticks {analysis) becomes an easy and quite a
natural effort. These early and associated exercises in addition
and subtraction might with advantage be repeated and extended.

At first, use should be made of small numbers, and these chiefly in mental
cakulations. For example : —

2 + 5 = 7 followed by... Take 5 from 7. Take 2 from 7.

4 + 6 = 10 ,, >, 6 from 10. ,, 4 from 10.

8 + 4 = 12 ,, M 8 from 12. ,, 4 from 12.

12 + 7 = 19 ,, ,, 12 from 19. ,, 7 from 19.

2. Subtraction of higher numbers.

The subtraction of numbers higher than 20 introduces the
use of either slates or paper, and also necessitates the simplifi-
cation of the exercise. A pupil cannot be expected, for
example, to take mentally the number 37 from 53. The sum

Simple Subtraction,

147

must be worked by means of a number of simple stages.
These simple stages are not usually recognized. If, however,
we intend to show why we take each step in the ordinary
working of a subtraction sum, we must not shrink from
attempting to make clear the principle upon which the method
of working depends. The following sketch of a lesson sets
forth the methods by which this principle may be taught.

How to explain the principle of subtraction by
'method of decomposition.'

the

EXAMPLES AND PRINCIPLES.

Examples with figures in the
subtrahend less than those in
the minuend.

(l) From 28 take i^.
By decomposition. Usual form

28 =
15 =

20 + 8
10 + 5
10 + 3

T.
2

u.
8
5

take 37.

5
3

(2)

59 =
2,1 =

From 59

50+9
30+7
20+2

u.
9

(3) Other examples like (l)
and (2).

First truth or principle stated.

We take one large number
from another when w^e take
the parts of the smaller num-
ber from the parts of the
larger number.

HINTS ON THE METHOD
OF TEACHING.
A

(a) The first exerci-e is that of splitting
up both minuend and subtrahend into
smaller numbers.

(1^) Any smaller numbers would do for this
purpose so long as (i) the parts of the
minuend are larger numbers than the
parts of the subtrahend, and (2) the
sum of the two parts equals the whole
number.

(cr) In the adjoining subtractions the num-
bers are split up into ' tens ' and
'units.'

{d) The class should be exercised in di-
viding many numbers into their
equivalents of tens and units before
the ^ usual form' of writing these
numbers is adopted.

(e) When the usual form is reached the
scholars should read each number (i)
as a whole, and (2) as made up of tens
and units.

Thus 28 = 2 tens 8 units.
15 = I ten 5 units.
&c. &c. &c.

How are we to know when the truth
which the above exercises are intended to
teach is known ? Evidently when the
scholars can state it. In order to lead
them to this result the children must be
taken over the steps of the above process
as follows : —

(i) Each number has been split up into
smaller numbers.

(2) These smaller numbers have in turn

been subtracted from one another

(3) The complete answer is made up of

the smaller answers.
V the children can state these steps they
understand the truth, and the statement
of the steps of working is the statement
the truth.

148

How to Teach Arithmetic.

Examples with the units of
the subtrahend greater than
the units in the minuend.

(i) Take 2b from 4J.
By decomposition. Usual form.
T. U.

43 = 30 + 13
26 = 20 + 6

3'^
6

10 -)- 7

(2) Take 2g from

62.

62 = 50+12
29 = 20 + 9

6-5
2

u.
212

30 + 3

3 |3

(3) Take 37 from

54-

T. U.

54 = 40 + 14
37 = 30 + 7

5
3

10+7

Second truth or principle.

Whenever the units figure in
the subtrahend is a larger num-
ber than the units figure in the
minuend, the units and tens
figures of the latter must be
decomposed, so that the tens
figure is reduced by i, and the
units figure is increased by 10.

The same method of decompo-
sition must be followed for tens,
hundreds, and any other higher
number.

(a) The method of decomposition changes
when figures in the subtrahend are
larger than the minuend. The neces-
sity for change could be shown by
attempting to work the adjoining
example by the above method.

{61 This change of the method of decom-
position must be made clear by many
examples, such as 43 = 30 + 13. ^^"d
care should be taken to make the
method of change quite clear before
attempting the full working Of 3. sub-
traction sum.

(c) The transition to the ttsual form should
be gradual. For example, at first it
would be well to mark the decomposi-
tion by small figures written by the
side of the tens and units.

id) Finally, the usual contracted form of
statement should be adopted accom-
panied by questions upon the actual
numbers into which the minuend is
decomposed.

In establishing the second truth the
preceding steps must be revised and
stated in the order of their occurrence, as
follows : —

(i) Recognise that the units figure of the
subtrahend is the larger number.

(2) Decompose the minuend and thus

increase the units by lo, and
reduce the tens by i.

(3) Subtract, and remember when sub-

tracting the tens figure that the
minuend is reduced by 1.

When the above steps can be stated in
their proper order the second truth is
known.

3. The chief difficulties of the decomposition method.

If all examples in subtraction resembled those
vTorked in the preceding lesson-sketch, the decompo-
sition method would be a simple and desirable process
to follow. The method, however, becomes difficult
to apply and explain when a succession of cyphers
appears in the minuend.

(a) Usual form.
TH. H. T. U.

From 5, o o 8
Take i, 2 5 9

Simple Subtraction. 149

TH. H.

From 4, 9

Take i, 2

For instance, in the example ' from 5,008 take ., „ .
1,259,' the former number must first be decomposed *■ ' "
to 4,99^8, Each figure of the subtrahend can then
be readily taken from those of the minuend. The
chief difficulty at this stage is to induce children to
remember the new set of figures in the minuend. The
changing position occupied by the cyphers in the
minuend presents a further difficulty.

4. Devices intended to lessen the difficulties of sub-
traction by the decomposition method.

{c) Transition

((7) In order to lessen the difficulties just stated, the ^H. H. T. u.

new figures (obtained by the decomposition of From 5, O O 8

the minuend) are sometimes written above the Take i, 2 5 9
original numbers, as in the example [c] adjoining.

TH.

oio

QlO

gis

1,2

5(3

{V) Another device is that of adding i to each figure ^/)
next to the left of the larger figure in the sub-
trahend, as in the example {d) adjoining.

This method entirely obscures the decomposi-
tion of the minuend. (It resembles most closely
the method of ' equal additions.') Whenever
this method is accompanied by the statements =^=^^^

' borrow ten ' and ' pay back one ' it becomes hopelessly obscure.
The method of decomposition has become mixed with that of ' equal
additions,' and the reason for the process has become inexplicable,
(r) A third and last device is that of subtracting the units figure of the
subtrahend (or any figure in the subtrahend greater than the figure
immediately above it in the minuend) from the 10 obtained by decom-
position, and by adding the result thus obtained to the figure in the
minuend. For instance, instead of taking 9 from 18 in the above
example the figure 9 would be taken from the 10 (obtained by decom-
position) and the l unit thus obtained would be added to the 8 units
in the minuend. The answer 9 would be the result, and this is a
correct result. It is obtained, however, by a method very difficult to
explain, and where explanations of all processes are demanded it should
not be used.

5. Subtraction by the method of ' equal additions.'

It has been shown that the explanation of the method of
decomposition becomes very difficult when cyphers are found
in the minuend, and in consequence another method has been
devised which obviates the difficulties found in the process of
decomposition. The method of ' equal additions,' as this
alternative process is termed, is based upon a simple principle
which may be stated as follows, viz. : — * that if we add the

15°

Haiv to Teach Arithmetic.

same number to both minuend and subtrahend the
remainder is unaltered.' The method of establishing the
principle, and of applying it to the working of sums in sub-
traction, may be best illustrated by means of the following
lessons.

Lessons* in Simple Subtraction (by equal additions),
arranged with a uiew of shoujing the reason for
each step in the working.

EXAMPLES AND RULES.

A. Introduction.

Examples to he worked jncntally :

3 + 5 = 8
8-5 = 3
8-3 = 5

7 + 5 = 12
12 - 5 = 7
12 - 7 = 5

To show the connection between
addition and subtraction and to
teach the meaning of the terms
'minuend^ and ^subtrahend.'

TEACHING HINTS,
ILLUSTRATIONS, &c.

Work examples in the concrete : —
ist. Adding together a number of

objects.

2nd. Reversing the operation to give

form to the simplest notions of sub-

tr.'iction

Pass quickly to operations in
abstract number, using those
which the children supply for
exercises, both in mental addition
and subtraction.

The terms are best learned by the
teacher using them from the first.

B. Examples in which each figure in
the subtrahend is less than the
figure of the same name in the
minuend.

Contracted

Method.

H. T. U.

8 7 5

Working

(0 5 (2) 70
2 50

n full.
(3)800
300

352 rt, 20

5 2 3

Answers collected

500

3 CO

20 (2)
500 (3)

523

Scholars who have been exercised
thoroughly well in numeration and
notation will scarcely need reminding
that the figure 5 taken from 7 repre-
sents the number 50 taken from 70,
and similarly th.at the figure 3 from 8
represents the number 300 taken from
800.

It will be well to work a few
examples both by the full and by
the contracted methods.

If an entire lesson be occupied
in this portion of the work, sound
results will follow.

* These lessons are made purposely complete. They introduce a revision of previous
work, and thus show the connection between what is already known and that which the
lesson is especially designed to teach. The lesson sketch might with advantage be split
into smaller lessons, and many examples added at e.ich stage.

Lessons in Subtraction.

151

. Examples in which the units figure
in the subtrahend is larger than the
units figure in the minuend.

I. To establish the rule of equal
additions.

1 = 2

2 = 2
6 = 2
8=2

{a) Simple Examples.

3 -
Add I to each 4 —

Add 5 to each 8 —

Add 7 to each 10 —

Add 10 to each 13 — 11 = 2

{b) IVkat the above examples show ; —

1. Equal amounts added to both
numbers in each example.

2. The answer unaltered.
{c) The rtile they teach : —

When the same number
is added to both minuend
and subtrahend the answer
remains the same.

This is a very simple form of induc-
tive reasoning, and should be con-
ducted in the following manner.

1. Use verj- simple examples. There
is no value in setting difficult
exercises at this stage. The mind
needs to be concentrated mainly
upon the processes by which the
answers are obtained, and in find-
ing out the sinilarities either in
the examples and results, or in
both.

2. Arrange the examples, fully
worked out, neatly on the black-
board, so that the common fea-
tures in the examples become
apparent, as far as possible, to the
eye.

3. Continue the exercises until
the scholars can make similar
examples after the teacher's
model.

4. Stop as soon as the scholars can
state the common conditions in
the examples in reply to questions.

5. The proof of success is manifest
when the pupils can state (in
their own language) the rule
illustrated by the examples.*

2. Application of the rule of equal
additions.

Example i.

Changed to:

H. T. U.

3 5 7 10 has been added

H. T. U.

3 5 7
I 2 8

2 + I o 10 has been added

229

Example 2.

Changed to:

H. T. U.

846
390

H. T. U.

8 I4 6
3+1 9

4 5 6

f 10 X 10 has been
( added = 100.
100 has been added

(2) It will not be necessary to work
in detail many sums. The class will
readily learn the rule, and at the same
time understand it.

At times when a sum is being
worked on the board and a
scholar is adding one to either
minuend or subtrahend, he should
be asked to explain fully what he
is doing and why he does it.

* These five stages of working exhibit a simple example of ' Inductive Teaching.'

152 How to Teach Arithmetic.

3. Statement of the rule as it is
applied in working subtraction.

{a) When any figure in the sub- <3) This statement in its entirety

trahend is greater than the "'"'^f "°^ ^^ expected from children
corresponding figure in the ^t this stage; they may however, be
minuend, add to the minuend S.""^^? '° state each of the three por-
a figure of the value of the "°"^ '"'° "^"^^ .t .s divided,
place next to the left.

(3) Then subtract.

{c) Complete the operation by
adding to the subtrahend a
number of equal value to
that added to the minuend.

SUMMARY OF TEACHING-

1. Subtraction is the reverse process to that of addition.

2. The 'minuend' is the larger number, and is placed in the top line of a sub-

traction sum.

3. The ' subtrahend ' is the smaller number, and is placed below the ' minuend.'

4. When equal numbers are added to both minuend an 1 subtrahend the answer

remains unaltered.

5. Statement of the rule, see above.

6. Criticism of the method of equal additions.

This method has the advantage of being based on a very
simple arithmetical truth, viz., that the same number may be
added to both subtrahend and minuend without altering the
answer. It has a further advantage in that the occurrence
of cyphers, either singly or in succession, does not in any
way increase the difficulty. The process, furthermore, does
not vary with different examples. The difficulties are com-
pletely disposed of one at a time. Finally, the reason for
each step may be understood and stated by children of average
intelligence.

It will be well in teaching subtraction to settle first the method
Dy which the difficulties of working the sum are to be overcome. If
correct answers only are required then it will not matter much which
of the methods described is chosen, but if the reasons for each opera-
tion are to be known and stated, then the method of equal additions is
best for young children. Whichever method, however, is chosen, that
method should be adhered to. Children should not be confused by
being taught a variety of methods at first.

7. Continuation of sums in subtraction.

It has been supposed hitherto that examples have required
only one equal addition each. The examples may be followed

Proving Sums in Subtraction. 153

by others in which more than one of the equal additions occur,
and these in diflerent parts of the sum. When sufficient facility
in the correct working of examples has been acquired, the class
may with advantage have problems set them somewhat in the
form of the exercises suggested below. Finally, problems
involving both addition and subtraction should be supplied.
For example, such exercises as the following are very useful : —

Liverpool has a population of 599>73^> Glasgow has a population
of 526,088 ; and Birmingham has a population of 447,912. The
population of London is 4,282,291. Find how many more people
there are in London than in all the three other cities named together.

Proving sums.

The answer of a subtraction sum is easily proved. The question of
proving sums is a matter of some importance. It is settled best by the
consideration of the aim we have before us in teaching arithmetic. If we
are most anxious to obtain correct answers, then proving sums will be of
some assistance. If, on the other hand, intellectual discipline is of first
consideration, then our scholars should be trained to use the rules they are
taught with the utmost care and precision, feeling certain that the correct
result must follow. A right answer is a stimulus to continued effort in the
same direction. An incorrect answer is the natural penalty for loose and
slovenly work, and its occurrence should be made the stimulus to increased
care in the future. The constant practice of ' proving sums ' tends to make
the learner less careful in the working stages, and hence one of the chief
effects of arithmetic as a means of mental training is weakened,

l/ary the Statement of the Addition and Subtraction
exercises. For example : —

(a) Addition. (/;) Sichtraction.

Add together Take ... from ...

Find the total of From ... take ...

What is the sum of ? What is the difference be-

Total the following tween .... ?

What will remain ?

By how much does ... e.x-

ceed ... ?
What must be added to ...
in order to make . . . ?

154 How to Teach Arithmetic.

SIMPLE MULTIPLICATION.

1. Multiplication and addition.

When a series of eqtial numbers need to be added together,
the addition of these numbers may be shortened by the use of
the multiplication table. For example : —

Bij addition. By multiplication.
8

8 8 multiplicand

8 4 multiplier

_S _

32 sum. 32 product

There should, at first, be abundant practice in mentally
working simple examples like the above by both addition and
multiplication. It should be carefully noted that the statement
' multiplication is a shortened form of addition ' is only true in
those cases where all the addends are the same.

The terms multiplicand, multiplier, and product should be taught
by placing them opposite the lines for which they stand. It should be
shown that the multiplicand may be either an abstract or a concrete
number. For example, we may multiply eight desks by 4, or we
may multiply the number 8 by 4 without reference to any objects
whatever. The multiplier is always an abstract number. It is
nonsense to talk about multiplying 8 sheep by 4 sheep, or 8 pounds
by 4 pounds.

2. The multiplication table.

We make very little real progress in multiplication until the
multiplication table is thoroughly mastered. How best to
secure this thorough knowledge is a question which now
presents itself. In the first place the tables of two and three
times should be worked out in both the concrete and the
abstract forms.

Concrete. Abstract.

Twice 2 are 4
Twice 3 are 6

Twice 4 are 8

Twice 5 are ic
&c, &c.

Marbles

Marbles.

and

= OOOO

and

_
OOOO

and

_ OOOO
~ OOOO

000

and

000

OOOO

= 00

OOOO

&c.

Simple Multiplication (Tables). 155

Do not continue the concrete numbers beyond the time when
they have served to explain the process by which the table is
constructed.

The above illustrates the ' experimental method of learning the
tables' recommended by H. Spencer.

3. Learning the tables.

The only secret of rapid acquisition in ' learning the tables ' is
the repetition of them until the association between the two
numbers to be multiplied and their product is perfect. When-
ever two numbers are to be multiplied together there must be
no hesitation to announce the product. Any halting; any
thinking over what ought to be the product ; and any repetition
of back numbers, so as to arrive at the required product, must
be regarded as faulty. Correction by further repetition of the
tables in which weakness is evident is the best remedy. The
following suggestions will prove helpful in ' learning the
tables ' :~

[a) Allcnu the class frequently to repeat a table sitmiltaneojtsly and in a Imv
tone of voice.

The association which we seek to form is that of sound chiefly, and
just as one note suggests the succeeding note in singing a tune, so in
tables, the sound of ' 5 times 5 ' suggests 25.

{h) Make the sound associations attractive by musical accompaniment, and
change the notes at intervals.

In twice times table, for instance, a change should be introduced
at 'twice 7 are 14' and at ' twice 10 are 20.'

{c) As association by sound soon loses its force, it ivill be better to repeat one
table several times than to repeat several tables once only.

The same rule holds when a new tune is being learnt by sound.
One line at a time is sufficient. In both the exercises of learning a
tune and learning a table it will be well to practise a portion until
the succession of sounds in it becomes familiar.

(d) Some sound associations are more quickly made than others. For
example, ' 6 ti7nes 6 are 36 ' is quickly learned, but ' 7 times 9 are 63 ' is
not so quickly learned.

If the reason why the first of these tables is quickly learned and
why the second is not so quickly learned be known, it will be possible
to arrange all the tables in two groups, viz., (l) those quickly, and
(2) those not quickly learned. The reason required is to be found
in the fact that in some tables the same sound is repeated again and,
it may be, again, as in 6 times 6 are 36, whereas in other tables there
is no repetition of sounds, as, for example, in 7 times 9 are 63, 12
times 7 are 84, &c.

156 How to Teach Arithmetic.

{e) Arrange the tables in order of difficulty, and repeat the most difficult
tables tuore frequently than those of less difficulty.

It will be found that the 5 times, the 10 times, and the II times
tables are most readily learned for the reason stated above, whilst 7
times, 8 times, 9 times, and 12 times tables are learned with greatest
difficulty. These latter tables, therefore, need most repetition.

(/) Fritit a fe^v of the most difficult numbers on a sheet of cardboard, and
hang them in front of the class, so that the scholars inay frequently see
them when their tninds are disengaged.

If it be remembered that the tables in which there are no repetitions
of the same sounds are learned with greatest difficulty, this sheet can
be readily prepared. It will contain '6 times 7 are 42,' but not '6
times 8 are 48'; it will contain ' 7 times 8 are 56,' but not ' 7 times
5 are 35.'
(g) Associate the tables which admit of it with other groups of similar
numbers.

Two times with pairs ; 6 times with \ dozens ; 12 times with dozens;
7 times with days in the week ; 3 times with three-penny pieces, &c.
These associations help to give a reality and an interest to the multi-
plication table, and they tend further to clear the tables of that air of
mystery with which children are apt to surround them when they are
simply committed to memory without such associations.

4. Stages in multiplication arranged in logical order.

{a) Multiplication by one figure.

When the fir.st multiphcation tables have been thoroughly
learned, the knowledge thus acquired may be used in working
easy sums by them. Care should be taken from the first that
the pupils are made to understand each step in the process.
The rule for multiplying a number by any figure is ba.sed upon
the principle that we multiply a number by any figure
when we multiply the parts of that number by the
figure and add together the several products thus
obtained.

For example : — Suppose the sum to be worked is ' 7 times 426.'
We work this sum by multiplying the 6 units, the 2 tens, and the
4 hundreds in succession by 7, and adding together the 42 units, 14
tens, and 28 hundreds thus obtained. It would be well to work out a
few examples in full, as follows : —

IT.

Tir.

TII.

II.

= 2

9 1

8 ,

1 2

Stages of Simple Multiplication. 157

{b) Multiplication by 10.

A number of examples should first be worked by 10 by
means of the ten times table. It would soon be recognised
that the figures in the multiplicand are repeated in the product
with the addition of a cypher in the units place, thus : —

357 X 10 = 3570.

A few examples will suffice to show that we multiply by
any number when we multiply successively by its
factors.

It is true that we scarcely ever set out in full the multiplication by
factors ; it is however equally true that whenever we multiply by a
number above 20 we do in reality multiply by factors, and if we intend
to explain every stage in the working of such sums, the truth stated
above must be known. The following example illustrates the above
statement : —

Example : —

Multiply 385 by 20.

(a) Working by factors.

385

3850 = 10 times 385
2

7700 = 20 times 385.

(i) Contracted working,
385

7700 = 20 times 385.

{d) Multiplication by the parts of a number.

Before proceeding to multiply by any number consisting of
two figures it is necessary to show that we multiply by a
number whenever we multiply by its parts and add
together the products thus obtained.

For example, suppose we wish to multiply 635 by 15. The full
working may be shown as follows, and the truth stated above, may,
at the same time, be illustrated.

* The term factor should be explained by means of simple examples, as, e-^., 6 X ? =
30, 6 and 5 are factors of 30 ; 3 X 8 = 24, 3 and 8 are factors of 24.

TH.

5
5

I
3

7
5

5=5 times 635
= 10 times 635

5 = 15 times 655

158 How to Teach Arithmetic.

The cypher in the second
line does not affect the value
of the answer, hence in ordi-
nary working it is omitted.

{e) Multiplication by any numbers of two figures up to 99.

It will be seen that between the multiplication by one figure
and any figure of two numbers there have been no less than
three intermediate stages. These stages have been introduced
in order that each step of the working may be understood.
That these intermediate stages are necessary will be evident as
soon as the working of a sum by a figure of two numbers is
closely examined. For example : —

Multiply 3,576 X 43-

Full working.
3.576

Explanation of each stage.

10,728 = 3 times 3,576.

14,3040 = 4 X ID = 40 times 3,576.

153.768 = 40 + 3 = 43 times 3,576.

The three intermediate stages are (l) multiplication by 10 by
placing the 4 in the second line under the tens figure ; (2) multiplying
by the factors of 40, viz., 10 X 4, to obtain the second line ; and (3)
the final answer is obtained b}' adding together the products obtained
by multiplying the top line by 40 and 3.

(/) Multiplication by any number.

The multiplication by numbers containing three figures or
more introduces no new principle. For example, the rule for
multiplication by 300 is an application of the principle of mul-
tiplication by factors. The factors in this case are 10 x 10
X 3. Multiplication by the two tens is accounted for by
placing a cypher in the units and tens places respectively.
When cyphers occur in the multiplier, as in the number 302,
the same explanation serves.

Simple Division.

159

5. Miscellaneous.

{ci) Before leaving the rule of multiplication for that of division the use of
the sign X should be introduced and frequently used. Examples
should be set in a variety of ways, as, e.g., multiply 857 by 9. Find
the product of 9,327 by 29. How many pencils are there in 25 dozens?
in 509 scores ? in 957 gross? 875 X 23. A scholar walks 394 steps
per day, how many steps are taken in a year of 365 days ?

[h) The usual method of starting to multiply by the units figure of the
multiplier is convenient but not essential. A few sums might be
worked in the reverse way, i.e., beginning with the highest number in
the multiplier. This exercise serves to recall and impress the principle
of multiplication applied in paragraph {d) above. For example : —

8,357,645 = multiplicand.
357 = multiplier.

2,507,293,500
417,882,250

58,503.515

= 300 times.
= 50 times.
= 7 times

2,983,679,265 = 357 times = Product.

SIMPLE DIVISION.

Connection with former rules.

The rules of arithmetic present a logical series of exercises.
One of the most fruitful efforts in teaching is to make quite
clear the connection of a new rule with those immediately
preceding it. Division may be shown to be a short method of
working a particular form of subtraction. It is also the reverse
of multiplication. A few examples should be worked to
illustrate both these connections.

(A) Examples showing the connection between Division and

Multiplication. (To be worked mentally.)

{a) By Multiplication.

(1^) By Division.

5 X 6 = 30

8 X 7 = 56

9 X 12 =108

30 -
56 -

108 -

- 6 = 5 ; 30 -

- 7 = 8 ; 56 -

- 12 = 9 ; 108 -

-5=6

-8=7
- 9 = 12

7 X 9 = 63

63 -

- 9 = 7 ; 63 -

-7=9

ID X 12 = 120

120 -

-12 = 10 ; 120 -

- 10 = 12

II X 12 =: 132

132 -

-12 = II ; 132 -

-II =12

i6o How to Teach Arithmetic.

(B) Examples showing the connection between Division and
Subtraction.

Ex. Hnv many times is 2 found in 10 ?

{a) By Subtraction. (l>) By Division.

lO 2 ) ID

^ 5 times. Ans.

— It should be pointed out that

4 division shortens subtraction

£ only when the succession of

2 subtrahends consists of the same

2 number

Ans. = 5 times.

Similar examples should be continued until the scholars discover
the connections between division and the preceding rules. The
examples used at this stage must be only those which can be worked
by the use of the multiplication table. •

Stages of teaching must be arranged in logical order.

The connection of division with multipHcation and subtrac-
tion having been shown, it becomes important to plan a series
of stages in strictly logical sequence. This series will prove
helpful to the learner in the effort to understand the reason of
the various processes he uses. There must be a full exposition of
the truth ' that any number is divided by another 7vhenever we
divide in succession the parts of that number and add together
the several quotients^ This truth may be shown in connection
with dividing a number such as 8624 by 2, in which there
are no remainders, to be followed by examples in which
remainders occur in differe-nt parts of the working. The exten-
sion of what is termed short division to division by factors next
claims attention, and finally the division by numbers beyond
the ordinary tables by the method of long division. Each
of these stages, together with allied topics, will now be
considered.

The principle upon which all exercises of division
are based.

This principle has already been stated in the paragraph
a,bove. It is one which in slightly modified form has appeared

Principles of Simple Division.

i6i

over and o\'er again in previous rules. In addition and sub-
traction, for example, the parts into which the numbers were
split were respectively added and subtracted ; and in multipli-
cation the multiplicand (in every example beyond the range of
the tables) was split up into a series of smaller numbers, and
the operation of multiplication performed on these smaller
numbers. There is, therefore, nothing new in the idea of
splitting up the dividend into a series of parts in order to
divide each of these parts instead of the entire number.

The new feature, and one whose explanation is difficult, is
the operation of beginning the division not with the units
figure, as in multiplication and the other preceding rules, but
with the highest figure in the dividend. The explanation of
this difficulty will be attempted in later paragraphs. We leave it
for the present, and proceed to introduce examples illustrating
the main principle of division.

Illustrative examples— 'i) without remainders: — Divide 8,624 by 2.

{a) Ordinary contracted method,
TH. H. T. u.
2)8 , 6 2 4

2 Ans.

The numbers actually divided,
and the value of each figure obtained
in the quotient by the above short
method, must be shown as below.

TH.H.T. U. TH. H.T. U.

2)8,000 = 4,000

2)600= 300

2)20= 10

'2)4 = 2_

4.3 I 2

(l>) Long division and less con-
tracted form.

TH.H. T.U. TH. H. T.U.

2)8,624 ( 4.3 I 2 Ans.
8 Thousands.
• 6 Hundreds.
6 „

2 Tens.
2 ,,

4 Units.
• 4 ,.

It will be well to select either of the above methods of showing
the numbers actually divided, and for a time to keep to the method
selected exclusively. Do not attempt the difficulty of dealing with
remainders until the main principle of division has been well estab-
lished through the working of many examples. Many teachers begin
with the long division form. They do this because in long division
the numbers actually divided at each stage of the working can be
more easily shown than in the more contracted form of working called
' short division.' The latter method should be introduced as soon as
the long division of a few simple examples is thoroughly understood.

l62

How to Teach Arithmetic.

Illustrative examples continued — (2) with remainders: — Divide 924 by 6.
(r?) Ordinary contracted method.

H. T. U.

6) 93224

I S 4

The small figures in the dividend
indicate remainders, each of which
is in turn decomposed to the value
of the following figure and added to
it to make the new dividend. In
the long division exercise this de-

composition is made quite clear.

(/>) By long division.

H. T. U.

6) 9 2 4 (l hundred 5 tens 4 uts.

6 hundreds = I54 Ans.

32 tens The decomposition

of the first remainder,
■viz., T. hundreds into

30 tens, and its addi-
tion to the 2 tens to
make 32 tens, must be
clearly taught. Simi-
larly the succeeding
decompositions.

The numbers actually divided by six, by either of the above
methods, are not 9 hundreds 2 tens and 4 units. What are the}-, and
how are they found ? These numbers may be founil by multiplying
each figure in the answer by 6, thus : —

100 X 6 = 600, the first dividend.
50 X 6 = 300, the second ,,
4x6= 24, the third ,,

The following stages of worhing the above sum by either
the contracted, i.e., the short division method, or by the
lonc^ method, must be pointed out in connection with the
working of many similar examples. The stages are as
follows, viz. : —

{a) The first figure in the answer is to be so many hundreds.
Now, 2 hundreds for answer would be too large a figure
because it would require 12 hundreds in the dividend,
whilst I hundred for answer requires only 6 hundreds in
the dividend and leaves 3 hundreds for remainder.
Place I hundred in the quotient.

{b) This 3 hundreds remainder is added to the 2 tens, making
by decomposition altogether 32 tens for the second
dividend. Now, to have 6 tens for answer would require
a dividend of 36 tens. Evidently, therefore, 6 tens is too
large a figure for the quotient. Try 5 tens. This will use
up 30 tens of the dividend and leave 2 tens or 20 for
remainder. Place j tens in the quotient.

((') There are left 24 units to be divided by 6. and this will
3-ield 4 units. Place 4 tinits in the quotient.

(d) Collecting the three quotients together makes a total of
154 = Ans.

Simple Division (by Factors). 163

The full and complete understanding (i) of the numbers actually
divided, (2) of the decomposition of the remainders in order to make up
each succeeding dividend, and (3) of the value of each figure m the
quotient, is only acquired step by step. These steps should be taken
in the following order and by the following means, viz. : — (a) The
long method of division by simple divisors with explanation of
each decomposition for finding the nevsr dividend. (/) The full
statement of the value of each figure in the quotient. (<) After
a few sums have been worked, and (a) and (/') have been taught,
there should be an attempt to recognise the actual numbers
divided. Lastly, the contracted m.ethod should be used, show-
ing at first by small figures the remainders and their decomposi-
tion in order to make the new^ dividend.

Why do we begin with the division of the highest
figure in the dividend ?

If there were no remainders we might begin with the division
of the units and proceed to the tens, hundreds, &c. The
difficulty of deahng with the remainders cannot, however, be
easily overcome when we work from the units to the higher
figures. We cannot change the units remainders into a given
number of tens, nor the tens remainders into a given number
of hundreds, and so on. But we can change the hundreds
that remain into a given number of tens, and when the
tens have been divided, those which remain can again be
changed into units, and these, along with the units of the
dividend, may be divided. In this way the reason for beginning
with the division of the highest figures in the dividend may be
shown.

Division by factors.

There are two points requiring special attention in division
by factors. These are {a) the truth that we divide by a
number when we divide by the factors of that number, {!>) the
rule for finding the remainder. The truth may be made clear
by a few simple examples worked mentally, such as, 36 ^
6 = 6. The factors of the divisor are 2 and 3. Now divide
36 by 2 = 18; then divide iS by 3 = 6. After working a few
examples by the whole number and then by its factors, the
scholars might be encouraged to make examples for themselves
and to work each by the whole number and its factors ;
when they do this successfully the truth {a) is understood. The

364 How to Teach Arithmetic.

rule for ' finding the remainder' should not be stated until it is
made clear by working a number of illustrative examples, such
as the following : — -

Divide 46 by 6. j^ „^^^j ^c made clear that the

^ -A first quotient consists of 15 threes

2 ) 15 a nd I remr. 1 and I unit remainder. Also that

7 and I remr. J 4 remr- ^]^g second quotient consists of 7

sixes and i three remainder. In this
way it may be shown that the last remainder is of the value of the first
divisor, and in order to obtain the remainder in units the last remainder
must be multiplied by three (the 1st divisor) and to this product the I
unit remainder from the first quotient must be added.

Long division.

The rule of ' long division ' has already been introduced and
the methods of working have been described. The exercises
in previous paragraphs were intended to make clear the more
or less contracted forms of short division, and the divisors were
such as could be managed by the application of the multiplica-
tion table. The ' long division ' now proposed is that which
deals with larger divisors than 12. Use should be made of the
simple examples already familiar in order to recall the rule,
and attention should be concentrated upon the difficulties
which follow the introduction of divisors above 12.

Example. Divide 8,769 by 23.

Remarks. — In working the e.x- Method of working.

ample on the right, we first try if XH. H. T. u.

23 will divide into 8 thousand and 23)8 7 6 9 (o thousands 3

yield any quotient of the thousand 5 9 hundreds hundreds 7 tens

value. As 23 is greater than 8 no T~6~6 tens 2 units

such quotient will result. The next 161 = "72 Ans

step is to decompose the 8 thousand " . ■

into hundreds and add these to the 5 9 units

7 hundreds, making together 87 4 o »

hundreds. We now divide these I 3 ""'ts remainder,

hundreds by 23 by finding what

quotient of the value of hundreds it will yield. If we try the number 4 we
find that 23 X 4 = 92, this number is larger than 87, so we try 3 times 23.
The number obtained by multiplying the divisor by 3 = 69. This product
is now placed under the 87 hundreds and subtracted from it, leavino- 16
hundreds still to be divided. This remainder is decomposed to tens and
the 6 tens in the dividend is brought down and joined with it, making in
all 166 tens. We try now to find a ten's figure that 23 will yield when 166
tens is divided by it. If we try 8 tens the product will be too great, so we
try 7 tens and thus obtain i6r tens. We then proceed to deal with the
itmaining stages of the sum as shown in the working.

The Place of Long Division. 165

7776 place of Long Division in the series of exercises
demands some consideration. There is no doubt that when
the divisors are large the working becomes very difficult, and
on this account should be delayed beyond the short division
stage. When, however, the divisors are less than 13 the diffi-
culties of finding the quotient by ' trial and error ' do not exist,
and then, long division, by being a less contracted method of
working, is more easily explained than short division. For this
reason it has been already suggested that the long form of
division by means of very simple numbers should be taken
before the contracted or short division form. Against this it
may be urged that children obtain correct answers more
readily by being introduced directly to the contracted form.
That may be quite true, but we are not so much concerned
about correct answers as we are about methods which the
children can understand. It is a very common experience to
find children (who have been taught only the usual contracted
method) quite able to obtain correct answers, but unable, at the
same time, to state the reason for doing so.

Dangers arising from leaving the consideration of reasons iinti!
the processes are mastered.

Whenever explanation of a process is left until the children are able to
use the rule so as to obtain correct answers thereby, a new difficult)'
presents itself. The children think they know all that is necessary ;
they can obtain correct answers, why. therefore, should they trouble
about reasons ? This unconcerned condition of mind is just the state
we ought to try to avoid. The greatest concentration of eftbrt is
needed in order to comprehend the reason for each stage in an}' arith-
metical process. It is by this aroused and concentrated effort that the
mind is most benefited. It is well to remember in this connection
that during the time a scholar is acquiring knowledge of a new rule he
is in the best condition of mind for laying hold of the reasons of the
processes he uses. We do well to seize the happv moment {i.e., when
the mind is in this enquiring state) to slowly unfold the explanations of
each step in the working. If we delay the attempt to teach reasons
until processes are familiar, the most favourable moment for acquiring
the reasons will have passed. The child is afterwards not under the
stimulus of feeling the necessity for this fuller knowledge, and, there-
fore, does not respond so readily as is desirable to the efforts of the
teacher to impart it.

Miscellaneous exercises in the first four rules.

Before leaving the simple rules it will be advisable to make
a series of exercises involving the combined use of two or more
of them. These problems (as they are sometimes called) do

1 66 How to Teach Arithmetic.

not follow the form in which examples involving one rule are
usually cast. The sums should not be of great length, as the
purpose is not so much to exercise the scholar in long arith-
metical processes as to awaken his power of applying the
knowledge of the principles and rules he has previously
acquired. Catches and mere puzzles should be avoided. The
purpose now is not to trip the learner. It is rather to encourage
him to put his knowledge to practical account. The problems
which provide exercises in several of the earlier rules yield,
furthermore, a valuable form of revision. They do this at the
same time that they maintain the interest and awaken the
brightest effort of the scholar.

The following sums provide exercise in all the previous rules :

{a) A traveller walks 25 miles on each of the first three days of a week.

He then walks 30 miles on Thursday and 20 on Frida}'. How far

must he walk on Saturday in order to walk altogether 144 miles?
(/') Suppose he wishes to walk the same distance on each day of the

following week of six days, hov/ far must he walk each day in order

to again walk 144 miles ?

MENTAL ARITHMETIC-MULTIPLICATION AND DIVISION.

If the method of introducing the various stages of multi-
plication and division throughout the preceding pages be
carefully examined, it will be found that each new process has,
in the first case, been almost invariably developed by means
of simple mental exercises. It will not be difficult for the
reader to make out for himself a complete series of mental
exercises necessary to establish the various stages of multipli-
cation and division in their logical sequence. The following
examples are intended to suggest the form of exercise. In
actual practice they should be still further developed and
varied : —

(.4) Exercises in Multiplication. (/?) Exercises in Division.

(i) Connection between niultipli- (1) Preparatory (connection with

cation and addition. subtraction).

2 + 2 + 2 + 2= 8; 2x4= 8 9-3-3-3 = 0; 9+3 = 3 times.

6 + 6 + 6 =18; 6x3=18 8-4-4 =0; 8-^-4 = 2 ,,

7+ 7+ 7 + 7 = 28; 7 X 4 = 28 18-6-6-6=0; 18+6 = 3 „

Mental Arithmetic.

167

(2) Multiplication by factors.
6x 4 = 6x2x2 = 24
5 X 6 = 5 X 3 x 2 = 30
8x 12 = 8x4x3 = 96

(3) Multiplication by parts of a

number and addition of the
products.

5 X 7 = vS X 3) + (5 X 4) = 35
4 X 8 = (4 X 5) + (4 X 3) = 32

(4) Vary the form of stating a
sum in multiplication. Thus :

(a) Multiph- 10 X 6 = 60.

(l>) Find the product of

than 9 ?
((/) How often is 12 contained

in 48 ?

(5) Mixed exercises.
(a) From the product of 8 and 4,

take the sum of 6, 3,
and 15.
(//) How much greater is the
sum of 15, 25, and 142,
than the product of 4
and 12 ?

(2) Preparatory (connection with

multiplication).

4X6 = 24: 24 -^6= 4

8 X 4 = 32 : 32 -^- 4 = 8

12 X 5 = 60 : 63 -^ 5 = 12

(3) What numbers are actually

divided

//; the folk

sums ?

84 -^ 6.

Ans. 60 and 24.

52^4.

,, 40 ,, 12.

104 ^- S.

,, 80 ,, 24.

(4) Vary the form of stating a
sum in division. Thus :

(rt) Divide 54 by 6.

(d) Find the quotient of

(d) How many times may 12
be taken from 60 without
remainder ?

((•) Share 81 pence ecjually
amongst three persons.

(5) Mixed exercises,
(a) Divide the product of 8 and

9 by 12.

(/') What quotient results from
dividing the product of 6
and 8 by their difference ?

Shortened methods of working mentally should be introduced after
the ordinary methods are well established. The following are examples.
Any good mental arithmetic will supply a full list : —

I. To multiply by 25, add two cyphers to the multiplicand, i.e.,
multiply by 100, and divide by 4.
To multiply by 99. add two cyphers as before, and subtract the

multiplicand from the result.
To multiply by 125, add three cyphers, and divide by 8.
To divide by 25, cut oft' the units and tens, and multiply the
remaining figures by 4. Add to this result the figure equal to
the number of times 25 will divide into the units and tens.
iS:c. &c. Sec.

->
J-

i68

Houi to Teach Arithmetic.

A device for obtaining a great variety of mental
examples in all the simple rules.

It is very necessary to place all sums for mental calculation
simultaneously before the entire class. As the sight sense is
the quickest and most accurate medium for receiving impres-
sions, the following simple appliance becomes very effective for
providing a great variety of examples in a clear and rapid way.

A. C

70612

S Q

A B C D is a small black-board with a square hole near the centre.
E F is a white lath made to slide behind the board so as to bring into
view in succession the figures printed upon it. Blackened card-board may
be used in place of the black-board.

How to use the apparatus.

1. For practice of addition, figures are written above the hole, or

below it, or both above and below it. By moving the lath the
figure in the hole is made to change. Without further statement,,
the scholar whose turn it is to answer announces the sum, product^
or quotient of the figures. Immediately this is done another figure
is brought to the aperture.

2. Subtraction sums may be set as shown in the figure, as may also

sums in multiplication and division.

3. A monitor should be employed to move the sliding lath. The

teacher is then left at liberty to deal with the answers of the
scholars.

THE VALUE OF MENTAL ARITHMETIC.

We have now indicated a series of exercises in the mental
arithmetic of the simple rules. These may serve as samples
of other series of exercises which each class teacher should
construct for himself, It may be well to note in

The 'Alternative Course of Arit/wietic.'' 169

passing, that no set of examples collected from a text-book
can possibly be equal in value to those constructed by the
teacher who has the special needs and conditions of a par-
ticular class in view. Upon a review of the constant use
made of mental arithmetic in preceding pages, it will be seen
that this form of arithmetic plays a most important part in
teaching. It is of high value during the acquisition of a new-
rule, and is not less valuable in the practical application of
any rule to calculations of every-day life. The scholar who
has had large experience in mental calculations acquires
thereby a facility in dealing with numbers which no amount
of slate-work can yield. For purposes of general education
there is scarcely any lesson which demands so much concen-
trated attention on the part of both scholar and teacher as
does that of mental arithmetic. In conclusion, it may be
pointed out that much of the ordinary paper or slate
arithmetic is mental, as are also the greater number of the
calculations of every-day life.

The above values of mental arithmetic will attach them-
selves to similar exercises in connection with the higher rules.
Suitable examples will be suggested in connection with each
of these rules, but no further statement on the value of the
subject need be made.

THE ALTERNATIVE COURSE OF WORKING THE
SIMPLE RULES.

In the code of 1893 an alternative course of arithmetic
appeared for the first time. This alternative scheme introduces
the pupil to exercises in all the four simple rules during the first
year, but limits the numbers used to those not greater than 99.
This course sets little children free from working with large
and unknown quantities, and leaves them at liberty to spend
more time in gaining a knowledge of processes. The numbers
with which the children are called upon to deal in this new
course admit largely of mental treatment, and this increase of
mental arithmetic may be expected to develop an aptitude for
dealing with the various relationships between numbers which
the long processes of slate arithmetic tend somewhat to hinder.
These small numbers, furthermore, allow of the illustration of
processes by concrete examples, and in this way a reality is given
to the first operations of arithmetic. The new course is a

I "JO How to Teach Arithmetic.

development of the ' useful ' exercises of the Kindergarten,
and may be made to provide an easy transition from the
counting and simple calculations of the infant school to the
more formal arithmetic of the upper school.

The new scheme of lessons must be carefully adjusted
to the intelligence of the learner.

Little children become confused when many new ideas are
simultaneously presented to them. ' One thing well ' is a maxim
which should be constantly borne in mind in teaching arith-
metic. At the same time we must be careful not to push this
maxim too far. It has already been stated that when a child
has put together the numbers 2 and 3 to make 5, it is in a position
both of knowledge and mind to see that 5 can be split up into
the numbers 2 and 3, and that if 2 be taken from 5 therefore
the number 3 will remain. These simple operations in addition
and subtraction may be attempted simultaneously. In the
same way when 5 is multiplied by 4 to make 20 it is easy to
see that 20 contains the number 5 four times. It will be a safe
precaution to bear in mind that not more than two related
operations should be attempted at the same time, and, further-
more, that these exercises should be limited to those small
numbers which can be dealt with mentally and in the concrete.
When numbers large enough to demand the use of the slate
are introduced it will be well to keep to one form of exercise
until it is thoroughly mastered. The following exercises are
intended to be introduced after a sound knowledge of all the
four simple rules has been acquired. They are to be considered
as samples only, and other examples should be constructed in
similar fashion with such numbers as 24, 36, 40, 48, 60, &c.

Mental Exercises on the number 12. Mental Exercises on the number 20.

[a) Count from i to 12 hy t7vos, as {a) Count by twos all the even
I, 3, 5, 7, &c. numbers up to 20.

Count by threes, both forward Count by twos all the odd num-

and backward. bers up to 20.

Count by fours, as i, 5, 9 ; 2, Count similarly by threes, fours

6, 10 ; 3, 7, II, &c. and fives forward and backward.

('>) Add to each digit in succession (/') Place the figures 3, 9, 12, 4, 15,
numbers which in each case 7, 19, 2, &c. , on the black-

will make 12. board, and then ask what

figure must be added to each
to make 20 ?

The Art versus the Science of Arithi7ietic.

171

Mental Exercises on the number 12

(continued),
{c) Put together two digits in any

order to make 12, e.g., 3 + 9 ;

5 + 1: &c.
{d) What number must be added to

4 + 3 to make 12 ? also to 2 +
6 ; to 3 + 7, &c. ?
{e) How many twos, fours, threes,

(Sic, in 12 ?
{f) What number multiplied by 2,

or by 3, or 4 or 6 respectively,

will make 12 ?
{g) What number is i of 12 ? What

number is i of 12, &c. ?
(Ji) Add 2 to the ^ of 12 ; add 5 to

the g- of 12, &c.
(/) Pence in a shilling ? in half a

shilling? How many sixpences

and how many threepenny

pieces in a shilling ?
(_/') RIonths in a year ? in half a

year ? in a quarter ?

Mental Exercises on the number 20

{continued'),
[c) Make groups of two figures which
added together make 20 ; e.g..,
9+II ; 2 + lS ; 7+13, &c.
Subtract each figure in para-
graph (l>) in turn from 20.
Make groups of three figures
which added together make 20;

(</)
('•)

.-.^"■.,3+12 + 5; 4+9+7, ^:c.

{f) What number multiplied by 2
will make 20 ? Similarly the
number multiplied by 4, by 5,
and by 10?

{g) How many times is each of the
following numbers found in 20,
viz., 10, 5, 4, 2, and i ?
Fmd the ^, the \., the \ and the

of 20.
What number must be added to
the fourth of twenty to make
the number 20? &c.

(_/) How many shillings in ^i ? in
a half-sovereign ? How many
shillings in a crown ? Crowns
in a pound ? &c.

The art versus
considered.

the science of arithmetic again

We are now in a position to state more fully than on page
133 the distinction usually made between the art and the science
•of arithmetic. The art of arithmetic consists simply of the
rules of arithmetic with their application to the solution of
sums. This knowledge may be acquired with but a very slight
accompaniment of insight into the nature of the rules. A
scholar who has learned the rules of arithmetic and who can
readily work sums correctly by means of them possesses a
knowledge of the art of arithmetic. In the preceding pages
there has been an attempt to explain every rule at the time it
has been introduced. No process has been used without
showing the reason why it yields the desired result.
The connection of every new process with those already taught
has been shown, and the principles of number upon which the
rules are based have, in every case, been illustrated and stated.
In some cases, where the principle has not been self-evident,
it has been taught by means of illustrative examples, as, for

172 Hoiv to Teach Arithmetic.

example, in the case of the principle on which the rule of
' equal additions ' in subtraction is based. When thus there is
(accompanying a knowledge of the rules of arithmetic) the
further knowledge of the principles of number upon which the
several rules are based, together with the knowledge of the
logical relationship existing between the succession of rules —
how each grows out of, and how each is dependent upon the pre-
ceding stage — then the knowledge of arithmetic becomes
scientific.

It now becomes evident that the study of arithmetic as a science is a far
higher effort than that of arithmetic as a mere art. We must be ready to
make the necessary allowances for this addition of effort so far as our
scholars are concerned. The additional work is somewhat difficult, and
will demand the expenditure of time and thought on the part of both
teacher and scholar. We must doubtless be content with making slow
progress through the simple rules. This need occasion no concern,
however, for slow progress in the first stages will be more than
made up by rapid progress through all the higher rules.

It was stated above that the art of arithmetic might be acquired
whilst but little progress was made with the science of nurpber. It
may now be stated that the science of arithmetic cannot be acquired
without a knowledge being gained at the same time of the art of arith-
metic. The true method of instruction in the science is to supply and
use an abundance of examples in illustration of the principles and
rules. In this way a double result is gained, viz., skill in the art of
arithmetic and knowledge of the science which underlies the art.

The advantages which follow the teaching of arith-
metic as a science.

Why put children to all this trouble ? Why not rest content
with an ability to gain correct answers ? Why attempt that
which demands skilful preparation, expensive apparatus, and
much patient effort on the part both of teacher and pupil, when
arithmetic for practical ends may be sufficiently secured without
them ? Such questions as these are sure to arise, and we must
be ready to answer them.

In reply it may be well to remind any one putting such ques-
tions as these that school-work in nearly every case has a two-fold
aim. In the first place it aims at developing mental ability, so
that the almost helpless child may grow into the wise and
trusted adult ; and in the second place it aims at imparting
knowledge, so that the ignorant scholar may develop into the
well-informed man. The terms ' information,' ' instruction,' and

Arithmetic as a Science. 173

' practical knowledge ' are sometimes used for the latter aim,
whilst such terms as 'intellectual discipline,' 'mental develop-
ment,' and ' education ' in its literal sense are used to express the
former aim. Now, arithmetic may be learned so as to yield
little more than information of a very practical and useful kind.
The subject, however, may be taught so as to afford a highly
intellectual exercise. Arithmetic taught as a science is capable
of yielding this double result. The ability necessary for
obtaining correct answers may be acquired in such a way
that the acquisition may be accompanied by the most valuable
training of the higher intellectual powers. It is to secure the
exercise of the reasoning powers, to secure the habit of con-
centrated thought, to arouse the spirit of enquiry so that no
step is taken without knowing on what it depends and to what
it leads ; — it is to provide these valuable intellectual exercises
that arithmetic as a science is taught.

It is true that this higher effort will entail trouble upon the scholar
and patient effort on the part of the teacher. These are not reasons,
however, against making the attempt. We may make the path of
learning too easy. Matter may be so skilfully prepared that its
acquisition calls forth very little effort on the part of the pupil. Not
so in this matter of teaching the reasons underlying the processes in
arithmetic. The highest skill on the teacher's part will still leave
opportunity for independent effort on the part of the scholar.

The science of arithmetic of the highest practical
value.

It should be further noted that whilst arithmetic acquired as
an art is of practical value to those who earn a livelihood in
the shop, the market, and the counting-house, that arithmetic
as a science, in so far as it develops the reasoning powers,
becomes of practical value in the highest and widest sense.
The power of connecting effects with their causes, and of
anticipating the results of such and such lines of action ; the
power, furthermore, of concentrated thought, of precision,
and of reaching exact knowledge ; — these powers, developed by
the study of science (arithmetical science among the others),
are of service not only in the limited sphere of the market and
the counting-house but in every condition and circumstance of
life. When, therefore, the highest practical value of arithmetic
is thought of, it should be associated with the acquisition of
arithmetic as a science.

174

Hoiv to Teach Arithmetic.

COMPOUND RULES (Money).

Different money values ; changes from one value to
another ; and money tables.

Children obtain a practical knowledge of the value of the
more common coins by the small purchases they make at
home. This objective mode of teaching should be continued
and extended in the school. Actual operations in recognizing
and naming coins, in changing coins of one value for coins of
a lower or higher value, and in adding and subtracting small
sums of money (first in the concrete and afterwards in the
form of mental arithmetic) yield the best introduction to the
compound money rules. Along with these concrete and
mental exercises it would be easy to introduce the class to the
farthings and pence tables, and to the mode of writing down
the different money values, as far as, and including shillings,
pence, and farthings.

The

farthings

tab/e.

farthings

.. I

- li

.. i^

.. If

.. 2

- 2i

.. 2^

■• ^*

•• 3

&C.

&c.

The pence

table.

s. d.

12 pence

I o

14 ,,

I 2

i6 „

■ I 4

i8 ,,

. I 6

20 ,,

. I 8

22 ,,

. I lO

24 „

2 O

&C.

If a table be either printed, or written clearly on a cardboard sheet, and be
placed in front of the class, good results will fullow. A few minutes each
day may be profitably spent in learning these tables. It is best always
to repeat a tabic with the numbers distinctly written in front of the class.
Sight and sound thus become mutually helpful in learning.

Compound addition— analogy betv/een simple and
compound addition.

The maxim ' proceed from the known to the unknown ' may
be applied at this stage with excellent effect. The class is
already acquainted with the different place values of the units,
tens, and hundreds in simple addition, as well as with the
operation of changing numbers of one name into numbers of
the name next higher in value. Use may be made of this
knowledge in teaching the new rule, if sums in simple and

Compound Rules (Mofiey). 175

compound addition containing the same figures be worked
side bv side, as follows : —

•>

1 2

3
4

5--'

8 10

The units figures amount to il, and the farthings column similarh-
amounts to II. Now charge the 11 units into I ten and i unit. Similarly
change the 11 farthings into 2 pennies and 3 farthings (qd. ). Set down
the I unit under the units column, and the 3 farthings under the farthings
column. Proceed now to add the i ten (obtained by changing the il units)
to the other figures in the tens column, amounting in all to 21 tens. Simi-
larly proceed to add the 2 pennies (obtained by changing the il farthings)
to the other figures in the pence column, amounting altogether to 22 pence.
Change now the 21 tens into 2 hundreds and i ten, also the 22 pence into
I shilling and 10 pence. Set down the i ten under the tens, and the lO
pence under the pence column. Complete the two sums by adding the 2
hundreds to the hundreds column, making in all 9 hundreds, and similarly
the I shilling to the shillings column, thus making eight shillings. Then
write down the 9 hundreds under the hundreds', and the 8 shillings under the
shillings' column.

A few sums only need be worked b}' both additions. Introduce
thousands into the simple addition, and pounds into the compound
addition sums, and be sure that the numbers in the different columns
are such that they will admit of the operation of changing from one
name to the name next higher in value. Accustom the children to add
up each column quickly as in simple addition, and make the change
to the next value after each separate addition exercise has been
completed.

Problems in addition.

After the completion of each stage of arithmetic the teacher
should put a series of questions into the form of simple prob-
lems. The problem is an excellent means of arousing the
thought of the class. It keeps the scholars from looking at
questions from a stereotyped point of view. It further enables
them to make practical use of their knowledge. The reason
why youths often appear to be unable to use their knowledge
of arithmetic after leaving school is often found in the fact that
they have not been accustomed to look at any question set
them from a variety of standpoints. Tell a boy to add up a

176 How to Teach Arithmetic.

column of figures, and he will do it quickly and accurately.
Ask the same boy how much a tourist spent in all after paying
35/- for his ticket, 15/6 for a pair of walking shoes, three
pounds and tenpence for hotel expenses, and 5/- in presents, and
(unless the boy has been accustomed to work similar problems)
he will most likely spend a considerable time in finding out the
rule, or how the sum is to be worked, and in the end will
probably fail to obtain the correct result.

Problems should not require long operations to solve them. The value
of a set of problems chiefly rests (i) in the application of two or more past
rules, and (2) in the variation of statement in which the same kind of
exercise may be presented. If the scholars do not see the solution of a
problem at once, it will be better to guide them slowly to its recognition
than to abruptly state it. A few well-chosen mental examples will generally
suffice to lead the class to the right solution. It is this effort to associate the
right processes of working with the problem that constitutes the chief value
of the exercise. A plentiful supply of simple examples gradually increasing
in complexity until one very much like the problem is reached exhibits the
sound method of teaching. If any steps in the process of working the
problem need to be told by the teacher, the preliminary training has been
faulty. The following ' notes of a lesson ' on a problem in compound addition
will serve to indicate more fully the mode of teaching.

NOTES OF A LESSON.
A Problem in Compound Addition.

The Problem : — A labourer earned 2/6 on Monday, as much more on

Tuesday, 1/8 on Wednesday, and twice as much as on Wednesday on

each of'the three following days. How much did he earn during the

entire week ?

EXAMPLES AND TRUTHS TEACHING HINTS, &c.

THEY TEACH. A.

, ., , , . ,- 1 , These and similar examples must be

A. Mental exercises-io hnd the mean- ^^,^^^^^ ^^, ^^,^^,^^^ ^^,^^^^j

mg of the t.rm as much more, .Vc. ^^^^ ^^^ ^^^^ ^^ ^^^ ^1^^^_

(a) 6d. -|- 6d. = l/- The idemity in meaning of the

(b) 9d. 4" 9d- = 1/6 terms 'double,' 'twice,' and 'as much

((■) five pence and as much more = The truth illustrated by these ex-

lod. amples will not be slated clearly by

„, , , T- c J I the scholars at first. Their statement

frw truth ftUed-.-lo find as ^^^^ ^^ ^^^p^^ ^ ^^^ ^^^^^^^ i,^^^

much more as any amount we ^^^ p^^p^^ ^^^^^

must add together two amounts

of the same value.

Notes of a Lesson. — Co7npound Addition.

177

B. Mental exercises continued — to

find the sum of a number of different
values.

(rt) A spent 5d. ia cheese, 8d. in
butter, and twice as much as
8d. in tea. How much was
spent altogether ?

(/') A boy's humming top cost 4d.,
a whip 2d., and a ship twice as
much as top and whip together.
How much did all cost ?

((■) In a family are 3 sons and 3
daughters. The father gives
5d. to the first son, yd. to the
second, and 8d. to the third son.
To each daughter he gives
twice as much as to the first
son. How much does he give
away altogether ?

T/u- iniih stated :— To find the
sum of a number of different
amounts, first find each of the
amounts and then add all these
together.

C. Tiie Problem : — Stages of working.
(n) Find the money earned each

day.
(/>) Arrange each day's w'ages as
below —

On Monday ...
,, Tuesday ...
,, Wednesday
,, Thursday...
,, Friday
,, Saturday ...

For the week... 19 2 Ans.

d.
6
o

8
4
4
4

Allow the class to stand, then state
the sum clearly once, and ask each
scholar to sit as soon as the answer
is ready. If difficulty arise, help the
scholars to set out clearly how much
is spent upon each article. Then add
these together.

In (/') the class must be encouraged
to work the sum stage by stage as it
is read out.

After each example is successfully
worked, the scholar who did it should
state fullj- the method of working.

This general truth will require the
same treatment as the one above.

After the scholars have had time to
re.'id and think over the problem, ask
any one to state : —

(a) The steps to be taken in work-
ing the example.
(/») The order in which these steps

are to be taken.
If these two questions cannot be
successfully answered, stage B must
be repeated. On no account must
the teacher suggest the answers.

The working is a simple effort. The
arrangement should be neat.

A similar problem as a test of D.

ability to deal with other sums of The test should be conducted with

like construction. perfect fairness. Scholars may stand

whilst working and sit when the sum
is fin's'ied. It will generally be well
to set two problems for test and allow
alternate scholars to work the same
sum.

BLACKBOARD SKETCH.

„, . ... . , (,?) The statement of the truths taught.

This will consist of :— J/^j .^.,^^ ^^^jj ,,.^j],i,ii. of the problem.

lyS How to Teach Arithmetic.

Compound subtraction.

Proceed as in compound addition, i.e., by working examples
of simple and compound subtraction side by side. Use the
method of ' equal additions ' whenever a figure in the sub-
trahend is greater than the figure of the same name in the
minuend. Children experience considerable difficulty in
decomposing a minuend like ^^20,000 os. o^d. into ;^i 9,999
19s. I id. + 6 farthings, whereas by the method of 'equal
additions ' the difficulty is very much lessened.* The following
examples exhibit the process of working in full. The small
explanatory figures may be omitted as soon as the process is
understood.

Example :— Subtract ^i 9s. 8|d. from ^8 9s. 4|d.

Simple Subtraction. Compound Subtraction.

From
Take

TH.

H. T. u.
giy 4I4 2^-i

9io 89 3
9 5 9

From 8
Take lo

s. d.
9-' 4!"^ f
9io 8y5

19 7 f

REMARKS.
I. After the

met

;hod of working

is known it wil

11 be well t^

statement of sums in compound subtraction as much as possible, e.g.,
' Subtract lys. 6d. frnni 25 sMllings ' may be stated as follows : How
much greater is 25 shillings than 17s. 6d. ? What must be added to
seventeen shillings and 6d. to make the amount equal to 25s. ?

2. Accustom the scholars to recognize the amounts stated either in
figures or in words, or in a mixture of both figures and words.

3. Before leaving compound subtraction for the next rule a plentiful
supply of problems should be introduced involving the use of both
addition and subtraction. In this way a thorough revision of com-
pound addition, as well as a variety of exercise in compound subtrac-
tion, may be secured.

Compound multiplication.

The rules of arithmetic adopted in simple multiplication
form the basis of instruction in compound multiplication. The
principles of number upon which the operations of simple
multiplication are founded are stated and explained on
pp. 156—7.

* Refer to the criticism on the method of equal additions on p. 152.

Compound Multiplication.

179

It will be sufficient to repeat these principles and the succession
of operations dependent upon them at this stage. In teaching,
however, each should be illustrated by a few examples.

A. Principles of number enume-
rated.

1. We multiply a number by any
figure when we multiply the
parts of that number by the
tigure, and add together the
several products thus ob-
tained.

2. We multiply by a number
when we multiply succes-
sively by the factors of that
number.

3. We multiply by a number
whenever we multiply by its
parts, and add together the
products thus obtained.

B. Succession of rules in
compound multiplication
stated in order.

1. Compound multiplication by
one figure up to 12 by means
of the multiplication and
money tables.

2. Multiplication by liigher num-
bers capable of being split up
into factors without remain-
ders. £'.,f., 24, 36, 42, 45, &c.
Multiplication by numbers s]3lit
up into factors with remain-
ders, d'.,ir., 23, 29, 34, 47, &c.

3. Multiplication by numbers up
to icoo.

4. Problems involving processes
of multiplication, addition,
and subtraction.

The three methods of working a sum in compound
multipUcation compared.

There are three different methods of working a sum in com-
pound multiplication. Each is based upon one or more of the
principles enumerated above. The three methods are shown
below, and the merits or otherwise of each are afterwards
discussed.

Example: — Muhiply ^^15 iis. 4|d. by 56.

{a) By j6 in one line.

£ s. d.

15 " 4t
56

By factors with remainder.

£ s. d.

15 II 4i X 6

;^87i IS

times,
times.

155

778

93
/871

7
8

6j =10 times,

ib) By facto;
£ s.
15 II

>-s of J 6.

4i
7

10 =56

8^ =50 times.

\^ = 6 times.

ID ==56 times.

108 19
;^87i 15

I So How to Teach Arithmetic.

REMARKS.

{a) In method [a) there are fewer reduction exercises, and the chances
of error, therefore, are lessened. It is also a short method. The
several multiplications and reductions should be shown at the side of
the sum. This would detract from the neat appearance.

(Ji) Method [b) is shorter than (c), and it also affords greater variety in
the multipliers.

{(•) The third method is the simplest of all. The factors are easily found,
and the number lo is easy to multiply by. It is the longest method
of the three.

Whichever method is chosen, that method should be regularly
followed until perfect facility of working is secured. Afterwards the
scholars may be encouraged to vary the method. The device of
writing side notes opposite each line to indicate its value should be
adopted in the early stages of working.

Compound division.

In compound division, as in simple division, it is necessary
to show that whenever tlie division of a number cannot be
determined mentally and by a simple use of the tables it
becomes necessary to make use of the following principle, viz.,
' that 7C'e divide one 7iuiiil>cr by another whenever we divide the
tarts of tlie dividejid by the divisor, and add together the results
tJius gained.' For example, a scholar would readily state that
the half of is. 6d. is gd., and that the half of 2S. 6d. is is. 3d.
These examples would be worked by a simple application of
the tables. If, however, an example like the following were
set, viz., to find the half of £^ig 7s. lod., the answer would
not be forthcoming. The amounts actually divided by two in
the above example are 18 pounds, 26 shillings, and 22 pence,
and the answer is ^^9 13s, iid. Now this answer could not
be determined at once, i.e., by means of an application of the
tables mentally. It becomes, therefore, necessary to show {a)
the principle of number upon which the rule of compound
division is based, and {b) the ai:)plication of the rule to the
working of sums. The following stages A, B^ C and D indicate
the order of teaching : —

Compound Division.

i8i

A. Examples, introduced to estab-
lish the principle of division.*

Divide 2s. 6c

s." d.
2)2 6

•by

In this case the two
parts of the dividend
are divided separately.
The two results added
together make the an-
swer. This simple example illustrates
the principle. Similar examples should
be worked until the princijie is fully
recog^nized.

Divide 5^-. 6d. by 4.

s. d. T 1 • 1 ,•

\ /T -In tn's case the di-

4 )_S vidend has been split

I 4.T "P into three parts,
= viz.. 4s., i6d., and S
farthings. Each in
turn has been divided by 4, and, as be-
fore, the three results together make
the answer. It will be easier at first
for the pupils to recognize tlie complete
shillings', pence, and farthings' divi-
dends. These are 5s., iSd., and S
farthings. Afterwards they should
state the actual amounts divided bj' 4.
Many examples like the above must
be worked at this stage.

3cl.

7 J-

The amounts ac-
tually divided by 3
are £^, 21s., and
2jd. The results of
the three divisions
added together form the answer.

B. The principle of division .'—We
divide an amount by a number
when we divide the parts of the
amount by the number and add
toijether the several results.

C. The rule of division stated.

The rule of compound division
may be briefly stated as follows : —
Find how many times the divisor is
contained in the amount of highest
value in the dividend. The remain-
der, if any. must now be changed
into the value of the ne.xt lower
amount and be added to it. The
sum thus found must in turn be
divided ; and if any remainder re-
sult it must be dealt with as above,
and the working continued until the
amount of lowest value is reached
and divided.

D. The rule applied.

Divide £8^7 i6s. (jfd. by 9.

£ •-. d. £ s. d.
9)857 16 9f (95 6
81

2 Pounds rcmr.
20

9") 56 shillings = "1
54 £2 'l6s. /
2 shillings rmr-
12
9)33 pence = 1
27 2s. 9d. J
6 pence rmr.
4

27 farthings =
27 6|d.

REMARKS :— The
method of long
division exhibit!)
the stages of
working more
fullv than short
division. The
side notes stat-
ing the value ot
each remainder
and eac h new-
dividend wi 1 be
helpful at first.
Discontinue
these as scon as
the stages ot

} working are
fully under-
stocd.

Problems upon the four compound rules.

The paragraph on tlie value of problems on p. 175 should be
read again at tliis stage. It will be possible now to make a
great variety of problems. These will yield exercises in the
revision of each of the rules, and at the same time afford

* Whenever a principle is to be established the examples should be
made as simple as possible.

1 82 Hoiv to Teach Arithmetic.

excellent opportunities for applying them in a practical manner.
The aim should be to provide sensible every day problems in
arithmetic. In this way the learner will be enabled to deal
promptly and successfully with similar problems when they
leave school.

Avoid such exercises as this, viz., 'With ;i^39 6s. lod. as dividend,
£Af 5s. 2|d. as quotient, and seven farthings as remainder, find the divisor.'
But accept the following : — A tradesman decides to share his property
equally between himself and his three sons. He has ;!f 1,080 lis. gd. in
the bank, fifty-five pounds in cash, and a stock which is sold for seven
hundred and thirty-nine pounds 6s. ii|d. He owes money to the amount
of ^99 IIS. lod. Find the value of each share.

The problem which deals with ordinary calculations, and which
requires the application of two or more rules, provides an exercise in
-both the art and science of arithmetic. There is exercise in the
working of rules, and at the same time there is exercise in determining
the rules to be used. This latter exercise is the higher of the two, and
can only be successfully attempted when the deeper or scientific rela-
tionships existing between the numbers used are understood.

NOTES OF A LESSON ON ''^'
A Problem in Compound Rules.

The Problem : — A tradesman decides to share his property equally
between himself and his three sons. He has ;^i,o8o lis. gd. in the
bank, fifty-five pounds in cash, and a stock of goods which is sold for
seven hundred and thirty-nine pounds 6s. Il^d. He owes money to
the amount of ;^99 lis. lod. Find the value of each share.

EXAMPLES AND RULES. TEACHING

A. Simple examples explanatory of DIRECTIONS.

the first portion of the sum. A.

. ,j ( i) Tliesec'xaiiiplesshoiild be worked

(1) 6(1. + 5(1. + yd. = IS. Od. by the class mentally, and similar

take away gd. Ans. ^= <)i\. examples should be set until

^~—'~~~~—'^ the scholars readily supply the

9d. -f lid. + bd. = 2S. 4d. answer.

subtract 4d. Ans. = 2S. Od. ^^^ ^Vork at first mentallv. Then

(2) A boy earns 1/- on ^b_)nday, i/J •'^f'^ ^'^ """f^' "■°^'^" '° '^" ''?'.
\-/ ■^'- ' J I J' 1^ class how the answer was ob-

on I uesday, 9d. on Wednesday, tained. Write out the st.ages of

and spends 2/6 on Thursday. working on the board.

How much is left? Ans. = 6d. (3) Continue similar examples until

,..,,.. , , . ., , the method of working the sum

(3) Additional and smiilar examples. j..,„ ,,j. supplied by any member

Method of luorliing:^ -Add together "^ '^^' ^'=^''''-

the several amounts received,
and take from the sum the
money spent.

Notes of a Lesson. — A Problem.

i8^

B. Examples leading to the full
statement of the method.

(i) 4d. + i/- + 6d. = i/io. Take
away 7d. and divide the re-
mainder by 5. Ans. = 3d.

(2) A farmer sells eggs for 2/6, butter

for 5/-, and cheese for 2/6. He
buys a whip for 4/6, and then
shares what he has left with
his three sons. What does each
receive ? Ans. = 2s. 2d.

(3) Additional and similar examples.

Full method of working stated: —
Add together the money received,
and subtract from the sum the
amount spent. Then divide the
remainder by the number of
persons sharing it.

Proceed as above, and give addi-
tional exercises until every pupil
is ready to state : —

(a) The three stages of working,
viz., (i) by addition ; (2) by sub-
traction ; and (3) by division.

(/') The full method of working.

The complete statement of
the rule is the most valuable
exercise in the lesson. At first
only a portion of it is to be
expected from the class. Ex-
amples must be supplied until
all the stages of working are
known and until their order can
be stated.

At first the scholars must
not be expected to make per-
fectly complete statements of
the different methods of work-
ing the sum. Their answeis
must be moulded into the
reouired form.

C. The problem worked.

1st step : —

7he addition of the moneys reeeived.

£ s. d.

1080 II 9 =in the bank.
55 o o =in cash.
739 6 ll| = stock.

£i^T^ 18 8^= Total.

2nd step : —
To find the money to be shared.

£ s. d.

1874 18 8^ = total amount.

99 II 10 = money owed.

i:i775

6 i07 = mone}' shared.

3rd step : —
To find the amount of eaeh share.

£ s. d.

4 ) 1775 6 10^

y:443 16 8i- 2 -The share
ofeach. An8.

Place the problem before the
class. Allow them to read it
over carefully. Do not suggest
the first or other step. Alter
sufficient time for thought has
been allowed, ask a scholar
to tell how the sum is to be
worked.

Do not be content with
a partial answer. If the
scholar cannot state all the
steps in order, the prelimi-
nary teaching above has net
been effective. It must be
repeated, and a fresh attempt
to solve the problem may then
be made.

After the three steps of working
have been stated, allow scholars
in different parts of the class to
work each stage in turn. Arrange
the sum neatlj- with side expia-
natorj' notes.

D. The blackboard notes would con-
sist of the statement of the rules,
and the three stages of work.

1 84

How to Teach Arithmetic.

Long Tots.

The code requires scholars in Standard IV. and upwards to
be able to ' add columns of pounds, shillings, and pence within
a specified time, in order to show^ readiness and accuracy.'

The adjoining effective
apparatus* affords prac-
tice in the above calcula-
tions. By moving the
screen in front of the
numbers, sums varying in
length and difficulty are
provided, and by rotating
the sheet a great variety
of exercise is supplied.

When using such an appli-
ance as the above the scholnrs
should have plenty of practice
in adding up each column, and
in changing the totals at once
into numbers of the next higher
value. The pupil should sim-
ply state the result of each
addition, thus —

(i) 6, i6, 24,

(2) 7, 13, 17, 19, 28,

(3) ^> 15. 21,

77-i6l0V\5657:9'
759 3 7'/2s 761-12-
1573/5 S'/2 IS 376' I-
653S- l-n'/i'>l657'1b-}0
SUn-S '^695-3'bfz

E.J. ARNOLD'S REYOLVIMG TOTS

3d.

The full size of the apparatus is
29 X 27 inches.
2,1, 40, 51 pence = 4s.
35, 45, 55, 65 shillings = ^3 5s.
25, 32, 40 pounds, &c., &c.
E.xercises such as the above tend to give a practical and commercial
value to the pupil's skill in arithmetic. Whenever a number is found to
present a difficulty in its addition, that number .should be noted and extra
practice in adding all such difficult combinations should be aftordcd.
All attempts to render the addition easy by seeking for groups of tens and
other simple combinations should be avoided. A banker's clerk scorns all
such aids, and ordinary scholars, by a little daily practice, become
remarkably proficient in rapidly obtaining direct and accurate results.

REDUCTION.
A. Money. Introductory.

Simple notions of change from money of one value to
money of the next higher or lower values have been already
acquired. A strictly logical arrangement (in consequence
of the simple operations in reduction required in working

* Issued by E. J. Arnold, Leeds.

Reduction.

185

the compound money rules) would place reduction of money
before compound addition and subtraction. The rules of
reduction are very simple, and it is proposed only to give a few
hints upon the best method of displaying the working together
with some advice upon the points where difficulty in teaching
is likely to arise. The following are the matters requiring
most attention.

1. Ascending and Descending Reduction.

The actual change of coins from one name to another will make the
meaning of these terms clear. Descending reduction was used in
subtraciion and division of money and ascending reduction was used in
addition and multiplication.

2. Tlio method of luorliing.
(<•?") AscENDiNc; Reduction.

Ex.—

Reduce 45,874 farthings to pounds.

4) 45-874 farthings.

Ans.

[2 ) ii,468^,d.

2,0) 95, ss. S.^d.

£47 15s 8^d.

U')

Descendinc; R

[i^^nUCTION.

X. —

educe ;^29 15s. 7fd.

farthings.

£ s. d.

29 15 7:^

595 shillings.

7147 pence.
4

28,591 farthings. Ans.

The use of side explanatory notes will prove of great service at tirst.
In descending reduction the additions of the shillings, pence, and
farthings present some difficulty during the process of multiplication.
For example, the 15s. is added along with the multiplication of ^{,29
by 20. An example cr two worked out in full will sufficiently explain
the process.

. Examples which present greater difficulty.

(^)

Reduce 143,897 three-pences to
pounds, shillings and pence.

4 ) 143 .897 three-pences.
2.0 ) 3S97,4S. - I over = 3d.
/^I798 14s. 3d. Ans.

Reduce ^^39 i6s. 8d. to four-pences.
£ s. d.
39 16 8
20

796 = shillings.
3 = number of 4d. in i/-

2390 four-penccs. Ans.

The remainders prove most difficult to deal with in 'ascending
reduction.' This will be met by requiring the scholars to state
the value of the numbers in the line from which each remainder is
taken. For instance, the remainder after divichng the three-pences by
4 is I. Yes, but what is this I? Ans. One three-pence; hence the
remainder in money is 3d.

1 86

How to Teach Ariihmetic.

In ' descending reduction ' the short method of bringing shillings
direct to four-pences, three-pences, &c. , should be adopted. The
only difficulty in the above example would be the change of 8d,
to four-pences. This happens to be an ecjual number of four-penccs.
Suppose the pence to have been ild. instead of 8d. ; then the four-
penccs would have been 2 as before and 3d. left for remainder.

4. Examples of greatest difficulty.

{a) Where one value exactly
divides the other.

(i) Bring 53,868 half-crowns to
three-pences.

53,868 = half-crowns

inultipliedbyiobecau.se
thereareiotbree-pences

in each half-crown.

538,680 Ans.

(3) Bring 687,345 four-pences
to florins.

6) 687,345 four-pences.

fl. 114,557 — 3 over = IS,

"Ans.

(/') Where one value does not
exactly divide the other.

(2) Bring 53,868 half-crowns to
four-pences.

53,868 half-crowns

32.

4) 1 6 16040 = pence.

404010 = four-pences.
Ans.

(4) Bring 687,345 three-pences
to four-pences.
687,345 three-pences

4) 2062035 pence.

5 1 5508 -3d. Ans.

Remarks. — The short method of working examples (i) and (3)
may prove difficult at first, but at this age children should be
expected to face such difficulties as these. Up to the stage now under
consideration we have advised the keeping to one method for the
solution of similar examples. There .should, however, now be allowed
opportunity for individual choice, and a short method, if correct,
should be preferred to the longer though simpler method.

B. Weights and measures (reduction).

According to tlie Code requirement the table.s of weights and
measures to be learned and used are those only which are in
ordinary use, viz., Weight — the ton, hundredweight, quarter,
stone, pound, ounce, and drachm ; Length* — the mile, furlong,
rod or pole, chain, yard, foot, and inch ; Area — the square
mile, . acre, rood, square pole or perch, the yard, foot, and
inch (boys only); Capacity— quarter, bushel, peck, gallon,
quart, and pint ; Time — year, month, week, day, hour, minute,
and second.

* The code of 1 895 removes the reduction of yards to poles in both
long and square measures to the work of .Standard VT. (Boys only).

Tables of Weights and Measures.

1S7

How to learn the tables of weights and measures.

The interest in the tables is greatly increased when concrete
examples or models are introduced at the time the table is
being learned and applied. Not only is the interest awakened,
but all arithmetical operations based upon a knowledge of the
tables become thereby much more real and practical.

Concrete examples and models.

1. For weight — a box containing each of the following weights, viz.,
4 drachms (5- oz. ), i oz. , l oz., i lb. , i stone, will be very serviceable.

2. For long measure — a ruler divided into inches and parts of an inch,
a yard measure, a long tape measure, a land chain (for boys).

The heights of the school, and of a doorway, and the length of the
upright side of the blackboard measured in feet and inches, together
with the actual distances of two or three well-known places from the
school, measured and painted on the school-wall ; all these will be
valuable.

The length, breadth, and area of the school and playground should
be carefully measured and the results put conspicuously on a school
plan.

For area and solidity

— the connection be-
tween long, square,
and solid measure may
be shown by means
of a stout cardboard
box marked as shown
in the accompanying
figure.

If the portion A B
be made movable it
will represent a lineal
foot divided into 12
inches.

Twelve such strips
make up the entire
side A B C D, /.c, a
square foot. This is

^^^^^^^^^

J-'i

'jU-j

y ■'

1 ''

T^-^—^--^^::^^.^^:^^:^^^:^^^::^^

-JB-

J^'

y"^

/
IX

Apparatus for showing the relation between
lung, square, and cubic measures.

seen to be divided into

144 square inclies.

If the front portion A B C D be made movable it will be seen that
twelve such areas an inch in thickness make up the entire solid or
cube, i.e., a cubic foot or 1728 cubic inches. If, further, the cubic
inch at B be made movable the entire piece of apparatus will show
in the concrete the relationship between long, square, and cubic
measures so far as the inch and foot are concerned.

1 88

Hoiv to Teach Arithmetic.

4. For capacity — measures of the pint, quart, and gallon may be con-
structed in cardboard. As the form of these is a regular cylinder, the
making of a set of measures would form a practical application of the
skill the upper standard scholars have gained in the manual training
classes.

The various tables should as far as possible be connected with the
home life of the pupils. Thus, connect pints with milk, yards with
length of calico, lbs. with weights of sugar and tea, and cwts. and
tons with those of potatoes and coals.

Whilit the above concrete associations lend interest and reality
to the tables of weights and measures they must not be allowed
to take the place ot a thorough mastery of the few tables which
scholars are now recjuired to learn. When the relationship between
the different parts of each table has been mastered the table itself
must be repeated until it is well known.

The rules of reduction of weights and measures.

These processes introduce no new arithmetical principle.
The rules suggested for working exam[)les in the reduction of
money (both ascending and descending) should be followed.
It would be well at lirst to show the reduction of various sums
of money to farthings alongside the reduction of tons, cwts.*
and quarters to pounds, thus —

2 to lbs.

£ s. d.
\.educe 89 13 2 to farthings.

Tons. cwts. q
Reduce 89 13

1,793 = shillings
12

1,793 =cwts.
4

21,518 = pence

7, 1 74 = qrs.
28

86.072 = farthings.

57,392
143,48

200,872 — lbs.

Multiplication by 5i and 30^, - Long and Square
measures respectively.

The chief diflicultifs in reduction of weights and measures
are those of multiplying and dividing by tlic mmibers 5^ in
long measure and 30.I- in s(|uare measure. In the case of
multiplication by 5-|, if it be remembered that we niuliipl\
by any number when we multiply by its parts and add together

* These terms should he explained when they are required. For
example, c. — hundred ; cwt. = hundredweight ; lb. = weight, to distinguish
it from £^ money.

Notes Of a Lesson. — Yaj-ds to Poles.

189

the results, the scholar need only be shown that it is neces-
sary to obtain {a) 5 times the number to be multiplied, and {b)
■i- times the nuniber, and add together the results. Similarly
with -T^o^, as shown in the following examples : —

Ex.

To multiply by 5h.

Bring 3594 poles to yds.

1 ) 3594 poles

^j po.

17970= 5 times 3594
1797 = 0- ,.

19767 = 5^ times ,,
= yds. Ans.

To multiply by 30{.
Ex. Reduce 157 sq. poles to sq. yds.

?) 157 = sq. po.
30^

sq. po.

4710 = 30 times 157
47401 = 30? times 157

Ans.

Division by 5^ and 30^.

This is by far the most difficult rule to teach in reduction of
weights and measures. An attempt, however, must be made
to show the reason for the process. The following lesson is
drawn up with the view of making each step in the process
clear.

NOTES OF A LESSON ON*
The Reduction of yards to poles (long and sq. measure).

Examples and truths they teach Teaching Directions,

and apply.

1st set.

Simple examples arranqed to
lead up to the required truths.

each dividend and di-
visor X by 2, 3 or 4.
12-^3 = 4 24 4- 6 = 4
20-f-4 = 5 8o-^i6 = 5
30 -^ 5 = 6 60 -f- 10 = 6
42 -f- 6 = 7 126 -4- 18 = 7

The truth taught : — When the
dividend and divisor are muki-
plied by the same number the
quotient remains unaUered.

Application of truth to the
division of a number by 5h.

1st set changed by X 2.

After working the ist set of simple
examples the teacher may change the
first two into the 2nd set by multiplying
each dividend and divisor by the same
figure.

Then direct the attention of the
scholars to the answers in both
sets of examples.
Allow the scholars to change the last
two. and let them asain note the simi-
larity in the two sets of answers.

These exatiiples must be con-
tinued until the scholars state the
truth. It must not be told.

(a) 22 -^ 5^
{!>) II -5

(0 33 -^ 5

= 44 -^ 1 1 =4
= 22 -^ II = 2

= 66 -^ I I :^ 6

After placing the examples («) (/') (c)
on the board, allow the class to sug-
gest the necessary change.

It may be necessary to suggest

the multiplication of each by 2 in

the first case.

* This lesson belongs properly to the work of Standard VI. and should be t.-iken
after the first four rules pf v.ulga.r fractions. It is retained here ;is an example of
'Inductive Teaching/

igo

Ho7v to Teach Arithmetic.

C. Rule stated. To divide by 5^
multiply both dividend and di-
visor by 2 and divide the former
result by the latter.

Ex. Bring 539 yds. to poles.

5k
2

539 yds.
2
= iyds.

II ) 1078

98 poles. Ans.

N.B. — In case of remainder it
must be pointed out that they
are ^ yds. and must therefore
be brought to yds. by dividing
by 2.

When they can make the change for
themselves the scholars know the rule.
Encourage the class to state it.

Whilst working the example place

the dividend and divisor as printed on

the left. Allow the class to suggest

the mode by which it is to be worked

If they cannot do this, then the

previous work must be revised.

Continue to place side explan.atory
notes luitil each line is understood.

D. Application of the trutfi tauglit
above to tiie division of a num-
ber by 301

1st set of 2ndset,eachdividend
examples, and divisor X by 4.

3of

6oi-

i2r-^3oi
iSiKsoi

-Soj

= 121 -4- 121 = I

= 242 -=- 121 = 2
= 484 -=- 1 2 1 =4
= 726 -^121=6

The same plan of teaching must be
followed as for the division by sj.

It will be necessary to change the
first example by multiplying the divi-
dend and divisor by 4.

Afterwards the class may be
asked to make the change from
the ist set to the 2nd.

E. Rule stated. To divide by 30:|-
multiply both dividend and di-
visor by 4 and divide the former
result by the latter.

sq. yds.
Ex. Reduce 3752 to sq. po.

3752 sq. yds.
4

121 ) 15008 (124 sq. poles.

121 Ans.

290

242

~^8

N.D.— Itwill 484
be necessary to . . . =: ^ sq. yds.
point out that — ,- I gn. yd.
the sq. yds. '■ ■'

have been re-
duced to quarter yds. Hence the remain-
der must be divided by four to obtain the
remainder in sq. yds.

The rule must be given as the result of
teaching and must on no account be
told.

If the children hesitate to state
the rule, more examples like those
under D must be supplied.
The dividend and divisor should be
placed in their ordinary positions by
the teacher. The children must sug-
gest the multiplication of each by 4.
The remainder will require a
few examples to show that it is
always of the same value as the
dividend.

Decimal and Metric Systems. 191

Inductive and deductive teaching.

The process of teaching the truths of number (as these are
apphed to division by 5^ and by 30;^ in the lesson just sketched)
is termed the inductive method. It is the method by which
children are led (by an examination of carefully arranged
instances) to the discovery and the statement of a truth, rule
or principle. The truths in the above cases are not announced
by the teacher. All the teacher is supposed to do is to place the
examples before the class, and to encourage the scholars to
discover the truths from a careful inspection of the examples.
Any truth or rule so discovered by the class is likely to be
remembered, and the exercise is of value, furthermore, because
it affords practice in one of the methods by which truths
generally may be found. If the teacher announce the rule and
if he work a sum in application of it, the scholars may, by these
means, learn how to work similar sums correctly. But they do
not thus learn why the right answer is obtained. They are
being taught by the ' telling ' or dogmatic"^ method, and not
by the inductive method.

The young teacher is advised to tell as little as possible. He should
make it a practice wherever possible (and especially wlien engaged in
explaining a new rule) to apply the inductive method of teaching.
In this way not only will skill in the art of arithmetic be gained, but
there will also be secured that intellectual training in reasoning which
arithmetic studied as a science is capable of yielding.

THE DECIMAL AND METRIC SYSTEMS.

Introductory.

The decimal and metric systems are extensions of the
notation with which children have already become familiar.
In the simple rules they have been accustomed to arrange
figures so that they increase or diminish in value by ten by

* In place of the word ' dogmatic ' the term ' deductive ' is sometimes used.

19:

How to Teach Aritluuetic.

being removed one place to the right or the left respectively.
In the decimal notation hitherto used the figures to the left
of the units' place (or those which are greater in value than the
unit) only are noticed. In the system now to be considered
figures to the right of the unit, and less than it, will be intro-
duced. Those numbers which are higher in value than the unit
are called multiples of it, i.e., they are tens, hundreds,
thousands, &c., times greater than the unit ; whilst those numbers
which are lower than the unit are called sub-multiples of it,
i.e., they are tenths, hundredths^ thousandt/is, &c., of the unit.

How to give first notions of multiples.

The notion of the different multiples of the unit may be taught by
recalHng for a moment the concrete method of presenting the different
values of figures in the units, tens, and hundreds places respectively.

Hundreds. Tens. Units.

There is no difference between the relative values of the multiples of the
unit in the new system of measures and i\\e /'lace or Av;?/ values of the tens,
hundreds, &c., which were learned in the simple rules. Children are
already familiar with the notion of increase in value by ten times as figures
proceed from the units towards the left. If, instead of beginning with the
units, they start with the hundreds figure and proceed to the tens and units,
the notion of decrease in value by tenths may be taught.

This notion of decrease by tenths must be fully understood in con-
nection with whole numbers before any attempt is made to carry the
same notion of decrease by tenths to numbers less than the unit.

Lessons designed to glue first notions of sub-multiples
and the use of the decimal point.

1st stag'e. — Recalling notions of fractions already taught.

The sub-multiplesmust be taught much more slowly than the multiples.
Children have already considerable knowledge of fractional parts. Their
notions of half-pennies, of farthings, and of the eight small cubes into
which the large cube of l^'roebel's Gift III. is divided should be recalled.
From the consideration of the familiar halves of half-pennies, fourths of

Decimal and Aletric Syste?ns.

193

farthings, and eii^hths of Gift III., the scholars should be led to the notions
of tenths, hundredths, &c. The following simple appliances will prove
helpful to them. Their introduction forms the second stage of the
exercise.

Units. Tenths. Hundredths.

I I I

2nd stage.— Concrete presentation of units, tenths, and hundredths
(sub-multiples).

A ruler marked inches and tenths of inches may be cut down to ten
inches in length to represent the unit. Another ruler similarly marked
may be divided into lengths of one inch ; each inch will represent a tenth
of the unit. Finally, one of these inches may be divided into ten equal
parts, each of which will represent a hundredth of the unit. The
diagram above represents 4 units, 5 tenths, and 3 hundredths.

The above lines are not drawn to scale. The scholars might be
taught to draw lines to scale in their exerci>e books representing units,
tenths, and hundredths. A set on a larger scale might also be drawn
on card-board and exhibited in the school-room.

3rd stage. — Exercises in re-arranging the tenths and units in the
concrete, accompanied by the ordinary decimal notation.

The children should now be allowed to see different combinations of
tenths and hundredths in the concrete, and with each new arrangement
there should be associated its decimal notation.

{a) Concrete* presentations by
means of sticks representing

units, tenths, &c.
I unit 4 tenths 9 hundredths

J >, O )» - »!

&c. &c. &c.

The fact that 4 tenths and 9 hundred hs
arc equal to 49 hundredths -.hnuld be
shown in the concrete. Tlie remaining;
examples should be similarly di alt with.

* Use the sticks of different lengths
shown in stage 2 for the purpose of
representing in the concrete each of
the following numbers.

(/') Decimal notation.

Units
I

6fcc.

tenths

&c.

hundredths

2
&c.

When the value of each place in the
above exainples is clearly understood,
then the scholars may be exercised in
decomposing each line, as follows,
viz. : —

(rt) I unit 4 tenths 9 hundredths
=*i unit 49 hundredths
= 149 hundredths.

194 How to Teach Arithmetic.

4th stage. — Combination of figures greater in value than the units
(multiples) with figures less than the units (sub-multiples).

Multiples.

Sub-multiples.

Hundreds

7
4

tens
2

7
5

Units
4
5
3
9

Tenths hundredths

5 6
2 3

6 9
I 4

The scholars should at first read each of the above examples after
the following pattern, viz., st-Ten hundred and twcnty-foiir yxa\\S., five-
tenths and six-hundrcdths. The last two figures may afterwards be
read as follows, viz., fifty-six hundredths, and so on for the remaining
figures.

5th stage. —The ordinary decimal notation, introducing the decimal
point.

Each of the above sets of figures should now be repeated, and instead of
distinguishing the units' place by means of heavier and larger figures the
decimal point may be introduced.

{a) Naming the value of each (/') Without naming the value of
column, each column.

H. T. u. tenths hundredths

724-5 6 724-56

4 9 5 ■ 2 3 495'23

I 7 3 ■ 6 9 I 73'69

3 5 9 • I 4 359' M

There arc three ways of reading each of the above examples. They are

learned in the following order, viz., {a) 724 units, 5 tenths, 6 hundredths ;

(A) 724 units, 56 hundredths ; {c) 724 decimal 5, 6.

The first method of reading should be adopted until the place value
of each figure is known. Then the second method of reading may be
introduced, and finally the third or contracted method.

The above course of teaching exhibits in outline the suc-
cession of stages designed to give children a general notion of
the meaning of the terms ' multiples ' and ' sub-multiples ' of
any unit. In teaching, it will be necessary to supply many
more examples in each of the stages. On no account should
fi stage be left for the following one until the former is

The Metric System. 195

thoroughly mastered. When the succession of exercises out-
lined above has been completed, it will be found that the
scholars thus taught are prepared for exercises in the ' Metric
System ' and in ' Decimal Fractions.'

THE METRIC SYSTEM.

An application of the decimal notation.

A substantial foundation has now been laid for the con-
sideration of the metric system. The system is, in fact, a
special application of the knowledge acquired in the previous
paragraphs. Hence, it will be found that a thorough grounding
in the relationships existing between the multiples and sub-
multiples of the decimal notation will prove a more valuable
preliminary exercise than will those of learning all the terms of the
metric system, and of committing the tables to memory. These
terms and tables may, however, be introduced at this stage
and the best method of teaching them may also be considered.

The prime unit of measurement in the metric system.

It is assumed that the size of the earth is fixed, and that any
meridian upon its surface will remain constant in length.
During the years 1792-3 many
eminent Frenchmen were engaged
in carefully calculating the length
of an arc along the meridian of
Paris between Dunkirk and Bar-
celona. They then estimated the
length of the meridian of Paris
between the North Pole and the
Equator. The distance thus deter-
mined was divided by 10,000,000,
and the quotient was made the unit

of length,* This unit is called a A B represents the distance divided.

metre, and is a little longer than ^^ '°.°°°.°°°-

an English yard. Its exact length is 39*37 inches.

* This statement is of historical interest. The accuracy of the measurements is not
universally accepted.

196

How to Teach Arithmetic.

A decimetre.

It is impossible on a page of this size to draw an actual metre.
The figure at the side represents the tenth part of a metre, i.e., a
decimetre. From this drawing it will be easy to construct a metre measure.
This is best done in card-board or wood. When made
it should be placed conveniently for reference and use
by the class. The scholars should construct for their
own use the figure representing the tenth of a metre.
They might further divide this length into tenths,
each of which represents ojie Juindredth of a }?ictrc, i.e.,
a centimetre. This hundredth might agam be divided
into ten equal parts, each of which would be one
thousandth of a metre, i.e., a viillimetre.

N.B. — Each measure is shown on the diagram.

When these notions of a metre and its sub-
multiples have been acquired, the terms deci-
metre, centimetre, and millimetre should be
associated with the length of each respectively.
It vvili be well at first not to spend time over the
derivations of these words The prime necessity
is to associate each word v.ith its length. On no
account should the derivation of the word be
made to take the place of the concrete presen-
tation of each length. After the association
between the words and the things they name
has been completely made, the meanings of the
Latin and Greek prefixes may be acquired.

Concrete notions of the multiples of the metre
might now be given.

For example, a line ten metres long might be
measured along the school floor ; another, ten times
as long (i.e., 100 metres), might be measured in the
playground ; and a third, ten times as long as the
latter, might be indicated along a well-known road or
street near the school. When these notions of a
metre and its multiples have been acquired, the terms 1° centrs. 4 inches.
decametre, hectometre and kilometre should be associated with the
length of each respectively.

The English equivalent of each multiple of the metre might be
given approximately ; thus, the Jdlometrc is about | of a mile ; the
hectometre is about lOO yards, and the decametre is a little over 32-8
i"eet.

The Metric System.

197

The metric table of length.

[a) Following the arrangement of
an English table of length.
10 millimetres = I centimetre
10 centimetres = i decimetre
10 decimetres = I metre
10 metres = i decametre

10 decametres = I hectometre
10 hectometres = i kilometre
10 kilometres — I myriametre

(d) To show the ualue of each length
expressed in metres (unit).
10,000 metres = i myriametre
1,000 metres = i kilometre
100 metres = i hectometre
10 metres = i decametre

I ""it 1=1 metre
of length J

•I metre = I decimetre

•01 metre = i centimetre

•001 metre = i millimetre

Exercises upon the metric table of length, showing
the simplicity of its application.

A few exercises in addition, subtraction, multiplication, and
division will serve to show that these operations are all
analogous to those of the simple rules. The simplicity of the
system may be further illustrated if two sums in reduction
be worked side by side — one by means of the metric system,
the other by means of the English table of length.

((?) English measure of length.
Reduce i mile to inches.

I mile
8

8 furlongs
40

320 poles

1600
160

1760 yards
3

5280 feet
12

(i) Metric measure of length,

Reduce i kilometre to
centimetres.
Kilometre

I
= 100,000 centimetres

The English measure requires the multiplication
successively by 8, 40, 5^, 3, and 12. The metric
system requires the multiplication by 10 to be re-
peated 5 times, and this is done by the addition of
5 cyphers.

63360 inches

198

Hoiv to Teach Arithmetic.

In ascending reduction the simplicity and shortness of the
metric system are equally marked. For example, 105473
centimetres are reduced to kilometres by dividing by 10 five
times in succession, or by placing a decimal point five places
to the left, thus, i '0547 3 kilometres ; whereas the English
measure requires the successive divisions by 12, 3, 5^, 40,
and 8.

The above examples show clearly how the metric system takes
advantage of the knowledge of number which the long practice of the
simple rules of arithmetic has provided ; whereas in the English
system, as soon as we get through the simple ndes and seek to apply
the knowledge gained to commercial and practical ends, we throw
aside very largely the decimal notation (which we have been at such
pains to learn), and we exchange it for other notations that vary with
every table both of weights and measures.

Remaining tables of weights and measures (metric
system).

The metric measure of length has been fully explained, and
the advice upon the method of teaching it has been made
fairly complete. The remaining tables must be taught in the
same manner as that of length. They cannot, however, be so
fully explained here, but their connection with the table of
length may be stated, and a few hints upon the method of
teaching them may be supplied.

(i) The metric measure of capacity.

The unit measure of capacity is best taught by constructing a card-board
cube, having each side one decimetre in length. The inside volume of this
cube is the metric unit of capacity. It is called a litre.

Each

dimension

is \ the

real size.

Fig. I. A cubic decimetre. Fig. 2. Ordinary form of the litre.

The cylinder is the common form of the litre. In figure 2 its dimensions
are shown one-fifth the real size. The height and diameter of the real
cylinder are 'loS metres, or I decimetre and 8 millimetres.

The Metric System. 199

(2) The metric measure of weight,

The unit of weight is obtained in the
following manner : — A small cube having its
sides (inside measure) I centimetre in length is
filled with distilled water at the temperature of
39° Fahr. The weight of the water in this cube ^ centimetre cube

forms the unit of weight. It is called a gramme. ^ ^'

(3) The metric superficial measure has for its unit a square area having
a side 10 metres long. The square thus formed is termed an are. A con-
crete representation of the are should be made in the playground. The
length of the side in English measure would be 39*37 inches X 10 = 3937
inches = 32*8 feet.

In constructing the table of superficial measure it will be found that
10 ares, i.e., a dekare, do not make a square ; nor does the tenth part
of an are, viz., a declare, make one. Hence there are only square
hectares (100 ares) and square centiares ('Oi ares) in this table. The
metric table of area follows the analogy of our square measure. It
will be remembered in square measure that 12x12 inches make i square
foot. In like manner 10 X 10 ares make i hectare. The terms dekare
(or decare) and declare are used, however, to represent 10 ares and
■Jj of an are respectively.

(4) The metric cubic measure has for its unit a cube with a side i metre
in length. This unit of cubical content is termed a stere. The sub-multi-
ples of the stere will be understood best by a reference to the English cubic
measure. An English cubic yard contains 12 X 12 x 12 (or 1,728) cubic
inches. In like manner the metric stire contains 10 x 10 X 10 (or i,oco)
cubic decimetres. Hence the tenth of a stere or a decistere = lOO cubic
decimetres, and the decastere =10 steres or 10 cubic metres.

(5) The decimal money table usually takes the franc as its unit. The
following example is worked by the method of simple addition : — 375 f. +
5-25 f. +4-5 f. = 13-50 f. Ans.

Remarks.

Each of the tables thus briefly described should be applied
in exercises, such as the one given under the ' measure
of length.' If illustrations of each measure and weight be
prepared as hinted above, very little difficulty vi^ill be experi-
enced in teaching the system. The entire series of weights and
measures has been shown to be related to the unit of length.
Pupils should be trained to find all the remaining units when
that of length is supplied. The exercise might be varied by
asking the children to draw correctly the front side of the litre

!oo How to Teach Arithmetic.

cube, or to make in paper the cube whose contents equal the
gramme, or to mark out an are in the playground. By means
of such concrete exercises as these a reality will be given to
the system, and an interest maintained throughout the entire
effort.

PRACTICE AND BILLS OF PARCELS.

Introduction.

The connection between practice and multiplication forms
the first step in teaching this new rule. The connection is
best shown by means of simple mental examples like the
following : —

(i) Find the cost of 50 sheep at £2 each.

This sum may be worked by two methods. We may multiply ^2
(the price of one sheep) by 50, and thus get the price of 50 sheep,
viz., ;^ioo ; or we may take ^^50 as the value of the sheep at £1
for each. Then multiply the /50 thus obtained by 2, in order to
get the price at ^2 for each sheep. This yields ^"100 as before.
The former method is termed 'multiplication,' the latter is termed
' practice.'

(2) Other examples to be worked by both methods.

Find the cost of 60 articles @ jCi each. Ans. ^iSo.
,, ,, 45 articles (§' ;,{^4 each. Ans. ;i^i8o.
,, ,, 54 articles (ai £2 each. Ans. ;,^io8.
&c. &c. &c. &c. &c.

Aliquot parts.

As soon as ability to work examples in which the price of
each article is an exact number of pounds has been acquired,
examples in which the price of each article consists of parts of
a pound should be introduced, as follows : —

((?) Examples with aliquot parts of a £ (to be worked mentally).

50 articles @; ^i = ,^50 o o
50 ,, @ 10/- = ^"25 o o
50 ,, (ql t,l- = £\2 10 o

50 articles fff 15/- = ^ 37 10 o
50 .. (« £i 15/- = ;^ 87 10 o
50 ,, (w,£2 15/- =;^I37 10 o

Examples like the last two may now be fully worked in order to

show the mode of stating a practice sum.

Practice and Bills of Parcels.

20I

{h) Example 1. Find the value of 50 articles @ £1 15s. each.

£ s. d. £ s. d.

50 o o := the value (a 100 each article.

25 o o = ,, (w. o 10 o ,,

10/-
5/-

iofi:i

h of 10/-

12 10 o =

£^7 10 o

® ;^I 15 O

(t) Example 2. Find the value of 50 articles @ £2 17s. 6d. each.

0/- =^,o[£i

£ s.
50

the

value @

„ @
@
@
@

each article

2
10

5
2

£2 17

Si- = A of 10/-
2/6 = A of 5/-

100
25
12 10

6 5

=
—
=
=

,,
,,
,,
6

£H3 15

After a few examples have been worked, the class may be led to see
that practice differs from multiplication in the following particulars : —
In compound multiplication we multiply the parts of the multiplicand
(£ s. d.) by the number of things whose value is to be found. In
practice we find the same value by a system of ' partial payments.'
The money is split up into ' aliquot parts,' and the prices of the articles
for these different amounts is found and then added together to yield
the required value.

Remarks and teaching hints.

(a) There is no reason why children who have passed through compound
division and multiplication should begin to work practice sums with
Id., ^d., i^-d., 2|d., for the values of the different articles. These
sums present more exercise in reduction than in practice. They are,
furthermore, quite as difficult as the examples worked above. There
should be variety in the examples, in order that the class may become
familiar with the modes of working sums in which the prices are shillings
and pence, and pence and farthings, but these need not be taken first as
they generally are in text-books.

{/>) When teaching, it is advisable not to allow all the aliquot parts to be
written out at once, and before the working by any of them is commenced.
The connection between each aliquot part and the line representing the
correct value for that part is best made by the two operations (viz , that
of finding the aliquot part and that of using it) being taken at the same
time.

202 Holu to Teach Arithmetic.

{c) The introduction of explanatory notes on the right-hand side of
every line of the working is very helpful to the learner. These should be
constantly used.

((/) When articles are named and their value at so much each is required, it
is confusing to multiply the articles by the money. Instead of doing this
it is better to write the articles in a line below and call them money,

'••.?■•—

2,357 articles @ ;^I5 7s. gfd. each should be written thus : —

^ s. d.
2,357 o o = value of 2,357 articles («^i os. od. each.
{c) Sometimes it is required to divide the same line by two aliquot parts.
Place all such aliquot parts close together and as nearly opposite the
line to be divided by them as possible.
(/) Children should be encouraged to find aliquot parts for themselves.
These parts will vary with different scholars, and especial notice should be
directed from time to time to the best selection of aliquot parts.

Compound practice.

In compound practice the price stated is not that of a simple
number of things, but is the price of a number made up (or
compounded) of several others of different denominations.
This compound number may be ac, roods, and poles, or it
may be cwts., qrs., and lbs., or any other of the weights and
measures. In all such sums the aliquot parts taken are those
of the weights and measures of lower name than the one whose
price is given in the sum.

The rule will present no difficulty if the children be reminded that
they have already been Shown that they can multiply the price of one by
the number of articles, as in multiplication, and obtain the same answer
as that obtained by simple practice. In compound practice we do, in
reality, multiply the money value of one ac, or one cwt., or one
yd., &;c., by the number of things given, and we take aliquot parts
in order to find the value of those quantities less than the one whose
price is given in the sum.

Bills of Parcels

May be introduced as soon as the compound rules are
begun. The practice of adding up a bill lends .interest to the
exercise of compound addition. Multiplication again affords
abundant opportunities for the making out of bills. Scholars
will work sums in the various compound rules with increased
interest when the sums are cast into the form of an account.

Rule of Three. 203

Bills should be constructed so as to afford practice in all the
foregoing rules, and the details should be the common sense
matters of ordinary trade. In order to give greater reality to the
working of ' bills of parcels,' a few actual specimens should be
collected and worked. The butcher's bill with its odd ounces,
and the school stationer's with its petty details and lengthy
additions, will yield excellent practice. The exercise may be
further varied by supplying each scholar with a bill in MS.
(copied by means of a multiplying process) for exammation
and correction.

Next in importance to the details composing a bill is the style in
which it is written. In order to secure the best style of displaying
a bill there is no belter plan than that of writing it on the black-
board. Allow each class, from Standard III. upwards, to copy the
bill so written once per week. This forms an excellent exercise in
penmanship, and when well done it materially brightens the pages of
an exercise book.

RULE OF THREE.

(a) By the unity method. (/>) By the method of proportion.

The unity method.

This may be approached by means of the following series of
simple exercises worked first mentally, and afterwards fully stated
on the black-board. The series of exercises should take the
order suggested below, viz. : —

^st series (mentally). Ans.

If I cow cost ^10, what will 12 such cows cost? = ;{^I20 o o

If I sheep cost ;^ I ids., what will 9 sheep cost? = ;!^I3 10 o
Continue to work similar examples until the class can state the rule,
viz. : — ' To find the price of a number of things, multiply the
price of one by the number bought.'

2nd series (mentally). Ans.

If 10 yards of silk cost £2, what will i yard cost ? = 4/-
If 12 stones of beef cost £6, what will I stone cost? = 10/-

Continue to work similar examples until the class can state the rule,
viz. : — * To find the price of one, divide the total cost by the
number of things bought.'

N.B. — So far the class has simply had an exercise in compound
multiplication and division.

204 How to Teach Arithmetic,

3rd series, a combination of the two preceding series.

(a) It has just been shown that if 12 stones of beef cost ;^6 that I stone

will cost lo/- What then is the cost of 5 stones ? — ;^2 los. Ans.
(/') If 12 stones of beef cost ^6, what will 9 stones cost ? = £4. los. Ans.
Continue similar sums until the class can state the rule, viz. : —
' Find the price of one, and multiply this amount by the number
of things bought.'

4th series (the above examples worked fully on the blackboard ).

{a) 12 stones of beef cost £6

.'. I stone ,, costs £6 -^ 12

.'. 5 stones „ cost £6 -4- 12 x 5 = £2 los. Ans.

Re-arrangement of stages in the unitary method.

After having established the unitary method of the ' rule of
three ' by means of a sufficient number of simple examples, the
convenience of multiplying first and of dividing afterwards may
be introduced to the notice of the class. Before leaving the
rule scholars may be encouraged to independent effort by
varying the mode of using the rule.

For example : —

(i) If 3 yards of calico cost 2/-, what will 18 yards cost?
(a) The cost of 3 yards = 2/-

(/') .*. ,, 6 yards = 4/- By multiplying (r?) by 2.
(c) .•. ,, 18 yards = 12/- By multiplying (/^) by 3.

Ans. = i2s. od.

(2) If 6 lbs. of sugar cost loid., what will 27 lbs. cost ?
(rt) The cost of 6 lbs. =: lo^d.

(l>) .'. ,, 3 lbs. = 5:j^d. By dividing (a) by 2.

Ans. = 3s. II:fd.

{3) If 2 gallons of oil cost i6d., what will 10 pints cost ?
{a) The cost of 2 gall. — i6d.
(/') ,'. ,, I quart = 2d.

('•) .'. ,, I pint = id.
(d) .'. ,, 10 pints = lod. Ans. = lod.

In the earlier rules it was deemed unadvisable to introduce much
variety into the vvorking of examples. The pupils are now, however,

Rule of Three by Proportioti. 205

becoming sufficiently advanced to make the introduction of some
variety of working a positive advantage. The class may be encouraged
to find shortened processes for themselves. Exercises which call forth
and develop independent effort on the oart of the pupil should be
encouraged by all means.

Proportion.

In dealing with the preceding rules a constant effort has been
made to lead children to connect each new stage of arithmetic
with one or more of the stages before it. One of the chief
advantages of the study of arithmetic lies in this recognition of
the logical order in which the various rules must be taken. If
a glance backwards be taken over the arithmetical processes
already considered, it will be noticed that they can all be
referred to the simple notions (i) of unity, (2) that one and one
make tico, and (3) that ttvo can be split up into one and one.

For illustration of the statement just made it would be well to remind
children that their notion of t^uo was originally gained from the addition
of one and one ; that ten was connected with ten sticks (units), and
that their first notion of one hundred was that of ten bundles of sticks
each containing ten sticks (units). In multiplication the product is
equal to the sum of a number of groups of units, each group having
the same number of units. Subtraction and division are extensions of
the process of taking two units and separating them into one unit and
one unit. It has been necessary to introduce simple fractions in order
to represent the parts of a penny, and also in order to form notions
of the submultiples of the metric system. Here again, however, it may
be shown that the fractional parts refer to one or unity. The term ' one
half is associated with the half of one. Similarly, ' one fourth' is one
of the four equal parts into which unity may be divided. In this way
it may be shown that the numbers in the various rules hitherto taken,
and the results obtained by their use, are all of them related to one
or unity.

The new relationship between quantities, viz., ratio.

The invariable rule to be followed, whenever a new truth in
arithmetic is to be acquired, is to present the truth through the
medium of very simple examples. The following are speci-
mens of examples which should be used to ^\\q. the first
notions of ratio.

2o6 How to Teach Arithmetic.

Numbers for comparison.

Result of comparison.

r^ . r 4. and 2
'^"""P '■ i 6 and 2

That 4 is twice 2
,, 6 is three times 2

'^-"p- { r»nd=:

,, 4 is one-third 12
,, 5 is one-fourth 20

c-p «'• { 'I i:l \l

,, 12 is two-thirds 18
,, 9 is three-fourths 12

Summary of results of comparison. In group i. the first number
is a multiple of the second ; in group ii, the first number is a fractional*
part of the second ; and in group iii. the first number is two or more of a
given fractional parts of the second.

Conclusion from the above summary, viz. , One number may stand
in relation to another as either a multiple of it, or a part of, or parts of
that other number. The term used for the above relationships is ratio.

Definition of the term ratio. Ratio is the relation which one number
bears to another of the same kind.f

The new relations between quantities should now
be recognised by the scholars.

In previous rules numbers are related to one or unity, but in
a ratio quantities are put into relationship with other quantities
besides one or unity. Having thus given scholars a notion of
quantities in this new relationship, it will be of service to
arrange a series of simple lessons gradually leading up to the
rule of three by proportion. The following five stages taken
in order represent such a series : —

1. How a ratio is expressed.

Instead of writing ' ^//e ratio of 2 to 4,' it is customary to write ' as
2:4,' which is another way of writing 2 -H 4. If the scholars have
sufficient knowledge of fractions they will see that a third way of

writing this ratio is -

4- _ _ .

2. To show that the two quantities forming a ratio must be of

the same kind.

Allow the scholars to attempt to compare the following quantities,
viz., 2 sheets of paper and 4 days ; 12 houses and 18 minutes, &c.
By way of contrast introduce examples which possess quantities which
can be compared, as, e.g., 3 shillings and 12 shillings ; 10 men and 50
men, &c. Continue to contrast the above sets of examples until the
scholars see that ' a ratio requires that the quantities composing it are
always of the same kind.'

* The scholars should have a notion of fractions already, otherwise this term must be
omitted.

t Sufficiently exact for scholars at this stage.

Rule of Three by Proportion. 207

To show that two or more ratios may be equal to one another
although the numbers composing them may differ.

The numbers changed by divi-
sion.

48:

24 :

12 :

6 :

Again, in each of these
ratios the first number is three
times the second. Hence
the ratios are equal.

The numbers changed by multi-
plication.

2:4 ^^ '^^ scholars examine

- ' these ratios, they will see

O : 12 that the first number in
g . lg each case is one-half the
second. Hence the ratios
10 : 20 are equal.

When the above changes are understood it will be evident that the

terms of a ratio may be multiplied or divided by the same numbers

without altering the ratio.

4. To show that ' proportion ' is an equality of ratios.

The ratio 2 : 4 is equal to the ratio 6 : 12. This equality is
stated in the following form, viz. : —

As 2 is to 4 so is 6 to 12,
or briefly, As 2 : 4 :: 6 : 12.
This last statement is the form which a completed sum in proportion
assumes. A very useful exercise at this stage is to require the
scholars to make for themselves a number of equal ratios, and to
arrange each pair of equal ratios in both the full and contracted
forms of a proportion statement.

5. To show that 'the product of the means is equal to that of
the extremes.'

If several of the proportion statements be examined the above truth
will be found to hold for them all. The truth may be graphically
stated in the following way, viz. : —

Product of 'means' = 12

As 2 :

Product of ' extremes ' = 12.

Rule of three by proportion.

Each of the five stages taken above should be illustrated by
many examples. When thoroughly mastered, they will prove
a complete preparation for the ' rule of three ' by proportion.
The connection of a proportion statement with the ' rule of
three ' may be established in the following way : —

{a) Place a proportion statement on the blackboard, as for example —

As I : 3 :: 6 : 18
{b) Allow the class to work out the equality between the ' extremes '
and 'means.' Take away the last term, viz., 18, and replace it by x.
The statement now stands as follows : —

As I : 3 :: 6 : X.

2o8 How to Teach Arithmetic,

(c) We have here one complete ratio and one incomplete ratio, and the
object before us is to complete the latter ratio. How shall we proceed ?
We may apply either stages 3 or 5 above. Suppose we take stage 3.
Then, from what is therein taught about ■ equality of ratios,' the figure
to be found must be as many times 6 as 3 is greater than i, i.e., 3 h'/m-s.
Hence, if we multiply 6 by 3 and divide by i the result is 18. The
full statement of the proportion is then restored, viz. : —

As I : 3 :: 6 : 18.

(d) Continue to work similar exercises until the class recognizes the
rule, viz. : —

To find the value of x multiply the third term by the second term
and divide the product by the first term.

The ' rule of three ' has now been estabhshed, and it has
been estabhshed by means of a series of logically arranged
stages. The result of each stage of working, furthermore, has
been acquired largely by the scholars themselves, and the rule
stands out as the final acquisition by the class. The entire
teaching effort may be quoted as an example of ' Inductive
teaching.'

How to state a rule of three sum by proportion.

I. What is the odd term ?* It has been shown that in every rule of
three sum there is a complete ratio and a ratio which is not complete. The
odd term is one of the terms of the incomplete ratio. It is placed, as shown
above, in the 3rd term of the proportion. There are cases in which the
phrase ' the odd term ' is apt to mislead, as when all the terms are sums of
money. For example :—// 5/- is given for the loan of£c„ -ivhat ought to he
given for a loan of £^0 ? A youth who is taught to look for the odd term
may experience some difficulty in solving this question. With the notion of
ratios as taught in previous paragraphs he is less likely, however, to make a
mistake. The two sums lent, viz., £t^ and ;,^5o, are at once seen to be
related ; they form the complete ratio. The interest on ^50 is the term
sought, i.e., X. When found, it (along with the 5/- interest given in the
sum) will form the second ratio. So that 5/- is the 3rd term.

2. What is the term which is like the answer ? * This question
is more likely to yield the third term (or term of the incomplete ratio)
than asking for the ' odd term.' In the above example all the terms are
amounts of money. The odd term appears difficult at first to find. Ask,
however, for the term which is like the answer or like the term sought.
Then the interest term, viz., 5/-, is readily recognized as the third term.

* By very little suggestion on the part of the teacher the connection of ' odd term *
and .-inswer term ' with the missing term of the incomplete ratio will be recognizea
by the class. *=

Ride of Three by Proportion. 209

How to arrange the terms of the complete ratio.

The arrangement of the terms of the complete ratio is the
most important feature of a rule of three sum. It demands
most thought, and only after many examples have been
worked does the young pupil become thoroughly master of
this part of the exercise. The following examples and sugges-
tions indicate the method of teaching : — ■

1st set of examples.— Direct proportion.

(a) If 5 men mow 3 acres of wheat, how many acres can 10 men mow?

Here the men arc doubled, and so the acres should be doubled, and
the arrangement, therefore, should be as follows, viz. : —
men men acres
As 5 : 10 :: 3 : X

■^ X 10 "^o acres

The working = — ^ — -^ =6 Ans.

5 5

(/') If ;/^io is sufficient to pay the wages of 12 men, how many will ;i^5 pay?
Here the money available for wages is one-half, and so the men to
be paid should be halved. The arrangement to produce this result,
therefore, is as follows : —

men
As ^10 : ;^5 :: 12 : x

men

T-u 1 • 12 X 5 60 , .

The workmg = -^ — - =6 Ans.

10 10 ==

Work many examples similar to the above until the scholars recog-
nise the following relation between the two ratios, viz., As the terms
of the complete ratio increase or diminish so the terms of the
incomplete ratio increase or diminish. The term ' direct pro-
portion ' may now be given to sums in this class.

2nd set of examples. — Indirect proportion.

(a) If 5 men mow a field in 12 days, in how many days will 10 men mow
the field ?

Here, evidently, as the men increase the time required to complete
the work diminishes, and the result will be obtained by the following
statement, viz. : —

men men days
As 10 : 5 :: 12 : X

days

The working = ^ = 6 Ans.

" 10 —

2IO IIo7v to Teach Arithmetic.

{/>) If 25 tons of coal are carted 4 miles, how many miles should 10 tons
be carried ?

In the exercise the tons to be carried decrease and the distance they

are to be carried should therefore increase. This result will be

obtained by the following statement : —

tons tons miles

10 : 25 :: 4 : X

miles
rr, , . 4 X 2t; = 100 .

1 he workm" = 3_ J _. = 10 .\ns.

10 10

Work many examj)lcs similar to the above until the scholars recog-
nise the following relation between the two ratios, viz. , As the terms
of the complete ratio increase or decrease the terms of the
incomplete ratio decrease or increase respectively. Now intro-
duce the term ' inverse ratio ' to this class of sums.

Cancelling.

The process of cancelling should be taught as follows. In paragraph 3
on page 207 it is shown that a ratio is not altered when both terms are
multiplied or divided by the same number. Let us take for example the ratio
144 : 156. Both terms are divisible by 12. The terms of the ratio by this
division become 12 : 13, but the ratio is not altered. .Sometimes it is
convenient to multiply each term of a ratio in order to clear it of fractions.
For example, i : J. If both terms in this case be multiphed by three the
ratio becomes 3 : i, but the ratio remains the same. The division of
both terms of the ratio by the same number is called ' cancelling-.'

Summary of stages in the ' rule of three by pro-
portion,'

1. Find the term of the same kind as the answer.

2. Place this in the third term of the proportion.

3. Determine, by reading through the sinn, whether the un-

known term of the second ratio is to be an increased or a
diminished term.

4. Arrange the two terms of the complete ratio so as to secure

the required increase or diminution.

5. Bring both terms of the complete ratio to the same name,

and, if possible, cancel in order to lessen the working.

6. To find the answer multiply the third term by the middle

term, and divide the product by the first term.

Measures and Multiples, 211

MEASURES AND MULTIPLES.

Measures.

The notion of one quantity being contained in another so
that it divides it exactly is not new. For example, a cwt.
is contained a certain number of times in a ton without
remainder; a foot in the same way is contained three times
in a yard without remainder ; similarly the sub-multiples of
the metric system are contained in the unit a given number
of times without remainder ; and in practice a number is an
aliquot part of another when it divides that number without
remainder. These examples, when recalled, will assist the
class in forming their notion of a measure ; at the same time
they serve to connect the new stage with those taken previously.

If difficulty arise in giving clear notions of the meaning of a ' measure,'
allow some members of the class to divide a yard length by means of the
foot rule. In the same way, if a six-inch rule be introduced it will be found
to divide or measure without remainder both the foot and yard. It is, there-
fore, a ' common measure ' of the two. Lastly, if strips three inches, four
inches, and six inches long be prepared, they will each of them measure
exactly the six-inch rule, the foot rule, and the yard measure. Each strip
is, therefore, a 'common measure,' but the six-inch strip is the 'Greatest
Common Measure' (G. C. M.) of the three lengths, viz., the six-inch, the
foot, and the yard.

Supplementary exercises (abstract numbers— mental).

Find numbers which measure 6. Ans. 2 and 3.

8. Ans. 2 and 4.

Find a common measure of 6 and 8. Ans. 2.

Find measures of 12. Ans. 2, 3, 4 and 6.

Find measures of 18. Ans. 2, 3, 6 and 9.

Find common measures of 12 and 18. Ans. 2, 3 and 6.

Find the G. C. M. of 12 and 18. Ans. 6.
If children be allowed to suggest numbers in lieu of those given
above, they will soon discover that some they suggest will not yield
• measures.' They will find that 2, 3, 5- 7. n. I3> I7. &«-•) cannot be
split up into numbers which measure them. Hence they are ' prmie '
numbers. In contrast it may be suggested at this point that the
measures into which a ' composite ' number may be split are termed
' factors.'

212 How to Teach Arithmetic.

How to find the G. C. M.

This is a very difficult rule to make clear to a class of young
pupils. Some think the attempt involves too much labour for
the return it yields. Others, who look upon arithmetic chiefly
as an intellectual exercise, will make the attempt, and to all
such the following suggestions may prove of service.

Stage i.

It may easily be shown that when two numbers are so related that the
smaller number divides the larger number without remainder the smaller
number is the G. C. M. of the two ; e.g., the G. C. M. of 6 and 12 is 6. Ans.

Stage ii.

Frequently the smaller number does not exactly measure the larger
number. For example, the G. C. M. of 12 and 30 is not 12. The smaller
number does not divide or measure 30
without remainder. It does, however, 12 ) 30 (2

measure 24, which taken from 30 leaves 24 = the No. ignored

6. Seeing that 12 measures 24 without re- —

mainder we may ignore the 24 and proceed 6 ) 12 (2
to find the G. C. M. of the divisor 12 and the 12

remainder 6. This we know to be 6. —

Working backwards, therefore, we find : —
That 6 = G. C. M. of 6 and 12
But 30 = 12 + 12 + 6.
.-. 6 = G. C. M. of 12 and 30.

The G. C. M. required = 6. Ans.

Stage Hi.

The first remainder will not always divide the smaller number without
remainder. In that case the G. C. M. of the second remainder and the
second divisor becomes the G. C. M. of the original numbers. Take, for
example, the two numbers 12 and •^t,.

We divide 33 by 12 and get 9 for 12 ) 33 ( 2

remainder. The number 12, therefore, 24 = No. ignored

is not the G. C. M. of 12 and 33. By con- —

elusions arrived at in Stage ii. we must now 9 ) 12 ( i

find the G. C. M. of 9 and 12. We, therefore, 9 = No. ignored

divide 12 by 9 and get three for remainder. The —

number 9, therefore, is not the G. C. M. of 9 and 12. 3)9(3
Using Stage ii. again, we proceed to find the G. C. M. —
of 3 and 9, which is 3.

Measures and Multiples. 213

Working backwards, therefore, we find : —

That 3 = G. C. M. ot 3 and 9

But 12 = 3 + 9

.'. 3 = G. C. M. of 9 and 12

But 33 = 12 + 12 + 9

.'. 3 = G. C. M. of 12 and 33.

G. C. M. required =

= 3-

Ans.

Multiple, common multiple, and least common mul-
tiple.

A few simple examples carefully chosen and worked mentally
will suffice to place the meaning of these terms in the minds of
the class. For example : — ■

What numbers will 6 divide without remainder ?

= 6, 12, 24, 30, 36, 42, 48, &c. = Multiples of 6.
What numbers will 8 divide without remainder?

= 8, 16, 24, 32, 40, 48, &c. = Multiples of 8.
Find from the two lists those multiples which are common to both 6 and 8 ?
= 48 and 24 = common multiples of 6 and 8.
Hence, 24 = least common multiple of 6 and 8,

The rule for finding the L. C. M.

There are three stages by which the rule is established, and
they may be taken in the following order : —

Stage i.

Take, for example, 6x8 = 48. The product of any two numbers is
evidently a multiple of both those numbers, and is also a common multiple
of them, but may not be the L, C. M. It is evident that 24 is the L. C. M, in
the example chosen.

Stage ii.

12 = multiple of 6, and of 3 and 2 (jhc factors of 6).

30 = ,, 15, ,, 5 and 3 {(he factors of IK,).

Hence, in finding the L. C. M. of 6, 5, 3, % wc may cancel the factors of
6, viz., 3 and 2, and find the L. C. M. of only 6 and 5 = 30. Ans.

Stage Hi.

In some cases it is possible to still further reduce the L. C. M. For
example, if the series of figures be 2, 4, 6, 8, lO, and it is desired to find
their L. C. AL, by applying the results ot Stage ii. the figures 2 and 4 may
be struck out. The figures that remain, viz., 6, 8, and 10 arc all
divisible by 2, i.e., they cOntlhi the common factor 2. So long as this factor

214 How to Teach Arithmetic.

is found once it may be struck out of the other numbers containing it. The
L. C. M. is then found in the following way : —
2 ) X, H, 6, 8, IP

3. 4, 5
L. C. M. = 2 X 3 X 4 X 5 = 120. Ans.

VULGAR FRACTIONS.
(What they are and how to teach them.)

Introduction.

We have found it necessary in the earher rules to introduce a
•^' Tew simple notions of fractions — as, for example, in dealing with
the different parts in which a penny is ordinarily divided,
and with the sub-multiples of the metric system. We have
also seen that all our notions of fractions are ultimately based
upon the notion of one or unity. Logically the consideration
of fractions should follow that of the simple rules. The rules
of fractions are generally, however, delayed until a knowledge
of the compound rules and of ratios as applied to proportion
is mastered. This delay is due to the value of a knowledge
of these rules for practical purposes. Logical sequence,
therefore, in this case is sacrificed to practical ends, and these
ends are considered of sufficient importance to justify the
arrangements adopted.

First notions of a vulgar fraction.

Children should have an accurate notion of what a fraction
really is from the commencement of the formal study effractions.
The following are specimens of both faulty and good teaching
respectively at this stage : —

Faulty teaching.

Recently, and before H.M. Inspector, a somewhat inexperienced teacher
commenced to give a first lesson on fractions in the following way : — After
breaking one of two sticks of equal length into irregular portions, he held
up one of the broken parts and the entire stick before the class, and told
the children that the entire stick represented o>!t\ and the part of the broken
stick represented a fraction. The teacher then proceeded to write on the
•black-board the following statement, viz., ' A fraction is a part of any

Vulgar Fractions,

215

whole/ Whereupon the Inspector, unable to restrain himself longer,
exclaimed — ' There I there I he is going to immortalize the error he has
taught, by writing it for tlie class to see ! ' Now, what was the error
which caused the Inspector to exclaim ? The answer may be best given
by stating the right method of teaching.

Good teaching.

Instead of two sticks, let the teacher obtain three sticks of equal length.
Allow one of the sticks to remain whole as at first. Then break one of the two
remaining sticks into three unequal

lengths. Proceed to measure (by
means of a tape or foot rule) and
to divide the third stick into three
ec^ual portions. Now call the atten-
tion of the class to the difference
between the parts of the two divided
sticks respectively. The unequal

Stick entire = one or unity.

Stick broken into unequal parts =
fragments.

Stick divided into equal parts
fractional parts.

partS-of the one and the equal parts of the other will be seen at once by
the class, and the terms ' equal parts ' and ' unequal parts ' will be given
to them. In similar fashion deal with
three apples.

Allow one to remain whole to
represent one or unity. Then break
a second into very irregular and
unequal parts, and a third ivjto
four equal parts. The terms ' unequal
parts ' and ' equal parts ' will be
connected with the different divisions
of the apples. At this stage the
term 'fragment ' may be associated ^PP''^ representing one or unity.

the equal
whether

divisions
the class

with the unequal divisions, and ^fraction ' with
of both stick and apple. If in doubt (as to
has formed a clear dis-
tinction between frag-
rhentsand fractions), other
examples may be intro-
duced. From the division
of concrete quantities the
teacher may proceed to
the division of abstract
numbers. Finally, the

definition of a fraction may be required of the class. In reply to the
teacher's question, ' What is a fraction ? ' Some children will say, ' the sann'
farts,'' the regular portions^ and the eqttdl partis, &c. Thbs^ dn6)iVei-& all

Apple divi.'.ed into 4 ccjual parts.

2l6

How to Teach Arithjueik.

show advance towards the correct notion of a fraction. The teacher
must guide the efforts of the children to a definition of a fraction something
like the following, viz., ' A fraction is one or more of the equal parts into
which a whole number may be divided.''

Mode of representing a vulgar fraction— numerator
and denominator.

■ The complete idea of a fraction can be analysed into two

simpler notions. The previous teaching has succeeded in

giving a knowledge of one or unity divided into two or more

equal parts. This is, however, only a portion of the complete

idea. Fractions vary in size according to the number atid

magnitude of the equal parts into which the whole is divided.

This double notion must now occupy the attention of the

class. The following illustration will help them to seize the

complete idea of a fraction.

Let the rectangle A BCD represent _ ^

one or unity. The dotted lines divide

the rectangle into nine equal (hence

fractional) parts. Each of these parts

is, therefore, a ' ninth.' The three parts

which are shaded are evidently ' th7-ee-

ninths' Other portions might be

shaded on the blackboard and the

scholars might be encouraged to name

them, as, e.g., fonr-ninths, seven-ninths,

&c. The class will thus be led to the

double notion of a fraction, viz., {a)

unity divided into a number of equal parts ; [b) the number of these parts

in the fraction named.

As soon as this double notion is acquired the appropriate name
should be associated with each part of it. Thus, ' denominator ' should
be applied to the number of parts unity is divided into, and • numerator '
to the number of these parts found in the fraction. At the same time
the symbols \, %, &c.. should be placed before the class, and the
appropriate names (numerator and denominator) should be associated
with the upper and lower figures respectively.

Vulgar fractions : — improper, proper, and mixed
numbers.

The different forms which a vulgar fraction assumes are
best taught in the first place by means of concrete illustrations.

Vulgar Fractions.

217

If card-board figures be constructed in place of the accom-
panying rectangular drawing, an effective teaching device
will be secured.

The drawing or card-board ^ P P

illustration may be used in
teaching after the following
manner. Let ABCD represent
one or unity. Extend the figure
so as to include two additional
squares similar to the ninths in
the large square. In the entire
figure there are eleven ninths —
written as follows, viz., -y-. The
fraction -g'- is greater than unity.
All such fractions are termed
' improper fractions,'' &ndi are to be distinguished from fractions less than
unity (as, e.g^^ f, ^, &c.). The latter are termed ^ proper fractions.'' It will
be well in teaching to supply other examples of both ' improper ' and
' proper ' fractions. The class will soon learn to connect the term ' improper
fraction ' with one whose numerator is greater than the denominator. The
next step is to change the --^ to its equivalent, viz., I^. That i^ is equal
to -g'- is evident from the above figure. After several improper fractions
have been changed after the manner of the -g-, the class will recognize that
the change is effected ordinarily by dividing the numerator of an
improper fraction by its denominator. The quotient is the whole
number and the remainder forms the numerator of a fraction of
which the divisor or old numerator is the numerator. All such
fractions as i-g- are termed 'mixed numbers.'

The rules of addition, subtraction, multiplication,
and division of vulgar fractions.

It is not the purpose of this book to supply a complete
compendium of arithmetic. The main object is to suggest
those methods of instruction which shall ' make the reason for
every step of the process intelligible and interesting to the
class.' The explanations of the various rules of fractions are
often best secured by means of concrete illustrations. The
simple piece of apparatus illustrc'\ted below has been designed
for the following objects, viz., (r| the explanation of the rules
of addition, subtraction, multiplication and division of vulgar
fractions, and (2) the comparison of vulgar fractions with
decimal fractions.

2l8

How to Teach Arithmetic.

FRACTIONS AT A GLANX'E.

^^d

Diagram designed to make the rules of vulgar raclions interesting and intelligible.*

Explanation of the diagram,

1. Each strip taken across the page from left to right
represents 07ie or unity.

2, Each strip is divided into a number of equal, hence frac-
tional parts. The lower strip into halves, the next above
into thirds, and so on. The uppermost strip is carefully
divided into tenths and hundi'edths to represent decimal
fractions,

3, Each fraction, printed on the sheet, represents the length
of strip, or the number of divisions, counting from the line
AB on the left side of the diagram. Thus, % is the length
of the strip from the line AB to the vertical line on the
right of the fraction.

4. The T-square, or any straight edge, will be found of
service whenever the various fractions are compared, c.i!;,,
as it stands on the diagram the T-square shows the
following facts, viz, : —

* This drawinjj is enlarged and mounted oil. cloth on rollers Air d'ass teactllngplif-
nose*. It is published by the \Vestminst<;r Scli.%1 Rook Dejiot, .S.W. , anil may also
be obtained tliro'igli Sinipkin, Mcr-^h'.i.ll, Kciil L>t Co., Ltd., and all booksellers.

Vulgar Fractions. 219

[a) That i = f .

(/') That when numerator and denominator are multiplied lij- the

same number the value of the fraction is not altered.
(<■) That the vulgar fractions ^ and | are equal in value to the

decimal fraction "75.

Directions for the further use of the apparatus, f

1. To give a correct notion of a fraction.* — Each strip
is divided into a number of equal parts, e.g., the lowest
strip into two equal parts, called halves ; the next strip
into three equal parts, termed thirds; the next into
four equal parts, called fourths, and so on. A fraction
is thus seen to be one or more of the equal divisions into
which a whole number or numbers may be divided.
Contrast also with irregular portions, termed fragments.

2. Meaning of numerator and denominator.* — In all

the vulgar fractions on the sheet, it will be seen that the
figure below the line is the number of equal parts into
which each strip is divided. This figure is called the
denominator of the fraction. The upper figure may
change, but on the same strip the denominator remains
always the same. The upper figure indicates the number
of the equal divisions (counting from the left) which go
to make up the fraction. This upper figure is called the
numerator.

3. Comparison of fractions.* — It has already been shown
that if it be wished to show that |- = /;, a T-square or ruler
may be placed as in the figure, so that one edge is level
with the f ths mark ; it is then at once seen that the ^ths
mark is level with the same edge. Hence the two portions
of their respective strips are equal and the fractions they
represent are also equal.

The same device illustrates the truth that * if the nume-
rator and denominator of a fraction be divided by the

same number, the fraction is not altered in value,' thus,
e -7- 2 _ 3

Exercises like the following may be readily worked by
moving the T-square along the sheet.

t In teaching- a class of beginners, it will be best to commehce with the lowest
strip, I.e., with the h, and gradually work upwards.

* Each paragraph marked with an asterisk is illustrated by the dia^raiti ' r"rac*
tions at a glance.'

2 20 Hoiv to Teach Arithmetic.

{a) In one-half there are four-eighths, three-sixths, or
two-fourths, {h) Four-sixths are equal to two-thirds, and
two-eighths to one-fourth, &c.

4- Meaning of common denominator.* — The above
process of changing halves to sixths, to fourths, and to
eighths, will prepare for bringing fractions having different
denominators, like \, \, and f, to other fractions, each
respectively of the same value as the original fraction, viz.,
I, |r, ^, but having the same (/>., a common) denominator.
The change of -^ to ^ may be shown by placing the ruler
against the \ and the |. They are seen to coincide ; so
on for the other fractions. It may be necessary to remind
the class again that when the denominator is multiplied
by two, or four, &c., that the numerator must be multi-
plied by the same number in order to preserve the value
of the fraction.

5. Addition of fractions.* — To add ^ 4- | -f 5. Proceed

first to show that these fractions must all be brought to
the same name or denomination. A reference to the
addition of 6 farthings, no pence, 25 pounds, and 54
shillings will help the class to the notion of bringing the
different values to the same name before adding them
together. By means of the T-square the class may now
be led to see for themselves that the \^ |, and |^ can be
changed to -|, ^, and 4 respectively. Then add the three
fractions together, thus making in all -''/-. If now we take
the whole of the upper strip to represent 1, it will be seen
that ^'- is equal to an entire strip, plus seven of the eight
equal parts into which a second and similar strip is divided.
Hence the -y- is seen to be equal to 1|.
N.B. — The meaning of an improper fraction and a mixed number

may also be shown after several additions similar to the above example

have been worked.

6. Subtraction.* — To illustrate the subtraction of-^^ from \.
As these fractional parts are shown upon adjacent strips,
the class will readily see the difficulty of finding what is
left after 0. of the entire strip has been taken from \. They
can, it is true, see what is left, but cannot state what frac-
tion of the whole it is. Now take both the \ strip and the

* Each paragraph marked with an asterisk is illustrated by the diagram ' Frac-
tions at a glance.'

Vulgar Fractions.

221

FRACTIONS AT A GLANCE.

Diagram designed to make the rules of vulgar fractions interesting and intelligible.

-^ Strip up to the strip divided into sixths, i.e., bring the
two fractions to a common denominator ; the class at once
makes use of the common denominator and states the
answer to be \.
The explanations accompanying the ' fraction chart ' are sufficient
to give the scholars a correct notion of addition and subtraction
of vulgar fractions. The method of bringing each of the fractional
addends to a common denominator by application of the rule for
finding the L. C. M. has already been dealt with. The scholars
know also that the numerator of a fraction must be multiplied by the
same number as the denominator in order to maintain the value of the
fraction. So that the necessary explanations, so far as the rule of
addition and subtraction are concerned, are supplied. These should be
followed by an abundance of neatly worked exercises.
7. Multiplication.* — To illustrate the multiplication of f by
■|. Place the edge of the T-square against the |, we
cannot tell by looking along the fourths strip what the half
of I is, but f is seen to coincide with the f , and the -^ 0/
|- may be read off, and found to be |.

* Each paragraph marked with an asterisk is illustrated by the diagram ' Frac-
tions at a glance.'

222

How to Teach Arithmetic.

We get the same answer by the following reasoning : —
If we multiply | by 1, the answer would be \ or %, but this
would be twice as much as is required when we multiply
by \. Hence % which is one half of f , is the correct
answer. Again, this answer may be obtained by multi-
plying the numerators together for the numerator in the
answer, and similarly the denominators together for the
denominator in the answer, thus, f x | = f . Hence the rule.

The use of the word ' of ' in the above statement needs further
explanation. We say, for instance, i x ^ = the half of i, f X j = i|
of \. &c. The class will see that the expressions are the same, if we
recall for a moment the meaning of multiplication as it was understood
by them in the simple rules. For example —

To multiply i by 2 is to take the multiplicand twice,

and thus obtain for answer 2.

J J J, 2 by 5 is to take the multiplicand five

times and thus obtain lo.
,, I by A is to take the multipHcand one-half

times and thus obtain h.
i.e., — one-half of I.
,j ,, I by :^ is (similarly) to obtain for answer \.

i.c., = one-fourth of i.
A few examples like the above will enable the scholars to seize the
following truths, viz. : —

[a) That to multiply by a number less than one {i.e., by a proper

fraction) yields a result less than the multiplicand.
{/») That the statements i X i, 2 X |, and | X i are equivalent to
the statements ^ of i, ^ of 2, and i of f respectively.

To show in the concrete how
J X f yields iw.

Make a square piece of card-board
A B C D to represent one or unity.
Then the portion A B G H = | of
the whole, and the shaded portion
A K H = I of J = VV-

immm&immmi.. -

K-

Vulgar Fractions.

223

The same result of multiplying j by ^ may be obtained by the

following processes of arithmetical reasoning, viz.

X 3 =

But

the multiplier in this case is four times greater than ^, therefore the
answer is four times too great. Instead of f , therefore, we require 6
fractional parts one-fourth as large as thirds, i.e.^ we require -f-^.

The same result is obtained by multiplying the numerators together
for the answer numerator, and the denominators together for the
answer denominator, thus, f X £ = yV. Ans. Hence the rule.

8. Division.* — To illustrate the division of^by i. Place the
edge of the square against the -^ division in the lowest
strip, it is seen to coincide with a in the eighths strip.
Now, -J- may be seen to be taken 4 times in i, i.e., in \.
Hence -J -^ ^ = 4 times. We get the same answer by the
following reasoning, viz. : — If we divide \ by 1, the answer
is \ times, but here we have divided by a figure eight
times more than \t. Hence we must multiply the answer
thus obtained by 8 and, thus again, by reasoning we get
the answer 4. In actual working, the same result is
obtained by inverting the divisor fraction and then pro-
ceeding as in multiplication, thus, -i x y = t = 4.

The above explains the rule of division in a very simple case. A
more difficult example (^ -j- f ) may be explained in the following way.
Recall the fact that in simple division when 12 is divided by 4, the
answer 3 is the number of times 4 is contained in 12. So, now again,
we wish to find how many times f of one is contained in 4 of one.
The accompanying figure will

help to explain the process. Let A .CD

the square A B C D represent one

or unity. Then A E F D = i, i.e. ,

the fraction to be divided by j.

Now, ABGH is f of the whole

figure and i-epresents the divisor.

But A E F D (?>., i) covers 12

parts of the figure, whilst ABGH

(i.e., f) covers only 10 parts of the

figure. The answer to the question

proposed, therefore, is 12 -^ 10 = i^

or lyjy. Therefore, the fraction =

is contained in 4 = Itit times.

k
I

E — ..-

* E.ich par.igraph m.irked with an asterisk is illustrated by the diagram ' Frac-
tions at a glance.'

2 24 How to Teach Arithmetic.

Difference between a vulgar and a decimal frac-
tion.* — Ask the class to notice the different sizes of the
divisions of these lower strips, viz., the ^, \, \, .\-, and -^-
respectively. We can make others, in fact, any divisions
we please. Vulgar fractions are thus seen to differ from
decimal fractions, whose divisions are seen above to be
either tenths of the entire line, or hundredths, &:c.

lo. Reduction of vulgar to a decimal fraction.* — To

illustrate this change, put the edge of the T-square against
one of the vulgar fractions, say the f ; look then at the
division with which the same edge coincides in the decimal
fraction scale. It is beyond the '7 line, and exactly
coincides with the '75 line in the hundredths division.
The vulgar fraction f therefore is seen to equal '75.
Similarly the \ line coincides with "25 and the \ with "5.
It may also be shown that \ in the vulgar fraction divisions
will not coincide with any of the lines in the decimal frac-
tion divisions. It is somewhere between '33 and '34. The
decimal fraction required is expressed thus, viz., '3333?
and is called a ' repeating decimal.'

Complex fractions, reduction of fractions, 8z:c.

The rules of addition, subtraction, multiplication, and division
of vulgar fractions may now be used in the simplification of
complex fractions, and in the solution of various sums which
arise in business and commercial transactions. Only a few
suggestions will be offered at the present stage. Any modern
arithmetic will supply directions for the explanation of these
advanced processes, and our scholars ought now to be suffi-
ciently intelligent to understand the explanations therein given

Example i. Simplify j Example ii. Simplify

15 It It

I -|of§

8 ^^S 8

H-T6 "^5 7 7 Ans.
I

I + I +1

= lXl=ih = 'iio Ans

* Each paragraph marked with an asterisk is illustrated by the diagram ' Frac-
tions at a glance.'

Vulgar Fractions, 225

The following points need attention in simplifying the above
examples, viz. : —

{a) In both examples to proceed to simplify one step at a time.

{b) In example i. to take care that the operations of multiplying and
dividing are completed before those of adding and subtracting are
commenced. For example, in simplifying I — -f of f , first multiply
I by |. Scholars need to be warned against subtracting | from I
first.

{c) In example ii. the first operation is to simplify y by multiplying

both numerator and denominator by 2, and thus obtain the
expression ^.
((/) In every case, to regard a fraction as a number which can be deter-
mined * by dividing the numerator by the denominator.'

Reduction of vulgar fractions.

At the commencement of this rule it will be helpful to the
learner to have some exercises in expressing fractionally the
part which one abstract number is of another. When the rule
of reduction has become, by this means, thoroughly understood
it may be applied to the solution of fractions composed of
compound and concrete quantities.

(a) Examples with abstract numbers.

i. What part is 5 of 10 ? Evidently -j^, i.e., |. Ans.

ii. What fraction is 6 of 15 ? From i. it will be seen that the required

rs = I Ans.

i I H

What fraction of f is J? = — = — x — = f. Ans.,

TAJ

Work similar examples until the rule can be stated, viz., ' That the
fraction which one number is of another is expressed when
the former number is made the "numerator" and the latter
number is made the "denominator" of the answer fraction.'

(/') Examples with compound and concrete quantities.

1
5 shillings 5

i. Reduce 5s. to the fraction of £1 ids. = -^ — = ^. Ans.

£1 los. 5(5
6
ii. What fraction of i cwt. 7 lbs. is 2 qrs. 14 lbs. ?
2 qrs. 14 lbs.

= By reducing to lbs. = fj'V = j^. Ans.

I cwt. 7 lbs.

?26 Ho7v to Teach Arithmetic.

The chief difficulty in all such examples as the above is that of
determining which quantity is numerator and which denominator.
Contrary to the general order in arithmetic, it has been advised in this
case to take the exercises in the abstract before those in the concrete.
Simple abstract examples such as those given above should be used
until the rule is thoroughly established. Care must be taken to distinguish
between the expressions, ' What fraction is equal to \ of J ? ' and
* What fraction is i of ^ ? ' The latter statement should be made in
the following form, viz., ' What fraction of 3^ is i ? '

DECIMAL FRACTIONS.

Connection with past work. — Meaning of * decimal '
and use of * decimal point'

In the chapter on the decimal and metric systems the local
or place values of figures to the left and right of the decimal
point, together with the use of the decimal point, were
explained. That explanation may be repeated again at this
stage, and the relation between decimal and vulgar fractions
established by a few exercises like the following : —

((7) Changing decimals to vulgar fractions.

11. T. U. ■ lij jQfj itnyfj

65-15 7 = 60 + 5 + tV + T^o +

4 7-3 8 6 = 300 + 40 + 7 + T% + T^ +

. 7 ^
1000

Turnr

5*09 6= S + T%+Tmj + -To%s

&c. &c. &c. &c.

It will be excellent practice if, at this stage, the class be required to
decompose such statements as the above. For example, the first line
may be expressed as follows : —

(a) 6 tens 5 units 15 hundredths and 7 thousandths
or (/>) 65 units 157 thousandths

or (c) 651 tenths 57 thousandths

&c. &c.

{•'j) Changing mixed numbers and vulgar fractions to decimals.

H. T.

1*0 Too

1006

35tV +

1 00

1000

• I 4

59t'u +

1 oiT5

I 5

• 7 3

8 +

Tou

4 =:
1000

• 5

&c.

&C.

&c.

Decimal Fractions. 227

(r) Place value of figures and use of the DECIMAL POINT.

The class should be made quite familiar with several such series of
figures as those above until they recognise : —

(a) That all the figures decrease in value ten times as they proceed to
the right.

(/') That all the figures increase in value ten times as they proceed to
the left.

and the distinguishing vulgar fractions from over the decimals
we need a mark to indicate where the integers end and the
decimals begin. In this way we may show the use of the
decimal point.

(d) That when we remove the distinguishing vulgar fractions from the

tenths column, the hundredths column, &c. , we remove what in
vulgar fractions would be called the denominator.

(r/) Definition of a Decimal fraction.

That a decimal fraction is one whose denominator is either
10 or some power of 10 ; that this denominator is not
expressed, but that it is indicated by the position of the
decimal point.

How to express a simple decimal by an equivalent
vulgar fraction.

After what has been shown in the above paragraphs it will
not be difficult to establish the rule for changing any simple
decimal into an equivalent vulgar fraction. It will be advisable
to start with very simple examples like the following, viz. : —

Example i. -5 = tV '8 = ru "6 = t"o-

These simple changes have been previously taught by means of the
' Fraction Chart.'

//. -45 = A + X = 40 +i ^ 45,
10 ICO 100 100

///. -075 = ° + -L + _1_ = 7o_+i ^ _ 75
10 100 1000 1000 1000

&c. &c. &c. &c.

Continue similar examples until the following rule is understood, viz. : —
* To change a decimal into its corresponding: vulg-ar fraction take
for denominator the figure i, followed by as many cyphers as there
are figures in the decimal, and take for numerator the figures

228 How to Teach Arithmetic.

forming the decimal, omitting cyphers immediately after the decimal
point.'

N.B.— (i) The scholars must be taught to reduce the vulgar frac-
tion answers by cancelUng both numerator and denominator, e.g.,

1 = 4 A z= 3 _75_ ^ A &c.
"^Gi 5 -^6) 5 tWGi 40

(2) The opposite process of changing any vulgar fraction to a
decimal should be delayed until after division of decimals has been
taught.

Addition and subtraction of decimals.

These rules follow the method of simple addition and sub-
traction of integers. The process of changing from one value
to the next of a higher or lower name will require thought.
Unless this is attempted there is very little educational discipline
in the exercise.

An example in addition in ivliich the method of changing from a
figure of lower value to one of higher is fully explained.

Explanations of carrying.

(n) The first column = tooo-

We split up this number into j^uu + ttt'oo'
Put down the i-^oo in the first column and
carry the -r^^ or ^ig to the next column.
{^) The second column = /^.

We split this up into t%% + y^^.
Put down the j^ in the second column and
carry the -^jP^ or j% to the third column.
(<f) Proceed as above until the sum is completed.

The rule of 'equal additions ' in subtraction should be introduced
and explained in the following way.

Example : 5"374-4"50 9-

It is necessary before taking j^jo from xo^
to add 1 JL_ or -j-^gr; to the minuend and thus
make the ^^ = tooo- Then 9 thousandths
from 14 thousands = xooo- Having added
-j-Iq to the minuend it is necessary to add j^^
to the subtrahend and proceed to subtract j^
from 1^ = -fg0. Proceed similarly with the tenths and units.

H. T. U.

Too

1000

3 5 •

7 •

8 9 ■

• 7

■^
J

1-2 Ai ■

• 3-2

146-

1
1

Too

1000

5-
4o-

^3
5

7
Oi

•

Decimal Fractions.

229

Multiplication of decimal fractions.

The multiplication of a decimal fraction by an integer follows
exactly the process of simple multiplication. Difficulty is only
felt when both multiplier and multiplicand contain a decimal,
and then the difficulty chiefly consists in explaining the position
of the decimal point in the product. Suppose, for example, it
is desired to multiply 3"57 by 2*3, the process follows that of
simple multiplication so far as obtaining a product of the two
numbers when multiplied together. How can we explain the
rule for fixing the position of the decimal point in the newly-
found product ?

Method of showing how to fix the position of the decimal point after
multiplication.

Example : Multiply 3*57 by 2"3.

/. Ordinary multiplication.

The number of decimal 3'5 7
places in the product is 23

shown by method ii. to

be three, i.e., as many i o 7 i
as there are decimal 714

places in multiplier and

multiplicand taken to
gether.

8-2 I

By vulgar

fractions

357
100

X —

8211
1000

Changing to a decimal =8211

The methoci of changing the vulgar
fraction to a decimal has been explained.
See under the first paragraph upon
decimals.

A few examples worked by both vulgar fractions and ordinary
multiplication will lead the class to formulate the rule for determining
the position of the decimal point.

Division of decimal fractions.

This rule follows that of simple division so long as the
divisor is a \vhole number. When both divisor and dividend
contain decimals, the following stages of explanations become
necessary.

1. Revise, by means cf simple examples, the following truth, viz., that
divisor and dividend may be multiplied by the same number without
affecting the quotient —

e.^., 64-2 = 3; also, 18 4- 6 = 3 ; also, 42 4- 14 = 3.

2. Apply the above truth to division of decimals in the following way :

Example i. Divide '28 by '07.

(a) Multiply both numbers by lOO

= 28 4- 7.
(d) Now divide 28 by 7 = 4.

Ans.

Example ii. Divide 2-376 by "025.

(a) Multiply both numbers by locxj

= 2376 -f- 25.
{!>) Now divide 2376 by 25 = 9504.

An?.

230 How to Teach Arithmetic.

3. The rule of division of decimals.

The examples should be continued until the scholars recognise in

every case 'that both dividend and divisor are multiplied by either 10

or some power of 10 sufficiently large to raise the divisor to a whole

number, and that the method of division afterwards proceeds as shown

in division by any whole number.'

The rule of division by a decimal embodied in the above remarks should

be stated by the class. If there be hesitation on their part to state the

rule, more examples must be supplied.

How to change any vulgar fraction to a decimal.

It has already been established that we may regard any
vulgar fraction as a number equivalent to that obtained bv
dividing its numerator by its denominator. This truth has
been applied in turning improper fractions into mixed numbers
and in simplifying complex fractions. If now the class takes
any vulgar fraction and divides the numerator by the denom-i-
nator (in the same way that it has been taught to divide a
decimal by a whole number), the same truth will again be
applied.

Example!. Reduce -V- to a decimal. Example ii. Reduce y to a decimal.
4)1 3 "oo 8)17-000

3*25 Ans. 2-125 Ans.

T, , ... ^ , The addition of cyphers to the right

Example 111. Reduce ^ to a decimal. ^„a ^t ^\, a- ■ -i a ^-wu

' « end ot the dividend until there is no

8 ) S • o o o remainder in the quotient formed a

• 625 Ans. portion of the teaching of division of

=-=^^ """" a decimal by any whole number.

Circulating decimals.

The exercise of changing vulgar fractions to decimals cannot
proceed far without bringing the learner into experimental
contact with certain vulgar fractions which cannot be changed
into their equivalent decimals. The following are examples of
such fractions —

Pure and mixed repeaters.

i = '3 3 3 3 +

• I I I I +

4 - -571428

i = -I 666 +
i= -142857

The terms repeating, recurring.^ or circidatiui; AQmwxX^ may now l)e applied.
When these examples are more closely examined it will be observed that

■^^ = -090909 +

Decimal Fractions. 231

some begin to repeat from the first figure after the decimal point — these are
called pure repeaters ; in the case of \ the first portion does not repeat, but
only the latter portion. Hence it is termed a mixed repeater. The contrast
just indicated will serve to impress the scholars with the exact meaning of
these terms.

The five new terms introduced into the above paragraph
should in every case be suppHed after the form of fraction
indicated by each has been learned. The teaching will then
present a good example of the following maxim, viz.,
* introduce a term when it is required^ or ' ideas before words.''

Conversion of a repeating or circulating decimal to
a vulgar fraction.

Addition and subtraction of these decimals present little or
no difficulty, nor do their multiplication and division by whole
numbers. When, however, the divisor is a repeater, or when
both multiplier and multiplicand are repeating decimals, it
becomes necessary to convert these decimals into vulgar
fractions, and afterwards to proceed by the rules for multiplying
or dividing vulgar fractions. At this stage, therefore, the
essentially new matter to make clear to the class is that of
converting a repeating decimal into a vulgar fraction.

How to convert a pure repeating decimal— the rule explained and stated.

Example i,

(«)

{h) Hence

{e) Subtract {a) from {(>) =

(d) Divide both sides by 9 =

Example ii.

(a) 72 = 727272 +

Id) Hence 100 X 72 = 72727272 +

Example Hi.

W '135 = '135135 +

(6) Hence 1000 x -135 = I35i35i35 "^

(d) Divide both sides by 999 = -135 = -^^5 ^"S-

The rule stated. The vulgar fraction, equal to a pure repeating decimal,
has for its numerator the figure or figures of the decimal which repeat, and
for its denominator as many nines as there are figures in the repeater.

232

How to Teach Arithmetic.

The conversion of a mixed repeater should be taught by similar
methods to the above. Intelligent scholars in the upper standards
should be able to understand the process. Any good text-book of
arithmetic will supply the needful matter. Practice in sums involving
the use of these converted decimals should follow.

Reduction of decimals.

The class may now be exercised in applying the rules of
decimals already acquired to various exercises of reduction.

Example i. Reduce ;^'0758 to the
decimal of a shilling and of a
farthing.

£
•0758
20

1-5160
12

= I '5 16 of a shilling

i8'i920

727680

= 72768 of a farthing
Ans.

Example

//. Reduce "625 of a

gumea

to the decimal of a

pound.

•625 guineas

625
1250

20) 13-125 shillings

•65625 pounds. Ans.

Example Hi. Reduce i cwt. 3 qrs.
14 lbs. to the decimal of a ton.
28 ) 14 lbs.

4) 3-5 qrs.

20 ) I "875 cwts.

■09375 tons
Ans. = -09375 ^^ ^ ton.

Example iu. Reduce 3 hrs. 15 min.
25 sec. to the decimal of 6 hrs.
30 min. 15 sec.
(a) Express as a ) 3 hrs. 15 min. 25 sec.

vulgar fraction/ghrs. 30 min. 15 sec.
(/>) Reduce numerator 11725 335

and denominator to = =

seconds 23415 669

Remarks. The examples i. and ii. will present no difficulty to
scholars who are well acquainted with compound reduction. The
addition of the quantity of the same name to each quotient will prove
the chief difficulty in example iii. When both quantities are compound,
as in example iv., they must be dealt with as a vulgar fraction first and
afterwards reduced to decimals.

Notes cf a Lesson. — Simple Interest. 233

ADVANCED RULES OF ARITHMETIC.

The applications of the various rules of arithmetic to
problems in interest, profit and loss, stocks and shares,
discount, &c., take us beyond the scope of this book. The
rules hitherto noticed have, in every case, been explained.
This has been rendered necessary from the fact that text-books
of arithmetic do not, as a rule, attempt to establish the reasons
for each rule with that fulness and clearness which is necessary
if these reasons are to be understood by beginners. When,
however, advance has been made to the higher rules of arith-
metic the text-book explanations become much more explicit,
and the intelligence of the scholar becomes sufficiently
developed to enable him to understand and to use the ordinary
text-book explanations. A few outlines of lessons on some of
the more important of the advanced rules are given below.

A series of stages leading to the solution of an easy problem
in simple interest will first be introduced. Each stage needs
expansion by means of examples gradually increasing in
difficulty. The problem in interest to be taught is stated
below. The teaching may be divided into two parts — the
first introducing rate of interest for a year only, the second
introducing rate of interest for a number of years.

Notes of a Lesson.

SIMPLE INTEREST-PART I.

Example: Find the interest derived from investing ;^3,54o
for 3I years at 4 per cent, per annum.

Examples and Truths they Teach. Directions and Teach-
A I- I ■ ± I I ± ' J. iNG Hints.

A Examples introduced to impart
the meaning of the terms 'per ^
cent. ,' 'rate,' and ' interest. '

I. A boy buys a peck of apples for i/- i. Each example must be con-
and sells the same for 1/3 ; what is sidered a sample of others

the gam ? = 3d. Ans. which shouldaccompanyit.

234

Hoiv to Teach Arithmetic.

Examples and Truths they Teach —
continued.

2. Suppose, instead of buying a shilling's
worth he invests £^\ in apples, and
sells these so as to gain in the same
ratio ; what will be the total
gain ? = 5s. Ans.

3. If he invest ;^20 and gain in the same
ratio, what is the amount of
gain? = £i^. Ans.

4. {a) If he invest £\<X) and sell at the

same rate, what will be the gain ?
= £2^. Ans.

{b') If he gain one-half of the above,
what will be the gain per;ifioo?
= £\2\. Ans.

{c) If he gain only one-fifth, what will
bethegain per;,^ioo? = ;,{^5. Ans.

Terms introduced and explained.

The £^, £i2\, and £2^ are the gains
upon investing ;if 100. Instead of gains
per hundred they are termed ' rates per
cent,' The moneys gained are also
termed 'interest,' and the moneys in-
vested are called the 'principal.'

Directions and Teach-
ing Hints — continued.

2. The ratio between gain and
investment must be asked
for, and this must be recog-
nized as the same in each
of the cases named.

3. If the stages taken by these
examples prove too diffi-
cult, others more easily
graduated must be inserted.

4. When example (4) is
reached, the idea of ;i^ioo
as an investment must be
repeated, and the terms
* centum'' and ' per cent.'' be
associated with the ;f loo.

In the same way the

different amounts earned

must be associated with

the term ' rate per cent. '

So long as a ;^loo is the

amount invested the terms

' rate ' and ' interest ' have

the same meaning. They

may, therefore, be taught

together at this stage.

B Examples of ' interest ' cal-
culated on larger amounts
invested.

Princh'al. Rate per cent. I.vterest.
£100 @ $ per cent. = ^^5. Ans.
;if5oo @ 5 „ = £2$. ,,

;^5oo @ 4 „ = /zo.

^/■looo @ 4 „ = ;{;40.

The truth illustrated by the above ex-
ample is as follows, viz. : — The interest
is the product obtained by multiplying
the number of j^^ioo in the principal
by the rate per cent.

These examples may be
readily worked mentally.
As soon as a scholar an-
nounces the correct answer
in any of the examples he
should be asked to state how
the answer was obtained.
These examples must
be continued until the
truth they illustrate can
be stated by the class.
The truth must not be
stated by the teacher.

Notes of a Lesson. —Sitnple Interest.

235

C Application of the truth estab-
lished under paragraph B.

Example. Find the interest upon_^25o
fcr one year @ 4 per cent, per annum.

I . Applying above truth.

(a) Find number of ;i^ioo in ;[^25o

_ 2_A!2

luo

[It) 2i hundreds X 4, i.e., the rate
per cent., = ;i^lo. Ans.

2. Tlie same Wirrkedhyfraetiotial statement.

250 X 4 __ ^jo.

100

Ans.

3. Full working- by the rule of interest.
\. Interest rule.

;i^25o=: principal.
4 = rate %

100) 1000

£0 =

Interest reqd.

ii. Showing the diffi-
culty of dividini
first by 100.

100) 250

2 10

£10

Int. reqd.

1. Stages {a) and {b) may be
worked mentally by the
scholars, and afterwards
written down by the
teacher.

2. This condensed form of
working must be recog-
nized as the same as the
exercise under paragraph i.
It is intermediate between
I and 3, and explains the
' rule of interest ' in which
multiplication by the rate
is taken before division
by 100.

The necessity of multi-
plying by the rate before
dividing by 100 is not so
evident in this example.
Others should afterwards
be introduced in which the
necessity would become
very evident.

Notes of a Lesson.

SIMPLE INTEREST-PART II.

D Examples introducing other
times than one year.

If ;^io be the interest for i year, then
what will it be for 2 years ? = ;!^20. Ans.
what will it be for 3 ,, =^30. ,,
what will it be for 6 ,, =^60. ,,

&c. &c. &c.

7'lie truth illustrated above, viz. : —
When interest is required for more
than one year, multiply the principal
by the number of years as well as
by the rate per cent.

These exercises are based
on the answer found in the
previous example.

They may be continued
until the truth they illus-
trate is recognized and is
stated by the class. The
scholars may then pro-
ceed to apply the truth to
the solution of an example
containing both rate and
a number of years.

236

How to Teach Arithmetic.

E Application of the above truth.

Example. Find the interest on ^{^aso

for 3 years at 4 7o P^r annum.
(a) Worked mentally.

2i hundreds X 4 X 3 = ^3°-
(<5) Worked fractionally.
10 I
!?5is( X H X 3 30

= — = Lip-

H
I

(<:) Worked by the rule of interest.

^250 = principal

4 = rate 7^

Ans.

1000
3

time

100) 3000

^30 = Interest reqd.

F The problem stated at the be-
ginning of Part I. worked in
application of the rule of
interest

^3540 = principal invested
4 = rate 7„

i) 14160

31= number of years

42480
7080

) 495'^ — process of dividing
20 by 100

12 00

Ans. =/'495 12 o

(a) This example is suffi-
ciently simple to be worked
mentally by the rules for-
mulated in the previous
stages.
(p) The class should recognize
in this form of working the
division by 100 as well as
the multiplication by rate
and time. This mode of
working prepares for {e) by
showing that we may mul-
tiply first and divide by
100 last,
(t) The side - notes explain
each line of working. The
class should be required to
announce each stage before
working it.

Call upon one scholar to

read over the problem, and
then ask for the three stages
of working.

If any doubt exist as to
either the stages or their
order, the exercises taken
in the early stages must
be repeated. To tell the
class one or more of the
stages will rob the exer-
cise of its chief educa-
tional value.
Allow the scholars to
state what each side expla-
natory note should be be-
fore writing it on the board.
Introduce the shortened
method of dividing by lOO.

Blackboard Sketch. -This will consist of a
statement of the truths in the order in which they
have been taught and of the full working of the
problem. ^^^_^___^^

Profit and Loss.

237

Profit and loss.

The sums in this class can generally be solved by * pro-
portion.' The gain or loss upon any transaction is nearly
always stated to be at a given rate ' per cent.' The advan-
tages of referring each gain or loss to a common standard of
cost should be made clear to the class by a few examples like
the following : —

Suppose, for instance, one article is bought for 10/- and sold for 11/-,
whilst another article is bought for 20/- and sold for 21/- ; the absolute
gain is the same for both cases, but the gain in proportion to the outlay is
not the same for both. How can the two be compared so as to show (i)
which is the better transaction, and (2) how much one is better than the
other ? This comparison may be obtained if they reckon the profit that
would follow the purchase and sale of ;^loo worth of each article at the
above ratios. The working would stand as follows : —

Example i. An article is
for 10/- and sold for il/-;

bought
what is

Example ii. An article is bought
for 20/- and sold for 21/-; what is

the gain per cent. ?

s. s. £
As 10 : II :: 100 :

s. s. £
As 20 : 21 :: 100 : X

N()5fe) X II

= ;^lo

5
^(5S X 21

— — X.I'0
I Gain %

— — /6IO5

I Gain % = £S

The gain is, therefore, one half as much in the second as in the first
example. By thus referring their transactions to a common standard
of cost, business men are able readily to compare the value of their
several transactions one with the other.

The following is a more difficult example, but need not occasion much
hesitation if the theory of proportion has been properly taught.

Problem. A horse is sold for ;^5i at a profit of 2 per cent. ; at what
price must it be sold to yield a profit of l per cent. ?

1st stage of working. — Simple examples to be worked mentally.

(a) A horse bought for ^100 and sold for ;^loo yields no profit or loss
per cent.

238 How to Teach Arithmetic.

{h) Another bought for ^loo and sold for £1 10 yields lO per cent,
profit ; if sold for ;^I20 it yields 20 per cent, profit ; but if sold for
£()o there is no gain but a loss of 10 per cent.

(c) A horse bought for ^50 and sold for £^i yields £i profit on £^0,
i.e., £2 per cent. ; if it is to be sold so as to gain only £1 per cent,
then it must be sold for ;,^5o los.

2nd stage. — The last example worked by proportion : —

Price obtained Price required Actual Required

per cent. per cent. price. price.

As 102 : loi :: ^^51 : x

5,"^ X loi loi

= = 50^ = ^50 IPS. Ans.

\^% 2
2

Stocks and shares.

The chief difficulty which scholars meet with here is that of distinguishing
between cash and stock. In order to clear this difficulty a few concrete
cases should be examined. For example, take the case of a new railway.
Its ^100 shares are issued for ^100 cash, and for a few years the concern
pays 4 per cent. Suppose, however, the enterprise succeeds until the
railway pays 8 per cent. The /^loo shares could not now be bought for
the original amount. Each share may rise to £160 or more. The
amount of stock does not increase — it remains ;!f 100 still — but the money
(cash) required to buy it has risen. The stock is at a premium. Sometimes
loss ensues, and then the price of ;^loo stock sinks below par, say to ;^8o.
The stock is then at a discount. Similar cases to the above should be
noted, especially those taken from the actual lists of stocks and shares in
the daily newspapers. Most of the examples are capable of solution by
proportion. It should be noted that stock should be compared always with
stock and cash with cash, and not cash with stock.

Scholars encouraged to construct their own sums
as well as work them.

When the higher rules of arithmetic are reached by our
scholars they may, with great advantage, be encouraged to
make a few examples of their own. The following are actual
sums made by boys and girls in Standard VII. of the Model
Practising Schools, Westminster. The working is also from
the same source.

Stocks and Shares. 239

Example i. What is my income when I have ;^68oo to invest, half in the
3| per cents, at 80, and the other half in the 5 per cents, at 75 ?

Investment. Investment. Income.

(a) As ;^8o : ;^3400 :: £1^ -. x

85
3i X 34^*5 297J

= = ;^I48 15s. = 1st Income,

^^ 2

Investment, Investment. Income.

(l>) As £7s •■ £3400 :: £s ■ x
680
5. X S4i5*5 680

= — = ;iC226 13s. 4d, 1= 2nd Income.

75 3

£ s. d.

148' 15 o = 1st Income
226 13 4 = 2nd Income

£37 S 8 4 = Total Income.

Example ii. What income do I derive from /'8650 stock in the 3 per
cents, at 745 ?

Stock. Stock. Income. Income.
As £loo : £86so :: £3 : x

173
3 X ^6S^ 519
= = ^^259 los. = Income.

tS|^ 2

240 Ho^v to Teach Arithmetic.

A FEW GENERAL RULES OF TEACHING.

Most of the following directions have already appeared in
connection with the explanations of the different rules. They
are collected here for revision and expansion.

1. Make the reasoning upon which a rule of arithmetic is

based quite clear before using the rule.

Unless this is done at the outset there will be difficulty in rousing chil-
dren to the effort of mastering the reasons of the rules. When, e.g^., a scholar
has applied the ordinary rule for the division of decimal fractions, and has
obtained a correct answer, he is not likely to trouble much about the reason
of that very simple process. Similarly, when the simple interest rule has
been learned, unless it has been previously explained, there is danger that
it will continue to be used without explanation.

There are a few rules, like simple short division, which will present
difficulty in keeping rigidly to this rule. In all such cases the reasons must
be mastered before the rule is finally left for the one succeeding it.

2. Apply the inductive method of teaching whenever a

new rule or principle in arithmetic is to be taught.

This direction has been followed throughout the teaching of this book.
A truth or principle, such as ' to add the same number to both minuend and
subtrahend leaves the difference unaltered,' is first taught by means of a
number of examples. Similarly, a definition such as that of a ' decimal
fraction' is supplied after the notion has been imparted by the inspection
and working of many examples. Finally, a rule like that of ' proportion '
is formulated after the examination and comparison of ratios have made
the reason of the rule quite clear. These are all examples of * inductive
teaching.'

The educational value of these inductive exercises has already
been stated in the paragraph dealing with ' arithmetic as a science.'

3. Note that whilst new rules are to be taught inductively,

the practice of working sums by the rules thus taught
is a deductive exercise.

By far the greater amount of effort in arithmetic is spent in the applica-
tion of a few principles of number. Hence arithmetic is mainly a deductive
exercise. The value of these deductive exercises should be recognised.
They have already been enumerated in the paragraphs dealing with the
• art of arithmetic'

A Feza General Rules. 241

All teaching of arithmetic should result in arousing self-
effort on the part of the pupil.

WTien rules are told, and sums are worked according to the rules, there
is a certain amount of mental effort aroused on the part of the pupil. What
that effort is has already been stated. It is not the highest kind of exercise.
It is chiefly a memory effort, and is sometimes characterized bv the term
'learning.' When, however, a pupil is led to the establishment of rules
and principles by himselt, the effort aroused is of the highest kind. It
is pre-eminently an exercise of self-effort. Because this effort is largely
that of comparing examples so as to identify and establish rules and
principles of number it is contrasted with that of ' learning,' and is termed
an effort in 'thinking.'

^^'e think, when we contrast and compare ; we learn, when we take
what others have prepared and reproduce it in the form in which it
was originally received. The study of arithmetic is of real educa-
tional value, largely on account of the exercise of thinking- —
comparing, classifying, reasoning (both inductive and deduc-
tive) — which the study affords.

Self-effort must be promoted by arrangements designed
to secure independent exercise. Copying must be
rendered impossible.

As the slightest assistance at a critical stage of working a sum is suffi-
cient to vitiate the entire exercise, no pains must be spared to secure
perfectly independent effort. The best class arrangements for securing
independent exercise are these which preclude all means of inter-communi-
cation between pupil and pupil. Let the scholars be placed so as to
prevent the possibility of copying. This may be done by giving different
work to adjacent pupils. If the scholars stand during the working of a
sum they may, with advantage, be allowed to sit as soon as their exercise is
complete, and, after turning their slates with the working towards the desk,
they may be required to wait quietly until their neighbours finish. A short
period of complete rest after the concentrated effort of working a sum will
not be out of place.

Independent effort on the part of the scholars must also be secured
during the working of a sum by the teacher on the black-board. In
order to secure this effort the teacher's questions should be directed to
those scholars who are specially known to need this form of direct
stimulus. Every scholar should realize the possibility of being called
upon at any moment to take his or her part in this class exercise.

242 Hoii> to Teach ArithjJietic.

CLASS MANAGEMENT DURING THE ARITHMETIC

LESSONS.

Arithmetic is influenced for good or ill more than any school
subject by the nature of the discipline of the class. The
subject of arithmetic requires for successful effort that the
learner be entirely and completely occupied with his work.
A divided attention, a talkative habit, a slip-shod style of
work, a state of mind careless as to whether or not success
attends the effort — all or any of these conditions will surely
make themselves felt in weakening the arithmetical and
intellectual results. On the other hand, a highly concentrated
state of mind, a neat and orderly arrangement of work, and a
desire to be accurate, and a determination to succeed — all
these will assuredly be followed by the most valuable mental
and arithmetical effects. Each of these conditions of successful
effort is worth fuller consideration.

1. Concentration of attention.

This is the prime condition of success in arithmetic. Whilst many other
subjects allow of a condition of mind open to suggestions from various
sources, arithmetic requires that the mind be entirely absorbed in the
sum and its working. The attention must be concentrated, furthermore,
throughout the entire effort. Let the order of thought be once disturbed
and the work is thereby and immediately rendered uncertain. Before
beginning the problem in arithmetic, therefore, we must remove all sources
of disturbance ; the class must be placed in orderly array ; if working on
slates, a standing position will be conducive to concentrated and steady effort ;
the scholars should keep the positions allotted to each of them until the
problem is finished, and then each pupil should quietly take his or her seat
and wait for the announcement of the result. Communication between the
scholars should on no account be permitted either during the working or
after it is completed ; and, finally, the teacher should take up a position in
front of the class so as to be able to detect the slightest indication of
diverted effort on the part of a pupil, and with a sign stimulate the
defaulting scholar without disturbing the efforts of the rest of the class.

2. Tiie orderly arrangement of tfie various stages of a sum

is necessary if tfie best results are to be secured.

This logical or orderly arrangement can only be secured where there is a
clear mental view of the entire series of arithmetical operations from the
beginning of the sum to its answer. This clear mental vision should be

A Few Gefieral Rides. 243

reproduced on slates or paper by means of the orderly statement of each
stage of working. The teacher's black-board work must always present
a model of arrangement. The free use of explanatory and side notes,
indicating in full the meaning of each stage of working, will be of service in
securing a logical and clear statement. All slovenly and ill-arranged
working should be corrected, and models of neat work should at times
be exhibited.

3. The desire to be accurate.

There are certain school tactics which foster a desire to be accurate
and a determination to succeed. Every time the scholar is successful there
is a measure of pleasure accompanying the successful effort. A teacher of
tact will take care that the sums his scholars are called upon to attempt
are fairly within their power. Whilst successful eftbrt to obtain correct
answers is followed by the desire to succeed, nothing is more disheartening
to a scholar than frequent failure. In addition to providing the above
favourable conditions of effort, the class teacher will take care to
utilise the stimulus which emulation between the members of his class
affords. Whenever scholars of nearly equal attainment are working
the same example this form of stimulus is present. Most scholars
like to do as well as their neighbours. Without pushing this form of
stimulus too far the teacher will take care to use it. If a record of past
work is kept the scholar's success to-day may, with advantage, be compared
with his work of yesterday. The record of his own progress will provide a
more healthy stimulus to accurate effort than that obtained by competition
with his neighbour. The stimulus derived from the pleasure accompanying
successful effort and competitive exercise may be augmented by the prac-
tical value which accompanies the obtaining of correct answers. If we
provide a good proportion of problems dealing with matters of everyday
experience — the workshop, the home, the field, &c. — a reality and practical
value will accompany the working of sums sufficient to provide additional
stimulus to accuracy.

Additional Class tactics during- the arithmetic
lesson.

A class of scholars requires slightly different treatment
according to the nature of the arithmetic lesson. The fol-
lowing suggestions cover lessons on a new rule, on problems
involving the use of two or more rules already taught, and on
lessons of revision or examination.

244 Hoiv to Teach Arithmetic.

{a) When teaching a new rule.

1. Provide an abundance of simple mental examples illustrative of the
new principle or rule.

2. Distribute the cjuestioning so as to arouse and sustain the attention
of all.

3. Allow the brighter members of the class (as soon as they have
mastered the new rule) to proceed with simple exercises in application
of it, whilst a further effort towards complete knowledge of the rule
is made on the part of the slower members of the class.

(/^) When teaching a problem.

1. As each of the rules embodied in the problem is or ought to be
known, it will be necessary to provide a number of siniple mental
problems which afford exercise in selecting and arranging the rules
required in working the problem. Scr notes of a lesson on a
problem, p. 1S2.

2. Continue these simple problems (arranged on the pattern of the
larger problems) until the processes of working, together with the
order in which they are to be introduced, can be stated by the class.

3. Do not be content when this statement can be made by the brighter
members of the class onh*. Other examples must be supplied until
the slower scholars can provide the statement in connection with
each new example.

4. When the rules to be used in solving the problem are known proceed
to work the problem on the black-board. Question all portions of
the class at this stage, and take answers from scholars selected
without show of hands, as well as from others who show their
ability to reply by putting up their hands.

5. As each stage of working the problem is completed, write its
meaning opposite the result.

6. Apply the knowledge gained by the oral teaching to the solution
of similar problems, taking full precautions against copying.

(<-) Exercises for revision and examination.

1. Choose examples which come fairly under the rules already taught.
Problems involving the use of two or three of the past rules afford
excellent tests of the value and reality of past work. They also provide
the pupil with material for the exercise of self-effort.

2. Prevent copying by any or all of the following devices : —

(a) Number the children A, B, C, each following the other, and set

different sums to each group.
(/-') Permit no working aloud, and take up a position well in front of

the class so as to detect the slightest attempt to communicate on

the part of a pupil.

Questions for Examination. 245

the result of each pupil's own eftbrt is that which alone 3-ields

any benefit.
{d) During lessons upon truthfulness and deceit, refer to the beneficial

effect upon character of cultivating the one, and the injurious result

of practising the other,
(f) Do not risk failure by allowing adjacent children to work the same

exercises until you are quite sure that their character is sufficiently

developed to bear the strain.
Introduce working from cards of examples for the following reasons, viz.,
{a) to provide new forms of example and fresh modes of stating them,
(/') to foster self-effort, and (c) to remove inducements to copying.
Exercise the class at times in the rapid working of short and fairly
simple examples on slates, in order to develop facility and confidence.
At other times encourage the careful working of longer and more diffi-
cult sums on paper in order to secure neatness and accuracy.

QUESTIONS FOR EXAMINATION.

Taken from Pupil Teachers' Examination Papers.

The New Code requires an exercise in rapid addition Make out a
column of figures suited for this exercise and say how vou would best
secure quickness and accuracy in performing it.

Take the following sum in long division : —

^^72,185 13s. 2d. -i- 163,
and work it so as to show fully the value of each separate figure in the
answer, and of each remainder.

Make four sums — two in direct and two in inverse proportion, and show
how you would explain to a class the working of one of them.

Describe the best system you know for teaching numeration and
notation.

Say how you would explain to beginners the rule for subtraction, and
illustrate your answer by this example : — 806 — 527.

Make some mental exercises on money suited for the First and .Second
Standards, and let them be as varied in form as possible.

Explain how you would make young children familiar with the right use
and value of the figures i and 7 as the notation for seventeen.

What are the shortest processes of working mentally the following
sums : — 57 X 25, 3 dozen articles at 72d. each, 85 x 99 ?

246 How to Teach Arithmetic.

Show by means of illustrations how you would explain to a class of
scholars the reason of one of these processes : —

{ci) Finding a common denominator of three or more fractions.
if) Reducing miles to half-inches.

Describe your method of teaching infants between six and seven years of
age ' to carry ' in addition, and say by what sort of visible illustration you
could be helped to make the rule intelligible to such a class.

Give examples of questions in mental arithmetic .suited to children of
the Third .Standard, which shall illustrate all the rules taught to children
of that Standard and shall prepare them for the work of the Fourth.

Taken from Scholarship and Certificate Papers.

Write out the rule for converting a pure circulating decimal to a vulgar
fraction, and work an easy example in such a way as to show the reason
of the rule.

State how you would explain to a scholar in the Third Standard the
value of the full remainder obtained in the division of 349 by 42. when the
division is performed by the factors 6 and 7 successively.

Show how you would explain to a class of beginners the reason of any
one of the following processes in arithmetic : — •

(a) Ascending reduction ; (/') Subtraction of fractions ; (c) Cancelling.

Multiply 74,oS6 by 909, and explain, as to the class, the process of
working, and the separate value of each line of figures.

State and explain, as to a class, the rule for the multiplication of a whole
number by a fraction.

Explain, as to a class of scholars, the rule for ' cancelling ' in either
fractions or proportion, and give some examples.

Show by what sort of visible objects and illustrations you could make
the rule for the addition of fractions intelligible to a class of beginners.

Additional Notes on AritJmietic. 247

248 Additional Notes on Arithmetic.

HOW TO TEACH GEOGRAPHY.

Introduction.

Geography is deservedly a very attractive and popular subject
of school instruction. This arises from many causes, amongst
which the following may be mentioned, viz. : — (i) it satisfies the
natural and almost universal desire to know something aboot
places and people beyond the range of direct observation ; {2) it
provides knowledge which the learner is immediately able to
use in his general reading; (3) the study is generally accom-
panied by attractive illustrations such as maps, pictures, models,
objects, &c. — any subject admitting of pictorial and objective
illustrations becomes thereby increasingly interesting and
popular ; (4) whilst awakening the interest and stirring the
imagination of the scholar, the facts of geography are acquired
without heav^y strain upon his mental resources ; and (5) the
study (in the main an exercise of memory and imagination) is
naturally well suited to the age and mental condition of child-
ren in early school life. The aim of the following chapters is
to set out the modern methods of teaching, and, at the same
time, to indicate the value of each method both for gaining a
sound and reliable knowledge of geographical facts, and for
making their acquisition a means of exercising and training the
intelligence of the pupil.

This double value, viz., that of gaining knowledge and of training
the mental powers, must be kept in view throughout the entire course
of teaching. Sometimes a young teacher (who is more anxious that
his pupils learn a host of facts, than that they acquire the facts <n
such a way that their intelligence may be developed) is led to think
that quicker methods of learning than those herein suggested might
be found. Let such a teacher, however, constantly keep in mind the
truth, that, valuable as the facts of geography may prove to the
scholar (as matters of mere information), the development of his intel-
ligence is a far more-ifiiportant concern.

250 How to Teach Geography.

/The starting point of geographical knowledge.

Suppose, for a moment, a child of ten years of age to have
been compelled to live all its days within the walls of a nursery.
To such an imprisoned child, the terms 'green field,' 'country
lane,' ' sea,' ' running stream,' ' hill slope,' and ' valley,' are mere
names calling up none of the delightful experiences common
to the minds of ordinary children. In such a case, the task of
imparting the facts of geography must prove very difficult
indeed. A start might be made by placing pictures and models
of these simple phenomena before the child. The little learner
would thus be very imperfectly put into the condition of know-
ledge possessed by most other children before they begin to
study the subject. For the ordinary learner, the home, the
street, the journey to school, the playground, the park, the
green field, the river, the sea shore, the down, &c. (together
with other special home features), form the natural starting
point for the acquisition of further knowledge. Without this
experienced knowledge, the teacher has little upon which to
base his teaching, but with these simple experiences in posses-
sion, the learner is able, readily enough, to gain very reliable
knowledge of regions beyond his own limited experience.

It has become a settled conviction that a firm and fairly wide basis
of direct and first hand knowledge must be laid before any really
reliable structure of geographical truth can be erected. We must not
think that lessons upon such topics as the 'journey to school,'
'the path up the hill side,' 'the babbling brook,' &c., are beneath
notice. Any lesson which perfects/ a child's knowledge of his
home surroundings, which arouses his interest in them, and which fills
his memory with vivid and agreeable images of them, is of real and
lasting value for the purposes of geographical instruction.

First lessons in Geography.

First lessons in geography should make the knowledge of
the child's surroundings as accurate and complete "s possible.
The observation of the learner should be exercised during
these early lessons upon the various features of the district in
which its home and school are placed. Obviously these
early lessons must vary with different districts. The country
child starts with knowledge which the town-bred scholar
cannot pdasess. The town scholar, on the other hand, gains

Plans. 251

direct experience of industries and of modes of life entirely
unknown to the rural child. For children again whose homes
are on the coast, the sea shore — its beach, cliflfs, promontories,
bays, and its estuaries, provides the most suitable and profitable
material for a series of first lessons ; whilst for scholars who
live in an inland county like Warwickshire, the several features
of the surface — hill, plateau, slope, valley, river, &c,, yield
a series of suitable and profitable lessons. All children, how-
ever, whether they live near the sea coast or in an inland
county, need to be able both to recognise and to state the
relative positions of the features which their observation has
made familiar, and for this purpose the first year's work in
geography includes a knowledge of a plan of the school and the
playground, together with the meaning of a map of the district
in which the school is situated.

There are special difficulties in the way of teaching geography to
children who live in crowded cities like London, Manchester, Liver-
pool, Birmingham, &c. The fact^ for direct observation by these
scholars are few, and can only be made with difficult3\ In order to
secure a wider and more attractive foundation of observed knowledge,
it is necessary to supplement wl^at the neighbourhood yields by knoW'
ledge gained through excursions, pictures, photographs, models, &c.
A very practical and valuable aid to the acquisition by young children
of the home geography of towns and their surroundings has
been provided by the educational authorities of some of our large
cities. It consists of the cast of a relief.model of the town and it^
immediate surroundings.

PLANS,

Introductory.

I / When the first-hand knowledge of home geography (gained
either by the informal teaching of home and school life, or by
the examination of a relief-model of the district) has become
fairly reliable and complete, we may begin to associate this
knowledge with the symbolic representation of it by means of
either a plan or map. In no case should the first map or plan
precede the more direct mode of acquisition. The plan should
be used only to record in a convenient form those geographical

252

Hmv to Teach Geography,

features which have been previously observed either in the field
or on a relief-model. In order to provide the simplest notion
of a plan it would be well to lead the class by very easy stages
from the knowledge of a plan of a simple object like a book to
that of the class-room in which the scholars are taught, and
finally to that of the school with its playground and immediate

surroundings.

Simplest notion
teaching.

of a plan— suggested stages of

Object, picture, plan (full size).

Show the class a book, or a small box, and accompany the presentation
of the object with a picture of the same object on the black-board. This
picture should be drawn by the teacher during the lesson for the observa-
tion of the class.

Picture.

Plan.

Picture.

Plan.

2. Ground-plan of object (full size).

This may be drawn by placing the book or box on a horizontal board,
and by drawing (or, better still, by allowing a scholar to draw) a line close to
the edges of the portion resting on the board.

Do not hurry over this portion of the exercise. Encourage the class
to make ground-plans of other objects, such as ruler, pencil, set-
square, &c.

3. Difference between a picture and a plan.

{a) The nature of a picture.

The difference between the picture and plan is readily seen. The class
will make no mistake in pointing out either the picture or the plan ; but,
if a.sked to state what this difference is, very fe\i , if any, of the class will be
able to state it. By the following method they may, however, be gradually
led, not only to see the distinction but also to state it. A painting may be
made so perfect that the eye may be entirely deceived. This painting is an
exact representation of what the eye sees when the object itself is before it.
■A .photograph presents all the appearances of the painting, except colour.

Plans. 253

Children never mistake the photograph for the real object. An outline
sketch, like the drawing made on a blackboard, is sufficient for the intelli-
gent scholar to see that it represents a book or a box. The sketch is a
mere outline of the chief features of the object ; sufficient is however
supplied for the scholar to see whether the drawing is that of a book or a
box. The painting, the photograph, and the sketch are all of them (as is
also any one of them) quite sufficient to indicate the object named. They
are all pictures of the object. Children may, in this way, be led to see
that all pictures agree in presenting an appearance which the eye at once
recognises as the drawing of a particular object. It is a representation,
more or less complete, of what the eye sees.

(/') The nature of a plan.

Direct the attention of the class to the ' plans ' ol both book and box.
Remove the pictures and the class cannot tell from the drawings which is
l)L>ok and which is box. The plan alone cannot give the child an image of
either box or book sufficient for it to distinguish one from the other. It is
true, that when the objects, or pictures of them, have been first shown and
the plans standing for these pictures have been drawn alongside them,
that, then, we may remove the pictures and the plans will enable us to recall
them. If, however, a child had never seen either a book or a box, it is ciuite
obvious that the plan, alone, would not enable such a child to distinguish
one from the other. What will a child (who has been guided thus far) be
likely to answer when the question ' What is a plan?' is asked. If it
should say, ' lines to show shape and size of the cover of the book,
or of the bottom of the box,' we may be satisfied with our teaching.
This difference between the picture (a representation of what the eye sees)
and the plan (lines to indicate shape and size of one side of the object) will
be as much as can be attempted at this stage.

Plans must be preceded by direct observation either
of objects or of pictures of them.

The above sketch shows how faulty is the method of teaching
/geography which begins with the map — the map being a
plan on an enlarged scale. It also shows the value of laying
in a store of knowledge of the various features by means of
direct and first-hand observation. After the child has obtained
a store of mental images of the various features of the world
around by direct observation, by pictures, paintings, jjhotographs,
and sketches, it is then in a position to make use of these
images in order to read intelligently the meaning of either a
plan or a map.

254

How to Teach Geography.

Drawing a ground-plan to scale.

The plan of the school or class-room forms a good exercise for teaching
simple notions of drawing a ground-plan to scale.

Ground plan ot a Class-room C
and of the School-room AB.

The plan selected, for teaching purposes, should be that of the particular
school in which the children are being taught. There will be no need to
distinguish, at this stage, between ground-plan and elevation. Whenever
the term ' plan ' is used in future, it will be in the sense of ' ground-plan.'

Suppose the class-room C to be 20 feet long and iS feet wide. A first
lesson in drawing a simple plan to scale should result in making lines
to represent the positions of the walls of the room, the doorways, the
gallery, and the desks. !

{a) The length of the class-room. j

One of the scholars should measure, by means of a foot-rule, the
length of the room. A straight line F should now be drawn by the
teacher to represent the line just measured. What length shall this
line on the board be drawn ? Allow the class to think over the
question. The child has measured a line along the floor 20 feet long ;
the teacher has drawn a long straight line F on the board, and wishes
to know how long this line must be. There will be \arious answers
to the f|ue.sUon. Probably some one will suggest half the full length;
another a quarter. Try if a line 10 feet long could be drawn on the
board. No. Then the line must be less than half The children have
now the notion of a line on the. board smaller than the full size. The

Plans. 255

teacher may suggest taking an inch on the board-line to represent each
foot on the floor-line. He may now ask how many inches long the
line on the board should be. As soon as 20 inches in reply is obtained,
a scholar should be allowed to measure these inches along the line on
the board. The parts of the line over and above 20 inches should be
carefully removed. The line remaining represents in plan the
length of the class-room and is drawn to the scale of i inch to
the foot.

(/') The breadth of the room, &c.

Deal similarly with the breadth of the class-room. A teacher ot
tact will allow the class to try to determine the direction this second
line must take on the plan ; and throughout the lesson he will allow
the scholars to make all the measurements and draw all the lines of
the plan with the exception of the first line. Future lessons will be
spent in putting the positions of doorways on the plan and in drawing
the plans of desks and gallery.

(<r) Extension of the class-room plan to that of the school, &c.

These lessons may be stillf urther extended by the drawing of plans
of the school and the play-ground. I

A plan of the school is drawn to scale on! the walls of many schoolrooms,
as is also the plan of the class-room on the walls of the rooms occupied by
Standards I. and II. These lessons on plans are especially valuable for
the exact observation of the surroundings of the school and its neighbour-
hood which they compel the children to make. They furthermore yield
elementary and accurate notions of a map on a simple and limited scale.

When we proceed to draw the plan of any area beyond that
of the school it becomes necessary to fix the relative directions
from each other of the several features to be drawn upon it. Map
makers have determined, so far as their drawings are concerned,
that the top of a map shall be north, the bottom south, and so on.
Surveyors of estates do not always adhere to this arrangement.
As our aim is to enable scholars to interpret maps and atlases,
it will be well to accustom them at first to the arrangement
adopted by the map makers. Before leaving the study of maps,
however, it would be well to show the class that placing the
North on the top of a drawing is a purely arbitrary device, and
that they must not be surprised to find special maps showing
a different arrangement. It will now be necessary to practise
the class in determining the four cardinal points in relation to
the school.

256 How to Teach Geography.

How to fix the positions of the cardinal points.

There are several methods of determining the cardinal points.
Amongst those more generally adopted are the following, viz. : —
(i) observing the position of the sun at mid-day; (2) using
the mariner's compass ; (3) observing the direction of the
shadow of a stick and taking this direction when the shadow
is shortest; and (4) noticing the position of the pole-star. It
will not be necessary to illustrate more than one of these modes
of determining direction. On a succeeding page, suggestions
are given for a lesson on the mariner's compass. The teacher
who wishes to mark out the meridional line on the floor or
ceiling of his school-room should take note of the following
corrections: —

1. True mid-day by the sun can be fixed by clocks keeping Greenwich
mean time only on the following days, viz., April 15, June 15,
August 31, and December 24.

On other days the clock is either fast or sloio. The amount of differ-
ence between the dock and the sun is given in any good almanac. It
the clock is fast 15 minutes, then the line must be drawn along a
shadow when the clock marks 12. 15 p.m.

2. Greenwich time does not give an accurate result for all towns. Liver-
pool, for example, is about 3° W. longitude. The sun moves to the
W. about 1° in four minutes. So that the sun would be in the south
of an observer in Liverpool 12 minutes later than to an observer on
the meridian of Greenwich.

3. The mariner's compass needs correction tor declination. True north
at present is a little more than 17° E. of the magnetic north.

Children should not be troubled with these corrections. They should
be observed, however, by those who wish to fix the cardinal points in their
schools and play-grounds by meridional lines and weather vane?. The
following is a sample of the lessons in direction which should be given to
children.

Aids recently adopted whilst giving a lesson on the
Mariner's Compass.

A most effective method of unpressing the construction
and use of the mariner's comi)ass was recently adopted in
a lesson given before one of Her Majesty's Inspectors.

The Mariner's Compass.

257

The following were the main features in the lesson : —

The scholar's compass.

Each scholar was provided with a small wooden circular box A like
an ordinary pill box. In the centre of the box a small pin B was placed
point iijnvards and in a vertical position. A short piece of magnetised
wire C, with a twist at the centre, was then supplied to each child. This
wire was poised on the pin by means of the central twist. Each child
was then supplied with a paper disc D on which the four cardinal points
were indicated as shown in the diagram. By the aid of these materials
the lesson was given ; the children gradually built up the entire structure ;
and, when the lesson was completed, each child was the happy possessor
of a working mariner's compass. The different parts of the instrument
were known and their uses understood. The Inspector joined the
children in making a compass for himself at the close of the lesson.

The teacher's model made on a larger scale.

A strong circular card-board box, such as those used for collars, supplied
the compass box. By inserting a large pin through the centre of the bottom
of the box a pivot for the magnet was provided. On the point of this pin
a magnetised bar was poised on which a circular paper disc was placed.
On the top of the circular paper the cardinal and other points were drawn.
The value, for teaching purposes, of this home made compass was increased
by the parts being left so that the compass could be readily taken to pieces,
and be as easily put together again.

A suggested exercise in hand and eye training.

An interesting ' suitable occupation ' might be associated
with the lesson on the mariner's compass. It would consist of
the cutting out and the bindincj of a card-board cylinder to
form the box of the compass. The needle with the central twist
must be provided, but the children might be taught to mag-
netize it, by passing a strong magnet over it a few times in the
same direction. /By experiment and by following the teacher's
movements the/class would be able to determine which end
should point /:o the nort/i and which to the south. The pre-
paration of tlVe paper disc would exercise the childrens' skill in
drawing lines at right angles to one another, and of making

258 Hoto to Teach Geography .

angles of different sizes. An important feature in an exercise
of this kind is the connection the manual effort makes with the
geographical knowledge taught. Both become mutually helpful.
The lessons in hand and eye training, devised for the children
in the lower standards of the school, should, wherever possible,
be connected (as in this case) with their knowledge-lessons.

Applications of the children's knowledge of direction.

Children should be taught to apply in their every-day ex-
periences the knowledge which these lessons on the compass
yield. The direction of the road from the home to the school,
and from the school to the home ; the direction of the shadow
at noon, in the morning, and at night ; the course taken by a
line of railway, by a river, or by the telegraph wire ; all these
may be used to fix and extend the knowledge of direction
already gained. Our geographical knowledge of areas unvisited
consists of the mental extensions of our observed knowledge.
The child whose observed knowledge is exact and full is thereby
put into the most favourable condition for readily and correctly
acquiring the geography of areas beyond his home and im-
mediate surroundings.

RELIEF-MODELS AND THE MEANING AND
USE OF A MAP.

Map to be preceded by relief-model.

The plan of the school and play-ground represents the relative
ppsitions of walls, galleries, doorways, &c., and, when viewed
as a wliole, it helps the observer to recall the shape of the
school building and the relative positions of the chief features
surrounding it. The plan may now be extended so as to form
a representation of the most striking geographical features of
the district. Such a plan when completed becomes a map of
the area. The best preparation for understanding this maj)
is the relief-model. The geographical features of the district
are on too large a scale for the scholars correctly and fully to
take in their relative positions. A relief-model of the area, on
a greatly reduced scale, most effectually assists the scholars to
realise the natural grouping of the various surface phenomena.

Relief- Models. 259

The following hints are intended to afford guidance to those
who are wishful to make and use a simple form of relief-model.

The construction of a relief-model of any district.

Maps of every district on a large scale and containing the roadways, tlie
principal houses, the railways, the rivers, lal^es, ponds, ranges of hills and
mountains (with their heights), lowlands, plains, and valleys, may now be
obtained. These maps have been prepared in sheets by the ordnance
survey. They supply all the information needed for the construction of
a relief-model of any district in the British Isles.

The material for making this model may be sand, clay, or putty.
If a permanent model be required, Parian cement will serve admirably.
It sets very hard, does not crack, and remains moist long enough to be
moulded into the desired shape. A convenient size for this model will
be 3' 6" by 2' 6". The cream white paste may be spread over
a frame made of match-boarding, strengthened at the back and sur-
rounded by a thin ledge 2'/ high. The vertical scale will generally
need exaggeration. Care, however, should be taken that this
exaggeration be not too great. These district relief-models should aim
at being ' works of art,' so far as the time and skill of both teachers
and scholars will allow. There are very beautiful models in both
the South Kensington and Jermyn Street Museums. When opportunity
serves, these excellent models should be seen by every teacher of
geography.

Sketch of a relief-model of the Isle of Wight, by Mr. Petty, student 1894.

260 How to Teach Geography.

The advantages and limits of the model.

The model, at best, only inadequately takes the place of
actual experience gained by excursions and travel. It must
necessarily be wanting in much that gives life and reality to the
scene it represents. Unless carefully constructed, and unless
especial care be taken to prevent a gross exaggeration of the
vertical scale, very erroneous notions may be given. The
model has the advantage (as before stated) of bringing an
assemblage of geographical facts under one view. In nature
these facts are often too widely spread and are on too large a
scale for scholars to see them in their mutual relations at a
glance. The model, when skilfully constructed, places before
the observer a bird's-eye view of the district, and when accom-
panied by actual and direct observation of the area, it becomes
the most effective of teaching appliances.

Children to be encouraged to make models for their own use.

When a school possesses a permanent model of the surrounding
district, the scholars beginning the study of geography will be benefited
by being allowed to make their own copies of this model. These copies
are best worked out in sand placed upon a large board or slate. When
children have become thoroughly acquainted with the model presented
for their imitation, they may be allowed to extend their modelling to
other districts well known to them, and beyond that of the copy.

Relief-modelling a 'suitable occupation' for the lower
standards.

The construction by the scholars of models in relief of the area
in the immediate vicinity of the school, of simple river basins,
and of coast features, might, with advantage, form part of the
' suitable occupations ' required by the code for Standards I., II.,
and III. Any occupation which naturally attaches itself to the
ordinary school curriculum, and which thereby helps to make
the instruction more real and interesting, must be a ' suitable '
exercise. The amount of geography covered by each year of
work might be lessened by this arrangement, but the thorough
character of the instruction would more than make amends
for the loss. Certainly the geography lesson would gain very
much in reality and life by a few such suitable occupations.

Relief- Models and Map Draiving. 261

Another suitable occupation.

The collection and arrangement, by the scholars
themselves, of specimens of the productions of any district
(especially if these specimens are classified and grouped so as
to exhibit in their arrangement a knowledge of the series of
changes which any natural product or manufactured article
undergoes before attaining its fully developed and perfected
form) call forth considerable skill and thought on the part of
the children. The exercises arouse their interest, cultivate
their observing powers, and result in the acquisition of
accurate and permanent knowledge. Not only is an intelligent
habit of observation cultivated by arranging these collections,
and not only are reliable stores of knowledge acquired, but
the exercises of classifying these materials, and of arranging
these products in an orderly sequence, are efforts which form
the basis of all processes of reasoning and judgment.

From the construction of a Model to the drawing of
a Map.

The model of a district naturally prepares the way for the
map of the same district. The map stands in the same relation
to the relief-model that the plan does to the school and
play-ground. When teaching, it will generally be found that
the more thoroughly the children are taught the relief-model,
the more readily and completely they will understand the
map. The value of being able to correctly interpret the con-
ventional and more or less arbitrary marks on the map becomes
at once evident, when it is remembered that nearly all their
geographical knowledge must be ultimately acquired and
retained by means of maps and word descriptions.

No labour should be spared, at the outset, to make the associations
between the marks on the map and the geographical facts which these
marks symbolise both accurate and vivid. It has been stated afready
that the model can at best only very inadequately supply the place of
actual experience. At the same time, it was stated that the model
possesses the advantage of bringing a large assemblage of geographical
facts under one view, and thus enables the scholar to see at a glance the
relationships in which the facts stand to one another. When the map
accompanies the model, the relationships of allied geographical facts soon
become as readily seen in the case of the mi.p as in that of the model.

262 Holu to Teach Geography.

The ultimate aim should be to make the map serve the place of both
model and actual contact with the facts. This aim can never be perfectly
realised any more than a description of a particular event in words can
ever take the place of actually witnessing the event itself. We do our
best for our pupils, however, when we associate correct geographical
features, or models of them, with the markings which represent them on
a map, and when we repeat the map representation in association with
the geographical features, or their models, until the connections are
thoroughly established.

The ability to draw a map from the relief-model marks the final
exercise in these preliminary lessons in geography. The map drawn by
the pupil should not at first be a copy of another map drawn by the
teacher. The scholar may be able to imitate a copy very cleverly and
not be able to interpret it. Our teaching at this stage may be considered
complete when the relief-model can be successfully represented by a
plan or map, and when a plan or map can be reproduced by means of
a model.

Sketch maps of the relief-models of their own and other districts should
be attempted by the scholars. The attempt on the part of the class to
draw these maps from the model may be followed, stage by stage, by
black-board sketches by the teacher. Finally, the class may be exer-
cised in reproducing the maps from memory.

Knowledge of districts beyond that of which the
children have direct observation.

When a thorough mastery of the geographical facts in the
immediate neighbourhood of the school has been gained, the
next step in teaching is to impart a knowledge of geography
beyond the range of direct observation. Very few districts
provide examples over the entire range of matter usually repre-
sented on a map. Advance to knowledge beyond direct
observation must be made by using the knowledge already in
possession. From the notion of the running brook an idea
may be gained of the river ; a neighbouring hill and hill range
may be enlarged to the notion of a mountain and mountain
chain, respectively ; a pond may suggest a lake ; a lake the sea,
and so on. A relief-model of any new district will greatly assist
this effort of the imagination, as will also photographs, bird's-
eye views, and maps.

We would suggest that the new district should be carefully selected
with regard to the knowledge already gained. It should be similar
in most of its features to the home district. The scholar in a Cornish

Physical Geography of Hills and Rivers. 263

school, e.g., should not be immediately taken from the geography of his
native county to that of the Midlands of England. It would be much
better to select the south-eastern section of England, because, whilst
providing matter of sufficient novelty to arouse the learner's interest, the
new district reproduces (in modified form) many of the coast and surface
features with which he is already familiar. From the S. E. counties
the next step would be to the double slope of the six northern counties.
The last area to be attempted by the Cornish boy would be the
Midlands.

PHYSICAL GEOGRAPHY OF HILLS AND

RIVERS.

The requirements in this branch of geography are vaguely
stated. They may be made either extremely difficult or very
simple. If an attempt be made to account for the distribution
of the hills, valleys and rivers of England, the eftbrt will be very
much beyond the power of a child in Standard IL If, on the
other hand, the names of the chief hill ranges, together with those
of the principal rivers be simply committed to memory, the work
can scarcely be dignified by the term ' Physical Geography.'
The teacher will do well to fix in his mind the amount of
knowledge fairly included in the phrase, and then to plan a
course of lessons best fitted to secure its attainment.

Aids to determining the most suitable course.

It will be entirely contrary to the principles of teaching
which have hitherto guided our methods, to attempt to teach
the distribution of the hills of England without trying, at the
same time, to give the scholars a mental picture of these hills,
as they are distributed over the surface. The scholars might
be able to repeat the hill ranges marked on the map, and
enumerated in a text-book, without knowing much more than
their names. A mere memory exercise like this would neither
meet the requirements of the Code nor benefit materially the
learner. The arrangement of hills and rivers and their names
have to be known, it is true, but they must be known in such
a way, that the knowledge includes a recognition of the natural
relationships between them. Something more than the names
must be acquired by the children, and the question to be
settled is, how much more ? The answer to this question must of

264 Hmv to Teach Geography .

necessity depend upon the answer given to a second question,
viz., how much these young pupils can fairly be expected to
understand ? If suitable apparatus be employed, it would not
be difficult to show a class of young children the following
truths of physical geography, viz. : —

1. That rivers have their sources in the high land.

2. That they have their courses along the slopes leading into the sea, or
into a lake, or a larger river.

3. That they make the valley lower by carrying down the loosened rock
towards their mouths.

4. That ridges of high ground (hills) are left outstanding, and separate the
streams running down the same slope.

5. That smaller streams run into the river from these ridges, and that these
smaller streams form tributaries to the main stream.

6. That rivers become deeper and wider the longer their courses are main-
tained, and that when they have very wide mouths, estuaries are
formed.

How to teach these simple truths of physical geo-
graphy.

It will not be possible, in these pages, to make sketches of
complete lessons in this portion of geography. A few sugges-
tions upon the arrangement of matter and the best mode of
presenting and illustrating it, are all that can be attempted.
The following method of teaching has been adopted with
success : —

{a) Appeal made to child experiences and to simple experiments.

The first two truths, viz. , that rivers have their sources in the high
land, and that they have their courses down the slopes leading cither to
the sea or a lake, should be introduced by a reference to such simple
experiences as the following : — (i) The children must have noticed rain
water falling on the road and then running down the slope into the ditch
or gutter. (2) Again, rain falling upon the uneven surface of the play-
ground does not stop where it falls, but runs along the nearest slope.
(3) Ky ^^3,y of experiment, two small boards or slates might be slightly
raised in the middle, and a little water from the fine rose of a water-can
might then be allowed to fall like rain upon the tilted boards. The
children, by this simpl^^ experiment, are at once led to recognise the
direction of the little streams thus formed, and as readily to connect
their direction with that of the slope of the boards.

Physical Geography of Hills atid Rivers.

265

(/') After these experiences and experiments, attention should be
directed to the model of the district in which the school is placed.

It may be that the neighbourhood does not lend itself readily to an
illustration of this truth. If not, it would be well to construct a rough
model of such an area as the six northern counties. The children should
be required to recognise and to point out the high land, the long slope
to the east coast and the shorter slope towards the west. Frona what
they have already observed respecting the course of the water on the
slopes of the road and the playground, the children should be able to
indicate the directions which the watercourses must take on the model.
The positions of the rivers should now be indicated, and the chief rivers
named, together with the high land on which they rise, and the seas
into which they flow.

(i) From experiment and model, the class may proceed to diagrams.
The following four diagrams illustrate the stages of valley, river, and
hill formation.

Bed of_ the runnel

Fie.3.

Diagram I. — Representing the formation of a tiny runnel on almost
level ground.

CeV of We runneJ

jmm^/xm

FJir.^

Diagram II. — Illustrating the deepening of the bed of the runnel, and
the gradual formation of a valley with higher land on either side.

HAMPSTEAD

■•J

Streiitn

Diagram III.-

-A representation of a section across an actual valley in
the north of London between Hampstead Heath and Finchley. The valley
is about two miles wide. The little stream is two or three yards across,

266

Hotv to Teach Geography.

at the bottom of the valley. Similar examples of hill and valley formation
are found in almost every part of England. The observation previously
made of the hollow formed in the playground or on the road side by the
runnel after a heavy shower, may now be recalled. The same force
(viz., running water) working during many years, has scooped out the
valley between Hampstead and Finchley and has left the hills outstanding
on both sides.

If a model of a valley, such as that between Hampstead and
Finchley be constructed, the class will be able to trace the formation
of a second set of streams and valleys, more or less at right angles to
the original stream. The term 'secondary valley' and 'tributary
stream ' are illustrated by this second series of valleys and streams.
They again, in turn, work their way to lower levels and leave ridges
of hills branching outv.'ards from the original ranges.

The following is a map of a district in which there have been the
various stages of hill and valley structure enumerated above.

Diagram IV. — A map of an ideal district illustrating the formation of: —

a) Primary valley and main stream, with a range of hills outstanding

on either side.
h) Secondary valleys and tributary streams, with branch hill ranges

(spurs) separating the secondary valleys from one another.

(«•) A wide estuary.

Physical Geography of Hills and Rivers. 267

Results expected from the above teaching.

By appealing to the experience of every school-boy, and by
using simple apparatus, sand models, inclined boards, &rc., the
series of truths stated on page 264 would be taught, in a simple
way, to young children. Not only would the truths be acquired,
but the relationship in which rivers and hill-ranges stand to one
another would be made clear. If some particularly bright
scholar should suggest that ' the rivers are the cause of the
hills,' the teacher may rest satisfied that he has awakened the
thought and enquiry of the learner. The ordinary surface
aspects indicate the dependence of the river upon the hill, and
this dependence is easily established, but the deeper and more
remote association, indicated by the scholar's suggestion,
should be accepted, and the boy encouraged to think out
similar associations wherever they present themselves.

Application of the truths learned to districts of Eng-
land and Wales.

The natural association existing between hills and rivers is a
most valuable one for young pupils to make. It should be
firmly established by reference to districts in England where
the same truths are clearly illustrated.

Examples of simple slopes drained by rivers.

1. The eastern and western slopes of the Pennine Chain.

2. The county of Cheshire.

3. The eastern counties of England.

4. The county of Somerset.

5. The southward slope of Dorset and Hampshire.

The basins of the Trent, the Great Ouse, and the Thames are not so
simple in their slopes and should be left until the hills and rivers in the less
complex areas have been taught. A rough model will greatly assist the
learner in his effort to associate the directions of these rivers with the
character of the districts over which they flow.

A case of special difficulty and how it is not explained.

When we come to the region south of the Thames, the truths
we are dealing with appear to be contradicted. The tributaries
on the right bank of the Thames appear to flow through the

2 68 How to Teach Geography.

North Downs. Their action cannot be explained to youno^
children. Only those who are able to realise the geological
truth, that at a time in the distant past the North and South
Downs were connected, and that the rivers flowed along the
long chalk slopes northward to the Thames and southwards
to the sea ; only those who can thus be led to understand that
these are old watercourses which have never broken through
a chalk range, but which have lowered their course in that
range by natural wear and tear, and have been continued
beyond the North Downs by the slow upheaval of the Wealden
area of Sussex ; only such can understand the physical geo-
graphy of the hills and rivers south of the Thames.

All this is beyond the power of a young child. In fact, it is matter
which is beyond the knowledge of some who have written on the
subject of physical geography for the instruction of adults. The rivers
of the south-east of England have been noticed, in so many case?, to
pass right through the chalk hills, that those who simply look upon
these rivers as they appear to-day have come to the erroneous
conclusion ' that chalk hills do not form watersheds, but that they allow
the rivers which approach to break through them.'

The young teacher will be careful to select the district for his first
lesson with a view to avoiding such difficulties as those presented by
the south-east of England. It will always be true that rivers must flow
along a downward slope. Plenty of examples may be found to illustrate
the truth, and to do that without the accompanying difficulties indicated
above. These difficulties are stated here in order to show that the
relation between the direction of hill ranges and river courses is not
always easy to understand. In all obscure cases the teacher should
leave the explanation of them until the children are capable of profiting
by it. He should, especially be on his guard against attempting an
explanation which (like the one suggesting that the tributaries of the
Thames have broken through the North Downs) is perhaps simple
but, at the same time, is incorrect.

The order in which the truths enumerated above
should be taught.

We are now in a position to review the order in whicli the

' various stages of teaching the geography of hills and rivers

' should be' taught. The highest land masses should be

indicated in the first place, and the direction of the slopes

should be examined on a relief-model, until the pupil is able

Physical Geography of Hills and Rivers. 269

to recognise (read) the same features on a map without the aid
of the model. The directions of the rivers should be inferred
by the children and their positions indicated by the teacher.
Riuer valleys follow next in order, and should be associated
with the work of the river. Hills are then introduced, and
should be seen to result mainly from the action of the river.
Finally, the smaller streams (tributaries) should be shown to
run along the slopes of the hills which separate the main
streams. When the nature of the connection between slope,
river, valley, hill, and tributary has been taught, it will not be
difticult to show that the longer time the river works, the
lower and wider the valley ; and that the longer the slope is in
space the larger and deeper must be the river.

It has now been shown how the most important truths of the physical
geography of hills and rivers may be illustrated by reference to the map of
England. The method of teaching has been indicated. A similar method
should be followed whatever may be the class under instruction, or the
district under investigation. The results of teaching geography by the
methods indicated will be far in advance of those which follow the method
of merely learning by heart the positions and names of the several physical
features, without any attempt to present them in their natural relations.

An objection raised and answered.

An objection may be raised against the attempt to teach
these truths to very young children, the objection, viz.. that it
is far too difficult. No doubt it would be folly to try to teach
such matters as fully as they must be known by pupil teachers
who have a similar geographical exercise in the first year of
their course. If, however, the plan of using simple relief-models
and of utilising simple experiments and experiences be adopted,
there is no reason why a beginning should not be made (even
at this early stage) to connect the features of hill, valley, and
river structures with one another, in a natural and rational way.

This is not the place to discuss the order in which subjects are
appointed to be taught, but rather to show trie best way of teaching
these subjects. The physical geography which does not attempt to
show how the high land inihiences the course and flow of a river;
how the river gradually scoops out its valley and leaves the hill inter-
vening between it and a neighbouring river ; and how the tributaries
of the main stream are eventually formed, is not worthy its name.
Unfortunately, the name has long been applied to tabulated statements

270 Holu to Teach Geography.

of mountains, rivers, hills, and tributaries, in which no suggestion is
made of any rational connection existing between the several facts.
With the aid, however, of the appliances for illustrating these connec-
tions (which have been repeatedly indicated in previous paragraphs),
and with the assistance of better teaching methods for presenting
them, it may be hoped that the teaching of this interesting school
subject, may, for the future, forsake the beaten track of the text-books,
and follow that arrangement of related facts which nature exhibits and
which the study of physical geography, worthy the name, demands.

GEOGRAPHICAL TERMS SIMPLY
EXPLAINED.

Contrary to usual custom and to the order of teaching sug-
gested by the Code, we advise that the teaching of these terms
be delayed until a fairly wide knowledge of individual examples
of each term has been gained. The reason for this delay will
be made clear in future paragraphs.

How to teach the meaning of geographical terms.

The teacher should not forget that the full meaning of
s vk geography can onl\- be taught by the methods
adopted when teaching the general terms of any other subjects
of study. A single example is not sufficient to lead the learner
to fix his attention upon the essential features of the group of
things so named, and, at the same time, to divest the notion of
its non-essential features.

Suppose, for example, the term cape is to be explained. The model
of the Isle of Wight, with the adjacent coast of Hampshire, might be
used for purposes of illustration. It presents a cape on the extreme
east. Suppose we describe the appearance of this portion of land.
It is bold, rocky, and pointed ; the cape furthermore is directed east-
ward, and is the furthest extremity of an island. After describing the
several features of the cape as graphically as possible, the teacher
might ask the class to state what a cape is. Let the teacher try to
realise what the children are likely to say in answer to this question.
Will the answer be ' a bold pointed mass of rock,' or will it be 'a mass
of rock at the eastern end of an island.' Either answer will show that
the child stating it has observed and remembered correctly. The class
should not be discouraged from giving these answers at this stage.

Geographical Terms simply explained. 271

They have not answered correct!}^, it is true ; but they are observing
carefully, and with a little tact may be led to the right answer.

The boy who answered first should be asked to come to the model
and try to find another mass of land something like the first. The
land now indicated may not be bold, pointed and rocky ; it may be
low, andlnot pointed, but may come down to the sea in a long and
ajjparentiy grassy slope. This also is a cape. Give the scholar time
to look at the two land masses. Then ask him, if he can see in what
they are alike. Yes, tbey both stahd out into the sea beyond the rest
of the land. Now ask'' the second biy to come forward and examine the

two capeb. He sees^ at once that the second cape is not on an island.
This chilcl will also most likely agree with his fellow scholar in leaving
out the ncition of '/ocky. ' After giving up both the words he used to
describe the capy^ before, this second scholar may be asked to notice
the points Ui which the two examples agree, viz., in projecting into the
sea. Both\bo/s will now, most likely, be of the same opinion, viz.,
'that a cape is land projecting into the sea.'

Other children in the class ma)', in turn, be asked to state what
they see alike in the two projections. They may be asked to point to
similar projections on the map. After many examples have been dealt
with in this way, the question • What is a cape?' may be put again to
the class. The answers will now be much more accurate than at first,
and will show that the required notion has become a part of the
knowledge of the class.

Criticism of the method.

It may be urged, that this is a long and tedious method.
Why not point to a cape and say, ' You see this land, children ;
it projects into the sea, doesn't it ? Whenever you see land
which projects thus into the sea, you must call such land a
cape. Now, what is a cape ? ' Atiszuer. — ' A cape is land which
projects into the sea.' This short method is very frequently
adopted, and it appears to be successful. The children can
answer the questions correctly, and there are all the outward
signs of knowledge. The method is evidently short and straight ;
the children have very little to do ; they are led at once to the
truth, and are able to state it. Then why should not this latter
method be followed ? Simply because children are not to be told
by another what they may be led, with a little effort, to acquire
for themselves. Children have minds which are to be exercised
and trained, as well as memories which may be crammed.
The process of acquisition may be made of more value to the

272 How to Teach Geography.

learner than the matter he learns. If children can be led, from
the outset, to gain knowledge in such a way that whilst
the knowledge acquired is sound and full, their thought is
aroused, and their self-activity and spirit of enquiry are stimu-
lated, surely we do well when we select the course which
secures this knowledge and encourages this enquiry and thought.

Conditions by which a model or a map of geograph-
ical terms becomes fitted to secure the higher
training.

In the example just quoted, the children could not be guided
to the acquisition of the general truth from the consideration
of a single example. Several capes, having different accom-
panying features, must be examined before children can be led
to single out for themselves the essential feature possessed by
all capes. On the model, therefore, there should be a lofty
cape, a pointed cape, a cape' on the mainland, and a cape on
an island, a cape composed of bold rocks, and another of grassy
slopes. When, from the examination of different capes, the
riass has been led to recognise the essential feature of all capes,
viz., land jutting into the sea, the map may be introduced.
It will now be seen that the map drawing of a cape exactly
represents the general notion we wish to form in the minds of
the children.

The places which the model and map should occupy with
respect to each other now become quite clear. After many
capes have been shown on the model, and the idea of a cape (z.t-. .any
cape and not some particular cape) has been acquired by the class,
the right time has arrived for the introduction of thcdrawmg of a cape
on a maj).

The remaining terms must be represented on the model and map in the
same order as that followed whilst teaching the notion of a cape. The
term ' river,' for examj)le, must not be tau&ht by reference to a single example.
One river should enter the sea; anothcA a lake ; a third should have its
rise in high land and possess a short aiiVl rapid course ; a fourth slujuld
meander about liie plain ; wliil.^t a liftiiUhouId be tributary to a larger
river. When these dilicrent rivers have iJben ol)served, and their several
conditions have been ncyted, the class may iL expected to select the features
which all the rivers l^di^scss, k\z., jtoit'ing\ovcr- ami draining the land.
When they can do this, they have found outVor themselves what a river is.
The model has done its work, the teacher may now introduce the map, and
the class, with the map before them, may attempt the ' defmition of the
term.'

The General Geography of England and Wales. 273

Summary of conditions helpful to tiie teacfiing of geo-
grap/iical terms, arranged in logical order.

1. That models and maps of geographical terms contain more than
one example of each of the terms they illustrate, and that each of
these examples be different in some of its aspects.

2. That children be allowed to observe a group of similar features,
(capes for example), and that they be encouraged to com-
pare them, aijid to state in what they differ and in what they agree.

3. That the general term be associated with the agreeing features,
and that a sketch-map be drawn to symbolise, in graphic form,
these common features.

4. That the definition come last, and when the children are able
to formulate it, that this ability be taken as evidence that the
scholars have acquired the knowledge for themselves, and that until
this ability is shown, we have no guarantee the knowledge has
been acquired.

5. That the children be allowed to apply their knowledge to the dis-
covery of other examples on an outline map.

6. That their self-activity be the main aim of the teaching, and the
most prominent outcome of the lesson.

THE GENERAL GEOGRAPHY OF ENGLAND

AND WALES.

The text-book arrangement is faulty for teaching
purposes.

In the present chapter it is proposed to indicate a method
of arrangement and of teaching which departs almost entirely
from the text-book mode of presenting the various geographical
facts. The text-book arrangement of these facts into groups
or tables of boundaries, capes, bays, mountains, rivers, &c., is
the arrangement generally followed in teaching. This is quite
natural from the teacher's point of view. He has acquired the
facts in this order, and they are remembered in the same order ;
it is therefore most natural and easy for them to be reproduced
in the order in which they have been both acquired and
retained. This order, however, so far as oral teaching is con-
cerned, is faulty. The faults may best be shown by taking

2 74 How to Teach Geography.

examples of the arrangement in the text-book, and by con-
trasting these with a new arrangement of the same facts for
purposes of teaching. The examples selected for this com-
parison may be the boundaries, the coast (capes and bays), and
the rivers of England and AVales.

{a) Boundaries not all to be taught at the same time.

These usually occupy the first paragraph in any written description
of England and Wales, and they are generally all taught at the same
time. Now suppose wc take any two out of this group, <■,;,'•. , the Cheviot
Hills and the St. George's Channel, and ask, why are these taught at
the same time? The Cheviot Hills arc naturally associated with the
mountains of the Pennine range and with the slopes to the south-east
and the north, and also with the rivers draining each of these slopes.
The Cheviot range should therefore be first taught along with these
natural connections, and not with the almost entirely different geo-
graphical fact, the St. George's Channel. When the characteristics of
the Cheviots are under review it will be interesting and natural to note
(i) that the traveller who crosses the range from the south, leaves
England and enters Scotland ; (2) that the rivers draining the northern
slope arc in Scotland, whilst those flowing to the south-cast are in
England ; (3) that along these slopes there were constant wars
between the Scotch and English, and that these contests are termed
' the border warfare;' and, (4) that the counties on l)oth sides of the
range arc called 'the border counties.' This teaching would fully
establish the notion of the Cheviots forming one of the boundaries of
England, and, at the same time, would not take the fixct completely
away from the geographical features with which it is naturally associated.

(/■') Coast — Cape and bay to be associated with hill and valley respectively.

The text-bo(jk arrangement takes the capes and bays as they occur
in order along the coast. In this way we get Elaniborough Head,
North Eoreland, Bcachy Head, Land's End, St. David's Head, i.\:c. ,
in the same paragraph. Now there is not such a close connection
between these headlands as to warrant us in teaching them all at the
same time. In fact, the association of them in this book order keeps
out of view another and far more fruitlul association. This deeper
and more fruitful association will be stated more fully in future pages.
Here, it will be sufficient, to state, that a very cursory examination of
a physical map will show that Flamborough Head should be associated
with the Yorkshire Wolds ; that the North Foreland should be con-
nected with the North Downs ; Beachy Head with the South Downs;
Land's End with the Cornish Heights; and St. David's Head with the

The General Geography of England and Wales. 375

granite ridges running through Pembrokeshire. Flaniborough Head
becomes a much more interesting geographical fact when it is seen
that the headland stands out as a bold hlulT ])romontory for the same
reason that the Wold's range, which it terminates seaward, stands
higher than the valleys on cither side. Evidently, Flamborough
Head should be taught, in the first mstance, in association with the
hill ranges of eastern Yorkshire, and not in connection with St. David's
Head in Fembrokeshire.

The bays along the coast are naturally associated with the valleys and
lowlands on the surface, and they should be learned in this association.
Children who learn man}' of these features in combination, and who
discover others, will, in time, enquire for the reasons of the associations
they discover. The teacher should carefully encourage all such
enquiries, for, when once the natural associations between mountain
and cape, and between lowland and bay, have been established, they
will bear abundant fruit in explaining similar associations the world
over. Should a scholar enquire why Bridlington Bay is taught along
with Mount's Bay, it would be ditficult to give any reason except
perhapu the following, viz., that the text-books supply this grouping,
and that the questions in examinations frequently require the same
• arrangement.

((-) Riuers should not only be taught in association with the seas they
enter, but with the slopes they drain and the ualleys they form.
The case against the text-book order for purposes of teaching may
be strengthened still further if the rivers of England be considered.
These are generally arranged in groups according to the sea into which
they flow. In this faultygrouping the Thames and the Yorkshire Ouse form
members of the class of rivers flowmg into the North Sea. This text-
book arrangement may be helpful to memory. At the same time it may
be shown to be almost destructive of those associations of naturally
related geographical facts which in teaching we should be always
striving to make.

Our meaning will become clearer if we select a river like the
Yorkshire Ouse, and state briefly the most natural geographical
associations which should be made in connection with it. These are : — ■
(i) the high land of the Pennine range on the west, (2) the slope
south-eastwards to the sea, (3) the valleys formed by the main stream
and its many tributaries, (4) the ridges of moorland separating the
various tributaries from one another, (5) the wide estuary of the
Humber, (6) the fertility of the surface along the middle and lower
reaches of the river, (7) the mineral wealth of the western and southern
regions, and (8) the occupations of the people, the towns into which
they congregate, and the modes of communication between these
great trading centres.

276 Hotu to Teach Geography.

It is manifestly a very superficial connection which merely associates
the Yorkshire Ouse with the Trent, Witham, Welland, Nen, Great Ouse,
and Thames, on the ground that they flow into the same sea. It is also
evident that in adopting this superficial connection (common in text-
books) we fail to notice those more valuable connections which serve to
establish the reasons for the direction of its course, for the character of
its flow, for the productions of its valleys, and for the industries of its
inhabitants.

Sufficient has been stated to illustrate our meaning when we
say that the text-book order must not be followed in oral
teaching. A new arrangement of the facts is necessary, and in
some cases knowledge not to be found in ordinary text-books
must be obtained. The text-book of geography which shall
take a country like England, and group the facts in the best
order for purposes of teaching is not yet written.* The teacher,
however, who devotes time to the discovery of the most natural
relationships between the geographical facts he teaches, and
who ignores almost completely the book classification of them,
will be amply rewarded. His class will begin to look for repe-
titions of these associations in every country they study ; they
will not be content with learning names merely, and they will
frequently ask questions about the causes of this and that
geographical fact. Such teaching will arouse self-effort on the
part of the class. Enquiries will take the place of barren
repetitions, and the geography lesson will become a means of
intellectual brightening instead of a dulling and wearying task.

A new method of geographical arrangement.

It is not sufficient to find fault with an old and well-worn
method. A better one must be suggested. Fortunately for those
who are anxious for improvement, a better method is daily coming
more clearly and fully into view. Amongst the more important
groups of geographical facts which the new method of teaching
has settled, the following may be briefly enumerated, viz. : —

1. Mountain ridges and their allied elevated surface areas to be associated
with bold coast features.

2. Land slopes to be connected with the flow of rivers, both as to rate and
direction, and these, in turn, with the formation of valleys.

* The physical geography and geology of the Rritish Isles by Professor Ramsey
is a hel[)ful book. No book, however, can supply die place of the teacher's own
arrangement.

The General Geography of England and Wales. 277

3. The development of secondary slopes with river tributaries and the
formation of secondary valleys.

4. Lowland areas, marshes, river openings (estuaries), and bays.

5. Climate and soil with productions, and these, in turn, connected with
the growth of important industries and with the towns engaged in them.

6. The local and imperial organizations for the promotion of industrial,
social and political affairs.

A series of lessons on the physical and political
geography of England.

It will not be difficult to illustrate the plan of arranging
geographical matter sketched in the above paragraphs by a
series of lessons on the geography of England and Wales. We
assume that the classes have already been thoroughly well taught
the geography of the district round the school, that they under-
stand the meaning of a map, and that they have acquired the
meaning of ordinary geographical terms. The plan about to
be suggested is subject to slight modifications dependent upon
the character of the home geography as the most suitable
starting point from which the geography of distant and unknown
regions can best be reached. In order to illustrate the eflect
of the home geography upon the first lessons on the more
distant geography the following examples may be cited. For
instance : —

{(?) The youth in Warwickshire will be most interested in tracing the
streamlets (taking their rise upon the plateau of his native county)
towards the Severn on the south-west, towards the Great Ouse on the
south-east, and towards the Trent on the north. In this way, nearly
all the geography of central England could be connected with features
with which the pupil is already familiar.
(/') The youth who has his abode on Salisbury Plain will be interested in
following the ranges of chalk hills radiating from the plain and giving
character to the Southern and Eastern counties of England. These
ranges are the South Downs terminating in Beachy Head ; the North
Downs terminating in North Foreland and South Foreland ; the Chiltern
Hills and the East Anglian Heights running north-eastwards to
Hunstanton Cliff; the Lincolnshire and Yorkshire Wolds extending
northwards to Flamborough Head ; and the Blackdown Hills running
westward through Dorsetshire. The character of these hills ; the nature
of the slopes ; the flow of the rivers draining the slopes ; the promontories
terminating each range ; the cliff structure of the coast-Hne ; the short
grass on the undulating surface ; the heavier soils in the valleys ; the

278 How to Teach Geography.

productions of the uplands (mostly dairy produce) and of the arable land
(mostly grain and root crops) in the valleys ; the general absence of
minerals and of large manufacturing centres : — all the above geographical
knowledge, in the order in which it is stated, would be learned with very
little effort by the Wiltshire youth.

Bearing in mind then the modifications stated above the
following scheme of lessons might be generally adopted. •

I. The general build of England and Wales.

After the connection between the direction of the Pennine,
Cambrian, and Devonian ranges of mountains and the greatest
length of England has been shown, and after the connection
between the extension of the ranges of chalk hills in the south
and south-east and the greatest breadth has been made clear,
then the triangular shape of the entire area may be indicated.
The length of England in this way may be connected with the
old and rugged ranges in the north and west, whilst the base of
the triangle — England's greatest breadth — may be associated
with the various chalk hills in the south.

The continuation of the old mountain ranges of the west through
Scotland and Scandinavia in the north, and through the Channel Isles and
Brittany in the South, would suggest the notion that England in its general
build is not so isolated and insular as the map at first glance suggests.
The same idea would be strengthened if it were pointed out that the almost
parallel chalk hills in the south and south-east of England are
repeated again in the north and north-east of France. The fact that a
slight elevation of the entire area would obliterate the North Sea, English
Channel and Irish Sea, would help the class to understand why England
(now a part of a small island) should be held to have been formerly con-
nected with the continent, and further they would see how small a
movement downward had caused the sea to separate England from the
rest of Europe.

The above teaching would result in the children knowing that
England was insular ; was triangular in shape ; had rugged mountain
masses in the N., the W. and S.W. ; had softer hill formations coursing
from W. to E. and to N.E. in the south ; and that shallow seas, viz.,
the North Sea, the English Channel, and Irish Sea surrounded
England on three of its sides. These facts of geography would be
known, and if the method of teaching suggested above were followed,
they would be learned in a much more interesting and thought-rousing
manner than could be the case if the same facts were merely seen on a
map, or repeated from tabular statements read in a text-book.

The General Geography of England and J] 'ales. 279

Distribution of mountains and liills and tlieir extensions
to the coast.

Shaded sketch of a relief model * of England and Wales.

The above relief-sketch has been prepared in order to explain
the method of teaching the distribution of the mountains, csic,
in England and Wales. A raised model containing the same
amount of detail should be constructed. The raised model
and the outline map (drawn as the lesson proceeds) provide
ample material for illustrating the teaching. The following are
the chief points to be impressed in the lesson.

1. The three groups of high mountain land. — The Pennines in the
north separated by the plain of Cheshire from the Welsh mountains in
the west, and these last in turn cut off b}' the valle^' of the Severn from
the mountains of Devonshire and Cornwall in the south-west.

2. The northern range in greater detail. — The group in Cumberland
separated by the Eden valley from the Pennine Chain ; the contrast
between the arrangement of high land in the chain and group ;

* By Mr. Kay, Student 1893.

2 So Hoiv to Teach Geography.

the names of the chief peaks ; and a graphic contrast between the
wild and rugged appearance of the Cumberland group and the
mon_::onous outline of the Pennine Chain.

3. The Welsh mountains (Cambrian Range) not one chain but many
ranges. — //i the north the Snowdon range terminating northwards in
Penmanmawr and Great Orme's Head, and southwards in Braichy-Pwl ;
in the south the mountains of South Wales terminating in Worm's
Head and St. David's Head.

4. The Devonian rartge, consisting of Exmoor, skirting the Bristol Channel
and rendering romantic nearly the whole of the North Devon coast ;
Dartmoor, similarly in the south ; whilst the Cornish Heights (the
back-bone of Cornwall), proceeding throughout the entire length of the
county, terminate in Lizard Point and Land's End.

5. The hills contrasted with the mountains as to height and appearance
and as to position. — The radiation of the chief hill ranges from
Wiltshire in the following directions, viz. : — (a) eastward, via the
North and South Downs to Beachy Head and to the North and
South Foreland, (i/) north-east, by the Chilterns, Gog- Magog, and
East Anglian Heights to Hunstanton Cliff; northward, by the
Lincolnshire and Yorkshire Wolds to Flamborough Head ; and west-
ward by the Black-down Hills and the Mendips.

The smaller hill-ranges should be taught in connection with the
details of the districts into which it will be well to divide the whole
country after a complete general knowledge has been acquired.

3. The more important slopes and drainage ar&as, the
rivers flowing through them, together with the valleys
which the riuers have formed and the openings by
which the riuers enter the sea.

The relief-sketch or the model may again be used, and the
chief slopes indicated thereon. There are several well defined
drainage areas. These should be selected for the first lessons.
For purposes of example we may select the slopes on either
side of the Pennine Range. These two slopes should be
contrasted, and the connection between the length of slope and
the length and rapidity of the stream should be associated with
them. The rivers draining the eastern slope, viz., the Tyne,
Wear, Tees, and Ouse form a group having many common
features. They might be taught together. Similarly the rivers
Eden, Lune, Ribble, and Mersey draining the western slope.
The contrast between the drainage of Durham and Cumberland

The General Geography of England and Wales. 281

would serve to establish the association between a group of
mountains and its drainage into lalces. Finally the various
openings of rivers into the sea would bring into notice {a)
Morecambe Bay and the mouths of the rivers Mersey and
Ribble on the west, (J)) the Humber and the mouths of the
Tees, Wear, and Tyne on the east. Connected with each river
is the valley through which it flows.

In the lessons on 'hills and rivers' already sketched, the valley is
shown to be due in very many cases to the river flowing through it.
This truth should be further impressed by reference to the valleys which
the rivers have carved out on both flanks of the Pennine Chain. When
the terms Weardale, Teesdale, Swaledale, Ribblesdale, &c., are used,
they should suggest not simply the valley along which the river flows,
but also the valley which the river has formed.

Following the treatment of the double slope of the Pennine Range
should be a similar treatment of the following slopes, viz. : —

1. East Anglia, including Norfolk, Suffolk, and Essex ;

2. Counties south of the Thames and bordering on the English Channel;

3. The central table-land, drained on the north and east by the Trent, oq
the south by the Ouse and Welland, and on the west by the tribu-
taries of the Severn.

4. Wales drained chiefly by the Severn.

5. The valley of the Thames.

6. The south-west peninsula of England.

The construction and use of a temporary relief-model of England
and Wales.

In a junior school where geography is very well taught, it is the custom
to make a sand model of England on a large scale once every year. The
model is made in the following way. A large linen cloth of butchers' blue
colour is spread on the floor of the school-room, and upon it are drawn the
coast-line, the chief mountains, hills, and rivers of England and Wales.
Sand is then passed through the spout of a small water-can along the
coast-line. In the same way the mountains and hills are raised, and the
water courses marked out. The level tracts of land are covered with sand
by means of a small shovel. The low lying areas are covered with dark
red sand, and the higher regions with silver sand, the highest points of
land being tipped with powdered chalk. Over the lowland and marshy
regions a little green powder is dredged. Thus, a very effective teaching
appliance is provided. By the side of the model, a sketch map, made
attractive by the use of coloured chalk, presents the same features as the
model.

282 How to Teach Geography.

An objection is sometimes heard to tiie effect tliat tlie sand model
is only a temporary appliance.

For those who cannot afford the time to make these models there
are permanent casts of- raised maps on a small scale which may be
bought. It may be stated, however, that the temporary nature of the
sand model is not without its advantages. It can be made on a large
scale. When one model has been constructed by the joint effort of
the teacher and his pupils, the latter are able to do the entire work
themselves. The scholars thus become very greatly interested in the
effort, and the knowledge which their own model represents becomes
very real and enduring.

Hints upon the use of the Model.

The introduction of the model is frequently accompanied by an entirely
mistaken use of it. The worst use to which it is put (though by no means
an unfrequent one) is to neglect it altogether during the teaching of the
new matter, and to introduce it merely for purposes of revision. The
following hints will be of service to those who use the model for the first
time : —

1. Begin the lesson with an examination of the model, and commence
the examination of the model by noticing the position of the high land
and the general slope of the surface.

2. Pi'oceed from the model to the sketch map, and develop the sketch
map on the black-board as fast only as the facts are learned from an
observation of the model.

3. Allow individual scholars frec|uently to indicate features on the
model, and then encourage them to place the same in position on the
sketch map.

4. From an inspection of the positions of the high land and the slope of
the district, require the scholars to infer the direction of the rivers.

This is exactly the reverse of the method adopted when the
teaching is only accompanied by a maj). The rivers are first
examined, and the slope is inferred from the direction which each
river takes.

5. Teach the coast features — capes, cliffs, bays and estuaries — along with
the distribution of mountain ranges, lowland plains, and river valleys,
and associate each of the boundaries of the district with the natural or
artificial feature near it.

4. The Geography of Natural Sections.

After the general structure of England and Wales has been

completed, the more detailed geography is best taken in

^^ sections. These sections might be {a) the six northern counties,

The Gaieral Geography of England and Wales. 283

further sub-divided into eastern and western slopes, (/') the
midland plateau, (r) the eastern counties, id') the counties
south of the Thames, (c) the south-western peninsula, and (/")
Wales, further sub-divided into North and South Wales. The
method of teaching each section should be the same as that
adopted for the general geography of the country.

5. Climate and Soil, together witli the productions of

the latter.

These form a group of related geographical matter. They
should be so taught that their dependence upon one another
becomes apparent. The moisture of the western areas is con-
nected with the preponderance of grazing farms, and of dairy
produce over arable land and root and corn culture. The
lowland plains of the east, with their heavy land and dry
climate, afford favourable conditions for the growth of
grain. Hence, in these localities, arable farming prepon-
derates over grazing. In the south, the warmer climate and
the lighter soils, yield suitable conditions for grazing on the
uplands, and for fruit culture in the valleys. Agricultural
markets are necessary in all the districts named, and the chief
towns providing such markets for the interchange and sale of
the various products of the land may now be stated. An
attempt may also be made to indicate the markets at which
merchants in fruit, corn, cattle, wool, &c., would most readily
obtain what they require.

Special productions such as cheese in Cheshire and Glou-
cester, hops in Kent and Sussex, apples in Devonshire and
Hereford, owe their position to climate and the nature of
the soil. The different breeds of cattle and sheep are
connected with variations of soil — the heavy breed of
■ — sheep in Lincolnshire contrasting with the small South-
down breed ; the sleek and well-formed Devon cattle
contrasting with the much heavier breed in Yorkshire.
Similarly, the heavy Norfolk draught horse contr;ist§ with
the ponies of Wales and the Shetlands,

6. Mining and manufactures and the great industrial
centres form another group of natutally related geographical
matter. The connection of coal with iron and the consequent
association of the principal iron and hardware industries

284 How to Teach Geography.

with the coal-fields should be noted. The introduction
of steam into all the important textile industries explains
the association of the woollen and cotton factories with the
coal-fields. By way of contrast it might be shown that the
hand and light machine industries of straw-plaiting in Bedford-
shire, of boots and shoes at Northampton and Staftbrd, of
tanning in Bermondsey, &c., are not associated with any
particular coal-field.

Instruction in this branch of the geography of England and Wales is
frequently made more interesting and thorough by some or all of the
following devices, viz. : —

1. By the exhibition of specimens of the more important minerals used in
the industries.

2. By collections of objects illustrative of the chief English industries
and showing the stages of manufacture from the raw material to the
finished article.*

3. By scrap-books of pictures of manufacturing centres cut from the
illustrated papers, and by photographs of factories, &c.

4. By specially constructed sketch and wall maps indicating the locality
of each industry, and the chief towns engaged in each.

The fishing industry employs thousands of people along our coast.
The chief fisheries should be described : — Cod fishing on the Dogger Bank
associated with Grimsby, Hull, and Boston ; the herring fishery with
Yarmouth and Lowestoft ; pilchards and mackerel with the Cornish ports.
In order to add interest to his descriptions, the teacher should provide views
of the fishing fleet and illustrations of the different modes of fishing — by
line, net, trawl, &c. Specimens of the different products might also be
shown, as e.^., oil, fish-glue, &c.

7. Commerce, routes of trade (ocean, rail, and canal),
and ports.

Following the account of our great industries should be that
of our commerce, our great trading routes, and our seaports.
We need raw material for our manufactures, and markets, both
abroad and at home, for the finished goods. Hence arises the
group of geographical facts now under consideration. Imports,
exports, and ports are closely related, and all three should

* A collection of t'-iese objects obt.iined from private manufacturing firms was exhi-
bited at the Health lixhibition, 1S84. A paper descriptive of their use in the teaching
of geograpliy was read by the author. Collections can now be bought. Those, how-
ever, which are made by the scholars and teachers arouse more interest than the
^>ought collections.

The General Geography of Efigland a7id Wales. 285

further be associated with the industries which have given rise
to them. For example, Liverpool and Manchester should be
associated with the cotton trade, Newcastle with coal, Cardiff
and Swansea with coal and iron, &c.

A railway map, showing the chief trunk lines radiating from London,
should be drawn in order to fix, with most effect, the directions of our
inland trade. If differently coloured chalks be used to distinguish the
more important railway routes, an eflective and not confusing result may
be shown. Canals should be indicated in the same way.

Ocean commerce may be made attractive by a descriptive account of
the chief routes, of the companies whose steamers ply along each route,
of their ports of call, and of the chief exports and imports. For
example, a lesson might be selected descriptive of our trade with
America and Canada. Attention would first be drawn to the large
supplies of cotton, corn, and cattle required by us, and which America
can supply. In return, America takes our manufactured goods, and
there are furthermore constant streams of passengers crossing the Atlantic.
Having thus directed attention to the nature of the trade awaiting transit,
the lesson would proceed to state and illustrate the various routes open
to the choice of the passenger and merchant. Cotton goods may be
taken by the Cunard, White Star, or Dominion lines from Liverpool or
Manchester. Passengers from London take ship most easily by the
American and German lines direct from Southampton. The calling places
for the latest mails, Queenstown in the south of Ireland and Moville in
the north, would next be noticed, and then the places of destination
would follow, viz., Quebec, Montreal, Halifax, Portland, New York, &c.
After the lesson, the scholars should have access to the illustrated guides
and pamphlets issued by the various steamsliip companies. Their
attention should furthermore be directed for a few days to the successive
notices in the daily papers of the sailings of a selected number of ships,
to the calhng for the latest mails, and the arrival of the ships at their
destination. By these methods, a continued interest would be main-
tained in the movements of our most important mail steamers, and
the power to make use of the shipping intelligence in the daily press
would be gained.

ti"^

Political g-eography — a misleading term suggestive
of erroneous methods of teaching.

The so-called political geography of England and Wales
cannot be entirely separated from that whicli is termed physical.
The prime aim of teaching throughout these pages has been to
discover the inter-dependence between the various facts of

5S6 Hotv to Teach Geography.

geography, and to associate the related facts so that their
dependence upon each other should be recognised by the
learner. It is upon this recognition that the value of geography
as an intellectual study mainly rests. Why then should we
designedly in our teaching pursue the familiar text-book
arrangement of matter, and reserve, until after the physical
features of a district have been learned, all reference to the
' condition and pursuits of its inhabitants and the names and
positions of the principal towns' ? We see no reason for this
unnatural method ; in fact, the industrial pursuits of the
inhabitants, and the position and development of the great
manufacturing, market, and sea-port towns have already been
shown to be dependent upon the area in or upon which the
raw matter is produced and worked. When teaching, therefore,
we advise the close association of the so-called political matters
— industries, towns, commerce, c\:c., with those physical features
•^climate, mineral wealth, soil and its productions, with which
they can be shown to be very closely related.

Examples of similar relations in other areas besides England.

The great plains have always been the areas of agricultural develop-
ment. What is true of the densely peopled plains of China and India,
of Lombardy and Belgium, may be shown to be true of the eastern
section of England.

The discovery of mineral wealth in any locality has frequently led to a
great influx of people. California, Australia, South America, South
Africa are familiar examples. The utilisation of steam has added to the
importance of the coal-field, and to-day the greatest centres of industry are
found on the coal-fields of England, Belgium, and Pennsylvania.
' Commerce,' says Mr. Keith Johnston, 'dependent on the variety ot pro-
ductions ot different lands and the exchange of surplus products or manu-
factures, is regulated in the paths which it follows by physical causes, and
brings men to the natural inlets of every country, the estuaries of the river
highways. In the ports, the business of the world is carried on, the
products of the interior are stored for export, and those of foreign lands
for distribution inward ; hence many of the great cities of the world have
grown up round their seaports.'

It would not be difficult to lead an intelligent class of
scholars to see tliat nations are influenced very largely by the
physical conditions of the areas they occupy. England shares
with all the powerful nations of the globe a temperate climate.
No nationality has ever developed tirst-rate rank under either

Geography and History. 287

tropical or Arctic conditions. Besides its immense mineral
resources and its favourable climatic conditions, England
possesses an insular and central position amongst the ether
peoples of the globe. Thus the pre-eminent place occupied
by Britain amongst the nations may be shown to be associated
with certain well marked physical conditions.

Geography made a starting point for the teaching of
History.

The teaching of geography hitherto considered, has, it is
hoped, enabled our scholars to understand the collecting
together of people in large industrial centres. The study of
the conditions under which people live in these crowded
centres naturally follows. This study would lead to an
enquiry into the various organizations for protection by the
local police, for the general supply of pure water, for the town
drainage, for the maintenance of highways, &c. These topics
could easily be connected with the levying of rates, and their
collection ; they would further prepare the way for lessons
upon Imperial Government, and the maintenance of an army
and navy, together with the imposition of taxes, so that the
burdens of expenditure may be spread over the community.
A simple course of lessons on the above subjects would prove
an effective preparation for the study of history.

The method of teaching the geography of England
and Wales, in the main applicable to the teach-
ing of the geography of other countries.

When once the true method of teaching the geography
of any one country has been determined, this method becomes
applicable to the teaching of the geography of other countries.
We need not, therefore, proceed to indicate the methods
of teaching the geography of Europe, India, the Colonies,
America, &c. Modifications of method will be advisable as
progress is made in the study. We plead for liberty in teaching
methods. Having escaped from the slavery of the text-book
arrangement, we must take care not to enter again into bondage.

A mountainous country like Switzerland needs to have its
geography treated differently from the geography of Belgium
with its plain and river structure. Again, the method of illus-
trating the facts of geography need not be the same throughout

2 88 How to Teach Geography.

the study. For example, the raised model is very helpful
in the early stages of instruction. As soon, however, as the
pupil is able to make good use of the map and atlas, the relief-
model may be discontinued. A trained geographer ought to
be able mentally to build up the contour of a country from the
representations of mountains, rivers, plains, coast-lines, &c.,
found on a map. Bearing, then, in mind a few such variations
in method as those above indicated, there will be found a very
general agreement in the method of dealing with different
countries.

The relief structure must be associated with the flow of the rivers
and the character of the coast-line (if any) ; the climate and soil must
in every case be very intimately connected with the surface produc-
tions ; and these, in turn, together with the mineral resources, will
continue to determine, very largely, the industrial, the social, and the
^political conditions of the people.

"he association of geography with other school
studies.

One of the encouraging features in the recent developments
of school method is the constant enquiry into the logical
relationships existing between the different parts of any parti-
cular subject, and also between that subject as a whole and other
subjects of school work. The object of all such enquiries is to
prevent the accumulation of masses of isolated and unorganized
matter. A memory may be crammed with facts, but unless the
logical relationships between these facts be known, very little, if
any use can be made of them. It has been the constant aim
throughout these chapters to show how the facts of geography
may be placed in their true relationships before the learner.
The connection of geography with other branches of school
study can only be briefly indicated. The reader may with
advantage expand the following notes : —

{(i) Geography and general reading. Books, for enlarging and supple-
menting the geography lessons, should be provided by the school
library. When, for example, the geography of Africa is studied, a
few modern works of African travel should be available, and the
attention of the scholars directed to them. Similarly, the geography
of South and Central America may be associated with the historical

Geography and Allied School Studies. 2 89

Works of Prescott, and that of Scotland with the poetry and some of
the novels of Sir Walter Scott ; of America with the biographies of
Washington and the stories of Cooper. During every reading lesson
the occurrence of any geographical term should be made an
opportunity for fixing its position on the map.

(l>) Geography and History. It has already been shown that a know-
ledge of geography provides the starting point for the formal study
of histor}'. Histor)', in turn, provides opportunity for considerable
instruction in geography. Most lessons in history may, with
advantage, be accompanied by maps and sketches. This incidental
teaching of geography is always effective, and should be encouraged.

(c) Geography and Drawing. This connection has been insisted upon
throughout the entire course of instruction. The sketch map of the
teacher should accompany his lesson. It should gradually develop
with the development of his lesson. The maps drawn by the scholars
should follow the lesson. Only after considerable instruction, and
when the power to interpret a map is formed, should scholars be set
to draw maps from copies without previous instruction in the descrip-
tive geography of the area. Next to the fault of getting up tables
of matter from the text-book may be placed that of the practice of
teaching geography, in its early stages, by means of map drawing
alone. If we wish the geography lesson to be a means of intellectual
brightenirg, map drawing must be relegated, in the early stages, to
its proper place, viz., to that of registering in a concise and attractive
form the results of the instruction otherwise given.

{(f) Geography and 'suitable occupations.' Whilst the early stages of
teaching were under discussion it was suggested that the making of
models of well-known areas in clay and card-board, and the collection
and mounting of specimens, might be made a 'suitable occupation.'
This occupation, whilst it affords exercises for both hand and eye,
will provide a very useful and practical knowledge of geography.

((■) Geography and arithmetic and composition. The calculation
of distances, the comparison of areas, and the determination of
latitude and longitude, &c., furnish exercises in arithmetic ; the
reproduction of the description of a country is a simple exercise in
composition, and at the same time the style of writing and arrange-
ment becomes an effort in penmanship and grammatical statement.

Maps and map drawing.

The maps of most service for teaching geography are those
which the teacher constructs before the class. These maps are
rarely overcrowded with names. If the map grows, as it were,

296 How to Teach Geography.

with the progress of the lesson, there are no confusing details
to distract the attention of the class. The sketch map, further-
more, presents the outline which the teacher wishes his pupils
afterwards to draw. If coloured chalks be used, the various
details may be readily distinguished, and a pleasing effect pro-
duced. For these reasons, we are of opinion that a sketch
map should be a prominent feature in every lesson in
geogi-aphy.

The Wall Map is of service when we wish to show the relationships
between the district we are teaching and the neighbouring areas. It is,
furthermore, of service for future reference by the scholars, and, when
bright and new, it serves to decorate the school walls. When the colouring
of a new map is gaudy, and when the features of an old map have become
almost obliterated, their appearance on the school walls becomes, in either
case, demoralising.

THE SHAPE, SIZE, AND MOTIONS OF
THE EARTH.

The most difficult portions of the geographical syllabus are
those connected with what is termed mathematical or astro-
nomical geography. The full and accurate study of these
difficult topics is beyond the powers of young children. In
former years the code syllabus, following the order of the text-
books, required children of Standards I. and II. to be able to
answer questions in these abstract subjects. Recently, how-
ever, the seasons (an effect of the earth's motions) day and
night, and latitude and longitude, have been delayed until
Standard V. is reached.

It has already been noted that there-,are topics connected with the
seasons, and day and night, whichAery young children can be led to
understand. Fur example, they i«nay be li;d to observe that in summer
we have long and warm cfci\s, *vhilst in *inter, the days are cold and
short. Very little childreiV 9/1 also be led to connect flowers, green
trees and fruit with summer ; whilst snow and ice, bare fields and
leafless trees may, ecjuaily well, be associated with winter. Children

Tlie Shape, Size, and Motions of the Earth. 291

in Standards III. and IV. might be led to connect the summer with
the observed height of the sun and the length of the day, and to
associate winter with the low sun and the long nights. It is only when
children reach the higher standards, however, that any attempt to
enquire into the causes of the long and warm days of summer, and of the
short and cold days of winter, should be encouraged. In arranging
a course of lessops in any of these W)pics, care should be taken to adjust
the lessons to the a^;e and intellectual ability of the children. Natural
phenomena, open to the observation of children, may be taken at a
very early age. Very obvious connections with these facts, but which
do not completely explain them, may be attempted at a later stage,
whilst the scientific explanation of the causes of the phenomena should
come last of all.

The shape of the earth.

Bearing in mind the conclusions arrived at in the previous
paragraphs, it seems that very httle can be taught respecting
the shape and size of the earth in Standard II. There is
nothing at hand for the scholars to observe. In fact, the results
of their observations upon the portion of the earth with which
they are best acquainted generally leads to a contradiction of
the accepted theory. It is true that we may tell the children
that the earth is i-ound. We may correct this statement by
informing them that it is not exactly round, but that it is
slightly iiattened at the poles, and that hence it is termed an
oblate spheroid. As yet, however, there is nothing but the
teacher's word to guide the children to the facts. The ' telling
method ' is the only method available at this stage.

We may attempt to illustrate what we tell the class, by introducing
. a globe to their notice, and, at the time of introduction we may tell
the children 'that the earth is round like this globe.' Still the method
is that of ' telling,' there are no phenomena for the children to observe.
The only phenomena to which we can direct their attention are the
disappearance of ships bene9.rifthe horizon, the earth's shadow on the
moon, and the fact that^s^lors have tftken tljsir ships round the globe.
From these facts children are expected j^Tearn that the earth must be
round. With the development of their reasoning poWers, the scholars
will be able readily to make the inferences we requirq. It is, however,
open to considerable doubt whether or not any of the children in the
lower standards can do more than merely accept, without question,
all we tell them about the earth's shape.

292 How to Teach Geography.

The size of the earth.

Trustworthy notions of distances and areas are very slowly
acquired. A mile in length, the distance between the school
and home, an acre in area, the size of the playground, the height
of the school room, its width, nay even the height of a door,
or the width of a passage through which children frequently
pass,- — all these will be found upon enquiry to be known but
very imperfectly. Upon this imperfect information the teacher
must depend, however, in order to impart reliable knowledge of
wider areas and greater distances. There are thousands of
children who can immediately state the distances round the
earth and through it, the length, breadth and area of Great
Britain, and the sizes of all the continents, who have never had
a yard tape or a foot rule in their hands. It is needless to
state that merely verbal knowledge of this kind is of very little
real value.

Methods used and found of service in yielding simple
notions of distance and size.

1. Actual experience of lengths and areas.

Children may be exercised in measuring with a foot-rule and tape
many of the simple lengths and areas mentioned above. For permanent
reference the length, breadth, height, and area of the school rooms may
be painted on the walls ; door-ways, black-board, &c., may be marked in
feet and inches ; the length, breadth, and area of the playground, and the
distances between several objects passed by children on their way to
school, may be carefully measured and placed in prominent positions,
as standards for reference when other and unknown distances and areas
are mentioned.

2. Estimated measurements of greater lengths and areas.

From these observed and carefully measured lengths, children may be led
to form notions of greater distances. The length of the county, for
instance, may be connected with the distance a boy walks to school ;
anil the time he takes to walk the shorter distance may be compared
with the number of days required to travel the entire lengtli of the county.
Use may be made of school excursions into the country, or to the sea-
side, provided that the rate of movement be corrected by reference to the
ordinary methods of movement, such as walking, &c. After a few
measurements of the county have been mastered, the area and extent of

The Shape, Size, and Motions of the Earth. 293

a country may be attempted, the children having frequent exercises in
comparing the lengths of known distances with these longer and unfamiliar
distances. Deal similarly with areas.

3. The dimensions of tlw globe should be generally associated with
distances and movements already familiar. Work out the time required
for a man to walk, or for a cyclist to ride, from John o"Groats to Land's
End. From this proceed to the time required to travel round the world
by steamer or railway. The apparent flatness of any small area which
we observe from any given standpoint is proof of the immense size of the
globe. The process of reasoning by which_ the apparent flatness is
associated with the immense size of tKe globe is beyond the power of
little children. All we can do is to show a very small ball side by side
with a very large globe. Then allow the children to decide by simple
observation which looks flatter when an area like that of England is
marked on the two globes and compared. We have stated sufficient to
show the difficulty of the task of attempting to give young children a
notion of the size of the earth. This difficulty was pointed out by
Professor Huxley many years ago in the following passage taken from
the preface to the first edition of his Physiography : —

' I do not think,' says the Professor, 'that description of the earth
which commences by telling a child that it is an oblate spheroid, moving
round the sun in an elliptical orbit ; and ends without giving him the
slightest hint towards understanding the ordnance map of his own
county ; or any suggestion as to the meaning of the phenomena offered
by the brook which runs through his village, or the gravel pit whence
the roads are mended ; is calculated either to interest or instruct.
The attempt to convey scientific conceptions without the appeal to
observation which can alone give such conceptions firmness and reality
appears to me to be in direct antagonism to the fundamental principles
of scientific education.'

Motions ot the Earth,— Day and Night, and the
Seasons.

Topics in astronomical geography are required to be
taken by scholars in the upper classes. These scholars are
required to state the phenomena and to understand their
causes. For the latter purpose, it will be necessary to construct
simple apparatus. The movements of the earth, giving rise to
the phenomena, are on too grand a scale in nature to be

294

Hoiv to Teach Geography.

directly observed. They must, at first, be imitated by means
of simple appliances. Fortunately the appliances are not
difficult to construct. The following will be found helpful.*

F and G are wire mounts. They hold the ball and the screen in position and allow
the teacher's hands to be free to turn the ball by means of the extended wire at H.

{d) Day and Night.

Obtain a large wooden ball. One can readily be made by a wood-turner.
Cover its surface over with gold paint. Mount the ball on a wire having a
wooden foot. See H and F in the figure. Make a cylinder of blackened
card-board, and enclose one-half of the ball in the cylinder. The stand G
holds the cylinder in position, so that the teacher's hands are free to rotate
the ball. A candle or lamp may now be placed in front of the ball to
represent the position of the sun, and a wafer may be placed on the ball or
globe at C. If now the teacher rotate the ball, the wafer will pass round,
and one-half of the rotation will be in the light whilst the remaining halt
will be in the dark. The three positions of the wafer, agreeing with the
rising, the setting, and the mid-day sun, viz., C, A, and B respectively,
should be indicated by the class. Afterwards the positions corresponding
to the setting, the midnight, and rising of the sun should be indicated.

When the' effect of a rotating earth in producing the diurnal changes
from day to night has been made clear, the class might be exercised in
finding out another explanation, viz., that of the sun moving round the
earth. They might be told that, many centuries ago, the earth was
supposed to stand still, whilst the sun revolved round it. This idea
required a body i^ million times the size of our earth to be controlled

* The following: diagrams are se'ected from the author's Graphic Listens in
Physical and Astioitoiiucal Ueograpliy.

The Shape, Size, and Motmis of the Earth. 295

by the smaller body, and not only so, but that all the vast community
of stars (bodies, i.e., resembling our sun) must similarly move round
the earth. In this way the second explanation could be shown to be
most improbable. The theory of gravitation propounded by Newton,
and now universally accepted, may be mentioned in proof of the
impossibility of the old notion. There are also experiments (like the
pendulum experiment of Foucault) which arc proofs of the earth's
rotation. The teacher must distinguish between an illustration and a
proof. At this stage the illustration by means of a rotating ball is all
that need be attempted.

How to show that the revolution of the earth round
the sun, with an incHned axis, causes the seasons.

Two globes should be provided
for this purpose. They should be
mounted so that the axis of rotation
is inclined from the vertical by 23^°.
If lines be drawn round these globes,
to represent the equator, the tropics
of cancer and Capricorn, and the
arctic and antarctic circles ; and if
both the axes be inclined in the same
direction, as shown in the accom-
panying diagram ; and, lastly, if
cylindrical shades be placed so as to
enclose the half of each globe (the
half, viz., furthest from the sun in
each case), the varying lengths of the
day for any selected parallel at the
summer and winter solstices, together
with the varying heights of the sun
at mid-day, will be apparent.

Allow the class sufficient oppor-
tunity to examine for themselves the
differences in the length of the day
during each of the solstices. Mem-
bers of the class should be permitted
to rotate the small globes, and should
be encouraged to state when the day
will be short and when it will be
long ; also when the sun at mid-day
will be low in the heavens, and when
it will be high.

c
SO

296 How to Teach Geography.

On no account should the class be told the conditions which bring
about the changes above-mentioned. They must be led to discover these
for themselves.

Assistance may be afforded in the following way. (i) Ask the class what
changes (if any) would occur if the earth remained in one position. (2)
Ask what must be done to the globes in order to effect the changes. Thus
lead to the notion of the revolution of the earth. Now place the axis
vertical and rotate the globe in both positions shown on the diagram with
the vertical axis, and ask if any difference in the lengths of the days is
possible in the two positions. Thus lead the class to see that the changes
depend not only upon the revolution of the earth round the sun, but also
upon the axis being inclined. The constant direction of the axis is a
matter of observation, and should be noticed by the class. The three
essential conditions upon which the seasons depend have now been illus-
trated, viz., (i) The revolution of the earth round the sun; (2) the
axis of the earth inclined 23F from the vertical ; and, (3) the constant
direction of the axis.

It may be well, at this stage, to caution any one against
attempting too much in one lesson. The ideas of the seasons
thus illustrated by the globes, are not easily realised by the
scholars. Not only should the globes be exhibited and
examined, but diagrams should be carefully drawn on the board
by the teacher to represent all that the globes illustrate. The
scholars also should be encouraged to make drawings of their
own, accompanied by written explanatory statements. It will
be noticed that the length of the days and the height of the
sun at the equinoxes have not been illustrated. These should,
however, be taught, and by methods similar to those already
indicated.

There are several remaining subjects of physical geography too ad-
vanced for full consideration in a work of this limited character. Special
works are published affording full directions upon the method ot
teaching such advanced topics as latitude and longitude, climate,
eclipses, tides, &c. The author's Graphic Lessons in Physical ami
Astronomical Geography sets out the matter to be taught in these
subjects, together with the mode of arranging the matter, and with
suggestions for the best method of illustrating and presenting it.

Geographical excursions and visits to museums.

For several years past it has been the custom to take a
company of student teachers over a well-known area in the
neighbourhood of London, in order to make a direct study of
the- more important geographical features of the district. This
first-hand study of phenomena in the field is followed by the

Excursions and Museums. 297

most encouraging results. The relationships between a great
number of geographical facts are rendered evident, and the
connection between the surface phenomena and the truths of
physiography and geology are discovered. The same kind of
investigation can be made in any part of the country. Similar
explanations become afterwards applicable in lessons upon
districts which cannot be actually visited. The geographical
excursion tends to brighten and to give reality to all future
lessons. The above effects are apparent in the teaching of
geography. When, however, we come to the learning of the
subject, the effects are still more encouraging. Scholars who
have thus been brought into actual contact with geographical
phenomena in company with their teacher, have a store of
reliable and vivid impressions to which they can afterwards
constantly appeal. Besides the use of this first-hand know-
ledge in class-room work, the scholar is trained to look upon
the world around him in a new light. Its hills and valleys, its
rivers and mountains, its chalk quarries and coal mines, become
(in place of dry facts to be learned, and, after examination, to be
forgotten) full of history and of life. Many a scholar may in this
way be started upon lines of activity which, filling his leisure
moments, may supply information of a most valuable kind, and,
at the same time, may provide a most enjoyable form of recreation.

Visits to Museums.

In crowded cities, where it might be difficult to make excuirsions and
collect specimens, a modified but very simiJar effect might be produced by
visits to museums. Increased facilities will, in all probability, soon be
afforded for visits of this kind.'* In order to make these museums of
greatest use for children, it will be necessary for a competent guide to
accompany them. The children should be in small batches. The visit
should have a definite aim, and until that aim is accomplished the attention
of the scholars must be concentrated upon the object in view. Preparation
by lessons previously given in the school should-arouse the enquiring and
expectant attitude of the scholar. It may be necessary to make special
collections of objects for the instruction of children. Very little good, for
example, would follow the inspection of a complete set of either botanical
or geological specimens. The effect would be confusing. If, however, a
few typical specimen cases were made up, having the objects distinctly
labelled, and a guide (teacher or curator) ready to give reliable information,
the visit would be of great value.

* Permission is now granted by Ait. 12 (g), New Code, 1S95, to make not more than
twenty attendances under proptr guidance to Museums, Art Gallerie-', &c.

298 How to Teach Geography.

Summary and review of the principles underlying
the suggested methods of geographical instruc-
tion.

The attempt to show the value of the study of geography for
purposes of mental training has been reserved until something
like a complete review of the principles underlying the adopted
methods of instruction could be obtained. That review can
now be made. When we look back upon the main features of the
suggested methods of teaching, we see that they may be stated
in the following propositions, viz. : —

i. No fact in geography stands alone,

ii. The relationship between many geographical facts can be
determined.

iii. When the relationships between the various geographical
facts have been determined, the true method of instruc-
tion is that which presents the facts so that the order in
which they stand related to one another can be discovered
either in part or entirely by the learner.

iv. The arrangement of facts which most completely con-
ducts the learner to the recognition of the natural
relationship between them is the best arrangement for
teaching purposes.

V. This arrangement is best for the following reasons, viz.,
{a) each fact becomes fully known ; (/>) it is therefore
readily remembered ; {c) the arrangement of facts for
one region can be applied equally well to new areas ;
hence, (^) this application of teaching method to
new regions encourages the intellectual activity of the
learner so that he now no longer remains a passive
receiver of knowledge imparted by another, but he
becomes himself an active participator in the discovery
of knowledgfe.

^t)^

The mental training which follows the adoption ot
the above principles of teaching can now be
stated.

"''he full value of the adopted method of geographical in-
struction for ])urposes of mental training will be best understood
when the student teacher possesses a clear notion of the various

A Mea7is of Mental Tra'ming. 299

operations of which the mind is capable.* At this stage a
simple statement must suffice. The following will not be
difficult to understand : — ■

1. The method of teaching requires the scholars to make the utmost use
oi \.\\&\x pmvcrs of ohscrvation. First lessons arc devised mainly with
the object of rendering as perfect as possible the knowledge of those
geographical facts open to direct inspection by the scholar. When
lessons advance to more remote regions the use of models, of pictures,
of maps, and of specimens continues the exercise of the scholar's
powers of observation. The method of instruction, throughout the
entire course, keeps in view the truth, that, so far as the scholar is
successful in realising the phenomena of other lands, he does this by
making use mainly of the facts which direct observation has supplied
in connection with the studj' of his own country.

2. After the scholar's powers of observation have been exercised in the
direct and exact inspection of the various geographical features which
his home surroundings supply, it would not be possible for him
to make much advance beyond his observed knowledge, unless,
when the objects themselves are absent, he could recall the
respective appearances which these objects present. This effort of
recall is an exercise of tJu- memory. Not only is memory exercised
during the initial stages of teaching, but throughout the entire course
of instruction, the retention of the geographical facts already acquired
is a prominent object, and one always to be kept in view. Hitherto,
the acquisition of geographical facts has been considered too exclu-
sively as an exercise of memory, and the various methods of instruc-
tion have been valued in proportion to the success, or otherwise, with
which they secured the retention of these facts. The most modern
methods of instruction, however, keep constantly in view the truth
that the associalioii of facts is the surest condition of their retention.
We retain best those facts which are brought into some form of
relationship with other facts.

For example, cheese with Cheshire might be remembered because
the first three letters are the same in both cases. Formerly, such
an association (of sound only) would be held to be sufficient. So
long as the fact • that cheese is obtained from Cheshire ' was
remembered, nothing further would be demanded. In the chapters
preceding this, a deeper form of association has been enforced.
Cheshire is the county of rich pastures. Accompanying these

* A simple account of the mind's capabiruies, and of the various school exercises
calculated to exercise these mental powers, is given in the autliors Principles of Oral
Teaching ami .}fi;>itiil '/'rai/tini:.

oo How to Teach Geoi:;raphy.

pastures, and consequent upon them, is the industry of dairy farming,

and cheese is one of the chief products of a well managed dairy. In

this way, a logical sequence between the moist climate, the rich

pastures, the dairy farm, and Cheshire cheese is recognised, and also,

in this way, the association of cause and effect (the most fruitful

bond of connection) is made. Whenever the learner can supply a

geographical fact, and, at the same time, can state why it exists,

the brightest and most enduring bond of association {i.e., of nieinory)

has been formed. Throughout the preceding chapters it has been

the aim so to teach the facts of geography that this highest and

most lasting bond between the facts should be formed.

If our pupils simply remember what they see, and retain what they

are told, their knowledge will be neither very wide nor very profound.

Our scholars may read over and over again long lists of names and

may call them capes, rivers, productions, &c. , and they may do this

so frequently that in time the names are remembered, and when

required they can be reproduced. Knowledge, in this case, will

be very superficial. Such superficial knowledge, however, is often

dignified by the term ' geography.' If this be the kind of geography

we seek to teach, no higher intellectual effort will be needed than that

of memory, and the memory exercise, moreover, will be of a very

low order. Methods of teaching, however, have been suggested in

previous chapters, having for their object a much higher effort than

that just named. Relief-models, pictures, collections of specimens,

maps, and graphic descriptions are all intended to assist the learner

in his efforts to realise, in tlieir natural grouping, the geographical

features of the country we wish to teach. The intellectual efforts

which these appliances and improved methods of teaching are

intended to stimulate, are [a) the imaginatiott by which the learner

pictures the natural scenery of the district under discussion, and

(b') the powers of reasoning by which he attempts to associate the

various natural features in the order of cause and effect.

Notes of a Lesson.

301

NOTES OF A LESSON.

RIVER CLYDE.

Standard IV'.
Apparatus.— Plaster model, sketch

INFORMATION.
IntrotTu'ctrbn.

The Clyde is the most important
river in .Scotland. It is situated
in the S.W. of the Lowlands.

Source.

Rises in the Queensberry Hills
(Lowthers) at an elevation of
1,400 feet. Takes a northerly
direction as a rapid mountain
stream.

Course.

Divides naturally into two parts
at the Falls, into Upper and Lowir
courses. 98 miles long. Runs
into the Firth of Clyde at Dum-
barton.

A Contrast.

{aj Country

(A) Soil and

Minerals .

(f) Valley ...
{li) Current

\(e) Water ...

UfiJ,cr.
Hilly, Pas-
toral.

Lower.
Low. Flat,
Cultivated.

Not Pro- Fertile,
diictive. Well drained,

Lead
Mining.

. Narrow,
Rock- bound.

Fast,
Impetuous.

Pure.

Coal
Mining.

Wide.

Sluggish,
2^ miles
per week.

Dirty,

unfit for

use.

(/) Tributaries ... Few and
small.

Man3' <-ind
Larger.

Revision.

From black-board sketch at this
stage of lesson.

Time 30 minutes,
map, wall map, coloured chalks.
HOW PRESExNTED.

Allow class to locate the district rep-
resented on the model by comparison
with a wall map. Ask for the most
important English river. Corres-
ponding Scotch stream. Announce
' River Clyde ' as the subject of the
lesson.

Trace course of river to its source.
Allow a scholar to point out the
highest ridge of land near, also the
highest peak. State the names of
both range and peak. Call attention
to the slope of range. Allow the
class to infer direction and nature of
the current.

Give short description of Falls.
Show picture. Why divided there ?
Compare with length of Thames,
about half length. Deal with width
similarly, half width. 'J'hames four
times as large.

Obtain as much material for contrast
as possible from class by examination
of the model.

Pentlani ■
'-.-■Sf, "'il--

Sketch Map of Ciydesdak

^yi'---^h:iH \

302

How to Teach Geography.

ship-building.

Tributaries.

((?) The mtlin slope is towards the

N.W.
(/') The secondary slopes are at

right angles to the main slope.

Right Bank — Leven, Kelvin.
Left Bank — Cart, Avon.

Productions and Industries.

1. {a) Mineral — Coal, iron, lead.
{!)) Vegetable — Oats, barley.
{c) Animal — Horses, cattle,

sheep.

2. ((?) Manufactures — Textiles,

niacliinery,
(l>) Agriculture — Fanning,

hnrsc-brt'cding.
{c) Mining — Coal, iron, lead.

Population and Towns.

Thickly populated in \V. of
basin only.

Lanark, on the Clyde, cotton manu-
factures ; scenery.

Hamilton, on the Avon, woollen
tartans.

Glasgow, on the Clyde, ship-build-
ing, cotton, chemicals.

Paisley, on the Cart, tartans,
thread.

Greenock, on the Clyde, Port, birth-
place of Jas. Watt.

These slopes must be observed by
the class. They determine the
direction of main stream and trib-
utaries. Point the tributaries out on
the model ; mark down on map ;
ask boy to point out on the wall map.

Obtain probable industries from the
productions, thus : presence of iron
and coal — manufacture of steel,
machinery, ship-building. Oats,
barley, horses — supplied only by
farmers, hence farming. Good
b'stuary — importation of raw mater-
ial easy — cotton, &C. Woollen
manufactures, silk, sugar refining.
Connect the towns with the in-
dustries, e.g., Ship-building with
Greenock and Glasgow.

Towns to be connected with their
industries and with some interesting
fact.

Associate the launching of the first

British Steamer with the rise and

development of ship-building or

Glasgow.

Hence probable seat of machine

factories.

Revision from Black-board Sketch.

1. Source. Queensberry Hill, flows N. and N.W., 98 miles long.

2. Courses, itpper and Lower, divided by Falls.

U/>/>cr. ' LolVi'r.

Countnj Hilly, Pasto?al. Low, Cultivated.

Soil Unproductive. Fertile.

Productions ... Unimportant. Valuable.

3. Tributaries. Leven, Kelvin, Cart, Avon.

4. Productions, Industries, and Towns.
(a) Coal, iron ; mining, manufactures.
(li) Agriculture, oats, horses.

((■) Gla.sgow, Paisley, Lanark Greenock.

Language as an Inheritance. 303

THE TEACHING OF ENGLISH.

Language considered as an inheritance and as an
educational force.

Suppose we attempt to realise the condition of a child born
amongst a people who use, in ordinary speech, not more than
300 words. These words would represent the inheritance of
ideas to which such a child becomes an heir. If it advance
beyond these words such advance must be by the laborious
eflbrt by which new ideas are formed, and by which words are
coined to accompany them. At most, the learner could^not
progress very far beyond the point reached by its ancestors.
If now, we take the case of many an English peasant boy a
century ago, he was, for the most part, in the position of the
above child. He could not read ; and the only language within
reach was that spoken by the people amongst whom he dwelt.
To-day the case is very different. Scarcely a child is allowed
to grow up without being able to read ; he is brought into
daily contact with teachers and scholars who are constantly
using language over and beyond that of the home ; the child,
by his ability to read, has, furthermore, the stored-up knowledge
of the entire community within reach. Now, how does this
surrounding (environment) of words (language) affect the child ?
In reply to the above question it may be stated that the mere
existence of an extensive literature around and about the learner
cannot do much of itself. A vast multitude of words may be accu-
mulated ; they may be arranged alphabetically as in a dictionary ;
the child may be presented with such a list, but all this scarcely
aftects the learner. He remains ignorant amidst the outward signs of
an abundance of knowledge. Let, however, the scholar listen whilst
either his brothers and sisters, or his teachers and friends use these
words in conversation ; let him read books, and let him use the
language in speech — tell, for example, to others what he has learnt
and what he has read ; let him find that he is understood by others,
and he soon becomes encouraged to attempt the further employment
-of the language he possesses. In this way the use of language by

304 The Teaching of English.

others, as well as by himself, whilst it does not create knowledge,
does stimulate the scholar to gain it. He strives to understand what
he reads, and he likes to know what others are talking about. It is
this striving after understanding, this wish to know as much as others
appear by their language to kncnv, that constantly stimulates the child
to acquire further knowledge.

The following paragraph on ' Language as an intellectual
stimulus ' * briefly repeats the above truth in other words : —

' Children are brought up in the midst of others older than them-
selves and of fuller knowledge. They hear words used in the home
and in the school which, at first, they are unable, full}', to understand.
This language becomes a stimulating influence over the child, especially
when the language is not too difficult. The learner strives to reach
the level of knowledge indicated by the words used. The questions a
child sometimes ventures to put to its parents and teachers reveal the
struggle after knowledge which is working in the child's mind ; and
the attempt to use language, somewhat in advance of its own
knowledge, marks the child's ambition to reach the level of its
superiors. The fulness of the language used in the home and the
school has its effect upon the child's mind, stimulating it much in the
same way that the language of a nation stimulates to intellectual
eftbrt all who listen to, or who use it.'

Special courses devised to assist the acquisition
of English.

The various subjects which contribute towards instruction
in ' the mother tongue ' cover a wide area. Every lesson, so
far as it makes the learner acquainted with language, may be
taken into the account — the conversational and recitation
exercises of the infant school ; the reading lesson, and the
oral instruction in grammar, in elementary science, or in any
of the other class subjects in the schools for older children ;
in fact, nearly every lessorr may be made to contribute some-
thing. There are, however, special courses of lessons devised
for instruction in English. It is ])roposed to limit our enquiry,
in the following chapters, to the method of teaching the
following branches of the subject, viz. : —

i. The granniiatiral and logical relations of words and sentences —
embracing the classificatinn of words into 'Parts of Speech,' the
analysis of sentences, and the formation of grammatical rules and
defmitions.

T;ilicn from Cowham's Principles of Oral Teaching, p. 209.

Position of Grammar in our School Course. 305

ii. Parsing and the analysis of sentences, i.e., the application of the

rules and definitions formulated in the preceding branch,
ill. The right use of words and sentences, exemplified by means of oral
and written composition.

The whole course to be an exercise of the learner's thinking powers,
and to be a means of enlarging his vocabulary.

When dealing with these branches it will not be
necessary to keep them distinct. The first two make up the
subject of English grammar. They may be taught so as to
furnish very useful practice in the construction of sentences
and in the right use of words, and the whole study, whether
that of grammar or composition, may be made a means of
exercising the learner's thinking powers and of increasing his
vocabulary.

Position of Grammar in our school course.

The position of grammar during recent years has undergone
some changes. Previous to 1890, any school taking a class
subject was compelled to take grammar. This prior position
of grammar no longer exists. At present there are indications
that ' elementary science,' in the form of simple object lessons,
may take a prior position. It may be well to set out briefly the
nature of the exercise, and from this endeavour to fix the posi-
tion which the study of grammar should have in any school
course.

The nature of the exercise and its value.

The full discussion of these topics must be delayed until
we are in a position to review the entire subject. At present
the following preliminary statements must suffice.

{a) The kinds of exercise which the study affords.

1. Classifying words and sentences. This exercise depends upon the
discovery of points of agreement between the functions which different
words possess in oral or written language.

2. Defining terms {i.e., setting out a truth in concise form) and
applying the truth so formulated to new cases : After words have
been grouped into classes it becomes necessary to introduce terms to
distinguish one class from another. Thus for the names of things we
use the term ' noun,' and for that about which we speak in a sentence
we use the term • subject.' These general terms need to be defined.

3o6 The Teaching of Etiglish.

i.e., we need a concise statement setting forth the essential features of
the classes named. These definitions are afterwards applied to new
cases, as in parsing and in the analysis of sentences. All exercises in
defining and in applying definitions are intellectual efforts of an
advanced kind.

(/') The values of the exercise.

1. Intellectual. The efforts of defining and of applying these definitions
arouse the learner's thought. In future lessons it will be shown that
these efforts are essentially exercises of the reasoning powers.

2. Practical. The guidance which a knowledge of the rules of grammar
afford in the correct use of language ; the power to recognise and to
correct faulty expressions ; the confidence which the knowledge giv.es
in the use of language — these are amongst the chief practical values
of the subject.

3. For general culture. This value is variously estimated. It includes
the other two values, and goes beyond both. It embraces the value
which the subject, as the handmaid of literature, possesses. It covers
the civilizing influence which a wide acquaintanceship with the
thoughts of others provides. It will be readily seen, however, that it
depends almost entirely upon the nature of the study as to whether
or not this culture value can be maintained. If the study of grammar
result in ability to pick out parts of speech by means of rules which
are vaguely understood, and which, as a consequence, lead to a con-
siderable amount of more or less shrewd guessing, or, if the effort be
guided by rules of thumb, which are not understood, but which lead to
correct answers, then the study will not lend itself to the development
of culture. If, however, the study of grammar be so conducted that
it leads to a more correct use of the mother tongue ; if it increase the
store of words and give greater facility in their use ; if it result in a
thorough understanding of the rules by which the exact use of
language is guided ; and, above all, if the study develop a love for
those rich stores of literature which our language pro\idcs, then it
will become a means of culture of the highest order.

The study of grammar reserved for the upper
divisions.

From the above statements it will be seen that the study of
grammar is of less value for practical purposes than for intel-
lectual ends. The intellectual exercises, furthermore, are
somewhat advanced in their character. They do not belong
to those early forms of intellectual life which a little child loves
to exercise ; they belong to a more mature state, and require

Place for Lessons in Grammar. 307

ability, on the part of the learner, to form general truths, to
define and to reason. Upon these accounts, it is argued that,
whilst the study of grammar is of high value, and should find
a place somewhere in every school course, its proper place is
not in the lower, but in the upper divisions of the school.

Lessons in Grammar to follow a course in Elemen-
tary Science and Geography.

The following points may be urged in favour of arranging
a course of lessons in elementary science and geography for
Standards I., II., and III., to be followed by lessons in
grammar for Standards IV., V., and VI.

(<?) The minds of the children in the lower standards cannot profitably
be exercised in mastering the rules and definitions of grammar. The
children will learn the rules by heart readily enough, and they may
be able in some cases to apply them with a fair degree of accuracy ;
but they are not sufficiently advanced to acquire the truths of grammar
by the inductive method of teaching, and, in this way, to extract
from the effort all the advantages which the study, as an intellectual
exercise, is capable of yielding. It is therefore urged that, in lieu of
the formal grammar lesson, young children should be occupied with
subjects and lessons which exercise their observing powers and their
powers of imagination.
(_/') A fairly wide acquaintanceship with words and sentences forms
a necessary preparation for formal grammar. This acquaintanceship
may be made in a natural and interesting way by means of object
lessons, by lessons in geography, and by readings in elementary
science, geography, Sec. In order to make as complete a preparation
as possible for the formal study of grammar, it should be one of the
chief aims throughout all these lessons to exercise and guide the
power of oral statement on the part of the child.

Thus it may be shown that a double advantage arises from
a little delay in the study of grammar. There is thus secured
the necessary material for the study. By means of object
lessons, &:c., words become familiar, and facility in their use in
language is acquired. Whilst this increase in familiarity with
the materials with which grammar deals is going on, there is
the gradual development of the intelligence of the learner, so
that bv the time a sufficient knowledge of words and sentences
is gained, there is the advance of the learner's powers of classi-
fying, defining, and reasoning sufficient for the intelligent study
of the subject.

3o8 The Teaching of English.

In Herbert Spencer's Education we find the following : — ' It may
without hesitation be affirmed that Grammar is not the stepping stone,
but the finishing instrument. Grammar and Syntax are a collection
of laws and rules. Rules are gathered from practice ; they arc the
results of induction to which we come by long observation and
comparison of facts. It is, in fine, the science, the philosophy of
language. In following the process of nature, neither individuals nor
nations ever arrive at the science first. A language is spoken, and
poetry written, many years before either a grammar or prosody is
thought of. In short, as grammar was made after language, so ought
it to be taught after language.'

How children acquire the habit of correct
speech.

A child acquires its mother tongue mainly by imitation of
language spoken by others. Those immediately surrounding
the child — its parents, teachers, and playfellows — influence its
language most of all. Next in order of influence are the books
it reads. For the acquisition of correct speech we have only
to place a learner in continued contact with correct models of
speech. A scholar, on the one hand, brought up in a cultured
home will naturally speak pure and correct English. On the
other hand, a scholar may learn many of the rules of grammar,
but, if he be constantly in the midst of those who speak
incorrectly, he will copy the faulty examples, rather than
follow the book rules.

It is not wise to say that the rules ot grammar, when thoroughly
mastered, have no practical effect upon either written or spoken language.
In school work, however, we may expect the scholar to be most effectually
assisted by the reading lessons, by the recitation exercises, by oral
instruction (especially if he be frequently required to take active part in the
lesson), by answering and asking questions, by exercises in composition,
and by being called upon, at times, to correct errors in both written and
oral statements. When the scholar comes to the age of reflection, the
rules of grammar will afford guidance btith in using and in understanding
more or less involved statements.

\Vc have hitherto considered the condition of knowledge and of mind
pre])aratory to the effective study of grannnar, and now proceed to
determine (l) what branches of grammar should be taught, (2) the order
in which these branches should be taken, and, (3) the methods to be
adopted in teaching them.

Early Exercises in the formation of Sentences. 309

First lessons in Grammar.

There are several alternative courses of grammar suggested
in the schedules of the code. The first course begins witli the
classification of words ; the second with the simple analysis of
easy sentences, and the third with simple exercises in oral
statement. The two remaining courses are modifications and
adaptations of the preceding courses, and need not here be
separately considered. Of the three courses briefiy described
above, the last is the one which accords most completely with
the principles already laid down. This third and newest
course encourages the acquisition both of language and of the
power of complete statement during the pupil's stay in the
lower classes. The enlarged vocabulary of the Standard III.
scholar, together with his increased familiarity with, and facility
in, the use of words and sentences, provides a most serviceable
preparation for the work either of classifying words into their
different parts of speech, or of entering upon a course of
lessons in the analysis of sentences.

The rapid progress made by children when they reach the upper
classes is evidence of the soundness of the plan suggested above. By
the time they reach the end of Standard IV. they have as sound a
knowledge of grammar as those scholars who have spent the three pre-
vious years in the study. The scholars, taught on the new plan, escape
the deadening influence of attempting, in the earlier standards, to learn
what, from the nature of the exercise, it is impossible for them to
understand, and, furthermore, they experience the relish and pleasure
which accompanies an exercise which is suited both to their age and
attainments.

Early exercises in the formation of sentences (oral
composition).

Children readily talk about anything in which they become
interested. Any object they examine, any event they witness,
and any incident they experience, may be readily made
a topic of conversation. If we wish children to practise
oral statement, we must first give them, by some or by
all these means, something about which they shall wish to talk.
The exercises of completing partial statements, and of correcting
faulty utterances, may be of some value when used as tests
after a regular and systematic course of instruction in
composition ; but, when introduced for the purposes of arousing

310 T//e Teaching of English.

and extending the power of oral expression, these exercises are
more depressing than stimulating. The same criticism applies
to the practice of writing on the black-board a long and
miscellaneous list of names, and of requiring each scholar to
state something about each. By what means, then, may we
best supply our young scholars with suitable topics of
conversation ?

In order to answer the above question, we fall back upon suggestions
already made. The earliest lessons in geography deal with the
features surrounding the home and school. The village brook, the
neighbouring hill, the shady dale, the path to school — its length, and
how long it takes to walk along it ; all these, beside many more which
a little thought will suggest, are topics which both children and teacher
know full well. A start need only be made, and the children will
readily enough hasten to express themselves. Again, during an object
lesson, no one ever fails to obtain statements from all parts of the
class whenever a specimen or a picture is exhibited. The scholars
know something about the object, and are immediately ready to
tell what they know, or to ask for information where it is wanting.
This last form of statement, viz., that of enquiry, should receive
especial attention and commendation, so long as it is prompted by an
evident desire to gain knowledge. After the completion of a
conversational lesson upon a more or less familiar object, or upon some
feature of home geography, if a few of the things passed under review
be named by the teacher, the scholars might be required to make a
statement in turn about each, or, all the class might be asked to write
down a .similar statement.

Lessons of information and statement ought to be
made mutually helpful.

The attempt to provide a series of exercises in sentence
forming for use in all schools is almost sure to be made. Such
a series of exercises may have very little, if any, connection
with the other lessons in the school. So far as the required
sentences are upon topics foreign to the school work, the
exercise will prove of little value. We strongly advise that the
course of instruction in sentence forming be associated as
closely as possible with other lessons, /.c, with the lessons in
geography, with the object lessons, and with the reading lessons.
Let these lessons not only determine the topics about which the
children's statements are made, but also the time when the
language lessons take place. Tliey should follow immediately

Sentence Forming in Grammatical Exercises. 311

after the knowledge lesson with which they are connected.
Whilst the knowledge is fresh and full, and before it has time
to lose its attractive form, scholars should be allowed to clothe
their ideas in language. This will give language a greater
reality, and serve, at the same time, to fix the knowledge more
perfectly.

Sentence forming in the more advanced grammatical
exercises.

The more advanced lessons, whichever scheme of instruction
is selected, may be made to yield abundant exercise in the art
of sentence forming. The teacher should have this constantly
in view in the preparation of his illustrative examples. The
sentence will take more time to prepare than the single word,
and will occupy more time in presentation, but the benefit to
be derived from their introduction will amply repay the extra
efibrt. The value of requiring children to express themselves
in complete sentences is enforced by H.M. Chief Inspector of
Training Colleges, H. E. Oakeley, Esq., in his annual report
just issued. He says : —

'A full answer — (i) promotes exactness of language ; each answer is an
exercise in grammar, placing the words clearly and in right order.
(2) Makes the boy think about what he states, and he will remember it
better. (3) Informs the other bo)-s also, especially those who cannot
answer the question, and do not guess the right answer by hearing one
word jerked out and (4) is nearly alwa3's accompanied b)- good discip-
line.'

Whilst conducting a grammar lesson the teacher will find
that the first step towards understanding a new stage in the
lesson on the scholar's part, will be his ability to embody the
new grammatical notion in an original sentence. It may be
furthermore urged as a reason for insisting upon the use of
sentences in teaching grammar, that there are some of the most
difficult portions of the study which cannot be taught without
reference to the sentence. For example, the case of the noun,
words like 'before' and ' that' which may be different parts ot
speech in different sentences, the distinction between the
transitive and intransitive verb, and the change from the active
to the passive voice.

If we watch a class when lirst called upon to frame original sentences,
it will soon become evident how little originality children at first appear

312 The Teaching of English.

to possess. They will repeat almost word for word the teacher's model
example, and only the most' intelligent children will attempt an entirely
new sentence. By practice in sentence forming, however, the power
which at first appeared to belong only to the exceptionally bright scholar
will become the possession of all. For purposes of a test, children may
write a series of sentences in application of any grammatical notion they
have recently acquired. For example, after a lesson on the active and
passive voices of verbs, a suitable exercise would be that of framing
sentences in which the same verb is used, first in the active voice and
secondly in the passive voice. Similar exercises in which the grammatical
knowledge may be tested, and the power to frame sentences developed
may be continued throughout the entire course of instruction.

HOW TO TEACH THE 'PARTS OF SPEECH.'

Introductory.

All the alternative courses of teaching arrive at a common
end, viz., the ability of the pupil to point out the ' parts of speech.'
They differ in the methods by which this end is to be attained.
One course, for example, requires Standard I. to be able to
point out nouns. Standard II. to point out nouns and verbs,
and Standard III. to point out all the parts of speech. The
course finishes with the analysis of sentences. This is the
usual text-book order of presentation, and only in recent years
has there been any departure from it. A second course
proceeds by the analysis of sentences, and introduces parsing
first in Standard V. A third course begins the study of
grammar by requiring Standards I. and II. to use language
in answering questions and in oral composition, and leaves the
exercise of parsing to be commenced in Standard III.

We have already indicated the course of instruction which appears to
be most rational for little children. We think, before cither parsing of
words or analysis of sentences is attempted, that exercises in the correct
use of language should be given, and familiarity with language through
reading should be gained. Of the two remaining courses, the one which
begins with the analysis of sentences is the more rational. It must not
be thought that little children cannot be taught to point out nouns,
adjectives and verbs. They can readily enough be taught to point out
some nouns, &c. If asked, for example, to underline the nouns in the
sentence ' the man gave a book to the boy,' even young children would
have scarcely any difficulty in pointing them out ; but they would find

Pointhig Old Nouns and Verbs. 3x3

difficulty in dealing with (.he verbs and nouns in a sentence like the
following, ' The good art loved, but the cruel are not. ' Assuming, then,
that there has been sufiicient preparation in language in the lower classes,
we can proceed t'^ examine the methods of teaching by grammatical
parsing and anal3'sis respectively.

Pointing out nouns and verbs.

Before arranging a course of lessons to enable children
successfully to point out nouns and verbs, it will be well to
settle the question whether it will be better to use words
or sentences in the illustrative examples. Will it be better,
Ihat is, to begin with an enumeration of the names of a number
of familiar objects and call these nouns, or to begin with simple
sentences containing a noun and a verb and allow the scholars
to distinguish the noun from the verb in each of the selected
sentences. The answers to these questions need not cause
much difficulty :—

A contrast is always a valuable aid in teaching, and, whenever wc can
arrange examples so that their points of likeness and unlikeness are
recognised, there is much more thought aroused than is possible when
isolated cases are observed. For example, I may take such words as boys,
girls, horses, men, sitn, school, &^c., and lead the class to see that they are
the names of things. The term ' noun ' may now be supplied and its
definition formulated. If, however, instead of taking nouns alone I make
a series of sentences like the following : —

Names of things.

What they do.

Names of things.

What they do

Boys

write

Men

\\-ork

Girls

skip

The Sun

ihines

Horses

gallop

The School

flourishes

and, with the co-operation of the class, distinguish between the words in
each sentence, viz., (a) the words which denote things, and {/>) those which
set out what the thing in each case does, I shall have taught that the words
boys, girls, &.C., are name of things, hence ' nouns ' as before ; but, at the
same time, I shall have taught that there are other words, very different from
the nouns, viz., words which set out what the things named by the nouns
do. I shall have taught, furthermore, that in a sentence the noun is some-
thing more than the name of a thing ; it is the name of the thing which
does something. This method of teaching nouns, by means of sentences
secures the following knowledge, viz. :- -

1. That a noun is the name of a thing.

2. That in a sentence the noun may be the name of the thing-
about which a statement is made.

2 14 '^^^'^ Teaching of English.

3. That there are other words in a sentence very different from
nouns in their uses. That these words which tell us what the
things indicated by the noun do are called Verbs.

Thus, three things are learned in place of one, and each is learned more
thoroughly than it could be if taken alone. Furthermore, there is
provided much greater opportunity for thought {i.e., of comparing and
contrasting) by means of such lessons as the above than could be presented
by taking either the noun or the verb alone.

Lessons on the adjective and adverb.

Lessons on the adjective and adverb should proceed exactly
on the hnes of previous teaching. Instead of presenting long
columns of nouns for the children to affix to each approjiriate
adjective or lists of verbs for them to write suitable adveibs
near them, let the class begin with enlarging the examples u-ed
in the previous lessons,* e.g.: — •

Introducing the adjective.

1. The little boy writes.

2. The healthy girl skips.

3. Young horses gallop.

Introducing the adverb.
Men work hard.
Brightly the sun shines.
The school flourishes w^ell.

(Care must be exercised in selecting illustrative examples, and in
arranging them, that children do not make false rules (inductions). For
instance, the above examples introducing the adjective might lead the class to
the following notion, viz., that an adjective is a word placed before a noun.
This danger is avoided in the examples introducing the adverb. The 7ts£
of the adverb in the sentence, not its position nor its form, is the notion
which the illustrative examples should establish.)

The second step in teaching is to allow the class to make similar examples.
When the class is abL-, readily, to supply examples of sentences introducing
the adjective and adverb, the scholars may be considered to have a
sufficient knowledge of both to be ready for the terms 'adjective' and
'adverb.' Finally, the class should attempt to formulate the definition of
each term.

* It is ;i sound rule in leacliing, applicable as trul)- in the grammar lesson as in the
arithmetic lessen, vi/., that the examples in loduced for purposes of establisliing a
truth lie simple. No thought, or at most very little thought should be demanded in the
effort to underst.Tnd the examples. All, or very ne.-irly all the thought of the h arncr
should he avail.il U- for, and concentrated in the effort o!" seizing and understanding the
truth illusliated.

Divisions of each part of Speech. 315

The method of teaching by contrast and compari-
son may be continued until all the parts of speech have been
taught. The following are subjects which admit of this mode
of treatment : —

Parts of speech (simple notions only),
i. The noun contrasted with the verb.
ii. The adjective ,, ,, adverb,

iii. The pronoun ,, ,, noun,

iv. The preposition ,, ,, conjunction.

The success, or otherwise, of the above methods of teaching,
depends largely upon the age and intelligence of the class.
We began the discussion of the teaching of grammar with the
general condition that, for the grammar lesson to yield the
highest value, it must exercise the learner's powers of classifica-
tion as well as his ability to form general notions, and to define
general terms. Very young children must not be expected
to do this ; but, with scholars of Standard III. and upwards,
i.e., with those whose powers of comparison and classification
(thought) have been fairly developed, a series of grammar
lessons, arranged on the above plan, will prove attractive to the
learner, and, at the same time, will serve to exercise and
develop his mental powers.

Divisions of each part of speech.— Inflexions.

From the recognition of the parts of speech, the pupil may
be conducted to the distinctions existing between different
forms of particular parts of speech. The method of teaching
by comparison and contrast may be continued throughout the
various inflexions which most of the parts of speech exhibit.
It will not be necessary to illustrate the method of teaching by
more than one example. The following sketch will suggest the
mode of determining the different kinds of adjectives: —

After many adjectives have been recognized, and a considerable facility
in pointing them out from amidst other parts of speech has been
developed, exercises may be set in finding distinctions between the different
kinds of adjectives. The process now becomes one of contrast. Many
words have been brought into a class and called adjectives, on the ground
that they all possessed the common features of qualifying or distinguishing
nouns. The process of division now begins, and this process depends
almost entirely upon the ability the scholars already possess (or else the

31 6 The Teaching of English.

ability they acquire through the teacher's guidance) of recognising the
following differences amongst adjectives. For example : —

i. Some adjectives are used to indicate ' number ' (quantity) as, e.g.,
the word twenty in the sentence 'there were twenty men present.'

ii. Some adjectives, on the other hand, are used to point out a
' quality ' as, e.g. , the word industrious in the sentence ' the
industrious man shall not want.'

iii. Others, again, simply point out, or distinguish as, e.g., the words
this and that in the sentence ' this work is well done, but that
is not.'

The following are the ' notes ' of one stage in a lesson
designed to bring out the distinction between adjectives of
' quantity ' and ' quality,' The examples throughout are selected
with a view to show the contrast between the two kinds of
adjectives. The scholars should be encouraged to find other
examples similarly contrasted.

Kinds of Adjectives taught by contrast.

Examples of adjectives indicating Examples of adjectives indicating
quantity. quality.

1. Many children came to see i. The obedient children were
the balloon. allowed to see the balloon.

2. There were forty sheep in the 2. The healthy sheep were in
fold. the fold.

3. All the boys were early to-day. 3. Successful boys are generally
Truth taught. — Some adjectives "^ tune.

are used to indicate quantity. Truth taught. — Other adjectives
These adjectives are termed are used to indicate quality, and
'adjectives of quantity.' are termed 'adjectives of quality.'

If the processes of thought exercised by the scholars in the
above teaching be examined, there will be found to be two
efforts quite distinct from one another, viz., the recognition of
contrasts and of agreement. The examination of the statements
on the right and left side respectively proceeds by way of
contrast, the differences between the uses of each couple of
adjectives (marked i, 2, antl 3) are first noticed. Afterwords,
the three adjectives on the left are compared, and, as a result,
they are seen to agree so far, at least, that they all indicate
'quantity.' Hence tlie notion of a separate class of adjectives

The Inductive Method of Teaching Grammar. 317

possessing the common feature of ' quantity ' is recognised :
and the recognition becomes much more distinct on account of
this class having been first contrasted with the second class,
viz., the adjectives of * quality.'

The above method is that by which every child gains possession o^ the
notions of adjectives of quantity distinct from those of quality. There must,
first of all, be the power to see differences between the uses of members of
the adjective group. Until this difference of use is recognised no progress
can be made toward the division of the great class of adjectives into smaller
classes. Whilst teaching, therefore, we do best for the child (and render
our own work more easy and direct) when we select the method which is
natural, and which the child must finally take. We adopt the natural
method when we proceed, first, by contrast to recog'nise differences,
and then group together the smaller class by identifying similarities
(comparision). Afterwards, we collect together, in our minds, the
agreeing features of the smaller group ; then we give these features
a term ; and finally we define the term.

The following inflexions of the different parts of speech
are examples of lessons which may be taught by the contrast
and comparison method, viz. : —

I. Nouns. j 3. Verbs.

(rt) Proper and common. j . .^ j Weak and strong.

{d) Concrete and abstract. j ^"' \ Regular and irregular.

. , P r I general. j i^>) Transitive and intransitive.

^''^ \ 2 collective. (c) Imperative and indicative.

2. Adjectiues.
(a) Quantity and quality.
(i) Ordinal and numeral.
((") Quantity and distinction.

(if) Indicative and infinitive,
(f) Active and passive.
&c., &c.

The inductive method of teaching grammar.

If the lessons already sketched be examined, it will be
observed, in every case, that the method of teaching
proceeds from examples to truths and definitions. In no
instance is the definition supplied first, as is generally the case
in the text-books. The method of teaching which commences
with the supply of a number of examples (selected by the
teacher so that each example embodies the new grammatical
idea) ; which then provides the scholars with sufficient guidance
to enable them to discover the new grammatical notion ; which,

31 8 The Teaching of English.

furthermore, encourages the class to embody the discovered
truth in examples formulated by themselves ; and which
succeeds in obtaining a statement of the grammatical truth
which the examples illustrate in the scholars' own words ; and,
finally, which supplies a new term to the new notion, and
requires the class to formulate its definition ; — this method, taken
in its successive stages, from the supply of examples to the
formulation of the truth and the definition of the new term, is
an example of Inductive Teaching.

The high position which grammar holds in the curriculum of our schools
can be justified mainly on the ground of its value as an intellectual exercise.
Recognising this, it should become our aim (as it is our scholars' interest)
to teach the subject so that the best intellectual results accompany the effort.
These intellectual accompaniments are best secured by the teacher preparing
and giving his lessons on the truths and definitions of grammar on the
inductive method.

Preparation necessary for inductive lessons in
grammar.

The inductive treatment of any subject of school study becomes possible
after an acquaintance has been gained with a considerable number of the
acts and cases included in the subject. In science teaching, for example,
a child is not expected to classify and arrange the facts and phenomena
ot any branch of study before he has become acquainted with a consider-
able number of them. This the learner does by means of his own experience,
by object lessons, and by simple experiments. The series of object lessons
in the infant school, and in Standards I. — IV., is intended to provide the
pupil with a considerable store of observed and exact first-hand knowledge.
In the higher standards, and in later years, the pupil will be properly
occupied in organising these stores of observed knowledge. He may, in
these standards, with advantage be required to classify facts, to establish
truths, and to define terms. It is thus seen that the higher exercises of
induction in the case of elementary science naturally follow the accumula-
tions of observed knowledge. In the same way we should treat the subject
of grammar. A considerable facility should first be gained in the meaning
and exact use of words and sentences. These, in reality, form the facts
which the formal study of grammar seeks to organise.

' Language first, then grammar,' is a maxim as true of the history ot
grammar as it is sound in the teaching of it.

In this way it may be made evident that we are working on
scientifically established methods, when we prepare our pupils
for the formal and inductive study of grammar by a thorough
grounding in the use of language both oral and written.

Parsing. 319

Words and sentences, not things, form the materials
lor lessons in grammar.

Considering the early age at which some have attempted the
study of grammar, it is not perhaps a matter for wonder that
children should have some difficulty in discriminating between
the thing and its name. What is a noun ? Ans. The name of
anything, as, e.g., chalk, air, John, etc. Again, An adjective
qualifies a noun, as in the example, "^ dL fine day.' Here the
word fine qualifies day. Lastly, The preposition is a word used
to join two nouns or pronouns together; as, 'The fire in the
stove is warm and bright.' The preposition ' in ''Joins fire to
stove. In each of the above cases, there is an indication that
the person making the statement is in danger of confusing
words with things.

All evidences of this kind of confusion in the minds of children should at
once be challenged. The chief difficulty rests in the detection of the
confusion. All our teaching methods should recognise the danger, and
should avoid it as far as possible. The grammar lesson should always be
made an exercise in full and exact statement, both on the part of the
teacher and learner. ' Did you say " Chalk is a noun." This is a piece
of chalk. You see at once that chalk is an earth and not a noun. Try to
correct what you said before.' 'You said just now that ///f liwn/ in yW/zi
fire to stove.'' Think again. 'You know that fne remains in the stove
because of the bars in front ; the preposition ' in ' does not keep the two
together ; what does it connect ? ' By these, and similar methods, the
dangers indicated above may be avoided.

PARSING.

A means of exercising and of testing previous
knowledge.

Unless the principles and definitions of grammar have been
thoroughly mastered, the parsing lesson will be constantly
beset with difficulties. Parsing should not be regarded
as a means of teaching ; it is essentially a method of
' testing, of revising, and of applying the knowledge already
acquired. It serves to discover where the previous teaching
has been faulty, and, also, to strengthen what is weak ; but,
above all, it gives facility in the use of the grammatical
knowledge already acquired.

>20 The Tearhing of English.

There is perhaps no school exercise in which we need to be mure
on our guard against the propensity of guessing at answers which
scholars manifest than in the parsing lesson ; and if we introduce the
exercise at too early a period, i.e., before the rules and definitions of
grammar have been fairly well mastered, we shall run considerable
risk of strengthening this habit.

How to conduct a parsing lesson.

Choose a passage mainly with a view to exercise the knowledge
previously taught.

We shall disappoint ourselves and discourage the class if we select a
passage for parsing which presents a number of difficulties for which the
previous teaching has not prepared the children. At the same time the
piece chosen should not be so easy as not to awaken effort. It should
make clear demands upon the scholar's power of applying the grammatical
truths already taught. If the class has been taught, e.g., the meaning of
the objective case of nouns and [irono'ins, it would be quite fair to introduce
a passage of prose or poetry in which the objective case occurs before the
verb. Similarly, after the nominative case has been explained an example
in which that case occurs afier as well as before the noun might very
properly be selected.

2. If the passage be a stanza of poetry, arrange it in prose order

before beginning to parse, e.g.,

' Nor board, nor garner own we now '
should be changed to : —

' We own neither board, nor garner, now.'

3. // the class understand the analysis of sentences, they should

distinguish the different parts of the sentence before attempting

to parse it.
It has already been pointed out that some of the most difficult features
in parsing become easy when the scholar has taken grammatical analysis.
For example, the cases of nouns, the verb, whether transitive or intransitive,
etc. If the scholars have not taken * analysis ' it will be necessary
to resolve an involved construction into a series of direct statements, and
to parse the more essential parts of the sentence, before proceeding to its
adjuncts and qualifying clauses. Take, for example, the following

passage : —

' Thus sung they in the English boat

A holy and a cheerful note,

And all the way, to guide their chime.

With falling oars they kept the time.'

Emigrant song, A. Man'ell.

Questions and Answers. 321

The structure ot the above passage should be simplified as follows : —
' Thus, in the English boat, they sang a holy and a cheerful note ; and
all the way they kept the time, with falling oars, to guide their chime,
' The proud— the wayward— who have fixed below
Their joy, and find this earth enough for woe,
Lose in that one their all— perchance a mite.' — Byron.
The above passage should be resolved into the following sentences before
any attempt is made to parse it : —

1. The proud lose their all in that one loss— perchance (it was) a mite.

2. (The proud) who have fixed their joy below.

3. And (the proud who) find this earth enough for woe.

4. Constant appeals should be made to the truths and definitions which
the scholars apply.
This is necessary, because many words either carry with them n their

construction, or acquire by their position in the sentence evidences of the

mode in which they should be parsed.

The frequent occurrence of the ending ' ly ' in the adverb, the nomi-
native case before the verb, the objective case after the verb, the
adjective before the noun, and even the size of the word — long words
being nouns and short words prepositions ; these are some of the
superficial conditions which a lazy scholar will seize and use in place of
the deeper truths of grammar which he should know and apply. Why
is the word ' well ' an adverb in the sentence ' he writes 7ve// ? ' Why
is that noun in the nominative case ? Which is the preposition and
which the conjunction in the passage just read ? Why is one word a
preposition, and the other a conjunction ?— the above are types of
questions which occur in every good parsing lesson. They form, in
fact, the life of the lesson. Without such questions the lesson moves
drearily along ; with them, not only is the matter of previous lessons
brought under review, but a special form of intellectual activity, namely,
that of applying knowledge previously acquired, is exercised.

^Questions and answers, and deductive teaching.

Questions and answers form so important a feature in a suc-
cessful parsing lesson that a little more attention may be given
to them. The questions quoted above require the scholar to
recall the definition or the rule in grammar upon which the
answer depends. The exercise of selecting and of recalling a
general rule, and of applying it to any particular case in the
paising lesson is an example of deductive teaching.

The loose use of the word ' deduce ' is a common fault, especially in
♦Notes of Lessons.' The above statement will help in the correct

32 2 The Teaching of English.

use of the term. Whenever a class recalls a general truth or
definition, and then proceeds, further, to apply either truth or definition
to a particular case, the effort is a deductive one. To talk about
'deducing a rule or truth from particular examples ' is absurd.

\l\le are now in a position to estimate the intellectual
value of the parsing lesson. We see, in the first place, that
success depends upon the possession of a considerable stock of
grammatical truths and definitions. Every step in the parsing
lesson demands the recall of one or more of these truths. This
recall is clearly an efl'ort of memory. But the exercise of
memory alone is not all we require. The special truth or truths
to be applied must be selected from the entire store, and this
effort of selection, and the further, but accompanying effort of
applying it to the particular case, is an exercise of our highest
intellectual powers, viz., those of reasoning.

Necessity for the careful preparation of the Parsing
Lesson.

A parsing lesson presents an excellent means of exercising
the teacher's powers of resource. Full knowledge will be needed
to explain all the difficulties which the scholars will meet with
during the progress of the lesson. It is true that points of
special difficulty may be anticipated, and a stock of illustrations
may be obtained and be held ready to solve them. When all
has been done, however, to meet the emergencies that may
fairly be expected to present themselves, there will still arise,
in almost every parsing lesson, doubtful points revealed by the
answers of the children. The difficulties thus sprung upon the
teacher during the progress of the lesson will call forth his best
efforts. A full and careful preparation on his part will provide
the best conditions for successfully overcoming the difficulties
of the moment, and will inspire him with the confidence
necessary for success.

GRAMMAR BY THE ANALYSIS OF
SEN TEN CES.

Introductory.

Amongst the ' alternative courses ' for teaching grammar, a
scheme is formulated for instruction through the analysis of
sentences. The ' instructions ' appended to the code give the
following statement explanatory of the introduction of the

Grammatical Parsing and Analysis. 323

different schemes. ' My lords believe that greater variety might
with advantage be secured in the class instruction. For example,
in one school the teacher of English attaches more importance
to the analysis of sentences as an intellectual exercise than to
grammatical parsing ; in another, oral and written composition
and the correction of common errors in the formation of
sentences are believed to be the most useful forms of exercise
in English.?'

Grammatical parsing and analysis are closely
related.

If reference be made to the chapters upon the methods of
teaching the ' parts of speech,' it will be seen that each ' part '
is taught by the examination of a series of sentences. It is the
use of the word in the sentence which determines its place
amongst the parts of speech. The difference between parsing
and analysis is mainly one of terms, as may be shown in the
following examples. When teaching the noun and verb, a
simple sentence may be introduced such as 'the boy writes.'
This expression is examined by the teacher and class. It is
found to consist of two distinct elements, viz., {a) the name
of the thing about which a statement is made, and {b) what we
say about the thing previously named. If, now, we wish our
pupils to proceed by grammatical parsing we call {a) a noun
and (U) a verb, but if we wish to teach by analysis, we call
(a) the subject of the sentence, and {b) the predicate.

Again, when we proceed to extend our teaching of the parts
of speech to the adjective and adverb, we do this by introduc-
ing a series of sentences like the following, viz. : Clever boys
write well. If the method of grammatical parsing be followed,
we term the word ' clever ' an adjective, and the word ' well ' an
adverb ; but, if analysis be preferred, we term the word ' clever '
an enlargement 0/ the subject, and the word ' well ' an extension
of the predicate.

Additional reasons for the early study of logical
analysis.

It has been shown that in order to obtain simple notions of
the noun, verb, adjective, and adverb, the entire sentence may
be used with advantage for the purposes of illustration. In

324 The Teaching of English.

this connection it may be repeated that some of the more
difficult notions in parsing can only be made plain through the
analysis of sentences. Such difficult matters as the cases of
nouns, the uses of the preposition and the conjunction, the
different kinds of conjunctions, and the distinction between
transitive and intransitive verbs, may be best approached,
for the purposes of explanation, through the analysis of
sentences.

It is absurd, says Mr. D. F. Fearon, formerly one of H.M. Inspectors
of Schools, to waste time over learning the cases of nouns which have
lost all their case endings, and have substituted for those case endings
structural position or logical relation in the sentence. The proper way
to teach English grammar is not to begin, as in the case of Latin or of
any other highly inflected language, with the study of the noun,
adjective, and verb, and their inflexions, but to begin with the study of
their logical relations ; or, in other words, to begin with the analysis
of sentences.'

Dr. Fitch, in his ' Lectures on Teaching,' states that ' long before
a child comes to the commencement of such a book (that is a manual
of English grammar arranged under the four chapters of orthography,
etymology, syntax and prosody), he has learned to speak and to use
his native tongue. He knows the meaning of sentences, and he thinks
by means of the language. That which in teaching French is the
ultimate goal of your ambition — conversation and freedom in using
words — is the very point of departure in the case of your own verna-
cular speech. Your pupil has already attained it. Hence the methods
of teaching a native and a foreign language are fundamentally different.
The slow, synthetical process appropriate in the one case of beginning
with words — in the case of German and Greek, even with the alphabet
— and building up at first short sentences, then longer sentences, is
wholly illogical and absurd in the case of the other. To a child a
sentence is easier than a word ; the cognition of a word is easier than
that of a syllable as a separate entity ; and the syllable itself is some-
thing easier than the power or significance of a single letter. And
hence the way to teach English grammar is to begin with the sentence,
because that is something known, and to proceed analytically. If
other languages are to be learned by synthesis, our own should be
learned by the opposite process of analysis ; and whereas we learn a
foreign language through and by means of its grammar, we must
learn and discover English grammar through and by means of the
la nguage.

The Method of Contrast.

325

Outline of a scheme for combining analysis of
sentences with grammatical parsing.

In the alternative courses of the code the exercises in logical
analysis of sentences are made gradually to merge into gram-
matical parsing. The following is the outline of a method of
teaching by which the two operations may be combined.
The scheme is suggestive only, and, in practice, should be
considerably extended.

Stages in analysis of sentences.

(rt) Subject and predicate of simple
sentences, introducing only in-
transitive verbs into the predi-
cate.

(d) Subject and predicate, and the
enlargement of subject and ex-
tension of predicate by single
words.

(d) Compound and complex sen-
tences

Corresponding stages in gram-
matical parsing.
(a) Nouns, pronouns, and verbs
(simple, not compound).

(d) Nouns, pronouns, verbs, adjec-
tives and adverbs.

(r) Inflexions of nouns, pronouns
and verbs ; adjectives, adverbs,
and prepositions.

(d) Different kinds of conjunctions ;
the relative pronoun and the
relative adverb.

The method of contrast and comparison may be

adopted in teaching analysis. Very frequently, it will be found,
that two contrasted topics, when taken together, are taught
in the time that it would require to teach one of them taken
separately, and (what is of more importance) each of the two
contrasted topics becomes, by this method, more thoroughly
taught. The following ten lessons in analysis of senterices are
arranged for teaching by the method of contrast.

1. Subject and predicate.

2. Enlargement of subject and

extension of predicate.

3. Phrases and sentences.

4. Words and phrase enlargements.

5. Words and phrase extensions.

6. Noun sentence and adjective
sentence.

10.

Adj. and adverbial sentences.
Simple and compound sen-
tences.

Principal and subordinate sen-
tences.

Compound and complex sen-
tences.

326

The Teaching of English.

The inductiue method of teaching analysis.

Th« inductive method of teaching may be applied to the analysis of
sentences in exactly the same manner as that indicated for teaching the
parts of speech. Truths and definitions should be established by an
investigation of examples. No definition should be applied until its
meaning has been made quite clear through the medium of examples.
During first lessons, examples should be carefully prepared by the
teacher, so as to illustrate the special truth to be learned. As power
to use the truths learned is developed, the scholars should be practised
in the analysis of simple selections of reading matter. Oral and written
lessons in analysis (see p. 328) form a deductive exercise, and should
be carried out on the same lines as those suggested for parsing.

-NOTES OF A LESSON

ON THE

COMPLEX SENTENCE.

A. First contrast.

Examples I. Principal Sentences.

(i.) I sat on a green bank
(2.) The seas are quiet

(3.) They went home

(4.) I questioned the man

Examples II. Subordinate Sentences.

(i.) When the sun was down.
(2.) Which are not disturbed by

the winds.
(3.) That they might do some

work.
(4.) Why he had acted in this

manner.
Method of using the examples.

Show by contrast the difference between Examples I. and II., viz.,
that Examples I. can be used independently, whereas Examples II. must
be used with another sentence. Give the name Principal Sentence to
those which can be used independently.

Truth taught.

A Principal Sentence is one which can be used independently.

B. Second contrast.

Examples III, Principal Sentences.

(l.) I sat on a green bank | and

I listened.
(2.) lie came a friend | but went

a foe.
(3.) The farmer sows seed in

spring I and he renps a

harvest in autumn.
(4.) I asked him a question | but

he did not answer me

Examples ! V. Complex Sentences.

(i.) I sat on a green bank | that

I might rest.
(2.) He went a foe | who came a

friend.
(3.) The farmer sows seed in

spring I which is to produce

a harvest in autumn.
(4. ) I asked him | why he did not

answer me [ when I spoke.

Metliod of Arranging Results on Paper. 327

Method of using the examples.

Point out that each sentence in both sets of examples is composed of two
parts. From Examples I. and II. the scholars will readily see and ^tate
that each of the two parts of Example III is a principal sentence.
Draw their attention to Example IV. and note that these differ from
Example III. This difference must be examined. The class will see
that the first portion of each sentence in Examples III. and IV. are
exactly alike. The difference, then, is in the latter portion. Read each
of these latter portions by themselves and ask what they need to complete
the sense. The idea of dependence will be recognised. When this is
done, the class will see that each sentence is composed of a principal
sentence and a sentence which is dependent on it. Give the name com-
plex sentence to the whole sentence and the name subordinate sentence
to that which is dependent. Expect the scholars to state the following
truths.

Truths taught.

A Complex Sentence is a sentence which is composed of a
Principal Sentence, and one or more sentences depending upon it.
A Subordinate Sentence is one which depends upon a Principal
Sentence.

C. Class exercise.

Allow the scholars to divide the following complex sentences, stating
which are Principal and which are Subordinate sentences : —
' It is true | that the comma is the weakest of all our stops ; | but there
are many pauses | which we ought to make in reading a sentence aloud"
that are not strong enough to warrant a stop.'

BLACK-BOARD ABSTRACT.
Examples I. Examples II.

Truth i. — A Principal Sentence is, &c.
Examples III. Examples IV.

Truth 2. — A Complex Sentence is, &c.

Truth 3.— A Subordinate Sentence is, &c.

Method of arranging analysis results on paper.

Selection of Poetry for Analysis.

There, at the foot of yonder nodding beech,
That wreathes its old fantastic roots so high.

His listless length, at noon-tide, would he stretch.
And pore upon the brook that babbles by.

328

The Teaching of English.

(a) The Tabular Method.

Sentence.

Kind.

Subject.

Enlrgt.

Predicate.

Object.

Extension.

His listless length at

noontide would he

stretch, there, at the

foot of yonder nodding

beech,

Princ.
Sent.

would
stretch

his listless
length

at noon- tide
(time)
There at...
...beech

(■place)

That wreathes its old
fantastic roots so high,

Subord.

Sent.

.Adj. to

that

wreathes

its old

fantastic

roots

so high

(place)

And pore upon the
brook

Princ.

Sent.
Co-ord.
with A.

(and)
(He)

(would)
pore

upon the
brook

That babbles by.

Subord.

-Sent.

Adj. to

that

babbles

(place)

A.
Principal
Sentence.

Subordinate

Sentence

Adj. to A.

Principal

Sentence

Co-ord. with

Subordinate

Sentence

Adj. to C.

lO.

II.

12.

13-

(/') Detailed Continuous Analysis.

He Subject to 2.

would stretch Predicate to i.

His listless length Object of 2.

at noontide Extension (time) of 2.

There beech Extension (place) of 2.

6. That Subject to 7 and connective

between A and B.

7. wreathes Predicate to 6.

8. its old fantastic

roots Object of 7.

Q. so high Extension (manner) of 7.

and Connective between A and C.

(He) .Subject understood to 12.

(Would) pore Predicate to 11.

upon the brook Extension to 12.

14. that Subject to 15 and connective

between C and D.

15. babbles Predicate to 14.

16. by Extension of place to 15.

The tabular statement is the easier method of the two, and it
relieves the learner from the necessity of subsequently repeating
the words subject, predicate, &c. The detailed continuous

Composition. 329

analysis requires more thought, and allows a more logical
display of the parts of each sentence and of the relation between
the successive sentences. Young beginners might be allowed
to adopt the tabular form, and, as power is developed, they
might be encouraged to adopt the detailed and continuous
form.

COMPOSITION.
Introductory.

\X The greater number of school subjects supply information.
The object lesson, for example, makes the learner acquainted
with the appearance and properties of thmgs around him ; the
readmg lesson brings within his reach some of the rich stores
of knowledge accumulated by the experience and research of
others ; the arithmetic lesson makes him acquainted with
numbers together with a multitude of combinations into which
various numbers may be arranged ; the geography lesson
supplies information about his own and other lands ; history
affords glimpses into the conditions of the past, and recalls
them for the guidance of action in the present ; and grammar
sets forth the laws which regulate the correct use of the
learner's mother tongue. It may thus be shown that most of
the subjects entered on the school time-table yield information
of a more or less useiul kind. Now, whilst it is very important
that our pupils gain information, it is equally important that they
acquire the power of communicating it. This branch of school
work has received distinct recognition in the ' English Alternative
Course B.' The course mentioned is evidently intended to
develop the art of communicating information with clearness,
fulness, and accuracy.

The connection between hnowledcje and power of statement cannot
be determined with absolute certainty. Sometimes the possession of a wide
range of knowledge is accompanied by an indifterent ability to communicate
it ; sometimes, on the other hand, the existence of a limited store of know-
ledge is atoned for by the power to present all that is known, in a clear
and attractive style. Other things being equal, however, it generally holds
that clear, full, and accurate knowledge is associated with the power of clear,
full, and accurate statement. The differences noted above may be due in
part to natural causes over which the teacher has little control. Experience,

330 The Teaching of English.

however, shows, that, with training, the power of expression (possessed in
some degree by all) may be developed, and the differences noted above may
be lessened or increased by different methods of teaching. For example: —
One scholar acquires a piece of information and is immediately ex-
ercised in communicating it to another. He re-states the matter orally at
home, and afterwards, writes it as a home-lesson. In each of the
statements thus made, the scholar will probably use a slightly different
form of words and thus a facility and flexibility of expression will be
developed. Another boy may acquire the same information and be
required to make very little, if any, further use of it. It is evident
that the two boys will, in course of time and under such widely
different conditions of training, develop a very different power of
statement.

The connection between statement and the permanence of know-
ledge is very evident. If we wish to retain any item of information
we do this best by stating and re-stating the same in a variety of ways.
When teaching, it will invariably be found, that knowledge presented in
many ways and reproduced by the scholars in a variety of exercises will
tend thereby to become permanent.

The examples of the two boys illustrate the connection between the
practice and the growth of expression. If, throughout the stages of
school life, we introduce a continuous and progressive series of exercises
in oral and written statement, we may expect the development of
considerable power in oral and written composition ; if,on the other hand,
we rest content with the acquisition of knowledge, and rarely, if ever,
practise our pupils in the reproduction of it ; and, if we constantly
permit the use of single words and broken utterance in the replies which
scholars give to our questions, we must not be surprised, if the majority
so taught manifest very little power of stating what they have learned.

A progressive series of exercises in oral and written
composition.

Different modes of statement become available, and indeed,
characteristic of successive periods of school life. In the
junior classes, statements may be limited to answering and
asking questions ; to stating what is observed ; telling a simple
story ; and to giving an account of a school or home experience.
The senior classes may be exercised in reproducing a story read
to them ; in writing a full account of a lesson from ' notes ' ; in
turning extracts of easy poetry into prose order ; in letter
writing and paraphrasing, &c. There is evidently a marked
distinction between the two stages. The earlier form deals

Composition by Oral Statement. 331

with facts and experiences closely related to the child's life
and demands the exercise mainly of his memory ; the latter
stage, on the other hand, takes the scholar out of the region of
his own experience, he is required to enter into the experiences,
the thoughts, and feelings of others. He can do this only by
the exercise of a vivid imagination, and by the development of
thought and feeling up to the level of that which he attempts
to describe.

Lx^/ea/" notions, and a desire to state them.

These two conditions are common to healthy effort in both stages.
Fortunately they are frequently associated. All teachers of young
children must have noticed that when the little learner has just gained
an item of knowledge, at that moment, the best form of expression
appears. When an object is before the class, the scholars become inter-
ested, and they can readily be induced to talk about it ; during, or
after the reading lesson, and whilst the topics are fresh and interesting,
it is easy to maintain a conversation with the scholars upon these
topics.

When this desire to communicate information is evident, we do well to
allow our scholars, as far as is possible, to satisfy the desire. We may
be sure that oral statements which are made when thought is active, and
when knowledge is fresh, will be characterised by both force and reality.
This time association between the acquisition of knowledge and its
embodiment in language is especially valuable in all exercises in the junior
classes. When we come to the work of the senior classes, i.e., to the
exercises of transposing, and of paraphrasing, &c., we must again secure,
not only the necessary knowledge, but, accompanying the knowledge,
there must be an awakened interest in both the exercise and its result.

/^Composition by oral statement, by questions and by
answers.

It has been shown that this form of exercise is best suited
to Standards I., II., and III. The forms which oral statements
in these standards may be made to assume have been
already enumerated. They are conversational exercises
between the teacher and his class upon (i) common things in
an object lesson, (2) the subject matter of a reading lesson,
(3) new scenes in a geography lesson, (4) simple events in the
life of a historical character, (5) a story, and (6) a school or
home experience. The following are methods which may be
adopted in any or all of the above lessons.

332 The Teaching of English.

Expansion of incomplete statements.

At first, it will be found that children shrink from the effort of expressing
themselves. They must, at this stage, be prompted by questions. The
answers to these questions at the outset will most likely be very brief,
consisting, it may be, of single words. In time our scholars may be
led to expand these single word answers into phrases and sentences. The
following exercise illustrates the method of expanding the brief answers
which children give : —

What name is given to Great Britain because it is surrounded with
water?

' An island,' is the brief reply.*

Where is Great Britain ?

* On the west of Europe.'

Now tell me two things you have learned about Great Britain.

* It is an island, on the west of Europe.'
What separates Great Britain from Europe ?
' The North Sea.'

Tell me all you know about Great Britain.

* Great Britain is an island on the west of Europe, and separated
from it by the North Sea.'

Correction of Errors.

Besides exercises in the gradual expansion of an incomplete expression
there will necessarily be at times the correction of erroneous statements.
These will require considerable tact in treatment. If the teacher encourage
the scholar to correct his own expression rather than accept the correction
of a fellow scholar he will, by this means, secure the best result. Sometimes,
however, the teacher may accept a corrected statement from another
member of the class. Care must be taken, whenever this is done, that
the scholar making the mistake is not discouraged, and, also, that the
scholar making the correction is not unduly elated. Mutual help should be
encouraged. Rivalry should not be over-stimulated.
Mutual questions and answers.

In a class of scholars of nearly equal attainments, exercises in asking as
v.'ell as in answering questions may be introduced. To frame a question is
as good practice in oral statement as to answer it, and for purposes of
revision is equally effective.
Written answers to questions.

After a lesson has been given, in which as many pupils as possible have
had oral practice in making statements, the entire class may be asked to
\vf 'te out full sentence answers to a number of questions. These questions
must be prepared with a view, not so much of testing the pupils' knowledge,

* This reply is all we should expect at this stage. We ought not to expect the
scholar to say, 'Great Britain is an island because it is surrounded with water.'

Composition in the Upper Classes. 333

as of exercising and developing their powers of statement. When the
exercise is completed the answers may be collected and a conversation may
follow upon them. Without mentioning the names of individual scholars,
the teacher may select a few answers for correction, and an exceptionally
good set of answers may be read as a stimulus to the rest.

i^/^omposition in the upper classes.

It has already been stated that ideas (knowledge) and an
aroused interest in the subject matter, together with an
awakened desire to state what is passing through the mind, are
conditions common to successful effort both in the upper and
lower classes. Besides these general conditions, the composition
lesson in the upper classes depends upon a good command of
language ; and, for clearness of expression, upon obedience to
a few simple rules. The following are some of the school
exercises which afford opportunity for the practice of
composition.

Home Lessons.

One of the lessons of the day might be reproduced as a composition
exercise. To assist the beginner, he might be allowed to have the use of
the black-board abstract. Sometimes allow the scholars to write in their
exercise books a brief statement of the result of teaching each stage of a
lesson. If an object lesson be selected, the scholar might be directed to
write half-a-dozen lines under each of the following headings, viz.,

1 . What the object is like — appearance and properties.

2. How and whence obtained.

3. The chief uses to which it is put.

The account of an historical character might be arranged in the
following stages, viz.,

1. Birth and parentage.

2. Education and other form of youthful training.

3. Public career and character.

4. Effects of his life upon the times in which he lived.

A few simple directions should accompany the earlier exercises,
such as, e.g.,
{a) The above headings to be borne in mind, and be used solely to

guide the arrangement of matter. They must not appear in the

composition.
(/') The matter under one heading to be completed before the matter

belonging to the next heading is comn>enced.
((•) The composition to be in simple language. Short sentences to be

used. Repetitions of the same word to be avoided as much as

possible ; and fme writing to be discouraged.

334 The Teaching of English.

2. Stones for composition exercise. This is, in the main, a memory-
effort, and does not take so high a rank as the previous exercise. The
stories selected for composition should be short, and the sequence of ideas
natural and striking. The scholars should be encouraged to reproduce the
several events of the narrative in the order in which they occur in the
original ; but they should endeavour to express the events in their own
language. The best exercises will be those of children who add to the
power of reproducing the ideas of the narrative in correct sequence the
ability to clothe the ideas in original language.

When conducting the composition lesson, it is important to note
that all general directions as to style of writing and of arrangement of
matter should be completed before the piece is read. If either a word
or a phrase in the narrative require explanation, it should be fully
dealt with after the first reading. The piece should afterwards be read
again without note or comment, and the scholars be asked to write the
piece from memory. Two or three excellent reproductions may be
read to the class without naming the writers ; and a model exercise (a
model both in style of writing and in matter, prepared by the teacher)
may then be placed near the class for their inspection.

Letter Writing.

The art of letter writing is an advanced accomplishment, and
is only acquired after considerable practice. The matter of
a school letter generally assumes either one or other of two
forms. It is either a communication of information to some
person supposed to be interested in the account, or it is the
presentation of a request for something which the person
addressed is supposed to be able to give. The aim of the
writer should be to express himself briefly, clearly, and naturally.
The oral statement can be amended, if obscure; it can be
repeated, if not understood ; but the letter communication does
not admit of being either amended or repeated. Hence the
necessity for making the communication definite and clear.
The tone of the communication will need to vary with almost
every letter written.

Letters written in school should be adapted to the scholar's thoughts and
life, otherwise a stiff and mechanical style will be developed. Scholars may
be encouraged to write to one another on some topic of common interest.
Applications for a situation are, generally, the last letters that boys do
well The youth who can scarcely put three lines together in decent style,
whilst applying for a situation during one week, will write to his brother
the following week a sheet of well-arranged matter descriptive of his new

Commercial Correspondence. 335

home and surroundings. The best preparation for acquiring a natural and
easy style of writing is to supply a number of topics in which interest has
been aroused. Directions should then be given on the methods of beginning
and finishing the letter. When the letters are completed they should be
followed by a bright and genial criticism.*

The form which a letter should take on paper is best taught by
means of a model, written by the teacher on the black-board. This
model letter should not be placed before the class in a complete state,
but should be developed gradually, as a result of an oral discussion
between the teacher and his pupils. The general directions as to style
of composition given on a previous page may be repeated here.

^/^ Commercial Correspondence.

After facility in writing an ordinary letter on a familiar topic
has been acquired, the pupil who is sufficiently advanced should
attempt the more formal style of correspondence adopted by a
commercial house. If a series of lessons in book-keeping be
given in the upper divisions of the school, the technical terms of
commercial life could be directly introduced into the correspon-
dence. If book-keeping be not taught as a specific subject, a
series of lessons must be arranged so as to make the terms
familiar. Scholars cannot be expected to use technical terms
correctly unless they have a practical acquaintanceship with their
meanings. The fact of the pupil having copied a few letters
of a strictly commercial nature from a book of model letters
will not be of much service.

Preparation for excellent work in this branch of composition must
follow the rules laid down in the opening paragraphs of this chapter.
Hence for success in the practice of office correspondence in schools,
there must be the inculcation of commercial knowledge of a special
character ; there must also be the association of technical terms with
the special knowledge acquired ; and there must be (accompanying
both the knowledge and the commercial vocabulary) an interest
awakened, in part by the teacher's enthusiasm, but mainly by the use
which the new acquisition is likely to be put by the pupil when, in
the near future, he quits the school for the office and desk.

* When making these criticisms it is always well to taliehalf a dozen in hand. The
scholars do not in that case know whose letter is being discussed. If only one letter is
taken for criticism, the attention of the class is divided between the criticism on the
letter nnd the writer of it.

33^ The Teaching of English.

The transposition of words and phrases in poetical com-
position into tiie prose order.

This exercise depends largely upon the knowledge which the pupil
possesses of the structure of a sentence. The best preparation for the
exercise is the course of lessons sketched under the subject of ' Analysis of
Sentences.' With this preparation the pupil may be led to select the
principal verb in a poetical composition. He will be able then to work
outwards (a) to subject and object ; (/') to the enlargements of subject
and object by words, phrases, and sentences, and (<) to words, phrases, and
sentences forming the extensions of the predicate.

Paraphrasing.

The conditions of successful effort are here similar in kind to
those required for successful effort in other branches of com-
position. They differ mainly in being higher in quality, so
high, in fact, that some consider they are beyond attainment by
our pupils ; and, for this reason, they do not encourage the
exercise. If, as some assert, the effort of paraphrasing should
only be attempted when the pupil can embody the most
beautiful thoughts that have found expression in our language,
in equally beautiful but original expression, then it becomes
reasonable to give up the attempt ; and if the effort result in
the merely mechanical change of words, with the effect of making
the meaning ludicrous, as, e.g., in the case quoted by the late
Matthew Arnold, where,

' As monumental bronze unchanged his look,' — GcrlTude of IVyomiiii^,

was paraphrased : —

' His demeanour was as unchangeable as ornamental iron -work ' —
' His countenance was fixed as though it had been a memorial of copper
and zinc ' —

it would be better to avoid the exercise altogether.

There is, however, a middle course. Our scholars may not
be able to clothe the thoughts of a difficult author in language
as beautiful as the original. Nor need they be allowed to render
themselves ludicrous by their first attempts being retailed for
the amusement of others. Patient effort on the part of those
who have the ability to para])hrase ; the kindly correction of
weakness (not by holding the pupil and his effort up to ridicule,
but by showing him his fault and helping him to amend it) ;
the joint attempt of teacher and pupil to realise the full

An Open Composition Lesson. 337

meaning of the author ; the possession of a good vocabulary ;
and, above all, the exercise of the imagination so as to gain a
vivid mental picture of the author's thought, and an accompani-
ment of feeling stimulated by the beauty of the images which
the words suggest ; — these conditions being fulfilled, there is no
reason why our scholars should not make the attempt.

Reading with expression is a very large part of the paraphrasing
exercise. It is the successful effcrt on the scholar's part to realise the
author's meaning, and is accompanied by feeling in sympathy with the
thought of the passage. There is only one additional effort required in
paraphrasing, and that effort is to clothe the thought and express the feeling
in new and suitable language.

The reading lesson in which the poetical passage is read with bright and
correct expression, and after which a lively conversation upon the subject
matter is held, until the thought and the beautiful grouping of ideas sugges-
ted by the poet's language have become the possession of the class, may very
well be followed by a paraphrasing exercise. The ordinary rules of compo-
sition should be followed in the arrangement and wording of the paraphrase.

An open composition lesson.

When moderate skill in composition has been acquired, the
scholars may be allowed to select a topic of their own. This
exercise might take the form of an oral description of an excur-
sion to the sea-side ; of a visit to a museum ; or of an event either
in their own experience or about which they have recently been
reading. In order, at times, to secure the simultaneous effort
of the entire class, a written statement might take the place of
the oral description. In the latter case, a few of the composi-
tion exercises should afterwards be submitted to the class — some
for approval, others for correction. A further variation to this
exercise would be afforded if, at times, a piece of good poetry
of the scholar's own selection were recited in lieu of the oral
description or written statement.

These open lessons afford an insight into youthful character. They
permit of scope for the exercise of the scholar's individuality. They
present the opportunity not only for the display of intellectual power on
the part of the pupil, but also for moral guidance on the part of the teacher.
A youth, when thus left to choose either his own recitation or his own topic
for composition, will, by his choice, manifest the kind of thought which
holds a commanding position in his mind. And it will not unfrequently be
in the teacher's power to chock what is unworthy, and to stimulate what is
noble in the minds of his scholars.

^-g The Teaching of English.

X)Special rules for composition.

The enumeration of a full code of rules for guidance in com-
position would require much more space than could possibly be
afforded in a work of this nature. Happily, the need of a
complete guide is not urgent. The reading of choice prose,
and the constant use of language (oral and written) under the
direction of a teacher, afford the best preparation for the
composition exercise. Children should, from the first, be warned
against fine writing. They should be encouraged to make their
statements in simple words, of which the meaning is quite clear
to them. All exaggerated expressions should be corrected.
Composition by means of short sentences should be required.
The frequent repetition of the same word should be avoided,
and especial attention should be directed to the necessity for
completing all that it is needful to state on one topic
before entering on the next. To the general directions just
enumerated, there should be added a few simple directions for
punctuation.

For a full statement of rules for guidance in composition and punc-
tuation a grammar, such as Prof. Meiklejohn's, should be consulted.
Dr. Abbott's book entitled ' How to write clearly,' will be of great
use to the teacher.

The following extract is taken from the latter work : —
/ 'Let clearness be the first consideration. It is best, at all
events for beginners, not to aim so much at being brief, or forcible, as
at being perfectly clear. When you are describing anything, endeavour
to see it and describe it as you see it. If you are writing about a man
who was killed, see the man before you, and ask, was he executed, cut
d wn, or shofi If you are writing about the capture of a city, was the
city stormed, surprised, or starved out J Was the army repelled,
defeated, or annihilated V

Relationships betiveen History and Geography. 339

THE TEACHING OF HISTORY.

^Relationships between History and Geography.

\ / A lesson in the history of a country at any particular time
1/ should be an attempt to picture to the minds of our pupils the
conditions under which the inhabitants of the country lived.
— The homes of the people, their work, their customs and
manners, educational advantages, their rulers, government, and
their religious observances, must all be passed under review. It
is evident that such a lesson must, in the main, be a reproduc-
tion of the commercial and political geography of the time.
Similarly, it may be shown that a series of lessons upon the
successive periods of the past must be closely related to the
commercial and political geography of the nation at the time
selected for each lesson. Not only is the commercial and
political geography of a country closely related to its history,
but the physical geography may be also shown to be intimately
connected with it. For instance : —

The industries of a district are ultimately based upon its productions.'
These, in turn (so far as surface productions are concerned) are dependent
upon climate and fertility of soil. When the mineral wealth of a country
is considered it is found for the most part to be due to the presence of
mountain and hill structures. The present condition of England, with its
thousands of operatives grouped in its manufacturing centres, cannot be
explained without referring to the mineral wealth deposited in the hilly and
mountainous regions of the country. Then, again, the pastoral and quiet
conditions of life on the eastern plains must be remembered when we wish
to account, in times past, for the more settled conditions of the people in
the east compared with the restless and warlike conditions of the inhabitants
of the west and north.

The physical geography of any country may furthermore be shown
to be closely connected with the character and activity of its people.
Neither the exploring Englishman nor the ubiquitous Scot could
have been produced in the centre of a vast continent. Britain's
insular position, together with the variability of its climate, is a factor
in physical geograjjhy which must be taken into account whenever an
attempt is made to explain the history and development of our Imperial
and Colonial possessions.

340 The Teaching of History.

The place of history in the school curriculum.

The recognition of the relationship between history and geo-
graphy affords assistance in determining the place which a
course of lessons in history should occupy in the school curri-
culum. From what has been already stated, it is evident that
a fair knowledge of the modern geography of Britain forms the
best preparation for acquiring a sound and rational knowledge
of its history. The political geography of England to-day — its
inhabitants and their distribution, their occupations and mode
of life ; the great commercial centres, with the government
(local and imperial) and the religion of the people, together
with their connections (social, commercial, and political) with
other nations — forms material out of which the future historian
will construct his narrative.

Conclusions.

It is clear, therefore, that the scholar who has a good knowledge of
political geography will have a substantial basis upon which to erect
his historical structures. Hence geograjjhy should precede history in
the order of acquisition. This order is in accord with the well-known
maxim of school work, viz., that in teaching we should proceed
'from the known to the unknown.' If, furthermore, the intellectual
pcnvers of the learner be taken into account, we shall find that the
above order is best. Geography presents considerable material
for the exercise of the powers of observation, memory, and imagination
— powers which are very active in early school-life. History, on the
other hand, affords scarcely any opportunity for sense effort, but it
demands the exercise of considerable powers of comparison, if Judg-
ment, attd of reasoning. On two grounds, therefore, we are forced to
the conclusion that geography should precede history. It is the
easier intellectual exercise, and the knowledge it affords is a sound
preparation for historical study.

The starting point in teaching history— two methods
contrasted and one selected.

It is customary for text-books of history to begin with the
description of ancient Britain, and to continue the account with
the gradual unfolding of the nation's growth through the Roman,
Saxon, and Norman periods, and thence to proceed through
the middle ages to the present time. There are some teachers
who hold that history .should be taught in exactly the reverse
order. These maintain that after a fairly complete knowledge
of physical and political geography has been acquired, the
history of the century proximate to our own should be taken,

The Ends in View in Teaching History, 341

and that this should be followed by the history of the century
further removed, and so on until the most remote period is
reached. A brief consideration of the nature of the study in
each case will help to determine the course we should select.

1. The method which begins with the present, and which works,
step by step, backwards to remote periods, requires a familiar acquain-
tance with the political and social conditions of modern times, and an
ability to recognise and understand the causes which have brought
about the present complex conditions of society. It demands, further-
more, the power to realise the social and political circumstances of the
immediate past, out of which the present conditions have been deve-
loped. This method evidently depends for success upon the pupil, so
instructed, being well informed in matters relating to the present, and
upon his possessing sufficient intellectual power to enable him to
connect the present with the past. The method is not suited to the
capacity of young children. If we are to teach history only to the
upper divisions of our schools, then such a method as this may be
adopted with the promise of good results, but underno other conditions
are these results possible.

2. The method which begins with the remote past, and which gradu-
ally leads the pupil from the simplest notions of an organised community
to the complex conditions under which the various forces of national
life are to-day arranged, appears to be much better suited to the
capacities of ihe children in our schools. Thi? method would make use
of the knowledge which children have of the present. It would
picture the Briton in his half savage condition, with his rude home, his
warlike disposition, and his ignorant and heathenish forms of worship.
It would contrast this Briton, living almost entirely by and for him-
self, with the Englishman of the present ; with his appearance, his
home, his knowledge, and his employment ; with his social, civil, and
religious privileges — the citizen of a grand Empire, and sharing in
the national life. There cannot be much hesitation in the selection of
the method best suited to the young pupil beginning the study of
history. The method of teaching which proceeds by strong contrasts,
which commences with a much less complex condition of life and
society, such as those indicated above, which appeals vividl}' to the
interest and imagination of the pupil, which demands far less initial
knowledge, and which makes less demands upon the higher intelligence
of the pupil, is the one best suited to the beginner of the study in an
elementary school.

The ends in view in teaching- history.

The teaching of history admits of very varied treatment, and
it yields equally varied effects. Amongst these effects the
following maybe briefly noticed, viz., (a) patriotism, (l>) citizen-
ship, {f) moral training, and (d) the development of general
intelligence.

342 The Teaching of History.

((?) Patriotism. If the aim of our teaching be patriotism, we shall seek
to bring out in bold relief the grand characters which history supplies,
and shall make the most of those heroic struggles for right and freedom
by which our forefathers gained the privileges we now enjoy. We shall
do honour to those pioneers of progress who, by their discoveries, made
it possible for England to grow into a mighty empire. In this review
of the forces which have tended to make our country what it is, we
shall not forget the work of such men as Tyndall, who supplied us with
our vernacular Bible ; of Caxton, who introduced the art of printing ;
of Shakespeare, who has embodied in words the noblest thoughts which
enrich our literature ; and of Newton, to whom we owe the discovery
of the laws which regulate the most subtle and far reaching of known
forces. To come to still later times, we shall not fail to notice the
developments in trade and commerce and in the social condition of the
common people consequent upon the introduction of steam, the develop-
ment of our system of railways, the circulation of a cheap and free
press, and the spread of popular education. These are some of the
achievements of which a nation may well be proud. A knowledge of
them would tend to inspire any English youth with that patriotism
which it is the teacher's aim he should possess.

{6) Good Citizenship. If this be our chief aim we must expand somewhat
the series of lessons enumerated above. These have dealt either with
the nation's progress as a whole, or with the achievements of her
greatest sons. The teacher's desire is now more particularly to inspire
the pupil with the duty which belongs to the ordinary or average unit,
or individual, of the community. Formerly this unit was, for the most
part, ignorant and willing to be led ; but now he possesses knowledge
and independence. History must therefore be taught him so as to
inform his judgment and guide his action when, in turn, he is called
upon to undertake the responsible duties of citizenship. The relation-
ship between capital and labour ; the effects upon trade and commerce
of disputes between employer and employed ; the evils of war ; the
consequences of monopolies and of bounties ; taxation and national
security— these and kindred topics must be added to those intended to
inspire patriotism. Unless these additions be made to our lessons there
is danger that the proud and arrogant spirit which sometimes charac-
terises the Briton amongst other peoples may manifest itself in the
dealings which various sections of the British people have with each
other.

(c) IVIoral Training. To secure this result, our lessons must seek, not
only to ins[)ire with an ambition to imitate the actions of the good and
noble, but they must be so arranged that the consequences of evil
conduct become evident. In this way we may hope gradually to
establish in our pupils' minds those standards of right and wrong action
which men ordinarily apply to conduct. History lends itself, perhaps
more than any other ' class ' subject, to this form of moral training.

{d) Intellectual Discipline. In every lesson there will be an exercise of
the memory in order to store up the more important events. It will
also be necessary to stimulate the learner to picture the past by an
effort of itnagination. The ability to 'picture out ' in words is a very

Arrangement of a Course of Lessons. 343

important element in the successful teaching of history ; and this ability
to ' picture out ' by the teacher should arouse a corresponding effort of
imagination on the part of the children. Every lesson, furthermore,
should be accompanied by enquiries as to the effect of this and that
action, and as to what led to this or that result. All such enquiries
indicate the exercise of the learner's judgment, and of his powers of
reasoning.

It may fairly be anticipated that the teaching of history will
secure all the ends above enumerated. With one teacher,
however, the patriotic aim will be a prominent feature ; with
another the moral aspects will be more completely emphasised ;
with a third the practical lessons of history, that is, the lessons
affording guidance in citizenship, will be most urgently im-
pressed ; whilst, with all, the training of the intelligence will be
an important element in the teaching.

Arrangement of a course of lessons.

The formal study of history as an organized series of events,
exhibiting by their arrangement the nation's development and
progressive life, cannot be attempted by very young children.
The earliest lessons should consist of simple narratives and
stories of an attractive kind. From these early lessons the
classes may be led to view a connected series of events as they
are found to group themselves round the lives of the more
remarkable historical characters. When a considerable number
of historical facts have been accumulated by the two preceding
methods, and when the mental power of the pupil has been
sufficiently developed, he may profitably be exercised in the
organization of these facts into an outline of English history,
and, finally, he may attempt the thorough and complete study
of a selected period,

{a) Simple stories for junior pupils.

The delight which a very young child manifests in a fairy tale is an
mdication of the form of story which early lessons in history should assume.
The power of the imagination is very strong during this period of school
hfe. The child's stock of mental images (the results of its own observa-
tion) is no doubt limited, but the power it possesses of elaborating new
mental pictures out of its original supply appears to be all but unlimited.
The child's imagination finds suitable material for exercise in such stories as
the following, viz., the visit to Rome of the Saxon youths, the exile of
King Alfred, the desolation of the New Forest, the discovery of Richard
by the singing of the bard, Oak-Apple day, &c. , &c.

344 The Teaching of History.

The following outline of method may be adopted in these early
lessons.

1. The teacher should graphically relate the chief events and interweave
questions, wherever possible, with his descriptive account.

2. He should introduce a picture, or better still, should accompany his
statement with a sketch on the black-board. This will prove of
assistance in fixing the interest, and in guiding the imagination of his
scholars.

3. The scholars may, afterwards, read the story from a book in which
the event has been related in language suited to their capacities.

4. The reading lesson should be followed by a rapid review of the chief
facts, by mean, of oral questioning.

{h) Stories continued, but with the aim of connecting together the
more striking historical events.

We may proceed from the selection of isolated pictures, taken from the
most attractive events of history, to the consideration of a series of the more
striking features in the life of a remarkable person, or in a selected period.
Whilst preserving the story style of narrative, each lesson should cause a con-
nected series of carefully grouped events to pass before the children's
minds. The life and habits of the ancient Briton contrasted with life in
England at the present time; the association of the appearance of the
Saxon youths in Rome with the introduction of Christianity ; the chief
incidents in the life of King Alfred, and of Canute ; the chief events
surrounding the conquest by William of Normandy ; an account of Richard
and the Crusades ; — these form examples of the story narrative which this
stage of teaching should provide.

Care must be taken that we do not attempt to deal with causes and
motives which are beyond the jrower of the child's understanding.
For example, we might picture the appearance of the captive Saxon
youths in Rome, and connect with their appearance the determination of
Gregory to send missionaries to England in the same way that we now
send missionaries to heathen people ; but it would be unwise to inform
our junior scholars of the gradual flisintegration of the Roman empire,
and the consequent withdrawal of the Roman forces from our shores.
The notion of an extensive empire must first be explained to them, and
the difficulty of defending the regions furthest from the centre of the
empire must be shown before the children could place any value upon
our statements. This knowledge belongs to a later stage of teaching.

Lessons in history beyond the preliminary stage.

Hitherto the matter of the history lesson has been fragmen-
tary and disconnected. It has been the means of arousing
interest, and has been adapted to our pupils' intellectual
condition, exercising for the most part their powers of memory

Lessofis beyond the PreVuninary Stage. 345

and imagination. It is now time, however, for our scholars to
begin to organize their historical knowledge. They must be
led to establish the relations which events bear to one another ;
how one form of action leads to one result, whilst another form
of action is followed by a result totally different. So long as
isolated fragments of history continue to be presented, this
study of growth and natural sequence cannot be pursued.
Where shall we begin this higher and more serious study of
history ? In reply, it may be well to begin by taking the succes-
sion of events as these group themselves round the lives of
remarkable historical characters. The events thus grouped will
certainly manifest an intelligible and natural sequence. They
will, furthermore, exhibit evidences of reality. Because of the
interest which the events connected with the lives of individual
men are likely to awaken, and because of the natural order
which these events must assume, and which it will not be diffi-
cult for our pupils to recognise, and because this course of
teaching is a natural expansion of the course adopted in the
previous courses of instruction, we think that history, through
biographical sketches, is well suited to this stage of teaching.

Brief hints upon the method of teaching this stage,

1. Oral lessons on each character should in the first instance be given by
the teacher. The reading lesson may then follow.

2. These lessons need not be invariably arranged on the same plan.
The following outline may generally, however, be followed, viz.
(a) birthplace and parentage, {/>) youth and education, (<r) public life
and character, ((/) historical effects resulting therefrom.

3. Contrasts between the conditions of life fiirza and i/ien should be drawn
at each stage of the lesson, and the scholars should take a prominent
part in the effort.

4. The conclusions as to the consequences of action and the character of
individuals should not be reserved solely for statement at the end of
the lesson, but should be drawn from the facts with which they are
connected as the lesson proceeds.

5. The facts should be grouped by the teacher, and when the grouping
is vividly realised by the scholars, the latter should be encouraged to
draw inferences therefrom.

6. When stating the facts, the teacher must adopt a graphic style ot
'picturing out.' At the same time he must avoid a purely lecture
style of statement.

7. Maps, diagrams, and materials should be introduced wherever possible,
and the chief points taught should be registered by means of a well
arranged abstract on the black-board.

34^ The Teaching of History.

Graphic oral instruction to be followed by the reading
of history.

The successful study of history very largely depends upon the ability of
the learner to realise, by means of mental images, the varying conditions
of the past. A youth with dull powers of imagination will rarely take much
interest in the history lesson. It becomes necessary, therefore, to introduce
methods of teaching which will stimulate the children's imagination. No
method will do this more readily than a graphic descriptive style (' picturing
out') on the part of the teacher. Afterwards, when by the aid of the
teacher's oral lessons the pupil has gained the power to mentally realise
the past, he may be encouraged to ' read up ' the subject independently,
and be thus prepared to enter, along with his class fellows and teacher, upon
a conversation upon the matter read. When, in this way, we are able to
arouse an interest in the independent reading of history, we shall have done
much towards securing an interest in the reading of general literature, and,
at the same time, we shall have developed a form of self-activity of the
most fruitful kind.

Reproduction of history lessons by the pupil.

The written composition should form the final effort ot each lesson.
Unless the pupil can write out a continuous and correctly arranged account,
we cannot be sure that the results of our teaching are satisfactory. The
aim of teaching is not merely the enumeration by our scholars of a series
of facts connected with the life of some great character, the aim is to obtain
an ability on their part to weave these facts into a connected and organized
statement — a statement, that is, which in simple language recounts in
orderly succession the chief events of the life, and which exhibits the rela-
tionship which exists between these events together with the lessons which
that relationship enforces.

The teacher's blach-board abstract will prove of great help to the
pupil in his attempt to reproduce the matter. This abstract should not
be actually reproduced by the scholar ; it should simply be kept in the
pupil's mind, and serve as a guide to the orderly arrangement of the
matter. With advance in intellectual power, the scholar might be
encouraged to accompany his own reading by an original abstract.
Of course the latter exercise should be entrusted to the pupil only after
he has gained some familiarity with such work. This familiarity will be
best accjuired by watching the teacher gradually unfold his abstract
as the oral lesson proceeds. The presentation of printed abstracts in
historical readers may serve a useful purpose at first. If constantly
allowed they become in time a source of weakness. There is no better
exercise tor either scholar or young teacher than the preparation of
his or her own abstract.

History of a Selected Period. 347

History of a selected period— a suitable exercise at
this stage.

This branch of the subject is the most advanced, and is
therefore reserved for the senior classes. Three processes of
preparation for the study have been concurrently at work.
These processes are {ci) the lessons in history already taken,
{b) the daily experience of the scholar living in the midst of a
civilized community, and {c) the general growth of the learner's
mental powers.

{a) Previous lessons. The historical story will have served to arrest
the learner's interest, and the biographical sketch will have made a series
of events to shape themselves into a simple yet rational sequence ; and the
multiplication of these sketches, carefully arranged, will have caused the
matter contained in them to broaden out into a continuous and connected
outline of historical facts. The pupil, thus placed in possession of the broad
outlines of history, will be able to arrange the fuller matter of the special
period in its proper relations, both in respect of that which precedes and
that which follows it.

(/>) Daily experience. Accompanying the above preliminary exercises
there has been an accumulation of experienced or intuitive knowledge.*
For example, the learner has been an observant inhabitant amidst a
community. Village, municipal, and national conditions of life have been
gradually forcing themselves upon his attention. The policeman on his beat,
the postman on his round, and the occasional visit of the rate collector ; the
election of a parish council, municipal elections, school board elections,
county council and general elections ; the magistrate's bench, the judges on
assize, the opening of parliament by the ruling monarch, the parliamentary
debates, and the passing of new acts of parliament ; a volunteer encamp-
ment or review, the marching of a regiment of the regular army, and the
account of a war ; all these forms of corporate activity have been passing
before the pupil's eyes, or reaching his ears, and each in turn has left some
valuable acquisition in the mind. By means of this intuitive knowledge,
and the knowledge gained by formal instruction, the learner becomes suffi-
ciently informed to ^iter profitably upon the complex aspects of a selected
historical period.

[c) Increase of mental power. Not only is a sufficient range of know-
ledge required, but the power to arrange and organize this knowledge is
necessary in order that the study of a period may become of the highest
service. The power to remember and retail the facts in sequence will not

* Knowledge gained without formal instruction is frequently termed 'intuitive.'

348 The Teaching of History.

be sufficient for the higher training of the senior scholars. They must be
practised in associating certain political effects with their causes ; the origin
and issue of remarkable social changes must be recognised ; great religious
movements, affecting the lives of the masses, must be traced through their
origin and development ;— these are samples of the higher mental exercises
which the study of a special period will demand. Evidently, then, the
study must be delayed until the powers of judgment and reasoning are
sufficiently developed to be capable of reliable effort.

Value of the study of a selected period.

From what has been already stated, it will not be difficult

to enumerate a few of the advantages which follow the study

of a special period. The method of study will form a model

which may be pursued in the study of any other period ;

guidance will be afforded in matters of social and political

Jmport ; the development by exercise of the intellectual powers

/of judgment and reasoning, and the formation of moral standards

/ for the direction of conduct may be fairly expected.

^ The kind of history to be taught.

Text-books of history, especially those of the smaller kind, are often mere
compilations of facts arranged in chronological order. These retail, for the
most part, the actions of kings, statesmen, and warriors. The narratives
in them become of most interest when a vivid picture is presented of some
sanguinary conflict, or when the steps are stated by which some plot or
intrigue is revealed, or when the measures that accomplished its defeat are
told. The scholar who reads history as it is frequently written must come
to the conclusion that England, as she appears to-day, is the result of a
series of unavoidable wars ; that the most important personages in its past
are either the statesmen who brought the wars about, or the generals who led
the forces to victory ; and that the most certain jjath to renown is to take
a prominent part in the butchery of thousands who have quite as much
right to live as those have who slay them. What more humiliating lesson can
any teacher give a class of young children than that of a war in which men
rushed into conflict simply because a depreciating remark had been made
respecting the corpulency of one of their leaders ! The patriotism that is
fed upon the renown which our forefathers gained in such conflicts as these
is dearly bought if children are led at the same time to applaud the utter
want of self-restraint which all such conflicts exhibit.

England has developed vastly more during the last, than during the
preceding centuries, and this marvellous growth is due to developments
in the .arts of peace rather than in those of war. When the history
of the nineteenth century is studied, the men who stand out prominently

Value of the Study of a Selected Period. 349

in English history are not warriors, but statesmen and men of science,
of invention and discovery ; men also who have become the leaders in
great political, social, and religious reforms. The history of the cen-
turies preceding the present may not present such a favourable
record.

If, then, we wish our scholars to be patriotic, and at the
same time to become worthy citizens ; if we desire them to
receive that moral training which the study of history is
admirably fitted to give, — the training, i.e., which shall develop a
high regard for the growth of their own powers and rights, whilst
/ they maintain a just regard for the rights and powers of others;
/ and if we wish to make the study of history a means of intellec-
tual discipline in the highest sense, then it will be necessary to
place in the background the conflicts, the plots, and the
intrigues which centre about a few individuals, and bring into
far greater prominence the efforts of those who have laboured
successfully for the moral, the social, the intellectual, and the
material progress of the nation.

The learning of dates in /li story

Dates are a valuable aid to the orderly retention of the facts of history.
As these facts must be kept in mind, the date with which each prominent
fact is associated will form an associating link by which it may be per-
manently retained and readily recalled. The leading facts of history should
be acquired, primarily, in association with those related facts which preceded
and gave rise to them, or with those which followed and resulted from them.
When, however, a central fact in history has thus been acquired, the date
of its occurrence should be connected with it. A few dates connected in
this fashion with the leading events of each reign will be of great service in
enabling the learner to keep the chronological order of his matter.

For example, the date 1688 marks a central and commanding fact
in history. There are events leading up to that fact, and there are
others which follow immediately from it. As soon as the date is
mentioned the entire range of associated facts should come to mind.
What is contended for is that dates should not be associated merely
with isolated facts, so that when a given date is mentioned the fact
associated with it comes alone to mind. If the fact is so isolated, and
is so insignificant that it carries with it no related facts, then neither the
fact nor the date is worth remembering. If on the other hand a
historical fact gathers others around it and controls them, then it
should be primarily associated with these other facts, the date serving
to call the entire series to mind, and to place the series thus remem-
bered in due chronological order with other series of similarly related
historical matter.

35° The Teach'mg of History.

Hints on the method of teaching the higher stages of
history

1. Make use of the knowledge the pupils already possess. For
example, if the subject be that of the government of the country, bring the
government you wish to describe into contrast with that of to-day. Simi-
larly, the relation between the different classes of the community in the past
should be contrasted with the relations between similar classes at the
present time.

2. Continue the oral teaching of history. The oral lesson is neces-
sary in order to make use of the knowledge already possessed by the class.
This is best known to the teacher, and he will frequently become acquainted
with it only as the lesson proceeds. The oral lesson is furthermore needed
to help the scholars to arrange and to organize their knowledge. In pre-
vious stages the oral statement was shown to afford the necessary stimulus
to the pupil in his attempts to picture the past by an effort of imagination.
In the present or higher stage the pupil needs to be led to reflect and to

ifer. An entire series of related facts and truths must be established.
/Causes must be followed to their natural effects, and effects must be traced
backward to their causes. Judgment must be passed on the nature of such
and such action — whether right or wrong. The opinions of the class
must be gathered, and their opinions must be accepted or corrected. All
these efforts belong to the higher stages of instruction, and may be most
successfully exercised by means of oral teaching.

3. Follow oral instruction by reading lessons, and gradually extend
the opportunities for the senior pupils acquiring historioal knowledge by
their own independent reading.

4. Make use of the following aids wherever possible.

Few countries are richer than our own in historical remains. Castles,
towers, mansions, roads, abbeys, and churches are available in almost every
locality. The teacher of history who is himself interested in these relics of
the past, will not fail to arouse interest in them on the part of his pupils.
Each may be made an attractive centre of historical associations.

Museums, both local and national, afford additional material, and
should be utilised. Pictures should be introduced into reading books,
and prints of larger size should be hung upon the school walls. The
series issued by the ' Art in Schools Association ' will prove an attrac-
tive and stimulating aid to the child. The Map should be introduced
into every history lesson. The association of an historical event with
a place gives additional brightness to the geography lesson, and the
localization of an historical event upon the map renders the event more
interesting and permanent.

How to Brighten the Teaching in Lower Standards. 351

OBJECT LESSONS AND ELEMENTARY

SCIENCE.

How to brighten the teaching of the lower standards.

It has long been felt that the transition from the interesting
and active work of the infant school to the almost exclusively
literary work of the schools for older scholars is too abrupt, and
it has become generally acknowledged that the work of the lower
standards in these schools needs brightening with work in which
the scholars take a much more active part than at present.*
The instincts of activity and curiosity which Froebel recognised
and utilised in his Kindergarten exercises do not cease to be
available for service when the child reaches the standards of
the upper school. There are several directions along which
the activity of these scholars may find exercise. Some have
already been indicated in connection with the teaching of
arithmetic, geography, and drawing. These are briefly recounted
below. The association of these more active exercises with the
ordinary and essential courses of school instruction appears to
be the direction in which good results will in future be obtained.
If skill of hand and quickness of eye can be developed in con-
nection with a scheme of exercises which serve at the same time
to render the child's knowledge of arithmetic more reliable, his
notions of geography more accurate, and his ideas of drawing
more perfect, it will be true economy both of the teacher's
strength and of the scholar's time to develop and follow such a
scheme.

* ' With constant, varied, and pleasant employment, the intelligence of children
develops ; without it, it shrivels up. If the children can be made to think (the hardest
of all work) whilst the teacher gives them an object lesson, the highest kind of school
work is done ; if not, the object lesson should be abandoned. The experience of my
childhood, and what I see in my own children, leads me to believe that work in which
children take spontaneous delight, as moulding in clay, building with bricks, construc-
tion in paper, each child for itself, is the most powerful agent in drawing out
intelligence.' — Blue Book, Air. AldU.

352 Object Lessons and Elementary Science.

The following exercises afford occupation for the hand and eye activities
of the scholars in connection with the ordinary lessons of the school. Addi-
tions may be made to them from time to time as the abilities of the scholars
develop. It will be seen tliat they may be made to form a part of the
scholar's work throughout his entire school course, and, further, that their
construction must tend to make the instruction associated with them very
real and enduring.

1. Arithmetic.

(a) Construction of concrete representations of 'place value.'

(l>) Drawing the above on paper by careful ruling and measurement.

Dividing these into smaller units by exact measurement.
((/) Cardboard figures to represent the exact dimensions of square inch and

square foot.

(e) Cardboard cylinders of a gill, pint, and quart. Neat work and exact
size required.

(/) The metric measures of length and capacity. Dividing the metre mto
decimetres and centimetres ; construction of the cubic centimetre for
gramme, and the cubic decimetre for litre, &c. See figures in ' //cnu to
teach Arithtnetic,' pp. 196 — 198.

(g) Strips of cardboard to illustrate different fractions of the same unit.
These may be further divided to show the addition, subtraction, &.C., of
fractions. See ' Fraction Chart,' p. 221.

{h) Similar strips cut into lengths to illustrate the terms 'measure' and
'multiple,' accompanied by drawings carefully executed and coloured.

2. Geography.

{a) The making of clay models ot river basins, ranges of hills, features

along a coast-line, &c.
{b) The drawing of maps to correspond with each of the models.
{c) The collection and arrangement of objects — specimens illustrative of

productions and industries.

3. Drawing.

(a) Construction of regular figures in wire and cardboard, see p. 114.
{b) Construction of models in cardboard, made to scale.

(f) Sections of regular figures, see pp. 115 — 117.

4. Object lessons and elementary science.

(a) Collection and mounting of specimens — botanical, mineral, &c.

(b) Drawing and colouring diagrams illustrative of (a).
{c) Construction of simple apjiaratus.

It should be observed that these lessons fespecially where exercises of
construction are made to accompany them) will demand a considerable
amount of individual direction on the part of the teacher. This will be
especially evident iu the early efforts of the children. The individual

The Aims of the Object Lesson. 353

teaching here indicated will absorb very much time, and will call for much
thought and ingenuity on the part of the teacher. The work is without
doubt soundly educational, and, in its effects, will make school life much
brighter, and make the knowledge acquired much more real and lasting.
It should be remembered, however, that the time of the scholar, and the
available effort of the teacher, have their respective limits. Allowance
must therefore be made for the inclusion of tliese new but highly disciplinary
exercises, by lessening the demands for almost absolute precision in such
exercises as spelling, the meanings and derivations of words distributed over
a wide area in reading, the exact reproduction of long lists of names in
geography, &c.

Allied to, and accompanying these exercises of hand and
eye are the ' object lessons ' which, in future, must be taken in
all the lower classes of the school. These will be a means of
brightening the lower standard work in the school. It is
of these object lessons, and the elementary science lessons
which grow out of them, that the following paragraphs more
particularly treat.

The aims of the iifeject lesson.

These aims may be briefly stated as follows, viz. : (i) the
development of the powers of observation ; (2) the awakening
of the child's interest in common objects and phenomena ;
(3) the employment of the scholar's instinctive activity during
the acquisition of knowledge ; and (4) the exercising (in the
higher classes) of the reasoning powers in tracing the connec-
tion between the observed phenomena and either their cais:s
or their effects. Besides the above aims, are others deserving
of notice. For example, every object lesson should impart
information ; it should also afford practice in the use of
language, and it should be made a means of moral training.

ow to secure the above aims.

We may now review the aims named above, and briefly
indicate soine of the methods by which each may be obtained,
leaving the fuller developments of each method to be worked
out in the class-room.

I, The powers of observation. An object lesson without
an object is a misnomer. Very often, however, objects are
provided and not used ; or, if used, they are kept almost

354 Object Lessons and Elementary Science.

exclusively in the hands of the teacher. Objects should not only
be provided for the lesson and the teacher, they should be
provided, as far as possible, for each scholar.*

In a lesson recently given before H.M. Inspector, a
specimen of the object — a flower in this case — was provided for
each member of his class. The pupils proceeded from an
examination of the more obvious qualities to detect those less
obvious, until a very complete inspection had been completed
of the different parts of the flower and their relative arrange-
ment. If the reader refer to p. 257, he will see an account of a
lesson on the mariner's compass, in which each child in the
class was provided with all the parts of the object, and was
taught to make the complete instrument. This first-hand
contact with objects stimulates the attention and awakens the
observation of the scholars most completely and successfully.

An experiment is a very effective mode of directing the observation
of the class. Some change is about to be made in the material before
them. The teacher knows exactly what will happen, the children are
full of expectation. It may be that having had some previous experi-
ence they anticipate the effect throughout the entire operation. They
are all of them most eager observers of both the process and the result.
An experiment becomes of the highest value when the scholars are
allowed to take an active part in it. This privilege cannot always be
secured. The teacher can generally, however, summon one or two ot
the class to the front in order to assist, and all the scholars may be
encouraged to attempt the more simple experiments afterwards.

Drawing is another mode of directing the observation. A sketch
may be made first by the teacher, showing in an exaggerated form the
special feature he wishes the class to observe ; it may then be attempted
by one of the scholars on the board before the class, or, best of all,
the drawing may be executed by the scholars throughout the entire
class. In The latter case the successful drawing is full proof that
the class has observed the desired feature in either the object or the
experiment.

2. The awakening of interest. 'A dull class' (the Senior
Chief Inspector, Mr. Sharpe, states) ' is the saddest of sights in
a school.' Whatever may be the case with other lessons, an
object lesson can only with difficulty be made a dull one. The

* No object (s.iys an Inspector) is suitable for an object lesson unless all the children
from their places can without serious effort discern all the points referred to. If the
object be too small for all to see together, each child should have one, when the highest
type of object lesson can be reached. For example, in a lesson on the acorn, each child
can take it from its cup, bite off its hard shell, rub off its coat, split the cotyledons,
observe the germ, and taste the flavour.

How to Secure the Amis. 355

faces of the children in a class brighten immediately they see the
preparations for an object exercise. Throughout the lesson the
class needs very little quickening. In fact, more frequently than
not, the eagerness manifested by the scholars is repressed
by a teacher who does not know how successfully to direct and
utilise it. In many schools the object lesson has been retained
for many years past, not with a view to examination, but for
the express purpose of interesting the scholars in the school
and its work. The interest in common objects and phenomena,
awakened by a series of object lessons, may be expected to
accompany the child during many of his leisure moments and
out-of-school rambles. In this way a habit of observation
may be induced, which in after life may become of the highest
value.

3. The employment of the scholar's instinctive activity
in the acquisition of knowledge by his own effort. The
independent effort of each scholar is in danger at the present
time of being weakened rather than strengthened. We direct
and guide the learner so continuously that, unless the warning-
be heeded, we may produce a community always in need of a
guide. The most valuable help we can give a scholar is to
enable him to help himself.

Throughout almost every lesson sketched in previous pages of this
book, the desirability of cultivating a certain amount of self-help has
been advocated. In the object lesson, more perhaps than in any
other, there is opportunity for exercising the self-directed activities
of the scholar. He will provide material ; he will be delighted to help
in an experiment ; he will scarcely wait for the specimen to reach him
when an object is submitted for class inspection ; and he eagerly
desires the front position in the class, where ever)'thing done is best
observed. All these familiar movements on the part of the pupil are
signs that in the object lesson we have the means of satisfying his
natural activity, and the opportunity for exercising and developing his
self-effort.

4. Exercise of the powers of judgment and reasoning.

Scholars in the lower classes are, as a rule, satisfied by asking
the question. What is it ? when a fresh object is presented to
them. They are content simply to know that * this fish is a
shark,' and ' this rock is granite.' Afterwards they will ask
such questions as the following, viz. : Why do you call this
animal a fish ? and that rock granite ? When, in answer to

356 Object Lessons and Elementary Science.

the first question, the attention of the scholar is directed to the
special feature — breathing by means of gills — which distin-
guishes the class ' fish ' from all other classes of animals, he
henceforth becomes able to distinguish two groups of animals,
viz., the group termed ' fish ' and that termed ' not fish.' It
thus becomes evident that the advanced questions beginning
with the word 'why' mark the ^period when the scholar is
ready to classify his knowledge. He is not satisfied with
merely retaining isolated scraps of information, but, instead of
this, he is prepared to organize these scraps into classes of
facts having common features. He goes further than this, for,
whenever a new animal is observed, he forthwith strives to
place it in one or other of the classes he has distinguished.
His ability to do this successfully is evidence of the exercise of
his powers of judgment and of reason.

During lessons on the common phenomena of aii-, water, &c. , the
senior scholar will not remain satisfied with a statement of faclo
merely. The cracking of a water pipe by frost is a fact which, at this
stage, must be connected with its cause. By the simple experiment
of exposing an open test tube, three parts tilled with water, during a
frosty night, it may be shown that the ice into which all the water
has been frozen, completely fills the tube. If another tube, having
its nozzle almost closed, be filled with water, and the nozzle be then
completely sealed, the tube will burst as soon as the water within
changes into ice. In this way the class may be led to connect ttie
cracking of the pipe with the expansion of the water upon freezing.

In order to engage the self-actiuity of the scholar in similar
experiments, tell him to fill a small bottle with water, to cork it
tightly down, and then to expose it to the frost. The cork will soon
be pushed out ; another cork will take its place, viz. , an ice cork ;
further exposure to frost will be followed by the freezing of the water
in the body of the bottle, and as the ice cork will not readily give way
the bottle breaks. Do not tell the scholar this. A hint or two will
be sufficient. The whole class may be expected to perform the above
experiment. The materials are easily obtained; all in the home
will be interested, and a most useful piece of domestic science will be
widely distributed.

During a lesson on 'Clouds,' the brief account of their appearance,
of their different kinds, and of their connection with rain, will not be
sufficient for the scholars in .Standards V., VI., and VII. They will
want to know how the cloud is caused, and what must occur before
the rain falls. The whole process may be exemplified by means of
a spirit lamp, a boiling flask, and a cold surface like that of a slato
on which to condense the steam.

How to Secure the Aims.

357

Boiling flask with steam issuing from nozzle of glass tube.

Whilst tracing the entire sequence of events, as above, either by
themselves or under the guidance of the teacher (the less the teacher
does the better), the scholars will find their activities (eye and hand)
agreeably stimulated, and, at the same time, their powers of judgment
and reasoning profitably exercised.

5. Increase and permanence of knowledge. Elementary
science lessons cannot fail to increase knowledge. This will
be in two directions. In the first place, the knowledge of
sundry facts and events gained through everyday experience
will be made more exact and complete ; and, in the second
place, the object lesson will bring under their notice entirely
new matter. The knowledge gained by the methods already
described will furthermore be of a more enduring kind than
that the scholar casually acquires. If any pupil, who has left
his school, be asked what lessons he remembers best, the
reply, with scarcely a single exception, will be the object
lesson. The reason of this is threefold, viz.: (i) the matter
acquired during these lessons is thoroughly understood ; (2)
the matter being of an interesting nature, is deeply impressed,
and (3) the facts, together with their causes and effects, are,
in part, if not entirely, gained by means of self-effort.

35 S - Object Lessons and Elementary Science.

The following instance of the effect of self-activity upon the
permanence of knowledge was recently observed : Out of a class ot
30 pupils one boy only could answer a question which arose during
the course of a lesson. Upon enquiring of the pupil as to the reason
why he remembered the matter so well, he stated that he was
selected to observe that particular matter when the lesson was gi\en
the month before, and was then required to tell the class what he
observed.

6. Increased power in the use of language. An essential
feature in every object lesson is the conversational method by
which it is conducted. The scholars are encouraged to state
in words what they see, and to reproduce in language the
sequence of events which has led up to, or v/hich immediately
follows, the phenomena they observe. The lecture style of
imparting elementary science is entirely avoided. These
lessons are primarily intended to arouse the intellectual
activities of the scholars, and only so far as the children
embody the results of their observation and th.ought in
language can the teacher be sure that the lesson is serving its
main object. It may be necessary at this point to caution the
beginner against accepting incomplete and scrappy statements
from his pupils. The method of conducting a conversational
lesson mainly by questions set by the teacher, and answers to
these questions given by the class, lends itself to short and
often single word statements by the children.

These short answers are sometimes unavoidable ; at the same time, com-
plete statements, and sometimes a lengthened account of an entire sequence
of events, should be received with approval.

To the question, ' What is the river on which the town of York
stands?' the answer is 'TheOuse.' It would be pedantic to say, 'The
river on which the town of York stands is the Ouse.' There are a great
many questions which admit of a similar mode of reply. When a question,
however, assumes the following form, viz., 'The price of a lb. of mercury
is 4s. 6d., how shall I find what it will cost to fill a tube containing 2 ounces ? '
it would be faulty to accept the answer in the single word ' Divide.'
That answer is correct as far as it goes, but it does not state as much as
the scholar should be required to know. The reply should be, ' Divide
4s. 6d. by 8.'

// a reading-booh be used to supplement the oral teaching, it
should generally Le introduced after the new ideas which the reading
lessons contain have been acquired through the oral lesson. The
object lessons in the lower standards should he entirely oral, and the
reading book should be gradually introduced as we proceed upwards
towards the higher classes of the school.

How to Secure the Aims. 359

The young teacher will see in the above an application of the
maxims ' Ideas before words ' and ' Use a word only ivhen it is required^
The reading-book often leaves the scholar with a vague notion
of the meanings of some of the words he has read. These notions
are gained mainly from the context in which the words are
placed. The ideas gained in the reading lesson follow the words,
and are not always clear to the mind of the scholar, In the object
lesson, on the other hand, certain properties of things are first observed ;
these properties in many cases are new ; the scholar needs language
to describe what he observes ; the ideas are first presented to the mind
of the pupil, and the word which follows is associated directly with
the idea. In this way it is shown that the object lesson may be made
a means of very thorough training in the exact u^e of words and
sentences.

7. Moral training through object teaching. There are
certain moral virtues which may be strengthened by the
training which accompanies a course of lessons on objects.
If we wish a scholar to have regard for a thing, the most
effective method of inducing this feeling is to lead him to
understand the object, and thus to become interested in it.
Animals are viewed with greater respect, and are treated with
more kindness, when they are made the subjects of our object
lessons. Some years ago Dr. Fitch publicly commended the
student who, in order to correct the mischievous tendency to
destroy the telegraph wires, which some lads manifest, pro-
posed to begin by giving them a lesson upon the delicate
structure of the instrument and upon its uses.

The power of sdf-appliialion may be strengthened, if not produced, by
the stimulus to activity which the object lesson affords. The patience and
perseverance with which the several stages in an experiment are noted and
registered^ are moral qualities which, when once developed, become
available in the whole range of human activity. The habit of exact state-
ment is in itself a moral virtue, and the ability to think clearly is accom-
panied in most cases by the power to act promptly. The marvellous adapt-
ability which many forms of animal and vegetable life develop in order to
continued existence, awakens a reverential feeling towards the Creator of
these existences. The recognition of the constancy between cause and
effect in the world of surrounding things, leads the scholar to expect the
same constancy of effect to follow his own actions.

For example, the plant, which is regularly watered and is placed in
the sunlight, grows and flowers, whilst another, hid away in the cellar
and allowed to become parched and dry, dies ; the west wind in
spring brings warmth and genial showers, whilst the east wind is
accompanied by cold and an uncomfortable and unhealthy dryness ; a

360 Ohjed Lessons and Elementary Science.

badly ventilated room causes headache; damp feet bring about a
severe cold ; regular food and exercise are conducive to health— these,
and a hundred more sequences of cause and eftect, are recognised by
the scholar. He soon begins to trace these and similar sequences for
himself. The relationship between effect and cause which he looks
for in the events happening in the world around he learns to apply to his
own actions. A due regard for the e'^ect of our actions upon ourselves*
and upon others is a moral conditior the attainment of which by our
youths is much to be desired. In t lis way it may be shown that the
lessons we give in elementary science may be ma le of service
for the strengthening of such moral habits as Kindness tu Animals,
Self-Ai'I'lication, Patience and Perseverance, Exact and
Correct Statement, Prompt Action, and a Regard for
Others.

Courses of object lessons and of lessons in elemen-
tary science.

The following considerations should be taken into account
in selecting these courses of lessons. In the first place, the
subjects should be closely connected with the surroundings of
the learner; the selections of horticulture for elementary science
in a town school, and of electricity in the country school, are
evidently faulty. Secondly, the object lessons taken in the
lower standards should prepare the way for the elementary
science lessons in the higher. Each of these conditions will
now be further examined.

1. Object lessons should tahe note of the child's surroundings. Many
reasons may be urged in favour of this. The material for each lesson can
be easily obtained ; the scholars are already familiar with some of the facts,
and thus there is a foundation of knowledge on which to construct the new
matter ; the pupil becomes interested in conversing about things which are
frequently brought under his notice, both in and out of school ; the matter,
being readily accessible, presents facilities for the exercise of the self-activity
of the learner ; and, finally, the knowledge gained becomes, in time, of
practical value in so far as it becomes of service when the scholar begins to
work with the material.

2. Object lessons should prepare for the more formal lessons of the
elementary science course. Suppose, on the one hand, it has been deter-
mined to take ' horticulture' for elementary science in a country school. The
natural preparation for this course would be a series of object lessons on the

* The most intelligent .Tnd roweiful leader of the working classes, both in and
out of Parliament, stopped H.M. Inspector of Schools in the street the other

day. 'Vou do not know me,' he said, 'I am . The lessons in physiology,

which you encouraged in the school, taught me the value of tiemperanoe and of keeping
niyselfunder healthy physical conditions.'

Courses of Object Lessons. 361

different productions of the field and garden. If, on the other hand, a town
school select the subject of chemistry, an acquaintance with the more pro-
minent aspects of all the common minerals and metals would prove of great
service. It will invariably be found that no solid progress in the scientific
study of any subject can be undertaken until a considerable acquaintance
has been obtained with the facts of which the science treats. The object
lesson of the junior classes should be framed with the view of su^Dplying the
matter to be organized into the science of the higher classes.

3. Examples of the progressive treatment of a subject— object
lessons a preparation for instruction in science. The construction and
use of the thermometer forms a subject of very thorough enquiry in the
' physics course of the specifics ' Children in the lower classes may be taught
to read a thermometer and to note its changes from day to day and during
each day ; thoce in the next higher classes may be exercised in noticing
the changes of readings during a week, a season, or a year, together with
the effect of cloud and of sunshine, of night and of day, and of height of
the sun upon the reading. The facts thus noted incidentally during the
early stages of school work becQme of great service when an enquiry into
the reasons for the phenomena are demanded of the scholars.

Another example of the way in which the lessons of the lowest and
the junior classes may become a preparation for the scientific enquiries
in the later stage is afforded by the following lessons on the seasons.*
Children in the infant school might be taught to relate their experiences
of the changes from the cold of winter to the heat of summer ; they
would associate with the latter the notions of green fields, flowers,
the sea-side trip, and long evenings for play, &c. With the winter
season they would connect the cheerful fire, the ice and snow, the short
day, &c. In the junior classes of the school for older scholars the
above would be remembered, but in addition there would be the
association of duration of sunhght and height of the sun with summer,
and the connection of short days and a low sun with winter. In the
upper standards the reasons tor the above phenomena must be taught,
viz., the earth revolving round the sun, the inclined axis, and the
permanent direction of the axis in space.

Seasonal lessons. Not only should the courses of object essons be
selected because of their connection with the school surroundings, and
because they naturally lead up to the advanced and scientific essons of the
higher classes, but they should be arranged according to the most fitting
period of the year. Lessons, for example, on snow, ice, the bursting ot
water-pipes, the shortest day, &c., should be arranged for the winter perio'l,
wliilst lessons on evaporation, clouds, rain, hail, a thunderstorm, a bird'i;
nest, &c., should be reserved for the summer season.

* The seasons do not form a part of any specific subject. It is a subject augh
generally in Echools, ai.d is selected for ihat reason.

362 Object Lessons and Elementary Science.

Object lessons must be adapted to each school
district.

No special course of object lessons can possibly be sui-ted to
the schools throughout the country. The code supplies an
outline of no less than eleven courses of lessons. These should
be carefully examined, and the one best suited to the school
district should be selected. If no course in the code appear
to be suitable a special one may be drawn up and submitted to
the inspector for his approval. The preceding paragraphs supply
the general principles which should guide the teacher in framing
a special scheme of lessons, A pupil teacher cannot do better
than study the course which has been selected for his own
school. The reasons for adopting the scheme should be sought
and any modifications of it from year to year should be carefully
noted.

HINTS UPON PREPARING AND GIVING AN
OBJECT LESSON.

Careful preparation necessary.

The teacher should make himself acquainted with the matter

by reading it up as widely as possible, by examining the material

to be used, and by rehearsing the experiments to be introduced.

Unless the lesson be thoroughly prepared, some of the material

will almost certainly be wanting when required, and many of

the experiments will fail. The class will require preparation.

They must be placed, for example, so that all can see what the

teacher is prepared to show ; a few bodily exercises and a song

will give them the necessary relief before settling down to the

concentrated effort of attention which the lesson will demand.

A brief outline or sketch of the lesson should be carefully

written by the teacher beforehand. This should not be exposed

to the class ; the effort of writing it will prove an eflTective

means of implanting the stages of the lesson in orderly sequence

in the teacher's mind. All illustrations — the picture, diagram,

objf'cts, (S:c., should be placed so as to be readily accessible

during the progress of the lesson, and a blackboard abstract

should be caref^ully planned before the lesson begins, and appear

on the blackboard when the lesson is completed.

How to Begin the Lesson. 363

The course which the lesson must follow will largely depend upon
what the children already know. If the lesson be given by the regular
teacher of the class the intellectual condition of the children will be
known by him, but if the teacher and class be strangers to one another,
the teacher must take measures to find out, as far as possible, what
the children already know, and construct his lesson accordingly. It
should be remembered that lessons sketched in text-books rarely afford
suitable material for a lesson to be given to any particular class. They
must not be depended upon entirely. The best type of lesson will be
that which is specially prepared for the particular class under instruc-
tion. Furthermore, it should be remembered that the effort of
arranging the matter of the lesson for himself will be the teacher's best
equipment for the task of giving it.

How to begin the lesson.

Very frequently the best beginning for an object lesson is to
show the object itself. If likely to be known by some of the
class, the teacher may ask those who know the object to tell
what it is. If the object be unknown, the name need not be
mentioned at first. A beginning might, in this case, be made
by asking the class to look at the substance, and to state what
they notice about it. If a series of lessons on related substances
be arranged, then a reference to the last lesson will often prove
the best introduction. Suppose, for example, a series of lessons
on the i)recious metals is being given. If a lesson upon gold
(already taken) is to be followed by one upon silver, a simple
introduction might assume the following form : —

Last week we had a lesson upon gold ; you were then taught that
gold was a precious metal ; this week we take another of these metals,
but one not quite so precious as gold. From what you know of the
value of coins, tell me the metal which stands next in value to gold ?
Ans. 'Silver.' Now compare the values of silver and gold, Ans.
'Silver is not so valuable as gold.'

Proceed then to enumerate different articles known to be made of
silver, and allow the class to join as far as they can in naming these.

From this enumeration of common and well-known forms of the
metal the lesson would naturally develop in the following directions,
viz., {a) the class would be introduced to specimens of the ore and would
be shown on a map the countries producing the largest supplies, (/')lhe
method of extracting the precious metal should follow, and (<) the more
important processes of manufacture by which the ore is made to
assume theappearance of coins, jewellery, household silver, &c., should
be illustrated and explained.

The selection of the matter of the lesson.

The selection of the lesson-matter demands the exercise of
considerable judgment. It must be selected and arranged so

364 Object Lessons and Elementary Science.

that at the dose of the lesson the scholars possess a complete,
evenly balanced, sufficient, and well arranged knowledge of the
subject. Care must be exercised, furthermore, to select matter
suited to the pupil's condition of mind and of knowledge, and,
at the same time, it must be sufficiently difficult to arouse
effort, and must be sufficiently valuable to be worth the effort
it arouses.

ia.) Complete, evenly balanced, and sufficient matter. If, for example,
the subject of the lesson be ' lead,' the scholars shi.uld, at the close, have
reliable and sufficient knowledge of its uses, its qualities (especially those
which fit the metal for its different uses), the mode of its occurrence, the places
whence principally obtained, the modes of separating the metal from the ore
and of manufacturing it into the various articles of commerce. An account
which only dealt with one or two of the above topics should not be considered
complete. Sometimes a lesson is heard in which nearly all the available
lime is occupied with the first half of the topics above enumerated. The
even balancing of the different parts of a lesson results from careful planning ;
unequal stress on the different parts invariably follows the lack of a care-
fully thought out plan.

(^.) Suitable Matter. Reading books, encyclopedias, dictionaries, and
text-books present matter in a suitable form for adults. The teacher ot
youth must pass the material obtained from these sources through his own
mind, and bring it down to the level of the child's mind. This is the
most important part of the teacher's work. If, when the knowledge to be
imparted is completely new, the teacher can present the actual material for
inspection by the class, he may impart this new knowledge with very little
reference to what the class already knows. Sometimes, however, it is
difficult to present the object itself, and, in that case, it becomes necessary
to refer the new substance to something that is already known —
platinum, for example, is harder than steel, the diamond more precious than
gold, &c.

Very much of the teaching art depends upon ability to bring the
new matter into relationship with the old, i.e., with that already
known. This process of breaking up the information found in text-
books and of putting it side by side with matter already in possession,
is an essential feature of a successful object lesson.

It is evident that the more the teacher knows about the information
already possessed by the class, the more likely he will be to
bring the matter he wishes to teach into effective relationship with it.
It is also evident that the selection of the matter of a text-book
prepared lesson (whilst it may afford some guidance in the arrange-
ment of the matter) must never be completely relied upon.

Hoiv to Arrange the Matter of an Object Lesson. 365

(<r.) The matter must not be too simple. Care must furthermore be
taken that whilst we bring the matter to be learned down to the level of
the scholar's intelligence, we do not make it too simple. It is equally faulty
whether we proceed above the heads of the class or beneath their level.
The skilled teacher gauges his position frequently and mainly by
questioning his pupils and by noticing the quality of their answers.

How to arrange the matter of an object lesson.

The importance of connecting the new matter with the old
has already been enforced. The value of a natural connection
(association) between the several items of new knowledge must
now be impressed. Isolated facts are rarely, if ever, remem-
bered, and, if remembered, are scarcely ever worth the effort.
Each new idea in the lesson must, as far as possible, be
connected in thought with the one immediately preceding it,
and it must lead to one immediately to follow. In other
words, the matter of the lesson must be logically arranged.

Suppose, for example, a lesson is to be given on 'cork and its uses.'
An ordinary cork is tirst shown. The question ' What is it used for? '
is asked. This question is immediately followed by a second, viz.,
' What is the quality of the cork which fits it for this particular use.'

Having settled these two questions, and associated the compressi-
bility and elasticity of cork with its use for the stopping of bottles,
another use to which cork is put is asked for. In ref ly, the children
may suggest ' for floating nets and for life-buoys.' In connection with
the latter uses, the scholars are again asked to name the quality
which cork must possess in order to render it a suitable float, viz.,
lightness and buoyancy.

Asking for a third use, the notion of cork mats, boot soles, or socks
may be stated, and then the scholars are led to associate with these
known uses the qualities of warmth, impermeability, and lightness.

In this way the class may be led to the association of a number of
ideas in the closest logical order.

Uses of Cork. Qualities fitting cork for each use.

1. For stopping bottles. i. Compressibility and elasticity.

2. In order to float nets and buoys. 2. Lightness, hence buoyancy.

3. For mats, soles of boots, and 3. Warmth and impermeability.

socks.

Faulty associations which lead to mechanical results.

There are other associations which are familiar. For example,
lessons are frequently arranged in which all the qualities are
associated in one stage, and the uses in a succeeding stage.

366 Object Lessons and Elementary Scie7ice.

The lesson upon cork, prepared on this plan, would assume the

following form : —

Stage I. — Qualities of Cork.

(a) Vegetable. . (f) Opaque.

\b) Solid. (/) Buoyant in water.

[/) Compressible. {g) Contlnistibh-.

\d) Elastic. {h) Impermeable.

Stage II.— Uses of Cork.

(a) For stopping bottles.

(/') Floating nets and buoys.

(<-) For mats, socks, and soles of boots.

It may no doubt be urged that it is quite logical to arrange all the
qualities under one heading, and the uses under a second ; hence in
text-books and in some 'Notes of lessons ' the qualities and uses are
arranged in the manner described. This text-book ordering, however, is no
reason why a more logical arrangement should not be attempted. Lessons
are often rendered most mechanical, both in their delivery and in their effect,
by stating all the properties of the substance in one stage of the lesson, and all
the uses in the following stage. Besides the mechanical effects which
result from lessons on objects being thus arranged, there is the further
weakening effect of bringing in a number of properties possessed by the
object which are of no real value so far as its uses are concerned.* In
order, however, to make up a list of qualities, these useless ones are
enumerated, and are often repeated over and over again in a series of
similar lessons.

If theaoove qualities of cork be examined, it will be seen, at once, that
the qualities in italics are not required when the uses of cork are being
considered. We advise the teacher first to collect the i/ses to
which the material is put, and then to find out the qualities which
adapt the material to its various uses, and finally to omit altogether
the other qualities for which no uses can be assigned.

* The following description of a faulty object lesson is, without doubt, overdrawn.
So far, however, as it is true, the lesson it describes would follow the faulty arrange-
n>ent already mentioned. 'I do not know,' writes an Inspector in the Blue Book,
' if it is the case with my colleagues, but there are certain so-called " object lessons "
that come upon me like the repetitions of a hideous dream. I seem to have heard
them all before in some previous stage of existence. I know what the questions will
be, I know what the children will answer, and I know what is coming next. And then
I see the fatal .apparatus got ready, the black-board and the chalk, and the picture-
card or the object — ' camel ' or 'lump of coal ' — and the victims are also ready on the
gallery, with an air nf ••esignation (for they know it all too), and the teacher with her

best manner survejs her class, and then

" Projicit ampullas et sesquipedalia verba."
and I am told (or rather the children are told) that the object before them is,
nopaque " or "tangible," or "transparent," or what not; or that the animal is
agregarious," or "carnivorous," or a "marsupial" and all this is carefully written
down on the blackboard and the words repeated by the children, and so on until the
fatal 20 minutes have expired- Anything more formal, dull, and mechanical than an
object les.son of this sort can hardly be conceivid.'

Frovi the Kiiown to the Unknoivn. 367

The matter must be arranged so as to proceed ' from
what is known to what we wish to teach.'

The educational maxim ' from known to unknown ' briefly
sets forth the principle which we wish now to impress. In the
lesson on cork, for example, the uses are well known.
They form a natural starting point in the lesson. Perhaps
the scholars have never thought of the qualities which
permit the cork to be put to its various uses. We wish to
teach these unknown qualities, and, in order to do this, and at
the same time to comply with the above educational maxim,
we begin with one of the uses of cork (the known), and
immediately proceed to associate wath it the quality (the
unknown) which gives the corks this particular use. Thus in
making the uses of a common object our starting-point, and
in proceeding to the qualities from the uses, we not only
arrange our matter logically, but we work in harmony with one
of the most widely accepted maxims in education.

The same holds true again if we examine a lesson on any of the common
English metals. If we start with the ore we begin with the unknown,
and we are obliged to proceed by telling the class a number of facts about
the ore ; whereas, if we start with the common and known uses
which are made of the metal, the children are immediately brought
actively to take part in the lesson ; they are easily and naturally led
from the uses to the qualities of the substance, and from these they
proceed to the method of producing it from the ore, and, finally, to the
areas in which the metal is found.

The matter must be presented so that the teaching
proceeds ' from the concrete to the abstract.'

In the higher stages of elementary science our lessons should
result in the formation of definitions, and the establishment of
principles. Comparison of objects leads to their arrangement
in classes. In order to distinguish by statement one class from
other classes, it is necessary to formulate a definition. If, for
example, we take a group of animals such as the cod, frog,
herring, crocodile, sole, whiting, and seal, we find that there
are two distinct classes into which they may be arranged, viz. : —

1. The class distinguished by living ~|

always in the water and breath- >Cod, herring, sole, and whiting,
ing by means of gills. J

2, The class distinguished by living 1 E- j-i j 1
V .^v • . ^1 1 1 ^ \\! rog, crocodile, and seal,
both m water and on and. J ^' '

2 68 Hoiu to Teach Geography.

North Downs. Their action cannot be explained to youn<T
children. Only those who are able to realise the geological
truth, that at a'time in the distant past the North and South
Downs were connected, and that the rivers flowed along the
long chalk slopes northward to the Thames and southwards
to the sea ; only those who can thus be led to understand that
these are old watercourses which have never broken through
a chalk range, but which have lowered their course in that
range by natural wear and tear, and have been continued
beyond the North Downs by the slow upheaval of the Wealden
area of Sussex ; only such can understand the physical geo-
graphy of the hills and rivers south of the Thames.

All this is beyond the power of a young child. In fact, it is matter
which is beyond the knowledge of some who have written on the
subject of physical geography for the instruction of adults. The rivers
of the south-east of England have been noticed, in so many cases, to
pass right through the chalk hills, that those who simply look upon
these rivers as they appear to-day have come to the erroneous
conclusion ' that chalk hills do not form watersheds, but that they allow
the rivers which approach to break through them.'

The young teacher will be careful to select the district for his first
lesson with a view to avoiding such difficulties as those presented by
the south-east of England. It will always be true that rivers must flow
along a downward slope. Plenty of examples may be found to illustrate
the truth, and to do that without the accompanying difficulties indicated
above. These difficulties are stated here in order to show that the
relation between the direction of hill ranges and river courses is not
always easy to understand. In all obscure cases the teacher should
leave the explanation of them until the children are capable of profiling
by it. He should, especially be on his guard against attempting an
explanation which (like the one suggesting that the tributaries of the
Thames have broken through the North Downs) is perhaps simple
but, at the same time, is incorrect.

The order in which the truths enumerated above
should be taught.

We are now in a position to review the order in which the
various stages of tcacliing the geography of hills and rivers
should be taught. The highest land masses should be
indicated in the first place, and the direction of the slopes
should be examined on a relief-model, until the pupil is able

Physical Geography of Hills and Rivers. 269

to recognise (read) the same features on a map without the aid
of the model. The directions of the rivers should be inferred
by the children and their positions indicated by the teacher.
Riuer valleys follow next in order, and should be associated
with the work of the river. Hills are then introduced, and
should be seen to result mainly from the action of the river.
Finally, the smaller streams (tributaries) should be shown to
run along the slopes of the hills which separate the main
streams. When the nature of the connection between slope,
river, valley, hill, and tributary has been taught, it will not be
difficult to show that the longer time the river works, the
lower and wider the valley ; and that the longer the slope is in
space the larger and deeper must be the river.

It has now been shown how the most important truths of the physical
geography of hills and rivers may be illustrated by reference to the map of
Enjrland. The method of teaching has been indicated. A similar method
should be followed whatever may be the class under instruction, or the
district under investigation. The results of teaching geography by the
methods indicated will be far in advance of those which follow the method
of merely learning by heart the positions and names of the several physical
features, without any attempt to present them in their natural relations.

An objection raised and answered.

An objection may be raised against the attempt to teach
these truths to very young children, the objection, viz.. that it
is far too difficult. No doubt it would be folly to try to teach
such matters as fully as they must be known by pupil teachers
who have a similar geographical exercise in the first year of
their course. If, however, the i)lan of using simple relief-models
and of utilising simple experiments and experiences be adopted,
there is no reason why a beginning should not be made (even
at this early stage) to connect the features of hill, valley, and
river structures with one another, in a natural and rational way.

This is not the place to discuss the order in which subjects are
appointed to be taught, but rather to show tne best way of teaching
these subjects. The physical geography which does not attempt to
show how the high land influences the course and flow of a river ;
how the river gradually scoops out its valley and leaves the hill inter-
vening between it and a neighbouring river; and how the tributaries
of the main stream are eventually formed, is not worthy its name.
Unfortunatelv, the name has long been applied to tabulated statements

37 o Object Lesso?is and Elementary Science.

NATURE-STUDY.

Nature-study is the exercise, first hand, of child observation
of simple and familiar objects and events and of the changes
these undergo with a view (^7) to increase knowledge of, and
interest in them, and (/') to develop the ability both to observe
and to record the results of such observation.

In answer to the question, ' What are we to understand by Nature-study ? '
Prof. C. Lloyd Morgan replies : ' A process by which simple natural
objects and events acquire meaning,'' and, he adds, 'the value of Nature-
study lies not chiefly in the imparting of a particular kind of information ;
it consists not so much in what is taught as in fostering an attitude of mind,
an attitude of observational alertness, of enquiry into the meaning of
familiar facts in the garden, Held, and hedgerow.'

Nature-study and Science.

Nature study must not be confounded with science. It should lead to
science, and, indeed, it should form the best preparation for science. So
long as the learner is noting simple changes in phenomena and events, and so
long as he is simply recording their sequences and their most obvious
natural associations, he is engaged in Nature-study, but when he advances
by an effort of imagination and deductive reasoning to the forming of
theories, or by further efforts of reasoning to the establishment of principles
he has left the realm of Nature-study and entered that of Science.

Whilst it is necessary not to confuse Nature-study with Science, it is
equally necessary to avoid making Nature-study a merely superficial
review of isolated and detached facts. Orderly sequences and organic
connections are sought out and recorded ; any fact or event is studied
in its relations to others with which it is naturally and organically
allied. For example, suppose the life history of a plant such as that
of the bean, from seedling to maturity, is being observed ; the series
of changes it undergoes are noted (drawn) ; at the .same time its
dependence upon soil, moisture, sun, &c., are recognised. In this way
the pupil not only uses his eyes and becomes able to state what he
sees ; he is led to see how many apparently different phenomena —
growing-plant, cloud, rain, sun, and soil, are naturally related.
lie is led from the use of his senses to the higher exercises of
thought.

Aims of Nature-study. These are many. The follow-
ing are the most important. Accompanying each is a brief
statement in explanation of it.

(7), To awaken interest in the Environment of the Home
and Sciiool.

One of the essential conditions of all Nature-study is that objects them-
selves, and not text-book descriptions of them, shall be presented. The
investigation of these objects, especially if they can be induced to assume
variations and change is invariably, even with young children, accompanied
by that pleasurable activity termed interest. This needs only to be stated

Nature-stttdv. 371

to the practical teacher. His difilculty lies in the fact that this presenta-
tion of objects direct to each child demands individual teaching, whereas his
experience has fitted him for dealing with classes of children. The reduc-
tion in the size of the classes under a given teacher becomes necessary, in
order successfully to interest young children in Nature-study.

{2). To supply material for evoking, and developing
intellectual effort.

What has been said on the intellectual value of object lessons and ele-
mentary science on previous pages may be recalled here. Young learners
never /oo/^ so intently as when observing some natural object, especially
when they know that something new is awaiting their view. Further, what
they themselves thus intently observe is permanently remembered, and if
the image recalled by memory is compared with some allied, but not present,
object, as when, for example, the recalled image of a thoroughly well-known
rabbit is compared with that of the rarely seen hare, or contrasted with the
still more rarely observed squirrel, an effort oi imagination is aroused ; and
should the exercise of contrasting and comparing a number of allied animal
forms be carried sufficiently far, type figures will be gradually formed and
the exercise of generalizing be aroused. Thus the intellectual efforts of
sense perception, memory, imagination, and the forming of general notions
are shown to be exercised.

It should be noted that the early lessons in Nature-study call into
play the efforts of sense perception and memory — dealing mainly
with the shape and structure of plants and animals, or with the more
obvious changes, which at different stages of life they exhibit. It
would be after a considerable number of somewhat similar objects had
been thoroughly examined and compared that the generalizing pro-
cesses have sufficient material for their successful exercise.

(5). The Higher Aims termed Moral and /Esthetic could not fail

to accompany the more intimate acquaintance with natural objects which
Nature-study encourages. The extreme beauty of flower, leaf, fruit, and
of animal form ; the habits of cleanliness amongst the latter and of
care for their young, — these must impress the learner much more power-
fully than woukl the abstract teaching of the school-room. Even the
struggle for existence which some organic forms appear constantly to main-
tain, such as the flower amongst weeds and insect pests tend to encourage
the learner to patient endeavour under difficulties. A greater regard for
lowly forms of existence and for life generally must ftillow the deeper
insight which Nature-study aflbrds.

(4). The Aim of Making other Subjects of School Instruc-
tion more Life-like and Interesting.

The Nature reading lesson, whethet poetry or prose, will be better under-
stood and hence will be accompanied l)y a livelier imagination and fuller
expression ; ilrawing, in which forms actually seen are reproduced, will
awaken a more exhilarating efibrt than that expended upon the most care-
fully produced but meaningless set of straight lines, curves and angles; the
lesson in geography, which is based upon a knowledge of areas actually
explored and hence familiar, will gain in reality and effectiveness.

In the lower quarters of certain large towns it has been noticed that
children in Elementary Schools appear to be quite happy and alert up

372 Object Lessons and Elementary Science,

to the ages of 9 and 10. After that age they tend to become listless
and are inclined to truant playing. This experience may be accounted
for, in part, by the fact that the work of the junior and higher classes
of these schools— largely literary in the past, finds little in the nature
of these children to which it can attach itself. The introduction of
objective study and of manual instruction will, it is hoped, tend to
make school work generally more natural and interesting.

(5). Increase of Knowledge.

This aim is placed last, not however because it is considered the most
important. The knowledge acquired in Nature-study is of little value com-
pared with those educational effects already enumerated. At the same time,
seeing that the matter of study is accounted of little value whilst the method
of enquiry and the educational effects are of highest worth, it seems not
unreasonable that subjects should be selected for study which are likely
to prove of greatest practical account. Herbert Spencer held that it was
against true economy that Nature should provide one set of exercises for
niental discipline and another for practical worth. He held that_ the
exercise of greatest utility would prove of highest value for educational
effect. Nature-study demands the observation and study of the objects and
events in the immediate vicinity of the scholar, and a thorough knowledge
of these, whilst providing for the wise exercise of intellectual, moral and
esthetic activity and feeling, will at the same time prove of greatest
practical utility.

Forms of Nature-study.

The form which Nature-study takes depends upon two
factors, viz. : (^7) the locality, whether urban, sub-urban,
country, seaside, manufacturing, mining, c\:c., and {l>) the
teacher and his special aptitudes and knowledge. Some
oiiginality should find expression in all Nature-study. Mere
repetition and imitation will not do. Work must be done
which both teacher and taught can legitimately call their own.

Recently, a class of pupils, working together near the banks of the
Thames were required, for a fortnight, to make the river a special
subject of observation. The movement and height of the water on
successive days very naturally formed a feature in their observations.
Most of the pupils embodied these in a tide-table. Some constructed
this from data obtained by observing the height of the river water
against steps leading to a landing stage. One of their number
uiliinalely found the official tidal gauge and succeeded in obtaining and
copying the curve 011 sciuire paper, representing very completely all
that the others had, with considerable dilficulty, found for themselves.
Now, although the knowledge gained by this particular youth was
more reliable than that of the others, yet, inasmuch as it wvas gained
Viy merely making a copy of what was done by another the exercise
failed as a I'orm of Nature-study.

Amongst tlie forms of Nature-study at present developed
and which yield the best results are the following : {a)
Studies on Living Things -Plants and Animals ; (/!»)

Nature-study. 373

Seasonal Studies including records, diaries and calen-
dars ; (r) School Journeys and rambles with geography,
physiography or botany as the guiding idea ; id) School
Gardening-,
(a). Studies on Living Things.

The Jiuiges' report on the recent Nature-study exhibition in London
states : ' We are inchned to put in the very first rank of merit, successful
and interesting work on hving things. The collecting, mounting, and even
study of a dead ol)ject, though it may be important when directed by a
spirit of scientific enquiry, is in general of much less value than the study
of the living.' Amongst instances of approved plant and animal studies
are the following : —

1. Dated drawings of stages ot growth of bean, pea, &c.

2. Drawings of developing leaf- and flower-ljuds.

3. Representations of the different parts of complete flowering plants
— dandelion and buttercup, with comparisons and contrasts, to be
followed by lessons connecting, as far as possible, structure with
function, and by experiments showing absorption of moisture and its
circulation through plant tissues.

4. The successive stages of silkworm growth from egg to moth, with
drawings from the objects themselves.

5. Similarly, from spawn through tadpole to frog.

6. Domestic pets — e.g., the rabbit, its structure, habits, and disposition,

7. Aquaria and vivaria.

(6). Seasonal Studies.

Very much of Nature-study must necessarily vary with each season.
Many changes in plant and animal life are determined by the changes of
season. The effect of temperature, of cloud and rain, of sunshine
and frost should form an integral part of the instruction. Nature
does not present us with scraps and tit-bits of information. The shoot-
ing star may appear to the casual observer to be a very detached and
isolated phenomenon, but to the astronomer the earth which attracts it and
the atmosphere whose resisting pressure fires it, both stand in most intimate
relation to it.

The construction of floral, bird and insect diaries, if kept for com-
parison with seasonal variations in successive years, may prove useful ; but
there is danger in this form of observation becoming formal and detached.

(C), School Journeys and Rambles should each have a definite
aim, and should be preceded by directions suflicient to keep the observation
of the scholar from dissipating itself upon a multitude of things, attractive it
may be, but not of value for the special object the journey is planned to
accomplish. The writer has found during a long experience in conducting
school journeys that the wriggling of a snake, or the sight of a ripe black-
berry has most effectiv-ely diverted attention for a linre from the physio-
graphic aims he had in view. The association of map, plan and section, is
absolutely necessary in all these journeys. They should be constructed and
studied by each pupil. The study of a given district by actual field
observation, accompanied by the construction of maps, &C., yields the best
preparation for the study of geography.* Joseph Lancaster used this

* Fuller accounts of three School Journeys arejgiven in ^ Sbhool "Journeys' (Cowham),
Westminster School Book Depot, S.W.

374 Object Lessons and Elementary Science.

method of teaching first notions of geography a century ago. He took his
pupils from his school in the Boro' to the open spaces of Clapham and
Tooting.

((/). Gardening.

'\'<j those who have been associated with Englisli education for many
years it is interesting to see how the new only reproduces the old. A
special feature in the three large playgrounds attached to the practising
schools at Westminster was the allotment in 1851 to each child of a border
garden plot. At Battersea, garden culture formed a special feature in the
training of each student. The last garden plot at Westminster disappeared
in 1865, three years after the introduction of the new code of Mr. Lowe.
The late Mr. Rooper, H.M.I., speaking at the congress on Nature-study,
said : ' the great educational problem of the times is how to secure the
acquisition of knowledge without sacrificing power to act. In the solution
of this problem one important factor will be found in the right use of a
school garden.' He further divided the subject under the following heads :
' The site and aspect ; scjii and its improvement l)y .spade-work, draining,
and manuring ; the build of a plant ; what a plant is made of; how plants
are nourished and their organs of nourishment ; sap and its movements ;
conditions of healthy growth ; germination; flowering, fruiting, and seeding
of plants ; annuals, biennials and perennials ; evergreens and deciduous
trees and shrubs ; the dependence of plants upon insects.'

' Besides positive knowledge the work of the garden cultivates a
love of industry, order and tidiness ; it builds up a feeling for beauty
of form and colour in flowers and trees and fruit, and touches the
heart of man as well as his brain. It is a natural gyjnnastic, and
bridges over the space that separates physical and intellectual growth.
It supplies a link between learning and life, and though it trains neither
the agriculturalist, nor the horticulturalist, in any immediate way, it
predisposes youths to interest themselves in these industries ; and if it
be their lot in after life to earn their bread in jnirsuit of them, it does
nothing to give a distaste for such occupation, and yet it by no means
unfits young people for any other.' \OjJkial Report of Nature-study
Exhibition, Blackic).

Connections with other School Studies.

The association of drawing witli every branch of Nature-
.study has been constantly uryed. The encouragement given
the pupils to converse and describe orally or by formal
composition ; the appreciation of the literature inspired by
Nature — poetry as well as prose; the ground-work supplied
for the teaching of geography and the introduction to the
formal study of the Natural Sciences are other important
connections.

Nature-study has its limits, ii does not provide for the study
of the accumulated exj)ericnces of past ages, and it leaves out of account
the important lessotis which these recorded experiences are intended to
teacli. Thougli it sui)plies means for tlie use of language, it omits all
systematic study of language. It cannot, except in a very limited
fashion, supply exercises for the formal study of arilhiiielical processes.

Appendix. 375

APPENDIX.

The Board of Education have issued a pamphlet of " Suggestions
for the Consideration of Teachers."* Very many of the methods
sketched in the foregoing chapters are enforced, and especial
emphasis is laid upon the necessity of stimulating the self-
activities of the scholar in all branches of school instruction.
The following paragraphs on the Teaching of Infants is re-
produced and represents very fairly the general style of the
pamphlet. It should be obtained and carefully studied.

INSTRUCTION OF INFANTS.

The leading principle which determines the methods of education suitable
to early childhood is the recognition of the spontaneous activities of the
children. These are immediately recognisable as a love of movement, a
responsiveness to sense impressions, and a curiosity which shows itself in
the eager questions of intelligent childten. Most children love to arrange
things and rearrange them, and young children are readily absorbed in
stories of strange or wonderful persons or events.

It is with these powers of childhood that the teacher has to deal, and the
process of education up to five or six years of age consists in fostering their
harmonious development, taking care, above all, that as little constraint as
possible is put upon free movement whether of body or mind.

What are known as " Kindergarten Occupations " are not merely pleasant
pastimes for children ; if so regarded, they are not intelligently used by the
teacher. Their purpose is to stimulate intelligent individual effort, to furnish
training of the senses of sight and touch, to promote accurate co-ordination
of hand movements with sense impressions and, not least important, to
implant a habit of obedience. Each Kindergarten occupation should have
its own purpose.

Care must be taken to see that the children are really occupied, and are
not merely mechanically repeating what the teacher shows. A Kinder-
garten occupation is not intelligently used if the children merely follow step
by step without initiative the procedure of the teacher, with intervals of
idleness during which the teacher visits each child in turn to adjust his work
if necessary. Whatever processes the child is called on to repeat should be
shown as a whole and repeated as a whole by each child independentlj'.
Better still the children should be allowed to devise their own applications
of the material given them in order that they may realise their own powers
of invention which otherwise may lie entirely dormant.

Formal teaching, even by means of Kindergarten occupations, is un-
desirable for children under five. At this stage it is sufficient to give the
child opportunity to use his senses freely. To attempt formal teaching will
almost inevital)ly mean, with some of the children, either restraint or over-
stimulation, with consequent dangers to mental growth and to health.

* Wyman & Sons, Fetter Lane, E.G. Price 7d.

376 Appendix.

Formal lessons may be given to children of five years of age, but any
attempt which may be made to reach a definite standard of knowledge of
reading, writing, and number at the age of seven should be subordinated to
the more general aims of physical and mental development and training in
hai)its of obedience and attention. The older children in some infants'
schools have been periodically examined. This practice should be entirely
abandoned.

The following lists of occupations will serve as a guide to teachers of
infants :—

For Children between Three and Five years of age : —

Games with music. Guessing games and others (without music).
Recitations of nursery rhymes and very simple verses. Picture lessons in
which the children tell in their own words what they can see in the picture.
Mosaic with coloured tablets. Drawing in sand, and with free strokes on
the blackboard or prepared wall. Matching colours from a heap of coloured
wools. Setting a table {e.g. carrying a glass of water without spilling it).
Knitting with large needles. Threading large beads in twos and threes,
and higher numbers. Arranging shells in twos, threes, etc. Arranging
pictures of number with cubes. The laying of sticks. Building with bricks.

For Children between Five and Seven years of age : —

To the above may be added — Brush drawing. Drawing with the pencil
on paper. Descriptive lessons. Observation lessons. Story lessons from
fairy tales, from the lives of great and good men and women, or from the
travels of explorers, retold by the children in their own words. Mosaic
with coloured paper and gum. Ruling simple geometrical forms.
Measuring and estimating length and weight. Modelling in clay. Basket
work. Cutting out patterns and shapes with scissors. Ball Games.

Throughout these occupations children should be taught the care of school
materials.

Lessons given to infants may often be associated with each other through
some leading idea or ideas, and each object or idea shnuld be treated so as
to call into play as wide a range of activities as possible.

For example, if the teacher takes a domestic animal as a subject for study
by her class, she may usefully give a lesson in order to explain its habits and
characteristics ; a drawing lesson to impress knowledge of its form ; a song
or story bearing on its association with human life. If the children have
reading books or sheets with information on this animal they will be
interested in seeing the written words at the same time as they are receiving
oral lessons. If the teacher makes sure that the children are actually able
to see and observe the animals chosen for the lessons, she can thus make the
scholars interested in them, and can foster kind treatment of them.

Each lesson should give the children new impressions, but each should
spring naturally from some other lesson, and should make use of the former
impressions of the class. Children should always be encouraged to say
without interruption and in their own words what they know, what they
want to know, and what they think, about any object which is made the
subject of a lesson.

Appendix. .377

OBJECT TEACHING.-Circular 369.

Education Department,

Vv'hitehall, London,

2Sth June, iSgj.

Sir,— It has been observed that in schools in which Object Teaching has been
introduced with most success the teachers have carefully distinguished between two
kinds of instruction which in other schools are not seldom confused. These two kinds of
instruction are — ' 1 1 observation of the Object itself, and (2) giving information about the
Object. This distinction is of importance, because the scope and method of the lesson
differ according to its nature. Object Teaching leads the scholar to acquire knowledge
liv observation and experiment ; and no instruction is properly so-called unless an
Object is presented to the learner so that the addition to his knowledge may be made
through the senses.

Junior teachers have not unfrequently given lessons before H.M. Inspectors which
were wrongly described as Object Lessons because in dealing with the topic selected no
suitable appeal was made to the eye of the scholar. A lesson, for example, on the
elephant to children in village schools who have no o;)portunity of visiting either
Museums or Zoological Gardens, may convey information and store the memory with
interesting facts, but it does not cultivate the habit of obtaining knowledge directly and
at firsthand, or develop the faculty of observation. However well the lesson may be
illustrated by diagrams, pictures, models, or lantern slides, if the children have no
opportunity of handling or watching the actual object which is being dealt with, the
teacher will be giving an Information Lesson rather than an Object Lesson. It should
be always remembered that in Object Lessons the imparting of information is secondary
to the cultivation of the faculty of observation.

Object Teaching should further be distinguished from Instruction in Natural Science.
It is Elementary Science onl)' in so far as it aids the child to observe some of the facts
of nature upon which Natural Science is founded ; but as it deals with such topics
without formal arrangement, it diff"ers vvidel)' from the .systematic study of a particular
science. The principles of scientific classification, the continuous study of one group of
natural phenomena, the generalization from facts and the search for natural laws, belong
to a later stage of mental discipline, which will be much more eff'ectual if it is being
b.ased upon the preliminary training of the senses through sound Object Teaching. It
is most important, therefore, that if, for example, Object Lessons are given on plant life,
no attempt should be made to treat them as a continuous introduction to the studj' of
Botany, or if the lessons relate to animal life, to the study of Zoology. In Object
Teaching, the chief interest in the lesson should centre in the Object itself.

The following suggestions, which have been made by practical teachers, will be
found useful : —

(i.) The teacher should select only so many of the Objects set forth in the appended
or other similar lists as can be dealt with in the year without overburdening the
scholars. Habits of observation are better cultivated by the thorough examination of a
few objects than by the superficial treatment of manj-.

(2.) No object should be chosen which the teacher cannot thoroughly illustnte
either by the Object itself or by some adequate representation of the Object, or by both.
All that is purely technical, v/hether in the mode of study or the language and
terminology, should be carefully avoided.

{3.) The children should be encouraged to bring with them to the lesson illustrative
speciinens which they have collected or borrowed from friends.

(4.) The children should be encouraged to make simple ura wings illustrative of their
observ.ations wherever possible, and in certain cases to make simple records on square-
ruled paper. Clay modelling and 01 her manual occupations may be employed to test
the accuracy of the impressions v.hich the children lorin, .and to fix them in their
muids. Teachers .also shuuM frequently illustr.ite details of the lesson by bl.ack board
drawings. Children who .ire j.iileil in five minutes by .a lecture will be open-eyed and
receptive for haU' uEihour while the teacher draws as well as talks.

378 Appendix.

(5.) Visits to Museums and other institutions of educational value are now recogni/.ed
by the Code, and may advantageously be undertaken where possible in connexion with
the Object Teaching. Occasional class excursions out of school hours (or, if the
instruction be in accordance with Art. 12 (y!) of the Code, in school hours), under proper
guidance, will enable teachers both to provide suitable Objects and to confirm previous
impressions. It should be borne in mind that Objects, when they are brought into the
class-room, cannot be there studied under their ordinary conditions ; and therefore it is
important by a proper use of such expeditions to let the children see what part the
Object plays in its usual surroundings.

(6.) If the scholars are to learn intelligently from their Object Lessons, the first
requisite is trained attention. The right method of securing this is to direct, in a con-
versational way, the attention of the children to the different parts of tlie Object in an
orderly manner, and explain the relation of each part to the whole. After the analysis
or study of separate detail, the Object should be again treated as a whole. It should
not be left in fragments, but the division into parts should be followed when possible by
the reconstruction of them into their original unity. Through such teaching the vague
and indefinite impressions which children receive from Objects when they are first
presented to them are gradually converted into clear mental pictures.

(7.) The attempt to teach children to be accurate in observation cannot be separated
rom tlie need of making them accurate in description. After the children have been
trained to observe a fact they should be practised in making a correct .statement of it in
a sentence of their own. This oral answering in complete sentences will lead to correct
use of the English language, both in talking and writing, and will store the mind with a
useful vocabulary. In the higher standards the children will be able to write briet
weekly compositions in which they may express in a written form the ideas which they
have acquired through oral instruction.

To sum up the main value of Object Teaching, there are three principal uses. The
first and most important is to teach the children to observe, compare, and contrast ; tlie
second is to impart information ; and the third is to reinforce the other two by making
the results of them the basis for instruction in Language, Drawing, Number, Modelling
and other Handwork.

There, are, however, other important uses of good Object Teaching. It makes the
ives of the children more happy and interesting by opening up an easily accessible and
attractive field for the exercise of brain, hand, and eye. It gives the children an
opportunity of learning the simplest natural facts and directs their attention to external
Objects, making their education less bookish. It further develops a love of nature and
an interest in living things, and corrects the tendency which exists in many children to
destructiveness and thoughtless unkindness to animals, and shows tlie ignorance a.nd
cruelty of such conduct. The value of the services which many animals render to man
should be dwelt upon, and the importance of kindly treating tiiem and preserving them
should Vie pointed out. By these means, and in other ways, good Object Teaching may
ay the foundation for the right direction of the activity and intelligence of the children
throughout the whole school.

I have the honour to be, .Sir,

Your obedient Servant,

G. W. KEKEWICH.

OBJECT LESSONS:—

The following lessons deal with the ordinary phenomena of common life and with
objects familiar to the children. The teacher's choice is not confined to these lists ;
other objects will be accepted suViject to the approval of the Inspector. Any of the
obiects may be dealt with at the discretion of the teacher in more than one lesson, and
although they liave been grouped for convenience of reference, it is not intended to
prescribe any specified number of them for a yearly course. With difXerent treatment
the same object may be adapted to more than one standard. .Some teachers may prefer
to deal with the same object in successive years, or to recur to it after a year's interval,
expanding the study to suit the growing powers of the scholars. 1"o meet the varying
requirements of teachers it will be noticed that in some cases the names of the objects
have been merely enumerated, while in other cases a few suggestions have been added
as to the mode of treatment.

I. Plant Life.

(a.) The study of plants as growing things. — Crow an onion in a bottle ot water
and note appearance of root ;ind stem. Make a model in cl.iy of the various stages of
growth at shoi ititcrvals. Grow mustard seed on d.iiiip tl.innel and note stages ot
growth. Notice a few curious roots.— The carrot. Cut ofT the lop of one and grow
it in .1 saucer of water. Contrast the root of a daisy (fi'orous). Koots which walk.

Appendix. 379

Strawberry or strayberry. V'iolet root. Contrast root of Iris and Solomon's Seal in
ttieir mode'i of extension. Stem. — Count the rings in a trunk that lias been felled.
Rings, how produced ; estimate age of tree ; the record of wet or dry seasons.
Climbing stems. — Ivy. Train bindweed up a stick and note that it turns to the right.
If you unwind it and force it the other way (to the left) note how it resumes its old
direction again, holding the stick with one of its leaf stalks to get a purchase for the
change. Simple experiments to show effect of light on (i) leaves and (2) roots.
Celery; blanching. Leaves of deciduous trees contrasted with leaves of evergreens.
Contrast leaves of holly, ivv, .Tiid box with leaves of oak. elm. and beech. Note
autumn tints. — Collect and pre^s k;i\es of various colours in autumn. Buds. — Leat
buds and flower buds. Parts of a flower. Fruits. — Diflferent kinds.

(b.) Blossoms, Fruits, Seeds, and Leaves. — Parts of a flower. Flowers of curious
shape. Pea blossom Insects and flowers. Colours of flowers and insects. Fruits.
How seeds are scattered. Shooting seeds. Flying seeds. Curious flowers, e.^.,
primrose: compound flower (daisy): water lily. Leaves. Shape, veining, arrange-
ment. Flowers as supplying (i) weather-glass, (2) clock, (3) calendar. Examine celery
plant. Cut leafstalks into thin sections to see how a plant is built up.

(c.) How plants are adapted to their surroundings. — A bimcli of spring, summer,
or autumn flowers (according to time of year). Flowers and the soil. Bog plants.
Riverside plants. Plants that grow in running water. Plants that grow in still water.
Meadow plants. Plants of the heath and moor. Plants of the hills. Plants of the
wood. Plants of the sea-coast and salt marshes. Sundew and flesh-eating plants.
Ferns. The spores of ferns. Grow some spores in a pan under glass and watch
growth and development of a fern. Contrast with growth of mustard from seed.
Mosses. Lichens. Funguses. .Simple experiments in manuring plants. How plants
help or hinder each other's growth. Parasites. Mistletoe. Plants which help or
injure man.

II. Animal Life.

(a.) The Cat (compare with Dog). —Eyes, rough dr\' tongue, soft pads and sharp
claws, teeth, method of holding prey, drinking, covering of fur, whiskers, tail. The
Cow (compare with Slieep and Goat;. — How she takes her food, teeth, chewing, milk
(cheese and butter), tail, hoofs, covering, ears, horns, nose. The Horse (compare with
Donkey) —Covering, teeth, hoofs, tail, mane. The Rabbit (compare with Hare).
Teeth, lets, feet, claws, covering, tail, whiskers, ears, eyes. The Mouse (compare
with Rat and Water Rat). — Teeth, paws, tail, whiskers, e\es, ears. A Fish. — How
titled to live in water, weight, shape, covering, temperature, movements. A Plaice
^ o iip.irc with Herring) — P^Iat, eyes on one side of head, gi!ls, movements. Animals
which sleep in winter. — Examples : squirrel, dormouse, common snake, frog, toad,
snail, slug. Preparation made for sleep.

fb.) Mole. — Shape, snout, teeth, paws, claws, eyes, ears, ur, food. Hedgehog.
— Covering of spines, hosv it rolls itself into a ball and why, head, teeth, food.
Common Snake (compare with Viper). — Shape, covering, teeth, how it moves, how it
swallows its pre}'. Frog (compare with Toad and Newt). — Movement, capture of
prev, breathing, winter quarters. Garden Snail 'compare with Slug). — Shell, mantle,
head, horns, eyes, food, preparation for winter sleep. Earth Worm. — Shape, rings,
locomotion, food, usefulness. Spider ('contrast with Bee). — Shape, segments, legs
eyes, jaws, spinnerets, web. breathing organs.

tc.) Paws and Claws and their uses.- Cat, dog, rabbit, mouse, mole, frog.
Tails and their uses. — Horse, cow, donkey, dog, cat, monkeys, harvest mouse.
Tongues and their uses.— Cat, dog, cow, woodpecker, frog. Teeth and their uses.
— Man, rat, cow, horse, rabbit, snake, fangs of poisonous snakes. Hair, Fur, Wool,
and their uses.— Cat, mole, dog, sheep, fox. Beaks of Birds and their uses, —
Duck, fowl, parrot, sparrow, goatsucker, heron. Feet of Birds and their uses. —
Duck, fowl, swift, owl. &c. Insects. — Examples: bee, beetle, butterth-, cockroach,
silkworm. Insect development, legs, wings, segments, mouth, breathing apparatus,
o\ipositors

III. The Sky, the Air, the Surface of the Land, and Water.

(a. J The 5/fiy— Sunrise, noon, and sunset. — Note the object over which the sun
Is seen to rise from month in munth. Note sun's position at noon, .and its varying
height above horizon. Shadow. — Note by aid of a spike erect on a flat disc the
v.arying length of the shadow .at noon. Study the shadows of objects. Variation in
sharpness and depth. Moon. — Note the changes. Draw the shape from week to
week. A few of the brightest constellations.— Make diagrams on sijuare ruled
paper rom a stuiiy of the sky itself. Gre.it hear and Pole Star; Lyre and Veg.a ;
Cassiopeia. Planets. — Note any planet visible when the lesson is given M.ark its
position on square ruled paper for a few weeks. Varying length of day and night.

380 Appendix.

(b.) The Air. — Wind. — Varying direction. Note and keep record of the direction
of the wind from day to day. Warmer and colder winds; rainy and dry winds.
Moisture in the air shown by seaweed ; string (changing tension). Wet cloth dries
in the wind (water turns to vapour). Vapour turns to water. Breathing on slate.
Clouds on hills. Evening mists. Clouds in the skj'. Three chief kinds : "heaps,"
" beds," "feathers." Rain. — Note size of drops. Raindrops on dust form little balls.
Note effect of heavy rain in tearing up roads. Note the channels so made, and the
arrangement of the sand and pebbles washed to a distance. Rainbow. — Note the
succession of colours. Note position of sun behind observer and of the bow where
the shower of rain is falling. Note that height of arch changes. When is it higher
and when lower? Rainbow colours on shells, film of tar, &c. Feathers of birds.
Dew. — Note when formed. Cloudless weather. On what does it lie thickest ? Hoar
frost. Snow. — Note size of flakes. Movement of flakes in the air as they fall. Snow-
drift. Snow squeezed into ice. Hail. — Note when it falls. E.xamine hailstones. Is
the hail accompanied by thunder? Thunder and lightning.

fc.) The Surface of the iawrf. — Level or sloping. — Simple way of measuring
slope. Height of school and neighbouring hill tops above sea level. Flow of water
over the land. — Neighbouring stream or streams. Water-pariings. 'J'he river basin
in which the school is situated. Construct a model fountain and make simple
observations on the pressure of water. Milldam. A "head" of water. Notion of
falling water as a motor. Soils. — Cla)'. sand, slate, granite, chalk, quarries near
school, gra\el pits, clay pits, brick works. Note how the rocks lie, in layers or in
masses without structure. Stones in the brook, water worn; pebbles on beach,
rounded; pebbles in gravel pit often with sharp edges, perhaps iceborne. Difl^erence
between sand and mud. Crumbling rocks. Efl^ect of frost on damp rocks. Caves by
the sea formed by the waves ; caves inland formed by rain dissolving limestone ;
stalactites. (A lesson for schools in limestone regions or near rocky coasts.) Building
stone, marble, slate, Bath stone, sandstone, &c. In marble, note shells, &c. Note
plants in coal. Volcanic rocks. — Lava, brimstone, pumice stone, basalt or whinstone.
(According to the nature of the district.) Rock salt ; crystals of salt. Salt in sea
water. Mineral in solution. Hard and soft water. — Rain water compared with
streams from chalk or limestone ; leavings after evaporation. Fur in kettles. Soften-
ing hard water. In certain districts, other minerals in solution, sulphur wells, iron
springs, medicinal waters. Mortar and cement, — Slake lime and make mortar : note
the heat, &c. Surface soils. — Crumbled rocks. Waterborne sand and mud. Vege-
table mould and earth worms. Vegetation and cultivation. — Forest, moor and
heath. Heathers. Hedgerow trees, elms, ashes. Trees of the forest, oak, beech,
birch. Evergreen trees, pines .ind furs. Evergreen plants and shrubs, holly, ivy,
bo.\. Contrast evergreen and deciduous leaves. Note changes at fall of leaf. Autiniin
tints. Press specimens. Riverside trees, willows, poplars, aspens. Hill pastures
and meadows. — Turf on the downs and hay in the valleys. Gardens and their
contents. — Garden fruits and wild fruits. Garden flowers and wild flowers.

(dj Waier^Standing water ; ponds, pond life. Springs and running water
— Clear water looks shallower th.m it is. Simple experiments in illustration. Study
of flow of a stream. — Where the flow is quicker (nj in the middle ; (/>) on one side,
outer and inner bend. Where the bank is eaten away and where sand is spread out.
V'arying bottom ; deep pools, shallows, sand banks. Confluence of tributary. Delta.
Measure the speed at which the water flows. Study of seashore. — Rocky and sandy
coasts. .Soundings. The rise and fall of the tide. Currents. Drifting sand. Effect
of frost on cIltTs. Breakwaters. Layers of soil and rock exposed down the side of a
clilT. Measure with thermometer the temperature of (a) a sprin,g ; (/>) a stream ; (c)
a pond ; (c/) the sea. Ice. — Stud\- hardness, mode of fracture ; splitting blocks with a
nee<ile. Does it sink or swim in water ? E.isy to make two surfaces of ice freeze
together. Simple experiments with ice. W.itch and record behaviour of thermometer
plunged in melting ice. Melt some ice carefully to find out whether it takes up more or
less room than the water into which it changes. Force a mass of ice into a lump of
clay and let it melt there. Freeze some water in a bottle and note bursting of bottle.
Bursting of pipes. Notes on expansion and contraction of substances illustrated by
beh.iviour of w.iter at different teuiper.atures Preliminary notion of thermometer.
Watch cold spring water being heated to boiling point in transparent glass vessel.
Note bubbles of air given ofT, and .as the w.Tter is he;ited bubble^ of steam rising from
below. Oliservc force of i;iimpr< ssed ste.im. Preliminary notion of steam engine.
Dribble powdered alum into clear water. — Hang thread in the solution and note the
formation of I rvstal. Alum .ind other crystals. I'^xpose to the air crystals of (i) s;ilt ;
(2) sod.'i. Note change. What dilference? Wli.it difference .according to weatlur?
ICxpose to the .lir crystals of saltpetre, and note result. Dribble salt into clear water
and note that it dissolves, (pucker at first, then slower, at last no more is dissolved.
I'l.'cce a frish egg in satur.Ued solution and aftcrw.ards transfer it to clear water. One
liquid is denser than another.— Compare water and mercury. Things which float in

Appendix. 381

mercury and sink in water. Upward pressure of water on bodies dropped into it.
W'liy bodies sink or float. Why steel ships float. Wliy cork floats. Simple e.\peri-
ments in displacement of water. Simple experiments in pressure of water and pressure
of air. Siphon. Squirt, pump. Diving bell. Distillation of water. Filtration
Water ; a combination of two gases, o.\ygen and hydrogen. Simple e.xperiments.

IV. Object Lessons for Town Schools.

(a.) The water we drink. — How obtained. Some of the simpler properties of
water. River (or canal), according to circumstances. Boats, barges, or ships,
with which children are familiar, according to circumstances. Other ships, e.s:-,
Atlantic liners. Bricks. — Their size, shape,_ and manufacture ; their size, &c., to be
ascertained by children's measurements. Bricklayer's work. — Arrangement of bricks
in 14-inch wall and in g-inch wall, shown with real bricks or with small wooden ones ;
mortar, &c. Coal. — Its simpler properties. How obtained. How transported, and
how used. Coal-gas. — It may be made in presence of the children. Gas works and
gas pipes. Petroleum. — How obtained : its simpler properties and uses. Lamps and
their dangers. Common stones used in building and road-making. Road-making
and paving. Quarries and quarrymen. Railways. — General sketch. Engines and
carriages. The work of railway men. The park or public garden.— General sketch ;
one or two of its more conspicuous trees ; and one or two of its more conspicuous plants.
Comparison between calico and flannel. — Cotton and its manufacture. Lancashire
and the cotton district ; mills. Sheep-clipping and rearing. The West Riding of
Yorkshire ; factories, &c.

(b.) Cart-horse. Donkey. Sparrow. Rat or mouse. Cat. Plants grown in
schoolroom. — Acorn in glass of water. Mustard and cress. Hyacinth in water or
pit. .'\ fern. Costermonger and what he sells. Some common fruits sold in streets
or shops, f. !,»■., pears and apples, strawberries, oranges, cocoanuts. Things seen in
grocer's window, e.g., tea, sugar, coffee, currants and raisins. The baker and his
work. The milkman. The addressing and posting of a letter. The postman and Post
Office. The sweep and his work. Dangers from fire, and how they may be avoided.
The fireman and fire-engines. 'Bus or tram drives. The policeman.

V. Object Lessons for Country Schools.

(a.) The farmyard.— Its buildings and their contents. Animals kept on a farm
and their uses. Necessity of cleanliness, kindness, and suitable food. The dairy and
its contents. — IJutter and cheese making. Bees. — Bee-keeping. Spring. — .Spring
flowers. Work in the fields in spring. The cuckoo and swallow. Record date of
arrival. Summer. — Different kinds of leaves and fruit. Work in the fields in summer.
Autumn. — Work in the fields. A mill and the work of a iniller. Winter. — Frost.
Ice. Snow. Birds. — Singing birds, as the thrush and nightingale. Birds of pre)', as
the hawk. Swimming and wading birds, as the duck and htron. Wild animals. —
The fox, hare, and rabbit. Minerals. — Amine. Three useful min rals. The lessons
on the seasons should correspond with the actual seasons of the year, and the difl^erent
operations explained should be taken while each is in progress. Leaves of trees may
be dried by simply placing them between sheets of paper and pressing them. Their
shapes may be used for the children to draw round on paper, which can afterwards be
pricked and then sewn round.

(b.) Springtime.— The waking of Nature. The lengthening daylight in the
morning and evening, the coming warm weather, birds singing, building their nests,
laying their eggs, the trees and hedges changing, buds and leaves, the bloom on fruit
trees. The local wild flowers of spring. The daisy, primrose, bluebell. Summertime.
— The local wild flowers of summer. Autumn. — The local wild flowers of autumn.
Winter. — The repose of Nature. The land. — Woodland, meadowland, ploughland,
moorland. The sky. A bird. — Covering, wings, beak, feet; motion: nests, eggs'
food. Local birds. — Thrush or blackbird, lark, robin, rooks. Birds which come for
the summer. Birds which come for the winter. Local wild animals. — Rabbit,
hare, fox, hedgehog. Animals on a farm. Miscellaneous.— Our village. The
carrier's cart. The cottage garden. The stream or river, its banks, the birds and
animals that live near it. A fish. A plant.

(c.) The garden in spring, summer, autumn, and winter. The farm in spring,
summer, autumn, and winter. The weather and wind. The soil; sunshine, sXr,
rain, frost, manure. The farmer's tools. — The plough, drill, reapin.g machine. The
crops. — Grass, corn, root-crops, whe.it, potatoes. Trees. — The oak tree, elm tree, and
apple tree. Evergreen trees. An insect.— The spider and his web. The butterfly ;
colours, beauty, history. Bees. The farmer's pests. The farmer's friends. A

pond. — \ frog. A ramble in a wood and what may be seen there. Miscellaneous.

The railway. Market-day in the neighbouring town. A newspaper.

382 Appendix.

VI.— Object Lessons in the Science of Common Things.

(3.) Water. — How carried, jugs, bottles, barrels, spouts, funnels. Wells. Things
that float, things that sink. Solids. — Hard and soft, in the room and in clothing.
Files. Hammer and nails. Buttons. Powders. — Flour. Pastes. — Paste, clay,
putty. Things porous.— Bread, sponge. Things that melt.— Butter, tallow, sealing-
wax. Ice, snow. Water. — Drying clothes, breathing on slates, frost on the pane.
The boiling of the kettle. The pot boiling over. Things that dissolve. — .Sugar,
salt. Air. — Bubbles, pouring water through funnel into empty bottle. A burning
candle. Fans, blowing feathers. _ Paper windmills. Forms of strength.— The floor,
joists and boards. Wooden bridges. Steps and stairs. Things that stretch. —
Elastic bands. Things that bend. — Bow and arrows. Cord, ropes. Machines. —
Tops. Roller for pastry, for garden. Perambulator. Movements. — Walking,
running, leaping, creeping, crawling. Musical Toys. — Harmonicon. Bell.

(b.) Water. — Pipes, taps, the fountain. Canals. Rafts, boats, aachors. Solids. —
Teeth, nails and claws. Sand-paper. Pins, needles, awl, gimlet. Hook and eye.
Powders. — Chalk, pencil. Pastes. — Mud in streets, brick-making. Things porous. —
Brick, chalk, springs of water. Things that melt. — Candle-making. Icicles.
Water. — Manufacture of salt from brine. Rain-drops, hail, spray, water-dust, the
cloud. Things that dissolve. — The manufacture of sugar. Air. — The chimney,
draughts. Waves and breakers. Winged .Seeds. Shuttlecocks, arrow, and kite.
Forms of strength. — The ceiling. The arch. Ladders. Things that stretch. —
A football. Things that bend. — Cart springs. Paper clips. Spider's web.
Machines. — Hnrjp, fly-whetl of sewing machine. Mangle. Waggon. Bicycle.
Movements.— Swimming. Musical Toys. — Musical bo.\, drum.

_'f.) Water. — Syphon, pump. Oil, cream. Solids. — Hinges, tires, and axles. The
grindstone. .Screws and screwdrivers. Powders. — Black lead. Pastes. — Poiterw
Things porous. — Blotting paper, towels, wicks, earth. Things that melt. — Lead,
iron. Water. — Salt lake-. I)istillation of water. Clouds and rain. Things that
dissolve.- — Crystals, hard water, \arnishes. Air. — The popgun, the fire-engine.
Winds. A sailing ship. Forms of strength. — The roof. Railway bridges. Cranes.
Things that bend. — Clock springs. Chains. Machines. — The loom. Thresliing
niacliine. Rolling iron rails. Coining. Movements. — Flying. Musical Toys. —
Tin whistle. Sounds from stretched cord.

VII.— Measuring, Weighing, and Testing.

A two-fiot rule. Measureirients of length — fir^t by eye, then with rule. Easy
measurements of a square — first by eye, then with rule. (Measurements in inches
only). Easy measurements of rectangles. The wire-gauge. Callipers. .Scales and
weights. Weighing of common objects — first by hand, then with scales; weight in
ounces only. Weighing letters. Plumb line. .Spirit level. .Steam — observations on
boiling water ; condensation of steam, &c. Mercury — weight of; c/. drop of mercury
and drop of water; eflfect of heat on mercury. Alcohol — efl'ect of he.it on it; its
evaporation. Thermometer, its m.innfacture. Tlierniometer — u.ses ; readii>gs in ice,
in boiling water, under the tongue, in schoolroom A candle — its composition. The
wick. Candle under bell-jar over water; candle in narrow-necked bottle. Chalk — where
found; its origin Clialk — its treatment wiih acid. Chalk — its reduction to quicklime
with blow-pipe ; lime-water. Sugar heated in test-tube ; wood heated in test-tube.
Sulphur heated in test-tube ; lead heated in test-tube. Magnet and iron filings. The
compass.

Additional Notes. 383

384 Additional Notes.

The Highest Prize iVIedai for Educational Works
was awarded to the following Books at the
Chicago Exhibition.

OF liOOKS ]iV
Master 0/ Method, IVestminster Trainitig College, Horseferry Rond, SAV.

GRAPHIC LESSONS IN

Designed to vieet the requirements of Male and Fevtale Candidates for Certificates,

and o/Pii/>il Teachers and Assistants in preparing for the Examinations at the end of

each year of Apprenticeship and for the Scholarship Examination, and also in

preparing Lessons in the Standard Geography.

New Edition. Price 4s. 6d.

1. The matter is arranged in the order of teaching.

2. Full and complete directions are given as to the mode cf

presenting each item of information to a class.

3. Nearly 200 Original Sketches and Blackboard drawings

have been introduced.

4. The matter covers in one book the entire course required

by Pupil Teachers and Students in Physical and Astro-
nomical Geography.

' We venture to predict for these Graphic Lessons a very wide distribution. Young
teachers will find in them the essential facts of the subject of their study, and experienced
teachers will often gather hints as to the arrangement and illustrations of their lessons,
which will save them a considerable amount of trouble. As the Master of Method in
the ^A7estminster Training College, whose pre-eminent success in this branch of
school management is emphasised in the Blue-Book just published, Mr. Cowham
can offer these "lessons" to young teachers with some authority. The engrav-
ings are very numerous and are bona-fide reproductions of work done on the blackboard
during actual instruction. Scientific accuracy has been combined with simplicity of
statement, and the profuse illustrations will be found to be helpful both to student and
teacher. The quality of the paper, the character and arrangement of the type, and the
general get-up of this work, cannot fail to give satisfaction to all for whom it is
primarily intended, and to whom we strongly commend it for the double use ot which it
is capable in learning and teaching.' — The Schoolmaster.

' Coivham's Graphic Lessons in Physical and Astronomical Geography cover a very
extensive area, comprising the Code work for the Standards, the Pupil Teacher's course
of geography, and the requirements both of the Scholarship and Certificate Examina-
tions. The lessons are arranged on a uniform principle. The left-hand pages contain
the information to be imparted in the course of the lesson, whilst the right-hand pages
are reserved for illustrations and teaching hints. Appended to each lesson is a summary
of the subject-matter and a set of questions for examination. A close scrutiny of this
admirable series of Notes and Lessons shows how simple and interesting even a
somewhat difficult subject may become when handled by a teacher who combines
sound knowledge with practical skill in imparting instruction. Great judgment
has been shown in the selection of suitable types, and the numerous illustrations,
most of which are intended for reproduction on the blackboard, evince the great
care that has been bestowed on the preparation of this useful manual. We
cordially commend this book to the notice of teachers.' — School Guardian.

For Specimen of a portion of one of the Lessons see the ne.vt t7i'o pai^es,

London: WESTMINSTER SCHOOL BOOK DEPOT, 128, Horseferry Road, S.W.;
also from SIMPKIN, MARSHALL, HAMILTON, KENT & CC. Limited.

24° Graphic Lessons in Astronomical Geographv,

Why is there not an eclipse of the moon every month, viz., at
every full moon ?

In reply : — ■

1. The moon moves round the earth in an orbit whose plane is
inclined about 5° to the plane of the earth's orbital movement
round the sun.

Particular attention must be directed to the moon's position
when crossing the second plane, and also when furthest away
from this plane, i.e., at C and X respectively, fig. 4.

2. The moon is represented -m opposition,' or full, in fig. A,
diagram 5, but it is not eclipsed because the moon is a considerable
distance above the earth's shadow.

3 The moon is represented 'in opposition,' or full, in fig. R, and
in this case it is eclipsed. Why ? Because it is not only full
moon, it is at the same time at, or near, the point where the
moon's orbit crosses the plane of the earth's orbit.

The earth's shadow always stretches away from the sphere with its
axis in the plane of the earth's orbit. Hence, when the moon at full
happens to be near the earth's orbital plane it passes into the earth's
shadow and is eclipsed.

4. The crossing points of the two planes which the moon must pass
every month, are termed nodes. When, therefore, the moon
is 'full ' and at or near its nodes it will be eclipsed.

Summary-

1. The shadow of a ball or globe is circular when cast on a screen held vertically
lo its direction.

2. The size of the sh.idow depends upon

(a) The size of the luminous object.

(/') The distance of the screen from the object casting the shadow.

3. When the luminous object is larger than a point a penumbra surrounds the
umbra.

4. An eclipse of the moon can occur only at or near full moon.

5. Tlie reason of this : —

{a) 'l"hc moon's orbit is inclined 5° to tlie earth's orbit.

(/■) 'the shadow of the earth is cast in the direction of its own 01 bit.

(i ) The moon can enter this sh.idow only when

(i) in opposition or ' full '; (j) when crossing the earth's orbit.

6. The moon is not eclipsed every ' full moon ' because often it is full and eiiher
above or below the earth's shadow.

7 Tile moon is alwaj's eclipsed when it fullils the following conditions; —
I. It is full moon,
a. .At or near, its 'nodes.'

111.

Notes of Lesson on ^Eclipses of the Moon.' 241

C. I. Fig. 4. Diagram showing
A, the upper half of one plane, cutting
a second plane B along the line CD.

Fig- 5-

2. Fig. A. Shows the conditions in which the moon, though_/«//, is not brought into
contact with the earth's cone of shade.

3. Fig. B. Exhibits the moon at full, at that part of its orbit most favourable for an
eclipse.

4. A model of a verj- simple kind is verj' helpful at this stage. It is made as follows : —
Take a sheet of cardboard to represent the earth's orbital plane, mark on it the

position of the earth's orbit. Then at the positions occupied by figures A and B insert
dilTerently coloured cardboard planes to represent the moon's orbit. With balls to
represent the position of the sun and that of the earth, and a movable ball to represent
the moon firstly as in fig. B and secondly as in fig. A, there will be very little difficulty
in realizing the conditions favourable for a lunar eclipse.

Questions for Examination.

1. F.xperiment wih the shadow of a plate
and a ball. .State any differences you
observe in the results.

2. When is the shadow larger than the
object casting it ?

3. Show by the aid of a diagram the
formation of a ' penumbra ' and an
' umbra.'

.(. What must be the astronomical position
of the moon in order to be eclipsed ?

5. At what angle is the moon's orbit
inclined to that of the earth ?

6. Draw a diagram showing the moon in
opposition and eclipsed.

7. Draw a second diagram to show the
moon in opposition, or ' full,' and not
eclipsed.

8. State the two conditions which must
be fulfilled for the moon to be eclipsed.

g. How often during the course of a
year is the moon in a position favour
able for an ' eclipse of the moon.'

IV.
Adopted by Commissioners of Education, Ireland.

■ ' Tlie method is based on the scientific pri)iiiplcs of psychology and ethics
with zuhich the author shows himself thoroughly acquainted.'' — JOURNAL OF
Education.

THE PRINCIPLES OF

OBOL wwm w piEKTflL wm^

An introduction to Psycholog-y and Ethics for Teachers.

By J. H. COWHAM,

PROFESSOR OF EDUCATION, WESTMINSTER TRAINING COLLEGE, S.W.

Designed, by referring to familiar School Exercises, to prepare Pupil
Jcachers, ex-P. T.'s, and Students for the Scholarship and the 1st and 2nd
Years' Certificate examinations, so far as these relate to the best fnethods of
school teaching, together xvith the reasons and principles upon which each

tnethod is based.

Revised and Enlarged Edition. Price 3s. 6d.

Spcci7nen copy sent direct and Post Free for 2s. i id., P.O.

1. PRINCIPLES OF EDUCATIONAL SCIENCE made easy by

an abundant reference to familiar school experiences.

2. A PRACTICAL GUIDE TO THE SCIENCE AND ART OF

'ORAL INSTRUCTION.'

3. Full guidance in the CRITICISM OF LESSONS.

4. Specimen Lessons and Model ' Notes of Lessons' in the

ordinary subjects of school instruction, all with a view
to Mental Training.

This book is mainly a reproduction of the instruction given by the Master
of Method to the Students of the Westminster Training College during the
year in which they secured the following published report from His Majesty's
Inspector of Training Colleges. (Gov. Blue Bock) : —

Of the School Management papers from Westminster, Mr. Brodie says, ' I can
report with real satisfaction. Last j'ear I spoke highly of this College, and the
papers this year show a very marked advance on those of last, and are, indeed,
taken altogether, perhaps the best set which I have ever revised. The papers
bear evidence of thoughtful training. . . Knowledge is ample, expression clear,
arrangement good.' Comparing papers from different bodies of students, Mr.
Brodie continues : — ' The best indeed, those of Westminster, evince very careful
training, and no less a desire on the part of the students to profit by what has been
so carefully inculcated. They are pervaded by that spirit which leads to excellence,
and approach that model of perfection which should always be kept in view.'

'With admirable skill, Mr. Cowham has epitomized the results of his long expe-
rience as the Master of Method at the Westminster Training College. The method is
based on the scientific principles of psychology and ethics with which the author
shows himself thoroughly acquainted ; and the ability with which these principles are
applied to practical class teaching is perhaps the most striking feature of the
book. . . . The hand of the skilled teacher is visible on almost everj' page. . . .
The be.sl book of its kind for students in training.' — yournal of Education.

Sctooi OrQanizatioii, Hygiene k ElUics:

Applied to School Work and Discipline.

Fourth Edition. Price 3s. 6cl. Post Free, 2s. lid.

'T'HIS book covers the curriculum of study for the Certificate Examination
-^ in the above subjects. It brings into one book matter which
hitherto has necessitated the use of several expensive works. The book
is full)' illustrated by outline sketches suitable for reproduction. It is the
outcome of several years' tuition of the students at Westminster Training
College.

'Thrice fortunate the schoolboy whose pastors and masters are actuated with the
spirit which animates the book, " School Organization, Hygiene and Discipline,"
written by Mr. J. H. Cowham, of the Westminster Training College. To the teacher
of youth this manual will be most valuable, for it is founded on practical experience.' —
TJte Daily Telegraph.

' New codes, new schools, new methods, and new teachers, render the supersession
of old books on school inanagement inevitable, and this work, by a skilled hand, is quite
qualified to fill the void. . . The chapters on School Hygiene are especially welcome
and the clear illustrations enhance the value of the text.' — Teachers Aid.

' Mr. Cowham lets us see, if we have not seen it before, how much tact, temper,
wisdom, and humour, the schoolmaster needs in all classes of schools.' — Daily News
Leading A rticle.

NEW BOOK, Just Issued.

THE SCHOOL JOURNEY.

A means of Teaching Geography, Physiography,
and Elementary Science. Illustrated by over
SO Maps and Photographs Price 2/6

/>> JOSEPH H. COWHAM, Westminster Training College, S.W.
With additional 'Journeys' by G. G. LEWIS, Bellenden
Road Higher Grade School, Peckham ; and THOMAS
CRAWSHAW^ Wesley School, Padihani.

Sir H. EVELYN OAKELEY, H.M. Chief Inspector of Training Colleges, writes in the
Departmental Blue Book concerning this Journey: — 'The value of thus connecting
the facts of Geography with their causes, and of exercising judgment and reason in
place of a mere remembrance of names, is obvious. This is the best way to teach
Geography, and I am glad to learn that some teachers who have been at Westminster
have taken groups of their scholars in a similar manner.'

Published by
WESTMINSTER SCHOOL BOOK DEPOT, 128, HORSEFERRY ROAD, S.W. ;

ALSO FROM

SIMPKIN, MARSHALL, HAMILTON, KENT & CO. Ltd., ST.VTIONERS'

HALL COURT, E.C.

COWHAM'S FRACTIONS AT A GLAHCE.

A Diagram designed to make the rules of Fractions
both INTELLIGIBLE and INTERESTING.

Price, Cloth on Rollers, 2s. 6d. ; can also be supplied in Sheets for

Mounting, Price, Is. each.

Ill

y " 10

J, 10

:zim

:::::|CM

"11

^ I

8 ^

6.1

6 ^

4 .

3 .

3 ^

2 ^

Reduced Drawing of the Chart "Fractions at a Glance."

1.— A. clear notion of the nneaning of a 'Fraction' is
given.

2.— By moving the T square along the Chart all the
rules of Fractions can be explained.

3.— Full directions for use are printed on each Chart.

4. — Much valuable knowledge is obtained by simple
inspection of the Chart by the Scholars.

B.— The reasons for the rules of Fractions may be
illustrated and understood.

The School Mistress, March 26th, 1891, says ;— "We have seen other diagrams, but none where the
arrangement is so simple, yet so effective."

The Daily Telei^raph, .April Sth, 1891, writes;— "A simple Diagram which performs the seeminglv
(iifficiilt task of making the rules of vulgar fractions interesting and intelligible."

The Teachers' /(jrf says:— " A mine of wealth to every intelligent Teacher."

WESTMINSTER SCHOOL BOOK DEPOT, 128, HorBeferry Road, S.W.; of Messrs. SIMPKIN,
MARSHALL, HAMILTON, KENT ft CO. Ltd., Stationers' Hall Court, E.G., and all Booksellers

VII.

NEW VOLUME BY J. H. COWHAM,

Westminster Training College, S.W.

THE SCHOOL JOURNEY

With additional School Expeditions,

By Messrs. G. G. LEWIS and THOS. CRAWSHAW.

A means of teaching Geography, Physiography,
and Elementary Science. Illustrated by
50 Maps, Plans, and Photographs,

Price ■ ■ 2s. 6d,

Press and otbcr notices.

SIR EVELYN OAKELEY, H.M. Chief Inspector of Training
Colleges, writes in the Blue Book concerning this Journey: — "The
value uf thus connecting the facts of geography with their causes, and of
exercising judgment and reasoning in place of a mere remembrance of names,
is obvious. I'his is the best way to teach Geography."

PROF. SEELEY in "School World" writes :— " An excellent record of what
has been done in a school outing. It is likely to stimulate teachers to take their
students to see the real geography in nature which cannot be taught from books
or in class rooms."

"NATURE" Reviewer writes: — "The book appears at the right
psychological moment. Here we have notes upon actual excursions, how
planned and performed, and, with these before them, teachers should have
no difficulty in arranging others."

THE "EDUCATIONAL REVIEW" writes:— "Any teacher who is
thinking of experimenting in this continental form of education will find the
hints given in this book invaluable."

THE " EDUCATIONAL TIMES " Reviewer writes :— " Full of
suggestions for the practical teaching of the subject. The accounts of these
three successful attempts should encourage others. The method adopted is
the important feature of the book, and we have nothing but praise for it."

THE "TEACHERS' AID" says :—" Teachers would be wise to secure this
instructive book."

WESTMINSTER SCHOOL BOOK DEPOT, HORSEFERRY
ROAD, S.W., and of SIMPKIN & Co. Limited.

Specimen Copies sent Post Free for P.O. Is. lid. by Manager,
School Booli Depot, Horseferry Road, S. W.

VUl.

Mulhauser's System of W riting is applicable to all slopes from the Vertica l,

Gowlam's piuiliaiisei Mn\ ol wntino.

For aU who wish TO ACaUIRE and TO TEACH a

Perfect Style of Handwriting-.

r-
m
a

r-
m

■n

c _.
■n (73

C B"

r* M

_. p

-n

o
-«

Prepared by J. H. COWHAM,

Westminster Training College, Horseferry Road, S.W.

Revised and Enlarged Edition, witli Capital Letters written in

Rhomboids. Price, ONE SHILLING.

RECENT SUCCESSES OF THE SYSTEM [see Blue Books).

The highest examination in Penmanship is that of the Government

Certificate for Teachers. In this examination, the following successes have

been gained by Candidates, taught on the Mulhauser system.

Certificate Exam.

(ist & 2nd • J

year) gained

(istyear) ,,

(2nd year) ,

(ist year) ,

(2nd year) ,

The marks issued to Training Colleges (November, 1S9S) show
that these candidates, taught solely on the Mulhau.'^er system,
gained an average mark for Penmanship 14 "^/q higher than the
next highest on the list.
An Inspector of Schools, commenting, in the Government Blue Book,

on the writing by Candidates for Certificates writes as follows : — " By far

the best writing was sent up by the Westminster men."

SUPPLEMENT to COWHAM'S MULHAUSER WRITING

MANUAL. Price 9d. _ , ., .

A Pupil Teacher and Scholarship Copy Book, arranged for daily practice
in every possible combination of letter forms. The book also contains
fac-simile of the Examination Papers set at the Scholarship Examination.
This book should be used in combination with the Manual of Writing. It
will be especially of value during the months immediately preceding an Ex-
amination.

1893 ..

Candidates

1894 •■

1896 ..

) *

1897 ..

)■

1898 ..

HIGHEST
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HIGHEST
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Marks.
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