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METHODS IN TEACHING

' A

j^aBHoaiJi^^

^?'''ii7Vt---:^w^A-'*,'MV'.'*''""'"' ';-''""'7(;-'y-^'*^-'"-Th',v:y - ■'^' " ./•:• •-•/•;■'■>. ^*;--'i:'r-"t-»'-,y!if

Methods in Teaching

\V. J. ALEXANDER, Ph.D., Prof,'ssor of Eui^lish, Uuiversih-

Colh'i::^, 'Joronto
R, K. ROW, 15 A., I'lce-Principal, AWmal School, Toronto
W . H. EELIOTT, B.A., Principal, Model School, Ifamilton
J. DiCARNlvSS, Inspector of Public Schools, East Middlesex
J. F. WHITE, Inspector of Separate Schools, Ontario
T. A. KIRKCONXia.L, B.A., Principal, /fi^^h School, Port //ope
W. SCOTT, B.A., Principal, A'orrnal School, Toronto
R. M. CIRAHAM, Principal Model School, London
A. C. CASS ELM AN, Draioim^r Master, Normal School, Toronto
A. F. NEWi.AXDS, Writing and Drawing A/aster, iXormal

School, Ottawa

Edited by J. J. TILLEY

Inspector of County Model Schools, Ontario

TORONTO
GEORGE N. MORANG & COMPANY, Llmited

1899

^HlR^//

L6I025

Kntcred acoordiiiK to Act of Pari i union t of C'anadii, in the year on<> thousand eight
hundred and i.inoty-nine, l)y (Jkorcik N. MoKANd & Cd.mi'ANV, I^imitkd, in the
Office of the Minister of Agriculture.

IMIKKACE.

At m irn'otin^r of the Traiiiiiii'' Dcpai'tiiicnl ol' tlic
Ontario Eflucation Association lu'M last year, the
Model Scliool niastors l)y ivsolntion expressed a dt'sii'c
tliat a text book on Metliods sliould l»e prepared lor
the use of teachers-in-trainino-.

It was su^^ested tliat educat(»i-s of well known
ability in the teachino-of particular subjects be asked
to contribute, in order that the book niioht set foi'th
the most approved modern methods of teachin<^^ as
developed by large experience.

This suo-gestion was adopted unanimously, and
the undersigned was re(picsted to make all necessary
arrangements and to ct as editor.

After much thou;j-^^ ind consultation with those
interested in the subj Mie gentlemen whose names
are given in the list of contributors, were requested
to write on the several sul)jects allotted to them ;
and the editor desires to thank the contril tutors for
the readiness with which they responded to his
request, and to acknowledge their claim to the greater
share of whatever credit may be awarded to this
publication.

Although the nature and scope of the work
undertaken by the different writers were discussed
and outlined when the subjects were assigned, yet
each contributor is to be considered as mainly respon-
sible for his portion of the work.

VI.

METHODS IN TEACHING.

The editor wislicH to ackiiowltulgu his indjihted-
ncHH t<j Mr. .}. Ilussoll Stuart, luspuctor of Public
ScliooJH foi- tli(! City of Stratford ; to J)r. Wau^h,
Principal of the Collegiate Institute, VV^iitby, and
to Mr. J. Sud<lal)y, Principal of the Model School,
Berlin, for valual)le assistance in the preparation of
his chapter on " Analysis of Method."

This text book is intended to serve merely as an
{issistant. The teacher should not allow it to become
a substitute for his own individuality, or to lead him
to relax his efibrts in devisinj.^ new methods for him-
self. The book is for ihe teacher, not the teacher for
the book. One cannot accomplish the best results
with the method of another, however excellent it
may be, until he has thoroughly assimilated it and
made it his own.

How far the contributors have succeeded in their
efforts remains for teachers to determine, but the
book is submitted in the hope that the main purpose,
viz.: The lessening of the arduous labors of Model
School masters, will, to some extent be effected, and
also that those who are not engaged in the profes-
sional training of teachers may receive some help
from its pages.

J. J. TILLEY, Editor,
Toronto, January, 1899.

les-
leip

TABLE OF CONTENTS
CHAPTER I.

PAOE

Analysis ok Mhthod, by J. J. Tilley 1

CHAPTER II.
LiTEKATUKE, by Prof. VV. J. Alexander, Ph.D. ... 30

CHAPTER III.
Language-Tkaining, by R. K. Row, B.A 67

CHAPTER IV.
English Grammar, by W. H. Elliott, B.A 92

CHAPTER V.
Reading, by J. Dearneas 146

CHAPTER VI.
Geography, Part I., by J. F. White 193

CHAPTER Yl.—{Gontinned).

Geography, Part II. (Mathematical), by T. A. Kirk-

connell, B.A 227

»mu wiiiM iM— aiM— ■WMMWMI

• • •

viu.

METHODS IN TEACHING.

CHAPTER VII.

PAGE

HiSTOiiY, by W. Scott, P.. A 240

CHAPTER VIIT.
Arithmetic, by R. M. Graham 261

CHAPTER IX.

Drawing, by A. C. Casselman 330

CHAPTER X.

WiiiTiNo, by A. F. Newlands 348

PAGE

240

METHODS IN TEACHING

201

CHAPTER I

ANALYSIS OF METHOD.

330

348

This book is not intended to teach Psychology,
but as inetliods of teachin<ij sliould be in harmony
witli the fundamental principles of education it will
be necessary to consider some of the truths made
known by this science.

The mental processes by which knowledtj^e is
acquired are discussed in three divisions, yet it must
not be assumed because they are considered separate-
ly, for convenience, that they are always distinct or
separate in action — that one ends before another
begins.

Our experiences of the world around us furnish a
starting-point for every form of mental activity.
These experiences can be secured only through the
medium of the senses. Without these the mind would
he left entirely to itself, and its activity could not be
conceived of. As Dr. McLellan says : — " It is impos-
sible to have knowledge whei-e there has been no
basis in presentation." (Applied Psychology, p. 15).

Mental life involves infinitely more than this, but
its initial point of activity must be consciousness of
stimulation of the sense-organs from without. The

METHODS IN TEACHING.

first stages of knowledge iniist be based upon and
determined by the realities which constitute environ-
ment. The abstract can never precede tlie concrete.

Although necessarily involved in what has been
said, it may be expressed in a separate statement,
that words of themselves do not convey ideas. Tlie
idea must be gained from the object of thought before
the word or symbol can have any significance ; for
" names do not inhere in things." It was the observ-
ance of this law that especially characttrized the
teachino; of Pestalozzi and of Froebel. Thev first
supplied the conditions of experience to the child, and
then directed his knowledge and his activities in
accordance therewith.

The means bv which human cultivation must bemn
is tersely expressed in the following (piotation from
Hinsdale: — '* A man blind from birth may learn the
whole color vocabulary, but he can have no concep-
tion of its meaning. The appropriate sense nuist
always furnish a starting point from wliich the mind
may work. Similarly language, writing and pictures
can never take the place of a suitable grounding in
the primal realities of sense and of the spirit. No
human beinor's cultivation ever befjan with words of
wisdom. The library is a sealed book save to him
who already possesses the keys of knowledge. A
volume is first a thing, then a book. The command
to keep out of the fire is significant only to those
persons who have already learned by experience what
the fire is. In this pi-imal sense, therefore, the educa-
tion of all men stai'ts at the same place, and proceeds
by the same steps." (Studies in Education, p. 31).
It necessarily follows from these facts that a

ANALYSIS OF METHOD.

poll and
environ-
jncrete.
las been
atenieiit,
as. Tlie
it before
nee ; for
e obaerv-
ized the

hev first

liild, and
\ities in

list begin

Ige.

rational system of teachinj^ must begin with the
presentation of external realities.

This method of teaching is known as the objective
method, and as it must furnish the basis for all
subsequent knowledge it should be understood in its
broadest sense. Any failure to grasp the extent of
its application will reveal itself but too plainly in the
limitation of its use. The teaching of " object-lessons,"
in which the realities are usually things which can
be seen and handled, has tended to restrict objec-
tive teaching to the presentation of visible things,
or to what is usually understood by the term
" objects." It should however be understood in a
much broader sense. Although it will be further
explained in subsecpient paragraphs, it may be defined
as teaching through examples of the thing to be
learned, or more briefly, as teaching any thing through
itself. It includes the teaching of everything whicli
is to be learned through the senses. When a child
hears any sound for the first time, or becomes con-
scious of the taste of an object, or by touching an
object learns of its smoothness, roughness, etc., or
when he learns sharpness by cutting himself with a
knife, or heat by burning himself, he is being taught
objectively quite as truly as when the teacher shows
him what coal is by placing a piece of coal in his hand.

It is however to the extension of this method to
the teaching of actions that atten.tion should be
especially called, because the advantage of its applica-
tion in this connexion is not recognized sufficiently by
many teachers. An action is an objective reality
(luite as much as is a tangible object, and it should be
taught in the same way. We teach a child what a

,l.^. 'Xl

METHODS IN TEACHING.

skate is by showing him the object skate, and in the
same way he should learn what skating is, that is by
seeing the action of skating performed. It is of the
highest importance that this rule should be observed
in the tear»,hing of arithmetic. What has been said of
words not conveying ideas, applies with equal force
to symbols of operations to be performed. The latter
are as meaningless to the child as are the former
until the actions which they indicate have been per-
formed before the child, or by the child, and the
meaning of the symbol grasped by the mind. 4+4 = 8
may be learned in its symbol form but the expression
has no meaning for the child until he has taken two
groups of foar things of the same kind and has noted
the result after having placed them together. The
expressioi\ is in no sense concrete except when
considered as a symbol, and can at first be of no
more service for thought-getting than can the word
red be to one who has never seen that color.

Pupils who have learned the multiplication-table
" by heart," and who can work figure exercises
rapidly and correctly, too often have but a vague
idea of what is meant by multiplication. If asked to
show by means of splints, or dots on their slates what
they understand 6 X 4 = 24 to mean, probably not one
in five will satisfy us that he has grasped the mean-
ing of the expression.

It is not contended that the child should dwell
too long upon the concrete, but he should be taught
in this way until he understands the operations, and
frequent exercises with the concrete serve as the best
possible test of his knowledge. When giving simple
problems to junior classes one or more type-problems

[id in the

hat is by
is of the
observed
sn said of
ual force
'he latter
e former
oeen per-
and the
4+4 = 8
xpression
iken two
has noted
ler. The
ipt when
be of no
the word

bion-table
exercises
a vague
asked to
ites what
not one
ie niean-

lld dwell

taught

[ons, and

I the best

simple

)roblems

ANALYSIS OF METHOD. 5

should be taught objectively preparatory to the use
of figures. Each child should be required, and
assisted if necessary, to perform the operations with
splints or other small objects ; then with the objects
before the eye, and the operations fresh in the
memory, the corresponding figures and the symbols
of operation when placed upon the blackboard will
have a real meaning for the pupils.

It is not enough merely to illiistiute with objects.
The operations should be performed by the pupils
again and again until the problem is thoroughly
understood.

A pupil may manipulate the figures quite readily
and yet have scarcely any idea of what is involved.
The true test of knowledire in all such cases is the
ability to do, and the best way to assist the child
in this connexion is not to call his attention to
figures on the board, or to give visrbal explanations,
but to lead him to examine liis own work, and thus
to correct his error if necessary. As a means of
broadening the pupil's conception of the solution of a
problem, and of affording him the pleasure which
always sp- ^ngs from the ac(iuisition of knowledge and
from the consciousness of power, the teacher may
point to the indicated operations as shown upon the
board and require pupils to take the necessary steps
with the splints, or he may perform the operations
and let the pupils point out or make the correspond-
ing figui'es or symbols of operation \\\)<m th<' board.
Such an exercise is always (Mijoyed by pu[)ils.

It will be belter to dcNote the whole time of ;i
single lesson to the thorough mastery in this way <>!"
one type-problem than to allow the pupils to solve a

^' ^' .>.< ..

■il

METHODS IN TEAOIIING.

dozen questions by means of verbal explanations and
imitation of the teacher s blackboard work.

This method of teaching is especially useful and
should always be practised in giving pupils their first
lessons in the compound quantities which are used,
and in the operations which are to be performed in
what are commonly known as Reduction and the
Compound Rules. These are fully discussed in the
chapter on Arithmetic. No learning of the " tables ''
from a book, and no subsequent working of an
indefinite number of examples with figures can
ever serve as a substitute for a thorough " ground-
ing in the primal realities " of quantity and of
operation.

There is another branch of education which comes
as fully within the purview of the objective method
as either of these already mentioned. It is the teacli-
ingof ethics, which is but the science of human action.
The child's first idea of what is right and of what is
wrong must be obtained as the beginnings of all other
knowledge are obtained, that is from the concrete,
from realities. The concrete in this case is action.
It is the child's own acts in relation to those in auth-
ority over him. He gets his first conception of right
from what he is permitted to do, and of wrong from
what is prohibited.

The child learns authority, government, restraint,
self-denial, obedience, etc., just as he learns the quali-
ties of objects. He learns them as objective facts or
realities. The little child will never learn the mean-
ing of truthfulness, kindness, gentleness, sympathy,
patience^ through the use of words ; he must be
taught through the illustration of these qualities

ia<^i&'&iiuk&^.

ANALYSIS OF METHOD.

tiony and

seful and
-heir first

are used,
'ormed in
I and the
3d in the

" tables "
ig of an
rures can
" ground -
Y and of

ich comes

e method

he teach-

an action.

what is

all other

concrete,

s action.

in auth-

|of right

ing from

|estraint,
ic quali-
Ifacts or
mean-
Inpathy,
lust be
ualities

in action. " Moral knowledge and natural knowledge
oriirinate in the same way."^ And teachers of experi-
ence know that better results are achieved in the
schoolroom by the observance of this fundamental
principle than by trusting to formulated precepts as
rules of conduct, however excellent these may be.

The force of a moral (piality can be readily
grasped when it is individualized in action, and
actions which touch the person ?*<3 more effective in
influence than those which appeal only to the under-
standing. Justice wlien administered by the teacher
in the schooh-oom and on the play-ground becomes a
living reality " know^i and read of all men." The
heart is the true schoolroom, through which deeds of
kindness, of sympathy, and of love come home to the
mind. For the teaching of those moi-al (pialities
which underlie a worthy character, no special pro-
vision need be made in the time-table. Given the
earnest, devoted teacher, in whose heart these (juali-
ties abound, and the necessary objective teaching will
be co-existent with the contact l)etween teacher and
pupil. If these qualities are not possessed by the
teacher, no constructed curriculum can serve as a
substitute therefor.

It was in this connexion that Emerson said : — " I
care but little what my daughter learns, I care much
from whom she learns : " and it was this truth, illus-
trated in private life which enabled Sir Richard Steele
to .my of Lady Hastings: — "To meet her was an
immediate restraint upon all improper conduct and
to be acquainted with her was a liberal education."

Such teaching will ]n\ assisted by the proper

1 Hinsdale.

maumiktMnm

"^v

METHODS IN TEACHING.

consideration of illustrations of human action fur-
nished in history! and in literature.

The relations of men to each other give rise
to morals, and as history sets forth these relations,
one of its chief uses is to form moral notions in chil-
dren. Men are object lessons in moral education.
Their deeds live after them to inspire and to warn.
History abounds in examples of courage, patriotism,
devotion to duty, nobility of character, in short ot all
the higher qualities which ennoble mankind. When
these are properly considered, with 4l^e many painful
contrasts found on the pages of history, thv3 mind is
led to form judgments thereon, which will have a
reflex influence on the character of the person form-
ing them.

McMurray, in illustrating this point, says: —
" When Sir Philip Sioney, wounded on the battle-
field, and suflerino- with thirst, reached out his hand
for the cup of water that was brought, his glance fell
upon a dying soldier, who viewed the cup with great
desire. Sidney handed him the water, with the
words, ' Thy necessities are greater than mine.' " No
one can refuse his approval of this act.

After telling the story of the man who went down
to Jericho and fell among thieves, and then of the
priest, the Levite and the Samaritan who passed that
way, our Lord put the question to His critics, " Who
was neighbor to him that fell among thieves ?" And
the answer came from unwilling lips, *' He that
showed mercy." Such moral judgments as these

1 The relation of history to ethics should be discussed in the second
part of tiiii) chapter, but on account of its close connexion with what has
just been (-aid, it is considered here.

j^^ ^^fgt^^»w^ ^

ANALYSIS OF METHOD.

stioii fur-
give rise
relations,
s in chil-
iducation.
to warn,
atriotisni,
ort or all
i. When
\y painful
le mind is
11 have a
3on form-

says : —
le battle-
his hand
ance fell
lith great
vith the
le. ' No

int down

of the

ised that

' Wlio

And

Le that

is these

spring up naturally and surely, when we understand
the circumst inces under which an act was performed.
On the otlier hand, it is natural to condenni wrong
deedt] when presented clearly and objectively in the
action of another, and later, the judgment must react
upon our own conduct."

The following ({notation from De Garmo^ fur-
nishes a very fitting conclusion for the discussion of
this part of our subject : — " All ethical instruction
should proceed from individual cases of action involv-
ing a liiorpJ content. Hence it does not suffice to
preach in school, except from the text of an actual
event. Children can best get the first points of
crystallization for moral truths from stories involving
a moral content. History fulfils its noblest mission
to the race on account of its ethical content, and of
the individual nature of the presentation. Every
deed of heroism, of benevolence, of charity, of patriot-
ism, is a concrete embodiment of a precious virtue ;
while every mean, cowardly, dastardly act is an
individual protest against meanness, cowardice, vil-
lainy. We can only continue the deposit about these
starting points, until at last the soul is strong enough
in itself to stand alone."

Ihe second
what has

W^e have seen that all knowledge must begin with
individual notions acquired objectively through con-
tact of the sense-organs with external phenomena,.
We have now to consider how this knowledi»e is
extended. These individual notions are not st{)i-e<l

1 "Essentials of Method," p. 65.

•1 t

METHODS IN TKACHINC.

hi'

away in tlu; mind as " dead treasures," but tliroujjfh
them the mind is enabled to take in new perceptions
more readily, and to extend them. The senses furnish
tiiese materials, while representation, ima<^ination and
judgment co-ordinate and assimilate them. New
perceptions are vo'^-'-red to the old, and are interpreted
and mastered ....^agh our former experiences. In
tliis way " old thought becomes material for new
thought."

We thus get at the core of apperception or the
assimilation of knowledge, which is that we learn
through what we have. De Garmo defines it as : —
" The condition of understanding through the sub-
sumption of new subjects under old predicates."
(Essentials of Method, page 31). Lange says : — " With
the aid of familiar perceptions, the child appropriates
that which is foreign to him and conquers with the
arms of apperception the outer world which assails
his senses;" and again, "One has no eye, no ear,
no receptivity, no understanding for that for which
one has no related thought, no connecting points, no
rich store of related concepts."

We shall next consider the use of words in rela-
tion to apperception.

When primal realities become subjects of con-
sciousness, through the senses, they constitute our
personal experiences, and when words or symbols are
associated with these experiences, they serve as
storehouses of thought. And when these words are
again presented to the eye or to the ear, the mind
through memory calls up into conscious concepts the
experiences with which the words were first asso-
ciated. These serve as apperceptive centres, and

!-^.^fiai»(*..V -.'■' it'

ANALYSIS OF MKTHOD.

throufj^li tlie constructive power of iinagination the
iiiind re-arraiif^es and transfonus them into new
fbriuH and combinations in liarmony with the way in
which the words are presented to it.

The followinfr illustration will serve to show how
this is done. I meet a child who lias seen only a
small wooden church buildinfjf, and I endeavor to <f\ye
him a mental picture of a church which I have seen.
As soon as I use the word church he calls up the
imaw of the church which he has seen. I tell him
that my church was high and large, and at once
throujrh his imamnation he sees his church raised
and extended in size. I tell him my church was
made of brick and that it had a bell placed above the
roof He immediately sees his church surrounded
with brick, and a bell placed above it as described.
Thus out of his stock of concepts or personal experi-
ences the child has constructed for himself an image
of tlie church which I described, in accordance with
the words presented to him.

It must be carefully noted that all the concepts
out of which the child constructed his image of my
church were previously in his mind. If he had had
no concept related to the word brick his church
would have remained wooden, and if he had never
seen a bell his church would have been unsupplied.

Imagination can construct, that is build together,
but it cannot create original elements. These, as has
been showni in part A, must be furnished to the mind
through the appropriate sense. The imagination can
form compounds and combinations wliich never
existed before, and in this sense may be said to

/ ?

I I

li;

METHODS IN TKACHINri.

creato, but in every case its creation is restrict(Hl
to eleiiKiiits that are already in the mind.

Tlie work of inia<^ination may he illustrated by
that of the blacksmith. He takes separate pieces of
iron, and after heatin<,s welds them to<;ether. He
creates the hors(!-shoe, but he does not create the
pieces of iron out of which it is made.

By this explanation the student will ^rasp more
fully the meaning of the statement previously made?
that words do not convey ideas. This may now l)e
bettor stated by saying that words do not create
ideas. The spoken word is but a sound, just as the
written word or symbol is but a drawing or picture.
Before either can become speech, it must, as has been
said, when recognized, call up and be associated with
some concept already in stock, by means of which the
mind can interpret to its own consciousness what the
speaker or writer desires to express through the word.
It is only in this way that " the word can become a
livl.ig force instead of a dead form." We are accus-
tomed to say, "Ideas first, words next." Realities
before sijmhoU would express the same rule in a
much broader way.

This method of teaching may be called the con-
structive method, and in view of what it involves
teache]'s should endeavor to find out what concepts
are possessed by the child before they attempt to
make use of it.

The nnportance of the work recently undertaken
by Dr. Stanley Hall and others, of leading teachers in
a systematic manner to take stock of children's
mental outfit befcn'e they begin to build thereon,
cannot be overestimated. Failure to do this too often

-'^■^inBBKSs^a-

ANALYSIS OF METHOD.

i restricted

istrated hy

te pieces of

jetlier. He

create the

^rasp more

•usly made?

[ly now be

not create

juwt as the

or picture.

as has been

ciated witli

P which the

p wliat tlie

the word.

become a

are accus-

Realities

rule in a

d the con-
involves
concepts

}tempt to

[dertaken
lachers in
Ihildren's
thereon,
|oo often

causes much loss of hibor and painful confusion of
thou<^ht. To define the lx)undaries of a piece of land
there must be a pcjint of be^'innin<^, and inih'ss \\i\
be^in at the child's starting point of knowledge we
cannot teach him intelligently. When we realize
this we can understand why it is tl\at what are
apparently absurd answers are often given to
(piestions in literature and other subjects by naturally
intelligent pupils. The cause of this in many cases
is that the pupils have no concepts by which they
can interpret the words as they stand in their new
relations, and in their desire to answer they rush to
concepts with which the words have been associated
in other relations, and as a result of their natural
effort they ar.e too often called or considered stupid.
If they have not material in store out of which
the mind can construct the necessary concept the
question cannot be answered.

A little boy travelling in Europe was told by his
mother that he was then in Switzerland, and was
asked how he liked the appearance of it. He looked
eagerly out of the window and replied, " I thought
it was pinker than it is." The little fellow had
evidently learned something from a wall map of
Europe, in which pink had been used to represent
Switzerland, and without any conception of the use
of the word Switzerland, he had simply assot iated
the sound of the word as used by the teacher with
the color pointed out on the map. Hence from what
he had learned though his eye and his ear, his answer
was a perfectly natural one. If all the geographical
concepts formed by pupils from the study of this
subject from books could be fully exposed to view

METHODS IN TEACHING.

we should Hud that mauy of them were equally
absurd. A teacher eudeavored to explain to his class
how spriiicrs were formed by showing a section of a
hill with the little streams percolating through the
soil to the reservoir below, and after this had been
done, an«i the effect of pressure explained, he asked
if any member of the class had ever seen a spring.
His feelings may be better imagined than described
as one of his pupils at once replied, "Please our
buggy's got two springs."

One of the many unavoidable difficulties with
which teachers have to contend is the use of the
same books for children who have been surrounded
by very different environments, and who have, in
consequence, acquired stocks of concepts that are
quite dissimilar. Bryant's description of the prairies,
for example, will " convey " but a feeble picture to
the child who has always lived in a city. The mean-
ing of " Dark hollows seem to glide along and chase
the sunny ridges," cannot be grasped in its fulness by
one who has never seen the sunshine and shadow
chasing each other over the meadow, or rushing in
quick succession along the surface of a field of waving

grain.

In teaching by what we have called the Construc-
tive Method, two things are especially necessary : —

(1) Such a review of the known as will prepare the
mind for the apperception of what is to be learned ;
and,

(2) A skilful rearrangement of the new matter
whenever this is possible, in order that the learner
may be enabled to detect the relation between the
old and the new.

ANALYSIS OF METHOD.

sre equally
to his class
section of a
1 rough the
J had been
1, he asked
sn a spring.
1 described
Please our

ilties with
ise of the
jurrounded

have, in

1 that are
le prairies,
picture to
The niean-

and chase
fuhiess by
Id shadow
jushing in
)f waving

/onstruc-
pary :—
;pare the
learned ;

matter

learner

^een the

It must not be assumed because the child has
already in his mind the necessary predicates that he
will, througli them, interpret the new subjects.
Experience proves that such is not usually the case.
The child is more likely at Hrst to regard each new
thing to be learned as a distinct entity than he is to
call up a related concept, and to associate with it the
new subject of thought.

Pupils who have learned reduction of whole num-
bers will see " Reduction of Fractions " printed at
the head of the page, and under the various rules
given will work all the exercises without perceiving
that the solutions are but new applications of what
they have already learned.

A pupil may have learned that the product of
the sum and difference of t a'o (piantities is eijual to
the difference of the squares of the quantities and he
may know at once that (a-fb)(a — b) = a^ — b^, yet
he will probably re(|uire some assistance at first to
see that (a— b + c— d) (a— b— c + d) = (a— b)^— (c— d)l
In preparing the mind for the new knowledge, the
teacher " who sees the end from the beginning," will
lead the child to note the point or points in the old
throuofh which the relation with tlie new is to be
established.

F'or example, when a child learns that a simjde
M^ord means one word, and that a comiJouiid word
means two or more words taken together, he has the
key by which the use of these words in many other
connexions may be undei'stood. The relation between
a simple sentence and a c<jmpound sentence, between
simple addition and compound addition, between
simple interest and compound interest, etc., will be

METHODS IN TEACHINCi.

readily seen when tauglit tliroiigh tlie idea of unity
and of plurality as found in the primal use of the
words simple and compound.

The teaching of the " compound rules " will fur-
nish excellent examples of what has been said about
" rearrangement of new matter." The new points in
these rules which will of course present difficulties to
the learner are, (I) the separation of the columns by
dots, (2) the names placed above the colunnis, and
(3) the different ratios between the quantities tlie
names of which are given.

The first and second difficulties may be easily
removed and a (question in the simple rules made to
resemble one in the compound rules, and although the
terms units, tens, etc., do not correspond to the names
of applicate numbers, this fact will not trouble or
mislead the pupil at this stage. In preparing for the
use of ratios which are not common, a question in
simple addition may be treated first as having other
ratios than 10 which are common to all the columns,
as 9, 8, 7, etc., and then as Iiaving ditferent ratios
between the colunnis. In this way the pupil is trained
to work (questions in the simple rules as if they were
in the compound rules and the relation between the
old and the new is easily seen.

Nearly every operation and every new term in
fractions can be taui^ht throujrh somethinix that has
previously been learned by the pupil. 2| can be
easily reduced to fourths when it is expressed as
2 units 3 fourths, and referred to the reduction of
2 bus. 3 pecks, to pecks. The value of a denominate
fraction as | yd. can readily be found when the

iimiHHilin iin-™«™™»-™

ANALYSIS OF METHOD.

idea of unity
ifil use of tlie

lies" will fur-
een said about

new points in
) difficulties to
lie columns by

columns, and
quantities the

lay be easily
: rales made to
1 although the
1 to the names
lot trouble or
parini;' for the
question in
having otlier
the columns,
fere lit I'atios
pil is trained
if they were
between the

new term in
ing that has

2f can be
expressed as
reduction of

denominate
1 when the

example! is treated as an ordinary (juestion in com-
poun(l division — 5 | 8 yds. ft. in. In changing a
proper fraction to its corresponding decimal the pupil
should not be tohl to " add a cipher to the num-
erator," but he sliould be taken back to simple
division, which we assume was done when compound
division was taught, and led again to see what act of
reduction was really performed in the expression
285 -f 6 ))efore he could say "6 into 28" and again
" 6 into 55."

In such preparatory exercises tlie teacher must
direct, and if necessary assist in changing the form
of the question ; b'lt ^n every case tlie work should be
done by the pupils, and if they are unal)le to solve
the new problem it is because the preparatory steps
have not been thoroughly understood, and these
should V)e reviewed.

The young teacher may think that this method
re(|uires too much time, but experience will convince
him that time is an essential element in all good
teaching, and chat the pupil's future progress will be
commensurate with the thoroughness with whicli
fundamental principles are mastered.

This method should be employed, wherever pos-
sible, in all subjects. The pronoun should be taught
through the noun, the adjective phrase and clause
through the adjective, the mountain through the liill,
the river through the stream, the country through
the school section, etc.

Points of dissimilarity and contrast will also assist
the mind to grasp new truths and to retain them by
the association of ideas. The diffeience I etween
the preposition and the conjunction, between th

■'?il

METHODS IN TEACHING.

compound sentence and the complex, between the
problem and the theorem, between the root and
the power, between the causes and effects of great
events in history, etc., will all become valuable aids
in teaching when they are properly compared and
distinguished.

This subject might be extended indefinitely, but
it is hoped that what has been said will emphasize
the importance of teaching subjects in their unity,
and will assist teachers in working towards this end.

i i'i

As has been said, the mind must begin with
individual or particular notions. The brute advances
thus far. The horse, for instance, has the notions
road, hay, dog ; but these, like the earliest notions of
the infant mind, must be very vague and indistinct.
The mind of man is further endowed with the power
of reflection through which it forms concepts.^ Known
objects are examined and compared, and their differ-
ences and likenesses discerned, and the mind forms
general notions to represent objects having common
characteristics, and groups the objects under these to
form classes. It discerns the qualities and relations
of things and affirms these as facts. From the
knowledge of particular facts derived either from
observation, or from testimony interpreted by our
personal experience, the mind is able by the power

1 Ah concepts and the generalizations of inductive reasoning arc
somewhat similar, they are discussed in the same section, though the
former might very properly have been considered at the beginning of
Section B.

^Jarff^r, it:^

ANALYSIS OK METHOD.

, between the
:he root and
Tects of great
valuable aids
compared and

definitely, but
dll emphasize
1 their unity,
ards this end.

}t begin with

)rute advances

.s the notions

iest notions of

nd indistinct.

ith the power

pts.^ Known

their differ-

mind forms

'in<r common

Inder these to

land rehitions

From the

either from

:eted by our

the power

re rea80uinK are
Ition, though the
Ihe boginniiiK of

of inference to soar beyond tlie limits of past experi
ence and to conceive those universal truths and laws
which explain particular fact, by revealing their true
relations, and thus to organize and extend knowledge.
The degree of intelligence to which any one
attains is determined chiefly by the strength of this
power to see the general in the particular, by ready
and accurate insight to grasp the true relations of
facts, to distinguish the essential from the non-
essential, and thus to infer correctly the underlying
principles. The generalizations of the child are
crude and inaccurate ; those of science clear and
definite. It is the chief business of the teacher to
train his pupils into the power ana the habit of
passinjj; easily from the particular to the general. ►So
far as the work of the teacher contributes to this
training, it can be secured only by the practice of
right methods of study. To cram the pupil's mind
with particular notions with no regard to their true
relations, or to requii'e or permit him to memorize
ready-made definitions of general truths, is not
educating him. Principles and truths cannot be
implanted in the pupil's mind by imposing upon him
the memorization of empty forms of words, mere
husks, which to him have never had any content.
They can be developed only by the self activity of
the pupil's mind, called forth, as has been shown in
Section A, by the suitable presentation of appropriate
objects, j'ud stinuilated and guided by the (juestions
and directions of the teacher. The teacher who
desires to be an educator cannot neglect the study
of those processes of thought which produce the
concept, principle or law.

METHODS IN TEACHINC!.

Tlio simplest general notion is that which repre-
sents a chiss of objects, Tliis concept represents tlie
characteristics which are connnon to all the objects
of a class. Each ij^eneral notion necessarily implies
individual notions from which it is derived, and
which are subsumed under it. The process by which
this concept is formed can best be shown by the
study of a particular instance.

The child perceives an apple, forming by a syn-
thesis of the several perceptive acts through the
different senses a sense percept or image of the object.
He perceives a second apple and forms an image of it,
and so on. When the second or succeeding' imajxes
are formed, the mind, at first dimly, but with increas-
ing clearness, compares the image with those which
preceded it, and which are more or less fully recalled.
It analyses and compares these images and perceives
the connnon parts and properties, such as the char-
acteristic shape, coloring, formation of parts, etc. It
then abstracts these characteristics, or conceives them
apart from any particular apple in which they are
exhibited. All the common characteristics are then
combined into a new thought-whole, a general notion
of this kind of fruit. This concept contains only
those characteristics which are common to all the
members of the class ; that is, only the parts and
properties necessary to make it an apple. It cannot
be imaged because it does not contain the individual
peculiarities of shape, color, proportion of parts or
flavor of this or that apple. The mind can express
it only b^^ a definition.

A large part of elementary teaching consists in
aiding the pupil in the actjuisition of new class

jp;

vijOTiRw 111 'WHIP ■vA.iiti mr.m>u-aiv,«KEimt

AXAUYSTS OF METHOD:

fc wliich repT'c-
represeiits the
all the objects
ssarily implies
'> derived, and
:)cess by which
shown by the

in^^ by a f^yn-
1 through the
3 of the object,
fin inia^e of it,
eedinp- imacfos
b with increas-
1 those which
fully recalled.
I and perceives
as the char-
)arts, etc. It
)nceives them
lich they are
tics are then
eneral notion
iitains only
1 to all the
e parts and
It cannot
e individual
of parts or
can express

consists in
new class

concepts, and it is impoi'tant that the method of con-
ductina' lessons of this kind be considered somewhnl
in detail.

A ])rimary condition of the lesson is evidently the
presentation of examples of the objects to be classified.
Who should give these examples, the teacher or the
pupil ? Some teachers assume that the pupil should
furnish the examples, on the ground that he can
better understand the objects which he himself dis-
covers, and also that these are more likely to arouse
his interest. An important objection in many instances
is that it is a serious waste of time ; the teacher can
prompth'' and judiciously select examples suited to
the child's development, and can ascertain by a
({uestion or two whether any are beyond his experi-
ence. Other objections are that it tends to discourage
the pupil through the rejection of his efforts, and that
it develops indefiniteness of thought, and a vicious
habit of guessing. It is also illogical, presupposing
a knowledge of the thing to be taught.

It forms no highly colored scene to picture a
teacher who misapplies the perfectly . nuid rule,
" that the teacher should not do for the child what
he can do for himself," conducting a lesson in this
fashion. His aim, let us say, is to teach the adjective,
and he proceeds to "develop" examples. Holding
up a piece of chalk he asks :—

T.—What is this ?

p. — That is a piece of chalk.

T. — Tell me something about it.

P. — You can write with chalk.

T. — Yes. Now Mar}' you tell me something
about it.

BBti>;

•""TIMII

METHODS IN TKACHINU.

P. — The chalk was in tlio box.

T. — Y-o-s. But t(,'ll 1110 .soiiiothiiif'' olso about it.

Is it any wonder if after sueli an exercise both
teacher and pupil are soon in despair and mentally
jL^ropin<j^ in a Fog*.

The second step — the first for the child — is the
examination of the examples presented. Here g'reat
care must be taken to direct the pupil's attention
without suggesting that which he should discover for
himself.

Having carefully examined the objects presented,
the pupils are then guided by the teacher to make
a comparison of their characteristics, stress being
laid first upon those which are common. Examples
should be multiplied, and the examination and
comparison repeated wath patience and thorough-
ness in order that the new concept may be clearly
developed. It is a serious error to try to obtain t!ie
definition before the pupil, by the careful scrutiny of
many examples, has firmly grasped the new^ notion.
The impatient teacher is apt to suggest to the
pupils by the form of liis cpiestions the wording
of the definition and to accept the pupil's repetition
of the borrowed language as proof that he has
acquired the new notion.

When, as a result of the careful analysis and
comparison of a suflficient number of examples, the
new idea defines itself in the child's mind, he will be
able to give expression to his thought. The new^ term
which designates the class may now be given, any
necessary improvements '*i the child's form of ex-
pression added, and the new definition made still
clearer by being applied to new cases.

ANALYSTS OF METHOD.

'Isc al)r)nt it.
exercise botli
and mentally

child — is the
1. Here i>"reat
pil's attention
Id discover for

ects presented,
icher to make
i, stress being
an. Examples
,mination and
md tliorough-
[lay be clearly

:o obtain the
ul scrutiny of
new notion,
ggest to the
the wording
nl's repetition

that he has

analysis and
examples, the
id, he will be
The new term
)e given, any
form of ex-
n made still

To illustrate the method suggested, let us take the
teaching of the definition of an island. The beat
presentation for this lesson is, of course, examples of
real islands as observed in a neighboring lake or
stream. The concept may, however, be clearly and
e(jrrectly developed, though with greater difficulty, by
representing islands on the moulding board or on
the blackboard. Having first aided the pupil's
imagination by referring to local examples of land and
water surfaces, to accept the surface of the moulding
board as representing water, and the little heaps of
sand as land, his attention is directed to the first
example. To make vivid the image which his mould-
ing board represents, the little fellow may in imagina-
tion row round the island, the course being traced
on the moulding board back to the place of starting.
The pupil then describes what he has observed.
" This is land. This is water. The water is all round
the land." As he scrutinizes a second example, he is
certain to make some vague comparison with the first.
Each succeeding example which the teacher directs
him to examine, calls up the others, and finally by a
systematic review the teacher makes the comparison
formal and exact. The pupil sums up the results of
his examination and comparison. " All these (point-
ing to the different representations) are pieces of land.
This is water. The water is all round each piece of
land."

The result of the comparison is that the child
abstracts the notion of this relation of land and
water ; that is, there is formed in his mind a general
notion of portions of land entirely surrounded by
water, without connecting it with any particular

METHODS IN TEACHING.

sland. He is now iTjuly for tlie tei'in /slu ih!, wliicli
dosif^nat(3H his newly acMiuircd concept, and under the
guidance of the teacher he makes a formal definition.

Having first directed the pupil's mind to discern
tlie essential common characteristics, his notion may
be more clearly defined by directing his attention to
the non-essential or accidental features or qualities
exhibited in individual examples, such as varying
size, elevation, outline, or material. He observes or
images some as mere patches of bare sand or rock,
some sustaining forests, farms, and towns, or forming
extensive countries. He perceives that some of these
characteristics are common to several or to many
examples, but he is led to see their non-essential
chai-acter, and thus his concept of an island grows in
extent and its essential characteristics are more clear-
ly defined.

Having dealt with a typical example of concep-
tive thought or classification, we have next to investi-
gate the method of forming a general truth, rule or
law. '' Take as an example of this the general rule
for forming the plural of nouns. Here again the
i^upil must begin with examples of the particular
cases coming under the law. The teacher writes on
the blackboard a list of familiar names of objects.
As each is written he obtains from the pupil the
statement that the nan^.e designates one thin^ of its
kind. The pupil may also give the form which
designates more than one.

Pen. Pens.

Book. Books.

Cup. Cups, etc.

Directed by the teacher's questions, the pupil

ANALYSIS OF MKTIIOD.

/s/ain!, wliicli
uid uiidi'i- tlie
iial definition,
iiid to discern
.s notion may
s attention to
s or qualities
li as varying
3 observes or
sand or rock,
la, or forming
some of these
or to many
non-essential
md grows in
e more clear-

3 of concep-
it to investi-
uth, rule or
eneral rule
again the
particular
writes on
of objects,
pupil the
dii^ of its
»rm which

[he pupil

MMMhscs tliis j)res('iitati()n and coiiiparcs llic words.
He notes tlie ditferent forms for each word, and the
corresponding difference in tlieir meaning. The
several judgments expressing his thinking are some-
what as follows: — Pen denotes one thing. Pens denotes
more than one thing. Pens is formed from j>C7? by
the addition of s. In a similar way he pronounces
upon the relations of book and hooks, cup and ^7/j).s',
and all the other examples placed before him. As a
result of his comparison of the words j)en, hook, cup,
etc., he forms an abstract notion of a name with a
sino-ular meaning:. He thus conceives a class of
names meaning one, which he is taught to call names
of the singular number. In the same way he forms
a class concept of names of the plural number. By
further comparison he discerns that the plural forms,
pens, hooks, cup)s, etc., are formed by adding .s to the
singular names pen, hook, cup, etc., respectively. As
examples are multiplied, with increasing clearness is
fo]'med the thought, that, since all the names exam-
ined form their plurals by the addition of s to the
singular, it must be true that all names form their
plurals thus. This is necessarily beyond his experi-
ence, but the thought develops in his mind from its
inherent tendency to attribute to nil the members of
a class, what has been observed to be true of those
which have been examined. Subsequent experience
teaches him the necessary modifications and limita-
tions of the grammatical rule which he has thus
discovered.

The act of thinking, by which the mind thus
reaches beyond the limits of experience, is called
Inductive Reasoning. It is through the operation of

MKTHODS IN TKACHINO.

tliis fni'iii of rojiHon tl»at all ^oncial tiutlis. mnxiins,
rules, and laws ai'c (IcvclDpcd in tlie iiiiml. In casos
of induction like that just described, tli<3 ouneral rule
is tlio montal product resultin^^ from the examination
and c()m})ai'iH()n of many exam})les. Tlie more num-
erous these are, the greater the confidence in tlie I'ule.

Havino- now Itriefly considei'ed the method of pro-
ceedin<>' from tlie ])articuhir to the j^'eneral, we have
next to deal with the application of the ji;eneral rule
or principle to particular cases. By this exercise the
pu])il obtains a cleai'er apprehension of the truth,
discovers new and perhaps unexpected applications,
as well as limitations or exceptions. Above all he is
pi'actised in the exercise of formal reasoning.

Formerly it was the practice of many teachers,
and of the text-book which they followed, to begin
the presentation of the subject witli a statement of
general facts and principles. Thus a text-book on
Grannnar began with a definition of the subject,
followed by definitions of its several divisions, and so
on. The order of development followed was first the
rule and then the examples subsumed under it. The
elementary text-book differed from the more advanced
only in being a thinner book, and in containing fewer
particulars.

However suitable this plan of unfolding a subject
may be for advanced students, who have already
much elementry knowledge which enables them to
attach at least some meaning to the definition given,
it is not likely to be helpful in the teaching of
children whose knowledge is meajxre and ill-defined.

Ti'aining in inductive reasoning is of great impor-
tance not only as the logical preparation for the

ANALYSIS OK MKTMOD.

ti'iitlis. innxims,
"H"l- 111 cases
(n3 oonei-il rule

lie examination
lie more iium-
iice ill the rule,
ii let hod of pro-
tieral, we have
10 ^reneral rule
lis exercise tlie
of the truth,
d applications,
■bove all he is
)nin<jf.

liMny teachers,
wed, to begin
statement of
text-book on
the subject,
•sions, and so
was first the
ider it. The
lore advanced
taining fewer

ig a subject
ave already
)les them to
lition given,
teaching of
fll-defined.
;reat iinpor-
lon for the

drdiiftiN »' treatment of the more advanced portions of
the sul'jcct, l)Ut also as a [H'cparatioii t'oi- tiic pradicMl
atijiirs of life. LVopK' usually airivc at ri,i:ht con-
clusions wlien their ])eliefs or princi})K!s are right. It
is a characteristic of the ignorant or careless, especially
when swayed by passion, to generalize from an
insutlicit'ut basis of facts, and thus to be influenced in
their coinluct by wrong opinions. The trained thinker
learns to withhold judgement until the facts are
closely studied, when a valid inference may be made.

The general rules or truths discovered by the
pupil from a careful study of observed instances will
not, however, he fully apprehended orretaine(l ])y the
memory unless they are applied to a sutHcient num-
ber of new cases. In each instance of such application
of a general rule or law, the pupil's thinking, when
formally expressed, may be set forth in three related
propositions, together constituting what is called the
syllogism. For example, the pupil's answer, " John
is a name ; therefore, it is a noun" implies a suc-
cession of related thoughts which when fully ex-
pressed take this form :

Words used as names are nouns.

John is a name.

Therefore John is a noun.

The first or general statement is called the
major 'premise, the second the minor premise, and
the third, resulting from a comparison of the first
two, is called the inference or conclusion. Fre({uently
one of the premises, usually the major, is not formally
expressed. In the above example, for instance, the
pupil has assumed the definition of the noun, which
forms the major premise. It helps greatly, however,

■mi^

METHODS IN TEACHING.

to a clnar ap])reliension of the diameter of the think-
ing performed to give it full expression in the form
of tlie syllogism. As an instance, take the correction
of the example of false syntax, " John and me went
to the fair." The lesson may proceed thus : —

T. — What eiTor is here ^

P.— Me shonld be /.

T.— Why ^

P. — Because I is in the nominative case.

T. — Why should you use the nominative form ?

P. — Because the subject of a finite verb is put in
the nominative case.

Re-arranged in logical order, the pupil's state-
ments are : —

Major. — The subject of a finite verb is put in the
nominative case.

Minor. — Me is the subject of the finite verb icent.

Inference. — Me should be changed to the nomina-
tive form /.

The teacher's persistent " Why " coming after the
pupil has stated his conclusion, requires him to
re-think his premises with greater precision, thus
giving him a clearer grasp of their relations. Practice
of this kind in logical thinking develops the pupil's
reasoning power, and also gives liim the habit of
analysing the facts which form the basis of his
inference. The proper method of teaching nuist be in
accord with the logical order of thought. First,
induction proceeding from the particular to the
general, and then deduction proceeding from the
general to the particular, is the unvarying and neces-
sary sequence. The mind first grasps individual
notions, then in succession are formed generalizations

ANALYSIS OF M?]TH()D.

f tiio tllillk-

iii the form
e correction
id me went

ve form ?
)> is put in

pil's state-
put in the

'erb irent.
e nomina-

after the
5 Jiim to
ision, thus
Practice
he pujjil's
liabit of
(s of liis
uist he in
First,
to the
:'rom tlie
\^\ neces-
idi vidua]
th'/,'itions

more and more comprehensive. Eacli trutli thus
establislied is then applied to particular cases, thus
storini;- the pupil's mind with new but properly
I'elated ideas. New conce])ts are clearly ojrasped b}-
being assimilated to that which was previously
known, and the pupil is trained into the habit of
dealing with new subjects whether presented in books
or in the affairs of life, in a logical way. He calmly
examines, compares and infers. " He is taught to
rise from the particular to the general as easily as to
<lecend from the general to the particular again."

■i

I'f

t t

.so

MKTIIODS IN TKACHIN(J.

CHAPTER II.

THE TEACHING OF LITERATURE.

Scope of the term Literature -as employed
in connection with the Readers— Tlie term Litera-
ture, altliougli perhaps the best that can l)e found,
is at once too narrow and too wide to indicate
accurately the sort of woi'k intended to l)e incUided
in tlie teaching of Readers in Public Schools. It
is too narrow because some of tlu; instruction liiven
in this connection is rather scientific than literary ;
it is too wide because a <>'reat deal of what is
most naturally su<i^gested by the term Literature
is beyond the comprehension and expei'ience of
school-boys and school-girls. With regard to the
first point: numy of the selections in the Readers
are manifestly not designed to introduce pu2)ils to
literature in its more proper sense, i.e., to written
thought which is marked by some special beauty and
power, of form and expression; they are inserted i'ov
the sake of the intvn'mation conveyed, in ordei* to
broaden the child's knowledgv^ and to stimulate his
interest in the world at large. They furnish an
introduction and preparation foi* that impintant part
of the reading of later years, which is motived, not
by the desire of aisthetic enjoyment, of gi'atii'ying
the literaiy instiiM-t [)r()[)er, l»ut by the appetite
for knowledge, by sympathy with mankind, and
by curiosity in regard to the history of the race

THE TEACHING OF LITERATURE.

KE.

IS employed

i term Litera-
;nii he found,
3 to indicate
) he included
ScIiooIh. It
'uction <;iven
lian literary ;
of what is
n Literature
xpei'ience of
^j^-ard to the
the Readers
ce pupils to
, to written
heauty and
inserted for
in ordei- to
iniulate liis
fui-nish an
ortant part
lotived, not
i^ratifying
<! appetilc
il<ind, and
f the race

and of the universe. Such lessons are the initial
st.ife of scientific rather than of literary work. But
since for ordinary people, knowledge must be
acquired, in a great measure, not first-hand from
tliin'i-s in themselves, but from books, the stinmlation
of such interest, the practice in acquiri'.ig knowledge
in this fashion, is fittingly enough comprehended
within the broad province covered by the Readers.

In regard to the second point: the somewhat
ambitious designation " Literature " is suggestive of
work unsuited to schools, and may tempt the
inexperienced teacher beyond the range of his pupils.
It is true that the more profound and many-sided
the teacher's own study of the selections, the wider
his reading nnd the more subtle his analysis of
literary effects, the better it is for his scholars ; yet
this width and depth of knowledge, should, in the
main, affect his teaching in an indirect way only.
To attempt to impose upon innnature minds the
higher results of literary investigation, is simply to
exhibit a lack of that sound sense and judgment
indispensable in ail good teaching. Advanced criti-
cism deals witli the analysis of the effects of literature
and of the way in which these effects are ])r()d need.
But at the elementary stage to wliich school-children
have attained, our business is with the production of
these effects, not with the analysis and classification
of them. Our end has been attained if we enal)le
the child to read easily, if we cultivate the habit and
stinuilate the desire of reading, and teach him liow^
to appreciate and enjoy what he reads. The attem])t
to analyse and account for the vague and nascent
literary perceptions of the beginner, will probably

1:1

*• A

i} ]

r**

'■.

■'^d

!lt

METHODS IN TEACHING.

result in destroying them, or, at least, in mingling
repellent associations with what ought to be only
pleasurable. The devotion of much time and thought
to the definition and classification of rhetorical terms,
figures of speech, qualities of style, and so forth, is
incompatible with the attainment of the real ends of
elementary teaching in literature. Here, as else-
vvliere, the student should be made accjuainted, not
with mere words, but with things, — in this case, with
the concrete experiences and feelings that literature
should afford. The boy, who, hearing tJte Mariners
of England, or Horatiut^ at the Bridge, feels his
pulse (piickened, his heart stirred in sympathy with
the sentiment or situation, who finds a pleasure in
the imagery and the swing of the verse, has had a
genuine literary experience and made a real step in
literary culture. And if the teacher succeeds in
arousing such elements or pleasure in connection
with a number of different pieces in prose and verse,
lie has opened the doors of literature to his pupil,
has put liim in the way of deriving permanent
pleasure, information, and culture from books — in
other words, he has attained what are the true aims
of the teaching of literature in Public Schools.

Aims of Teaching" Literature in Public
Schools — More explicitly, then, the object of the
teaching of the Readers is, (1) To show the pupil
how to read, how to turn the printed symbols into
the ideas which they represent; (2) To broaden
knowledge, to quicken intellectual curiosity, to stimu-
late that general interest in men and things which
belongs to every cultivated man, and which depends,
in a great measure, upon books for gratification ;

THE TEACHING OF LITERATURE.

,, in niinglin<j^
t to be only
3 and tliought
itorieal terms,
d so fortli, is
e real ends of
lere, as else-
(|uainted, not
his case, with
hat literature
tlie Mariners
Ige, feels his
nipathy with
a pleasure in
se, has had a
1 real step in
succeeds in
connection
se and verse,
o his pupil,
permanent
books — in
le true aims
ools.

in Public

ect of the

the pupil

mbols into

'o broaden

, to stimu-

lings which

h depends,

atification ;

(8) To awaken the appreciation of literature proper,
to develop the ability to feel the beauty and power
of literature in its narrowest and highest sense.

Importance of Interest in the Study of Litera-
ture — Now, the taste for reading, the sense for the
beauty of literature cannot be developed except
pleasurably ; if the method be dry or repellent, tlie end
cannot be attained. Hence, there is something unicpie
in this subject. When a pupil is engaged in the study
of arithmetic, or grammar, or writing, mental dis-
cipline is given, and practical skill is imparted, whether
the pi'ocess be an agreeable one or not ; but tl^e chief
end of the study of literature cannot be reached,
unless the associations therewith are pleasant, and
the pupils are borne i'orwanl by their own interest
and enjoyment. But, if for this reason the diffi-
culties of teaching the subject are enhanced, on
the other hand, they are lessened by the variety and
. scope of the matter treated and of the methods that
may be employed. While remembering the evils of
needless desultoriness, we vMiy yet say that any
passage from good literature that appeals to the
intellectual curiosity or to the taste of the pupil may
be studied, and that any method may be used which
serves to bring the subject in hand into relation with
the reader's previous knowlec'ge and experience, or
into touch with his sympatliies and emotions.

How to Stimulate Interest- How, then, may

interest be stimulated ^ First of all, by In'inging
what is read into relation with actual thino-s,
by making the pupil realize tlie statements, the
situations, the persons of the lesso-.i. For the beginner,
at least, the mere fact that ideas are conveyed
3

111:

) '\

'4 ' a

METHODS IN TEACHING.

tlirough the printed pa^^e, is enougli to impart
an unreality and aloofness to them. It is extra-
ordinary how a child may understand each word and
sentence, and yet somehow the thoughts contained
may never penetrate beyond the surface of his mind.
Nearly all mature persons have had a similar
experience of the unreality and remoteness of the
facts, for example, of Greek or Roman history, — an
unreality of which we are scarcely aware, until some
touch of nature, some commonplace incident awakens
in us the sense that Greeks and Romans were real
men who, like ourselves, lived and felt ; we at length
realize facts which we had all along understood. In
like manner, the skilful teacher will change the
vaguely and feebly apprehended ideas of the printed
page, into vividly realized conceptions similar to
those v.^liich are produced by the pupil's own
experiences.

To attain such results in the case of those extracts
which are not specially literary, but are primarily
designed to waken 2uriosity and broaden knowledge,
the methods employed will rather be those of science
than of literature. For instance, when reading the
selection entitled A Piece of Coal, the teacher will
exemplify in actual specimens tiie various assertions
of the author. When the lesson is on Canadian
Trees, not only will he exhibit, as far as lies in his
powei', leaves, bark, etc., but he will, by questioning,
make sure that his pupils recognize the various
species; he will find out what they themselves have
noted in regard to trees, will cultivate habits of
observation by drawing attention to the branching,
liabitat, and other peculiarities of familiar varieties.

THE TEACHING OF LITERATURE.

li to impart

It is extra-

icli word and

its contained

5 of his mind.

[I a similar

eness of the

history, — an

e, until some

ent awakens

US were real

we at length

erstood. In

change the

the printed

similar to

mpil's own

ose extracts
primarily

knowledfife.
of science

leading the

acher will

assertions

Canadian

llies in his

estioning,

various

)lves have

Ihabits of

[ranching,

1 varieties.

Ill the case of lessons — historical and other — that
have to do witli the life of the race, the outlines
should })e tilled up with interesting dr'tails from the
teacher's own readino-, and should be illustrated l)\'
some familiar parallel cases. If, in preparation for
such work, the teacher each session broadens his
own ac(|uaintance with the subjects treated, the
lesson will uain a new interest for himself; and even
when the newly ac(|uired information is l)eyond the
range of the students, his own freshened perception
of the significance of the old theme, will lend that
animation and interest which are essential to the
successful teaching, an<l are yet difficult to retain in
coiniection with luickne3'ed work.

Oral Reproduction— Tlie special bar interposed
between the pupil and the ideas of the author, by tlu^
fact that they are conveyed in literary form and
through written symbols, may be partially (jvei-come
by the oral reproduction of them in more conversational
and familiar style. That such a bar does exist, is
shown by the observation of the young, and of persons
unaccustomed to reading. Little children greatly
prefer to have a story told in the natural langua<i'e
of the narrator, rather than read from the printed
page. In maturer life many can follow a lecture
with pleasure and advantage, who would find a
chapter in a book, on a similar ♦^heme, nmch less
attractive and profitable. And this difference does
notarise aerely from the v\(jrds being addressed in
one case to the ear, and in the other to the eye : for
the speaker who uses a n anuscript or recites from
memory, is at a great dis.M.lvantage with a jiopular
audience, as compared with him who employs

: tj

1 I !

!lM

! i

i«

■^ ^

METHODS IN TEACHING.

laiit;iiM|;e mikI iU'V<'lups tlio blionie on the suggestion of
the nionicnt. The ohstacle cfiused by the untkniiliar
iiiediuiii sliould he smoothed away by tlie teacher,
until j^radually the turning of the printed symbols
into tlie requisite tlioughts, images, and feelings, may
become second-nature ; as it is second-nature in the
case of every cultivated man. One method of begin-
ning this process is to prepare the pupils for the
printed text by oral reproduction in more familiar

Thi

'ill

illy

d'ul

I junior

classes. If the teacher's treatment is successful, the
pupil comes to his task with his curiosity already
quickened, and his mind predisposed to catch the
chief points of the lesson as well as its general
bearing. The teacher need not, and, as a rule, should
not, limit himself to a bare paraphrase of the original ;
he should emphasize and enlarge upon those points
which are likely to be the most interesting and
suggestive, tilling out details, illustrating from the
pupils' own knowledge and experience, and so forth.
For higher classes, this preparation may often be
superfluous ; but in certain lessons, it will prove not
less advantageous for them than for younger students.
To do this sort of work really well re(|uires both long
practice on the teacher's part, and special preparation
for each day's lesson. Such oral reproductions
should not be memorized ; the language employed
and o;eneral form should be left to the suo-o-estion of
the moment.

Reading* Aloud — Another method for the stimula-
tion of interest and for the interpretation of a selection,
especially of those pieces which have marked literary
excellence, is reading aloud. That the reading ma}^

THE TEACHING OF LITERATURE.

'Ill

siip^nostion of
lie unlamiliar

tlio teacher,
ited symbols
feel in OS, may
ature in tlie
liod of beffin-
ipils for the
lore familiar
111 in junior
iccessful, the
sity already
bo catch the

its general

rule, should
3he original ;
[;hose points
and
from the

d so forth.

y often be
prove not

er students,
both long

)reparation

)roductions
employed

,"gestion of

e stimula-
selection,
id literary
di

•esting

ing may

be effective, the teacher must, first of all, himself feel
the writer's power. He should be able, in the s'3Cond
place, in some measure at least, to put his feeling of
the charm an 1 beauty of such a piece as The Vision
of Mirzd or Gntf/'s Elcfji/, into his vocal rendering.
Successl'ul reading re(pures perfectly clear and dis-
tinct enunciation, so as to impress itself upon the
ear of every pupil without any effort on his part.
Slovenliness of enunciation and weakness of voice are
utterly destructive of attention. It must further be
remembered that reading, particularly the reading of
poetry, should be leisurely, so that the mind may
have ample time to catch and connect each idea. Each
piece, even if familiar, should have been read aloud
repeatedly by the teacher in preparation for the
class ; for the proper rendering of the sense of a
passage requires the adjustment of many elements
which camiot be left to the impulse of the moment. A
great source of charm in reading lies in the physical
peculiarities of the voice, the proper use of the organs
of utterance, the control of the breath, the seizing of
the proper pitch and tone. The dramatic rendering
of the thought is not here referred to; but simply the
manaijement of the voice, so that it shall be frc*^ from
hoarseness and the sense of strain, and may flow with
ease and smoothness. These are all qualities which
majT", in a considerable measure, be cultivjited. In
other respects, of course, the reading should be as good
as possible, and the voice suitably varied in harmony
with the sentiments. The last result is, perhaps, best
attained unconsciously by a reader who has a properly
cultivated voice, and a prope)* (uiderstanding and
feeling for the passage upon which he is engaged.

ifi

METHODS IN TEACHING.

But ho-cjiIIlmI <h'(( iiinlir readini;' should bo avoi<l('(l :
Jiuytliinj;" is tu Ihj shunnod tluit distracts the atten-
tion h()\i\ wliat is read, to i\u\ reader. The hitter is
the mere medium i'or the eH'ective transmission of the
writer's tliou<,dits, and lie should, as far as he can,
eti'ace himself. Besides, dramatic readiuLj;- even at its
best, oives an opportunity for burlescjue, and the
schoolboy's sense of the ridiculous is keen.

The Specific Work of the Student of Litera-
ture — What has been said so far, applies to the
Lessons of the Readers in <>'eneral ; let us now turn to
what is more especially our theme, the consideration
of literature in its more proper and narrow sense, and
to the third of the aims mentioned above as belonjj^ino-
to the subject with wdiich v/e are concerned, — the
awakening of the sense of the beauty and power of
literature. What, we may ask, is the business of the
student of literature as such ? It is his function to
understand exactly and fully what the author means.
The printed symbols represent somethini;' in the
writer's consciousness : it is the aim of the student of
literature to reproduce within himself, the state of
mind of the writer which is indicated by these
printed symbols. In certain cases this is a compara-
tively simple matter. For example, Mr. R. A. Proctor
knows certain facts about the heavens, which are set
down in the lesson on Fixed Stars. The process of
understand ino- him is a simple and purely intellectual
one ; on the other hand, in the case of the lesson
entitled National Morality the reader who appre-
hends merely the ideas, and the line of argument of
Mv. Bright, has not caught the com])lex mental state
which the orator intended to convey. Besides

THE TEACHING OF LITERATURE.

;.li

313 avoided ;
tlu! atton-

\iv latter is

ssioii of the
as lie can,
even at its

L', and tlie

of Litera-

ies to the
low turn to
nsideration
sense, and
; belonorino'
rned, — the
power of
less of the
motion to
lor means,
in the
tudent of
state of
by these
eonipara-
-. Proctor
li are set
rocess of
lellectual
Ic lesson
appre-
linent of
lal state
i>esides

understanding^ the thoughts, the person wIjo truly
appreciates this selection feels also the <:;1()W of
enthusiasm with which Mr. Bright legards his facts,
and catches through the form and st^de the contagion
«)f lofty emotion. The latter selection is literature in
a fuller sense than tlie former : it has beauty, it has
power beyond the mere thoughts conveyed ; its form
and expression are shaped by the writer's feelings,
and, to a person of literary culture, communicate
these feelings.

Literary Interpretation— In the widest sense of

the word " literature," all recorded thought is
literature, and all recorde<l thought recpiires a
process of interpretation : we must understand
the words in the sense in which the writer em-
ploys them ; we must put them together so as
to get at his assertions ; we must perceive the
relations of the assertions to one another; we must
gr isp the whole outcome of the passage. In the case
of writings pn^'ely matter-of-fact or scientific, the
literary student's work is tlien complete. But if the
work under consideration belongs to literature in its
narrower sense, this is merely the first stage of
interpretation. When we have thus attvained the
substantial meaning, we must further feel fully the
way in which these substantial thoughts shaped
themselves in the author's mind, the way in which he
looked upon them, and the feelings which he had
about them. All these conditions in the writer's
mind modify his form and expression. The account
of Canadian trees in the Third Reader, is a bare
statement of facts ; since the modifying conditions of
f«'(>ling are absent, the expression is almost without

■, i

METHODS IN TKACHING.

lit r

literary character. 80 .soinetiines we find a writer
narratiii*,'' a Hcries of lii.storic events, almost without
arranj^eiiH'iit or connection other than is imposed hy
the events tliemselves, — without indication as to which
were the more imp(jrtant, and which the less impoi-t-
ant Tacts. Such a one is a mere mechanical recorder.
But ail historian like Macaulay marshals his facts,
brings certain events into prominence, subordinates
others to them, and, merely in virtue of his doing so,
his work becomes literary. His view of the fact is
indicated in the form — in the paragraph structure,
for example. Accordingly, if a reader (as young-
children are aj^t to do) mei'ely takes che facts as
they come, without perceiving the connection and
relative importance given them by the w^riter, he
fails to apprehend the litei'aiy <{ualities of the work.
Hence the teacher should, by ((uestion, ascertain wdiat
the pupils think is the outcome of a passage, should
test by means of oral or written reproductions,
whether they have grasped the coiniection and
importance of ideas. He should point out how the
paragraphs are framed, how successive paragraphs
are related to one another, and so forth.

But still, we are not in the domain of literature
in its fullest sense, but in the realm of such written
thought as is chiefly valuable for the information
that it gives.

Literature Proper — We recognize that the oral
reading of a passage which is valuable merely for
the facts conveyed, is a much easier matter than
the reading of such ])ieces as the scene from Kivg
Jolin, {Foarfh Ratder, No. CI.), or LucJilnvar, which
are not valuable as information. The substantial

THE TEACHING OF LITERATURE.

meaning' of these two Helection.s nn<:jlit, indeed, be
conveyed in the simple and unvaried style of a
passage written for information only. I>ut there is
something beyond what is thus eonveyed — a some-
thinir which does not exist in the matter-of-fact
lesson, a something represented by the varied
modifications, tones, ijifiections, of a good reader's
voice. The elenuuits lepresented ))y the Jilay of
the voice are the purely and essentially literary
elements. Such reading brings out, for instance,
the music and cadence of the lines and the changes
of feeling in keeping with the ideas expressed. The
child shouhl be taught to apprehend and feel these,
as well as that substantial meaning which might
be produced by a monotonous vocal ivndering or in
a prose paraphrase. The best method of attaining
this end is, as has been already said, good oral read-
ing. But the teacher should also dogmatical!}' i)oint
out such literary (qualities as are within the ])upirs
comprehension — that the rhythm of the line is suit-
able, the imagery beautiful and suggestive, this or
that passage particularly effective. Let not an exag-
gerated reverence for the de(bictive method lead the
t(3acher to abandon his real position of superiority.
He is able to perceive much that a child cannot
perceive for himself, and which the most skilful
questioning will never educe. The pupil should be
informed, with a judicious consideration for the
limitations of his powers, that such and such ([ualities
exist in a passage, that it should awaken such and
such a response in himself: he should be urged to
read and re-read the passage with this information in
mind. In time, some, at least, of the qualities

■

METHODS IN TEACHING.

1 i

I s

I 5

coutninud, will gradually <lawn upon his perception.
No nictlioil is more eii'ective than this ; tor after all,
the greatest iiistrunicnt of literary culture is con-
tinued familiarity, under competent guidance, with
suitalile examples of good literature within the
compass of the })upirs ap[)reciation.

We are now in a I tetter position to comprehend
the worth and the ])ermanence of true literature.
Such litei.iture possesses power and beauty apart
fi'om the substantial facts or thou<rhts to which it
gives expression — a power and beauty which must
therefore be containe<l in the expression, in the form.
If a book is valuable only for the bare ideas contained,
wlien we liave mastered these ideas, we cease to read
the book ; and books of this character sink into
oblivion, with each generation. But when tliere is
some special charm or force in the expression, to
recall the suV)stantial thought does not produce upon
us the effect of the ))ook itself : the actual words
uiust be before us, either inscribed upon the material
page, or upon the tablets of memory. Hence the
perma lence of literature, the preservation of such
books as thv II'k((1 through ages. Hence, too, the
inexhaustible vjuiie of literature for eacli individual
reader, and its unending solace and charm.

Examples of Essentially Literary Qualities-
Let us illustrate, in a s])ecific example, the difference
between mere recorded thought and literature
proper. We miglit find in a purely matter-of-fact
treatise, somr such statement as the following : '* The
extinction of man mid of all that he has produced, is
assured by the action of certain forces on the terres-
trial globe, which must ultimately result in the

THE TEACHING OF LITERATURE.

destruction of tluit body and its return to its |)riuii-
tive nebulous condition." Tlie saniii substantial sense
is contained in tlie well-known passage ot" Shake-
speare's Tempest : —

" And, like the baseless fabric of this vision.
The cloud-canped towers, the <i;orge()Us palaces,
The solemn temples, the great globe itself.
Yea, all which it inherit, shall dissolve
And, like this insubstantial pageant faded
Leave not a wrack behind. We are such stuff
As dreams are made on, and our little life
Is rounded with a sleep."

The substantird ideas contained in these two versions
are the same. But the aim of the |)i'ose passaoe is
merely to convey them intelligently to the mind ol'
the reader. In the prose passage intellect is address-
ing intellect ; there is no attempt to give beauty to
the language or to indicate what the writer may
have felt in regard to tlui matters stated, or to
produce an emotional effect of any kind upon the
reader. Yet if we actually believe and realize

ft/

these facts, there will be a stimulation of certain
f(!elings in regard to them. Now, Shakespeare
states the same fundamental ideas in such
rhythm, language, .-ind im;igery as will naturally
excite in pei'sons of literary aj)(itude a befitting
emotional accompaniment, — a sense of the awfulness,
the gi'andeur, the solenui import of the facts. It is
conceivable that a readei* may not feel the stimulus
of the form: thei'e ai'e many hai'd-headed people,
little ()])en (o n'sthetic impi'essions, who would g<'l
nothing moi'e than the substantial sense of the
passage, and by whom the (pialities ol" expression in

■h

\ II

METHODS IN TEACHING.

! «

whicli the poetical differs from the prose passage,
would be regarded as frivolous and meaningless
verbiage ; in such persons the literary sense has not
been developed. The teacher, whose Vjusiness it is
to awaken this sense, will see not merely that the
substantial meaning is apprehended, but further — a
more difficult matter — that the literary effect is also
felt. The reading of such a passage should stimuhite,
should (juicken and elevate the feelings, should
impart the sense of ex(juisite beauty and charm. Of
course such results cannot, indeed, be fully attained
with immature minds. Literature is written for
mature men and women with wide experience and
developed sentiments, and much literature is (|uite
unsuitable for schools. It is not, hovvevi^r, to be
granted that only what is wholly within the range
of the child's mind is to be read; but for careful
study, pieces should be selected, of which the main
sentiment and (jualities are within the pupil's
comprehension.

Imagfinative Literature— A very large and very
important ])art of literature proper — the drama, the
epic, narrative poetry, pi'ose fiction, description —
aims at presenting the conci'ete, — what in real life we
apprehend through our senses, what we see, hear, or
feel. The authors of such literature possess power-
ful imaginations ; they can summon before the mental
eye, with extraordinary clearness, images sinn'lar to
those impressed upon the consciousness by the
external world ; it is the aim of their writings to
enable the I'eader to apprehend, with \ ixidness, thes(!
visions of theirs. Accordingly, just as in the case
of lessons with regard to natural objects and

THE TEACHING OF LITERA ^URE.

111 id

plienomena, it is incumbent on tlio teacher to see that
the pupil has these objects and plienoinena clearly in
his inind, instead of mere words, or vague conceptions ;
so, in the case of imaginative literature, he mu<^t see
that the pupil forms concrete pictures in his brain —
and these as vivid and accurate as possible — of the
persons, scenes, and situations presented. The details
should be vividly conceived, and should take their
proper places in the completed picture. Diagrams,
or illustrations from more familiar experience may be
employed to give reality to these imaginative con-
ceptions. It should be further noted that the
language of poetry is pictures(pie, even where the
theme is not ; such language can only be appreciated
when the imagery awakens the appropriate concrete
images in the reader's mind.

Poetry — The fullest exhibition of literary (piali-
ties and the utmost perfection of litei'ary form is to
be found in poetry ; and although the great mass of
poetry treats of experiences, and appeals to feelings,
beyond the range of childhood, yet children are
sensitive to poetic effects within certain limits. They
Jiave, for example, marked susceptibility to the
rhythm and metre which are distinctive of poetiy;
and are undoubtedly stimulated and pleased by poetic
passages which they only vaguely understand. In
the case of poetry, particular care should be given to
minute interpretation; for its language presents many
difficulties, which familiarity sometimes leads the
more mature readei* to overlook. Its phraseology is
often extremel}' pregnant and condensed, the links of
connection in thought omitted, the order of words
confusing, the vocabulary unfamiliar, the imagery

I i

'• 'il

Lit

;.>!

i!,f

• -4

« >

METHODS IN TEACHING.

full of su^ij^t'stivcnoss and pictiiros([ue efi'cct Ques-
tions jiiul explanations are needl'ul to elucidate these
various points. But, after all, it should be remem-
bered th.at the ^'eneral meaning and outcome, the
stimulus to the pupil's imagination and to liis sense of
beauty are the matters (jf greatest importance, and
with these the study of the poem should begin and
end.

Method of Studying* a Poem— li my one reflects
upon his own method of studying a poem, or of any
other piece of literature which presents similar
dilHculties, he will find that it is gradual advance
from the obscure and vague to the clear and <let lite.
This is the nat\n-al method and should generall}'' be
followed iii teaching. We do not determine exactly
the meaning of each word and phrase as we come to
it, and in this manner arrive at the drift of the whole.
Such a method of procedure cannot be consistently
carried out; the possibilities of meaning in words and
phrases are too numerous for so straightforward a
course. The process we actually go through is similar
to that of the learner in translating a sentence fiom a
foreiun lan<»uam'. He has an idea, more or less elastic,
of the meaning of all or most of the words in the
sentence, l)ut he is not sure of the exact sense in
which each is used. This vague knowledge of the
i)articulars Liivcs him a sunjicstion as to the diift of
the whole sentenci'. l^pon this hypothesis he pro-
ceeds, and ascertains if it can be maintained on a
more e.xact scrutiny of the individual woi'ds. He
probably Mnds, if the sentence be at all diflicult, that
the more detailed examination will lead liim to
modify hiw conception of the whole outcome. So a

THE TEACHING OF LITERATURE.

■'tti
• ij

i.l

species of mental see-saw ^oes on : at eacli staj;;*' hy
tlio inihience of the details upon tlie wliolc, and
aj^ain of tlie whole upon the details, he niak(\s a
closer and cioarer approximation to the real sense.
So it is with a poem. After heini;- I'ead, tlie pn[)il
should be interrogated in some o-eneral fashion, as
to the subject, — what it is all about; then, what
the first stanza or sentence contrilnites to that
g'^neral outcome, and so on. The first answer
accepted will probably re(|uire to be modified by
the light thrown upon it by answers to subse(juent
(juestions. Some fairly true ^-eneral coi jeption
liaviniT been thus arrived at. the more detailed
investio-ation of the force of each word, phrase, imaoc
should follow. This <n'neral conception will thus be
filled out and probably modified. When the piece
has thus been carefully examined, the initial
questions should once more be put and answered.
Finally, the special beauties, the sicrniticance, the
truth of the poem should be pointed out, and the
piece read aloud as effectively as possil)le, by teacher
or pupil.

An Example — Take, for example, such a poem as
Scott's Lochhivar {Foarfh Reader, No. IJ V.), a sort of
poem well suited to the youni,^ because it deals with
active life, indicates a story, is rapid in its movement,
and throujijh its very condensation, stinp .ates the
exercise of imagination in tilliniL;- u}) links and
suggested details. After the pupils have familiaii/cd
themselves with this j)iece, and the teacher
has read it aloud with spirit and feeling, a
succession of (piestions might be put: — what is the
main thing narrated ; who was f^ochinvar; what was

' i'

i I

i
I

METHODS IN TEACHIN

luH clianicter; wliat otlier pei'soiis appear in the poem;
tlieir relations with tb.e hero; why we sympathize
witli liim ; could such an event as this happen in our
time ; what conditions of society does it indicate.
The teaclier may liere give an interesting sketch of
the state of the Bordei's at the supposed period of
the story, and its causes. Then the pupils might
be asked to describe in detail the picture suggested in
the third stanza ; what is the next scene presented ;
and so on ; the purpose of tlie first stanza, of the
repetition in the last two lines, etc. The story might
then be told as a consecutive narrative (not in the
fragmentary method of the poet) by one of iae pupils;
and subsequently it might be written by all as an
exercise in composition. Attention should be drawn
to the metre, — its suitability, the rapidity of its
movement caused by the frequency of trisyllabic feet;
the characteristics of the stanza might be further
brought out by comparing it with other stanzas to
be found in the Reader, e.g., with that of Gray's
Elegy. The detailed interpretation should follow ;
words like brake, oneasure, gdlliard, etc., must be
explained, and the understanding of more common-
place words, dauntless, ford, craven, etc., be tested
by (questions ; attention should be drawn to the
purely poetical character of some words like steed,
quaffed ; the comparison contained in the first two
lines of the 4th stanza will require a full explana-
tion, and so on. Then the distinguishing qualities
of the poem may be pointed out in simple language :
its animation, its wonderful condensation and sugges-
tiveness, its picturesque force, its development, its
unity.

THE TEACHING OF LITERATURE.

Uage :
gges-
\l, its

Detailed Examination of Lang-uag^e— In tlie

teachiiiix of the Readers a jxreat deal of work
may be done in the detailed examination of the
meaning of words and phrases, the reasons for their
use, the effect of the substitution of synonyms, and
so on. The nature of this work is })retty fully
indicated in the Regulations of the Department of
Education, and need not here be further dwelt upon.
It may not be amiss to insert a caution that the
teacher should see that interpretation does really
interpret. Definition is often purely formal, the
substitution of one word or phrase for another, but
definition ought to bring the word from the sphere of
the unknown to the known. Tlie language employed
in definition shouhl be such as to have substantial
meaning for the child. Explanation sliould, by sub-
stitution or comparison, bring the thing explained
into the sphere of the familiar. Further, it should be
remembered that this detailed work ought not to
overwhelm the truly important matters : the real
appreciation of literature, the understanding and
feeling for the whole. The temptation is, of course,
to spend the time on this less profitable but easier
work of detailed annotation, but that is not the way
to teach literature or to instill the taste for read i no;.
Finally, it is better to employ part of the time
assigned to lessons in literature to supplenu^ntary
reading, or to the reading aloud by the teacher of
suitable extracts of which th(^ pupil is reciuired to give
an outline from memory, than to overdo the
interpretation of the pieces in the Readei*, and to
destroy the interest and enjoyment by excessive
4

:;'

^ #

dabAdMSMikiAi&

METHODS IN TEACHING.

niiiuiteness, or by entering upon Uiemes and matters
beyond the pupil's capacity.

Lesson based upon a Prose Passag^e— Thus

far, we liave been indicating, in a general way,
what we may aim at in teaching selections from
the Readers, what methods may jjrove useful ; and
finally, we have endeavored to bring clearly into
consciousness what literature does for its readers,
and what is its special function in its truest and
narrower sense. These last points are of special
importance because the lack of clear apprehension on
the teacher's part of what literature is and what it
does, often leads to vagueness in the teaching of the
subject, and the employment of methods which do
not subserve the real purposes of literary instruction.
In order to make still clearer the aims and methods
of the teaching of literature proper, it will not be
amiss to show in detail what may be done with a
specific piece of literature in the class.
• Now, it is impossible to exemplify on paper, actual
teaching. Actual teaching, as all other practical
matters, is in a large measure determined by circum-
stances and conditions which are never twice the
same. A large part of a teacher's skill lies in the
sympathetic perception of these conditions, and in
the power of adapting himself to them on the spur of
the moment. The teacher should have a definite
aim in view, and a general conception of the proper
method to be followed ; but these will be modified by
the character of the pupils before him, of the answers
given, of the manifestation of interest, and the com-
prehension of the various points brought forward. A
question quite proper in one case, will be quite out of

P
1)

P<
W

TH?] TEACHING OF LITERATURE.

I coni-
A
it of

place in {inotlier. Wliat kii()vvl«Ml;;x' slionld ])v impartod
by the instructor, wliat elicited tVoni the pii})ils them-
selves, what matters dwelt upon, what li;^"htly passed
over, — these thin<ifs can only he determined hy the
actual circumstrjices. The teacher should he especially
careful not to reject an answer wholly, hecaust; it is
partially incori'ect. Tlie only answer to he I'eceived
with rebuke is one wliicli is the result of carelessness,
or inattention. In other answers tliere will usually
be some <;erm of truth ; upon this the judicious
teacher will seize, and by furthei* ([uestioninn- elimi-
nate what is superfluous or erroneous. He will not
rigidly hold to the line he intended to follow, but
develop that to which the answers naturally lead.
All of this ooes to show tliat in attemijtino- to work
out a lesson on paper, w'e are indicatini;' roughly what
might be done, — not wliat necessarily should be done.
Let us take, first, the following- prose extract from
the Third Reader entitled

NATIONAL MORALITY.

"I believe there is no permanent greatness to a nation
except it be based u])on morality. I do not caYe for military
greatness or military renown. I care for the condition of
the people among whom I live. There is no man in England
5 who is loss likely to speak irreverently of the Crown and
Monarchy of England than I am ; but crowns, coronets,
mitres, military display, the pomp of war, wide colonies,
and a huge empire, are, in my view, all trifles light as air,
and not worth considering, unless with them you can have
10 a fair share of comfort, contentment and happiness among
the great body of the people. Palaces, baronial castles,
great halls, stately mansions, do not make a nation. The
nation in every country dwells in the cottage ; and unless
the light of your Constitution can shine there, unless the

'■': <: fl

'i^ 'Sfffi ^ f^^*''^' ^" -*^*'*'^'- *■'■

METHODS IN TEACHING.

15 beauty of your legi.shvtion and the excellence of your states-
manHhip are iinj)roHsed there, on the feelings and condition
of the people, rely upon it, you have yet to learn the duties
of yovernnietit.

" I have not pleaded, as you have observed, that this

20 country should remain without adequate and scientific
means of defence. I acknowledge it to be the duty of
your statesmen, acting upon the known opinions and
principles of ninety-nine out of every hundred persons
in the country, at all times, with all possible moderation,

25 but with all possible efficiency, to take steps which shall
preserve order within and on the confines of your kingdom.
But I shall repudiate and denounce the expenditure of every
shilling, the engagement of every man, the employment of
every ship, which has no object but intermeddling in the

30 alfairs of other countries, and endeavouring to extend the
boundaries of an Empire which is already large enough to
satisfy the greatest ambition, and I fear is much too large
for the highest statesmanship to which any man has yet
attained.

.'35 "The most ancient of profane historians has told us that

the Scythians of his time were a very warlike people, and
that they elevated an old scimitar upon a platform as a
symbol of Mars, for to Mars alone, I believe, they
built altars and offered sacrifices. To this scimitar they

40 offered sacrifices of horses and cattle, the main wealth of
the country, and more costly sacrifices than to all the rest
of their gods. I often ask myself whether we are at all
advanced in one respect beyond those Scythians. What
are our contributions to charity, to education, to morality,

45 to religion, to justice, and to civil government, when
compared with the wealth we expend in sacrifices to the
old scimitar ?

" Two nights ago I addressed in this hall a vast assembly
composed to a great extent of your countrymen who have

50 no political power, who are at work from the dawn of the
day to the evening, and who have therefore limited means
of informing themselve" on these great subjects. Now I am
privileged to speak to a somewhat diflferent audience. You

O.)

THE TEACFIINf} OF LTTKRATURE.

represont those of your groat coniiminity who havo a tnoro

55 comploto education, who have on some [)oints greater
intelligence, and in whose hands reside the power and
influence of the district. I am s[)eaking, too, within the
hearing of those whose gentle nature, whose Hner instincts,
whose purer minds, have not sutfered as some of us have

60 suffered in the turmoil and strife of life. You can mould
opinion, you can create political power — you cannot think a
good thought on this subject and communicate it to your
neighbors- -you cannot make these points topics of discussion
in your social circles and more general meetings, without

65 aflfecting sensibly and speedily the course which the govern-
ment of your country will pursue. May I ask you, then, to
believe, as I do most devoutly believe, that the moral law
was not written for men alone in their individual character,
but that it was written as well for nations, and for nations

70 great as this of which we are citizens. If nations reject
and deride that moral law, there is a penalty which will
inevitably follow. It may not come at once, it may not
come in our lifetime ; but rely upon it, the great Italian is
not a poet only, but a prophet, when he says —

'The sword of heaven is not in haste to smite,
Nor yet doth linger."

*' Wt have experience, we have beacons, we have land-
marks enough. We know what the past has cost us, we
know how much and how far we have wandered, but we are

80 not left without a guide. It is true, we have not, as an
ancient people had, Urim and Thummim— those oraculous
gems on Aaron's breast — from which to take counsel, but
we have the unchangeable and eternal principles of the
moral law to guide us, and only so far as we walk by that

85 guidance can we be permanently a great nation, or our
people a happy people."

Remarks Introductory to the Selection. — The
author of this extract is John l^rioht, son of a cotton
spinner and manufacturer in the north of England:
the family were Quakers. John Bright attracted

1 1

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MKTIK)DS IN TKACHTN(i.

iii))l

i(* ii()tic(^ in ooiincctiDM \vi

til tl

ic M<;Mtati()ii .•i.i'jiinst

tii<'('()i'ii laws, WMS elected to INiflifUiieiit, and heeanie
one of the most distinguished orators and puMic men
of his day. As a speaker \ni was distinenished for
his skill in exposition, tor the simplicity, smoothness,
id enei'gy oi* his style, and i'or the power which
comes from hioh charact(3i\ sincere convictions, and

tin; constant a])[)eal to lofty motives and i(h'als. Tt
must he rememb(n"(!d that a speech is intended to he
spoken, and a mei'e i-eader lal)ors under e-reat
disadvantages: he loses the charm of tone and
utterance, and (especially in the case of a man of
IJri;L;ht's stamp) the weight that comes from character
and feeling — things ea-;ily perceptible when we liear
and see the orator himself, but much less manifest on
the pi'inted page.

The extract before us is merely tlie conclusion of
a long speeeli attacking tlie foreign policy usually
followed by English statesmen, which, as Mr. Bright
thought, too often involved the nation needlessly
and wrongfully in war. It was delivered at a
ban(juet given at Birmingham in Bright's honor,
October 29, 185(S. During the thi-ee years innnedi-
ately preceding, ill health had prevented him from
appearing on the public phitform. At the date of
this speech foreign affairs were threatening, and the
Crimean war (LSS'i-lSSG), was fresh in the minds of
his hearers ; it seemed a fitting time to raise his voice
against an almost universal tendency (to which he
was himself on principle opposed), to regard military
achievements as the highest part of a nation's
activity and its greatest glory. He believed that
true national greatness lay in other things ; for

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THE TEACHING OF LITERATURE.

exainpl<%in tlie happiness of the people at larj^e. He
coiisi(lore<l that there ('(jul<l Ix' no ti'ue (jfreatneHs
which was not based upon molality, ij'., npon the
same principles of conduct as we acknowledge to be
ri<jfht when individual men are concerned. Now, in
general, no such moral stan(hird seems to be held as
regards nations ; for example, a man who takes by
force liis neighbor's property, does not thereby win
the admiration of his fellows, but is punished ;
wliereas the seizing of the land of one nation by
another is often considered a glorious exploit. Mr.
Bright strives, in the extract we are about to study,
to disabuse the minds of his hearers of these views —
immoral and pernicious as tliey seemed to liim.

Some remarks of the kind given in the last
paragraph should serve as an introduction to the
piece, and we will suppose that the pupils have
subsequently had an opportunity to read the exti'act
carefully over by themselves. The study in class of
the piece in detail may then be begun.

First Paragraph. — Wh »/ does the orator begin with the particu-
lar assertion contained in the first sentence ? It states the thnme

of the whole extract. Wh]/ does lie make a negative asi,ertion^

instead of the positive one, that the permanent greatness of a
nation is based )(pon moridity? The proposed positive assertion
IS not so strong, for it is quite consistent with military glory
being one factor in the greatness of a nation, and that Bright

does not believe. What connection has the second sentence

liiith the first ; or, in other words, why does the orator make the
assertion contained in the second sentence at this particular point?
In the first sentence he states that he is going to maintain : in
the second that he is going to argue against. It will be noted
one of the best ways of making clear what a person asserts is to
express what he implicitly intends to deny by his assertion.

1,1

METHODS IN TEACHING.

:i ;

11 )

Thoso firat two seiitonces, then, are introductory to the wht^Ie
extract.

St<Ue hriejlij uihat is the snitjecf of the rest of the paragraph 'f
The comfort and happiness of the people at large is the true

test of national success. What is a " coronet 'i " a '* mitre '{ "

(lines 0-7). — What is really meant here by '^crowns, coronets,
mitres'^" Kings, nobles, bishops, and the state and grandeur
that pertain to them. What sort of lamjuage is this ? Figura-
tive. Has this kuuinaae any peculiar appropriateness here?

The words employed make us think of the external splendour
connected with these orders of the State ; and it is their
side)idoi(r that is in point here ; compare the next phrases,

''military display^ the pomp of war." Wltat is the exact

meauintj of ^^pomp'^" (line 7). Shoio its s\iitahilit\i in this

connection. (Consult dictionary and etymology). Note the

alliteration in the enumeration of details in lines 7. Again
note the picturesque language, " i)alaces, baronial castles,"

etc., (lines 11-12). What relation does the sentence beginnintf

''^ The nation,'^ (line 12), bear to the preceding'/ E.»plain

how the '■^beantij of legislation^' and ^^ excellence of states-
manship" may be impressed *^on the feelings and conditions of
the people." By helping them to be contented, ("feeling ") and

prosperous (" condition "). Why does the speaker introduce,

after the first tiro sentences, these sentences asserting the supreme
importance of the comfort and happiness of the people at large'!/
As his audience might be little inclined to agree with his views
as to military greatness, he introduces something to which they
will naturally assent, which is, yet, inconsistent with military
exploits being regarded as the main factor in a nation's great-
ness ; for war is evidently at variance with the comfort and
hap{)iness of the people at large.

Second Paragraph. — State briejig the stdtstance of tliis para-
gr((ph. The speaker does not object to military expenditure if
limited to puri)oses of defence and maintaining internal order-

Wh((t rel((tion does this subject bear to irhat has gone liefore'f

It serves to explain or define the position that he has taken up
against needless wars ; or it serves to meet an objection that
might be made to his position. — WJiat hro parts does this
paragniph nat\irallg fall into f An assertion of what he deems

THE TEACHING OF LITERATURE.

ye f

if
)r.

justifiablo ;i8 regards military expenditure, an assertion of what
he deems unjustiliable. Observe, how, a«ain, we have the
positive and negative sides in order to define his position with
the utmost clearness. — The clause, "acting upon known
opinions the country " (lines 22-24) is intro-
duced because Bright has in mind the principles of the Quakers,
«vho are opposed to war under all circumstances ; although he
may in his heart sympathize with these principles, he does not
object to the government acting in accord with the opinions of

ninety-nine hundredths of the nation. What is the meanintj

of ' ' repudiate" (line 27)'f Note the circumstantial and detailed

character of lines 27-29. Wind is the effect of this rurum-

sttintidlitij and det<iil f It gives emphasis and strength to the

speaker's assertions. Note the difference between the spirit

of the latter part of this sentence (lines 29-ii4) and the
imperialistic ideals and tendencies of our own time.

Third Paragraph. — What is the meanimj of "p/o/(nt<" " {line
S5) here'f — What is the more common mi'a)ii)ig in ordinary
coni'ers((tio7i 'i — The most ancient of profane historians is

Herodotus. Who irere the lSc]itltiansi' — Who ii> Mars f— Into

what two parts does this panujrapli fall, and what does each
part Ho ? The first part states some facts about the Scythians,
the second applies these facts to the English nation, or suggests
a re;^emblance to certain facts true of the English.

It is difficult for people to look impartially on the actions
of their own nation, as it is difficult for men to judge in«i)artially
the actions of the members of their own families. Hence the
common device of leading a person unconsciously to judge his
own case in the case of another ; so admirably illustrated by
Nathan's parable to David (See II. Samuel xii. The story
might bo told to the children). So, Bright hero attempts to
make his audience feel the undue v-alue they place upon war
and its barbarous character, by hinting a certain resemi)lance
between the attitude of Englishmen towards war and that of the
bloody and barbarous Scythians. Besides this, a sudden
riiference to a remote and seemingly unrelated subject has the
effect of rousing the attention and relieving thu strain of a long
treatment of a single theme ; f«)r it must be remembered that
this extract in the Reader is but a small part of a long speech.

METHODS IN TEACHING.

Wlidl <i'liiii,iitii(ip is there in the speaker^s <iiihi)i(i riuestions
nishdil of iiKihiiui usHertians at flic close of the panufrdph f It is
often nioro effective to suj'j'est somethin'' txud to let the hearer
think it out for himself, than to aflirm it ; especially when the
assertion is painful or uncomplimentary to the hearer, and

might rouse opposition on his part. To what does the speaker

vt'ffi' ill the " ireallh ire expend in sacrifices to the old scimitar? "

Whii is the phrase ^^sacrifices to an old sCiinitar^'

cmplotjcd rather than some direct expression like " warlike expendi-
ture T^ It serves to keep before the mind the real resemblance
botwei!!i the barbarous sacrifices to Mars, and the sacrifices
modern Englishmen mike to the warlike spirit.

Fourth Paragraph. — What is the ora.tor's aim here? Ihnv
does it differ from his (dm in the earlier part ? Hitherto he has
been trying to convince the intellect of his hearers of the truth
of his position, now he tries to move them to act upon this
conviction. It is the natural thing at the close of the speech,

to introduce the practical application. To irhom do you

suppose the speaker is referring hi " ifonr conntnjmen who ....
. . siifijects" (lines Jf9'52)? The franchise in towns was at
this dite confined to householders who paid an annual
rent of f^\2 ; this excluded a very large body of workingmen.
Two nights before, Mr. Bright had addressed a public meeting
on the very subject of the extension of the franchise and

parliamentary reform. Tit irhom is reference made in ''^ those

trhose (jcntle nature af life^' {lines FtS -GO)? Women.

Wliij is the phr<(se " irithin the hearimj " {line FtS) empUnted

instead, of the simple ^^to?" The ladies were not actually at
the bancjuet, but only present as spectators in the galleries.

(h're the reasons for the choice <f each <»/ the epithets {lines

r)S(!0) irhich lie ((pplies to iromen, so as to shoir irhtj he prefers

these to hian\i others irhich <(re etptallij appVuudile to iromen. —

What is it that ".so»h«' (f us have suffered ?^^ — What is the

practicid course Jw now unjes his hearers to adtipt ? To think over

and discuss these subjects of which he has been talking.

Wh((f ijeneral principle, ffs to the waiithe EiKjlish ijoreounentacts,
u)iderlies this sentence ? That government will i)e intluenced by
))ublic opinion.

In the following sentence, "May I ask," etc., (line ()(}),

THE TEACHING OF LITERATURE.

he
rer

'),

Bright indicates a fundaniental principle of his at variance

with that of perhaps the majority of men. W'IkiI ii'iomn

Is then' fur llw (lljf'i rent sliindnrd llnil icf i(pi>hi h> llie urtions
of men (ts indiridnuls, (DuI of tne}t (i:'tin(j fi.s nuli(nf<f For
exdmple, is there ^oiij reosmi ichii it is more justijittlde for
(I Hidion to t(d<e possession of territonj Inj forre, than for <( nutn
to seize upon (foods by force f If one mon thinks that onother
is i)i possessio)i <f his propertij, yrJiot dot's he do, if he octs

properli/'^ He appeals to the courts. Is there onij court for

(I notion to oppeol to otidinst (diother ntdion f No. St > there

is no other miii tisutdUj tt> settle ti dispute except Inj rectmrse to
tiruis'/ Is this ansirer td)sotutel\i true; do notions erer tippenl
ttt 'I third pttrttj to decide tlie ct(se ticcttrdimj tt> its Uterits !' Yes,

in case of arbitration, as in the Alabama claims. li'hot is the

ijreot difference beticeen the r'onditions tf prirtite ptuties (joi)k(j
beft)re a Court, and ntditms tiefire tt Ctturt (f Arbitrtdittn f In
the case of nations, there is no external force to compel the
parties to submit to arbitration, or to comply with the award ;
in the case of individuals, there is. So we see it is more ditlieult
to arrive at equitable decisions as between nations, than
Ijet^een individuals ; and this tends to make nations resort to
force, to the principle that might is right, rather than to the

princijjles of justice. "The great Italian poet" is Dante.

Whttt is the sultsttintitd meonintj if the poetictd ijuottition i'

Fifth Paragraph. — Whttt litertdUj <ue the thintjs nferred to
in " l>e((rt,ns " tmd " Ittndmttrks " (line 77) f -Whtd hos the pttst
cost them 'i There is doubtless a special reference to the loss of
life, suffering, etc., of the Crimean war, which had recently been
brought to an end. The vast national debt of England is mainly

due to war. Whtit tjuidf htire ire'f This is indicated below,

"the unchangeable and eternal principle of the moral law."

" Urim . . . . brea.st," (line 81) see Exod. xxviii, .'{0, a pair of
jewels on the High priest's breast -plate, employed as an oracle
in critical junctures.

After the selecticm has been carefully studied, it should be
read aloud either by the teacher or the best reader in the class.
Finally, a brief outline might be written out by each of the
pupils to exhibit the main thoughts of the [lassage and their
proper connection.

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METHODS IN TEACHING.

Teaching of a Poetical Selection— In order to

exoiiiplify the te{icliin<j;; oi" poetry, let us take tlie
following sonnet from the Foarf/t Render :

SONNET.

"Mysterious Night I When our first parent knew
Thee from report divine, and heard thy name,
Did lie not tremble for this lovely frame,
This glorious canopy of light and blue ?
5 Yet 'neath a curtain of translucent dew,

Bathed in the rays of the great setting flame,
Hesperus with his host of heaven came.
And lo I creation widened in man's view.
Who could have thought such darkness lay concealed
10 Within thy beams, O, Sun I or why could find
Whilst fly and leaf and insect stood revealed.
That to such countlees orbs thou mad'st us blind I
Why do we then, shun death with anxious strife ?
If light can thus deceive, wherefore not life ? "

Let us suppose that the pupils have been recjuired
to prepare this poem ; further, that the teacher has read
it aloud, so as to In-ini;- out, as far as may be, the
meanino- and I'eelino- of the poet and beauty of the
rhythmic melody. He may then proceed, after the
usual method, to ask for a brief and sim])le state-
ment of the thou*^ht of the poen), and so forth. Or,
perhaps better, since the sonnet is likely to be
obscure to the youni^ student, he may adopt
another course aiid develop the general meaning from
an invcstioation of the sijxnificance of the successive
statements. This metliod, at least, we will follow
here.

First ({uatrain. — IVhal is tin' fust tliin<i that llif parm muke.s

IIS think iitnt'it f Night. -Who is referred to in ^' our Jir.tt

parent" {line 1)/ IVhat is meant by " report dicine " {line 2) 'i

THE TEACHING OF LITERATURE.

An account from God himself (see openiui^ chapters of (Jenesis

where God is represented as speaking with Adam). Wlmf is

the ordinarif meaniiKj of mwfpiil — Whut Is i\fi'.rri'd to i)i the

words " this lovely frame //j//// and Idne " (line S-/f) '^

— What, theUy is the sHt)st<riti<d meanimj <>f the first tiiidtrain'f
When Adaui first heard about Night, without liaving seen it,
did he not dread its appearance, and fear that it might forever
blot out tho beautiful blue dome of the sky f

Second (][uatrain. — IVhdt isthe ^'■tircat settliKjjldme" (li)ie ('>)f

The setting sun. " Hesperus " is the classical name for the

evening star. What is the ^* host of heareu' {line 7) f The

stars in general. What is the meanimj of " creation widened in

man's rieir" (line 8)'f The darkness of night enabled Adam to
see the vast multitude of heavenly bodies, and thus he got a

w^ider view of the exter. L of the universe. Everyone must

have noticed the sense of immensity and grandeur produced by

the sights of the starry heavens. What, then, is the sid>-

stantial meaning of the irhole of the second ifiialrain'^ When
Adam beheld the first night that he ever experienced, he
became accjuainted with a large part of the universe hitherto

unknown to him. Indicate the connection in thought hetireen

the first and second quatrains ; or vhat reasm has the poet for
saging ^rhat he s<(gs in the second stan'^a^ after irhat he has s((id
in the first stan::a ''^ The first stanza tells what result Adam
might naturally have feared in connection with night, when
he had only heard vaguely about it ; the second what was the
result of his actual experience of night.

Third <{uatrain. — Wtiat is meant tnj saying that ^^ darkness
lag concetded irithin the t>e<(ms of the sun " {line 9-10)!' J'nt the
thought in simple prosaic langioigt-. The rays of the sun hid

something. What iras it ttiat the rags of the smi hid'f

The universe of stars. Is thai actnidly trnef Observe it is

a fact that the light of the sun does prevent us from seeing the
vast universe of which our earth is but an insignificant speck ;
whereas night reveals the universe to us. Notice also how the
poet puts this in a very striking way. So that something of
which we are all, of course, aware, is made fresh and vivid to
us. This is a special example of that which poetry
in general is fitted to do and is continually doing — the

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METHODS IN TEACHING.

imparting (jf freshness and iinpressiveness to what is familiar.

Wlwn in it Unit ^\H\i vnd leaf and insert (ire )rre<iled "

(line 11) f In the day-tiuio. WJnj (we tltene thimja esperiidbj

selected^ Wind coninion ju'c>di<irit)f h<(re Jliea, tea res and
inserts, that leads tlai poet to mention tlieni'f They are all small

and insitjiuHcant. What is the orditiary meani)i<j af orh't

What are the ^'' roiinlless orbs" referred to in line iJf

Observe that the second exclamation is a repetition, in a

more emphatic form, of the lirst exclamation of the (|uatrnin.

What eilectdoes the poet gain by putting these two clauses

in the form of exclamatory (piestions, rather than in the form
of assertions, " No one would have thought," etc., and " We

would never have found that whilst fly," etc. >. The third

([uatrain, then, substantially states in general what was said
in regard to Adam in the second quatrain, that while the sun
reveals the earth and the various objects which it contains, ic
conceals a vastly greater and nmre stui)endous world.

Final couplet. — 2*M< ^/('' suhslioilial vteani)t\i of the unestion

of line 1-i in simple lamjiaaje. Why do we dread death i

How does liijht dereive ns{line IJj) ^ It leads us to think that
what we see in the day time comprises the whole universe. In
the earlier part of the poem, our attention was directed to the
fact that night gives us a wider and completer view of the

universe than day. "^Wherefore not life i"' Kxp<ind this

(inestio)i la/ supplijinii the ellipsis. Wherefore may not life
deceive us ?

Development of thought.— Now let us see what is the
connection in thought between the earlier part of the poem
and those last two lines. What did ve Jind as the Jirst idea

presented Inj the poet /n the poem!' Night. The poet was

thinking and speaking of night in the earlier part of the poem,
telling us something that it does, and com])aring this with what
something else it does. What is titis '' soniethimj else" f Day.
In the earlier part of the poem he si)oke of night and Hay.

What is he Udi;inij ((htnit in line l.l f Death. A)h{

H^tial is the sid>jert orthiiKj tlial he is sprai^inii <dnnif inlinr I J) f

Life. Is there anti ronnerfiiai, then, ahiih om' nniimdhi

notires between niffht and da\i, <>n the tnte ha)ui, and death mat
life on the other ( Can yon renieni,bei any pli rases commonly

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THE TEACHING OF LITERATURE.

()8

iised, 07' ((Hij i)ass<([ie in hoohs tluit you hare rend, irjiirh Indimte
a re.iernbli(nce or connection hettrcn thest' 'nh'(is f " Tho dark-
ness of the grave," "night of death," eternal life is often
styled " eternal day," etc. "Work while it is called to-day,
for the night cometh when no man can wc^rk. ' John ix. 4.

There is <i re,sembl<nice citmmonbj traced (tetiri'fu itifjlit (i)td

deatJk, and dii\j <ind lif^" i and that doubtless sutjiji'sted to thi- pni-t
the brin^jimj of these ide(is together in the sinuiet. hi the last line
there is a quest i(ni ash^'d, ichich is }iot ansirered (irhat is calh-d
a rhetorical ijuestion) ; such titiestions art' aliraiis intended to
siKjtjest a}i onsirer ; irhat is the ansirer siojijested bij thr ijiws, inn

of the last line'f Life may deceive us. What rrason dot's

the poet sutfjest for supposimj that life maij deci'ire ns .■' Day

deceives us. I}i wlait respect did i re find that dmi deceives ns'^

7'fte p'.ici evidentlij insinuates that life inaij deceirr ns in a

similar iraij ; hoic then miifht life deceive ns/ By making us

think that what we see in this life is the whole of existence.

Norr, tlifce is anothrr rhetorivid ipiestion in line /->, irhtd is the
ansirer intended f We have no reason to be afraid of death.

Is there iiny mention of fear or dread elseirhere jh this

poem? Was Adam's fea^' of ni(jht justified vhen he artiadlii

experienced niijid ? It did mm no harm; on the contrary, irhai

— OI)serve in this line 13, the 'word " then " is used :

did it do 'f-

what force has tliis'f It indicates that the two assertions iniplied

in these two lines are the result of what has been said in the

earlier part. Th<' ^^ then" indicates that tlwre is <( reason in

the previous part of the poem for the implied assertion in this
line that we luive no tjround to dread death ; wltat is thr reason!'

Adam had no real ground for dreading night. Nat onli/ did

ni(jht do him. no httrm, we htive seen thai it receah-d to him thf
immcnsitii and (jrandenr of the universe — showed him a world
iiivisible tnj day. Now, since the pnet is evidentlij thiulii>ui of a
resemlla)we lietween nitjht aiid death, dinj and life, he is insinu-
atiu<i or suiitjestinii that death }na>i proordilij have some fffert
similar to th((t which nii/ht ha<l to Adaui ; whot u-mttd lie a
similor effect I That death should reveal a vastly greater and

grander state of existence than life reveals. What u-as the

difference between the thiutjs noted taj the poet as revealed tnj ihnj,
and those revealed btj niyht ? The former were trivial and

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1 1

METHODS IN TEACHING.

small, the latter great. And so irhaf ironld he lihcly to ho fhr

diffemice in the character of things rere<ded hij the present life,

an the ane hand, and hy death an the. other? St((te Jiriejlii the

snbstantiid meanintj <f ttie fimd couplet. We need not be afraid
of death, any more than Adam needed to be afraid of night ;
for, not improbably, the view we get in this life, that the
present existence is the whole of existence, and that death
ends everything, is just as ill-grounded as Adam's thinking
what he beheld in the day-time to be the whole of the
universe.

The poem as a whole. — Harintj ijot an idea of the meaninff
of the poem, sngged some appropriate title for this sonnet.

Night, Imm »*tal'Ly, Night and Death, etc. Is there any

reason to Ite i '. fi>" the second of these titles, as compared irith
the first f Do i, ti i, h the idea of " Night " or " Immortalitg "
is (f mitre importance iii. ^'-se. poet's mind in writing this poem?

The latter. -What relation has the idea of Night to that of

immortiditii i)i the poem? It serves to suggest it, and intro-
duces it. 1)1 irhnt part of the poem, then, is the principal idea

e,r.pressed? In the final couplet. And what purpose does the

rest of the poem serve ? To introduce this idea, give reason for
it, give impressiveness and picturesque power.

The teacher may point out that a certain force is given to
the main idea by thus including it concisely in the narrow
limit of the couplet, whereas the introductory matter has a
more roomy expression in the quatrains.

Form and Thought. — What do you notice with regard to the
rhymes of the first and second gnatrain respectively ? They are the

same. This common rhgme serves to connect these t/iro stanzas

titgefher hg the form —to make the^n stand together, and apart from
the following giadrain, irhich does not rhgme ivith them. Are the
guatrains likeirise connected i)i thoxajht? Yes ; they describe the
incidents, the facts about night and day, which occasion the
chief idea of the poem.

It will be noted that the third quatrain gives expression to
reflections suggested by the incidents mentioned in the previous
lines ; and that the final couplet contains the principal thought
which is the outcome of the whole. So the natural divisions
of the sonnet made by the arrangement of rhymes correspond
to stages of thought.

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THE TEACHING OF LITERATURE.

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Iht

Miscellaneous points. — Let us note some further points
in the poem. *' Myaterions NUihty'^ (line 1). Is Ucre «?«//
special appropriateness in this adjective Jiere? What is
the meanin<i af ^^ mifsterionsV Full of mysteries, i.e.,

full of hidden things, of secrets. And is this aspect of

niijhty as full of hiddeyi things, important in th is poem 'f Evidently
it is the fact that night was full of hidden things that were
revealed to Adam, that leads the poet to think that death may
be a revelation of another existence.

Lines 3-4. — Apart from langnage and expressioyi, is there ang
special heanty in these lines f The beauty of the picture sug-
gested of the starry heavens. Notice, these lines make us
think of a beautiful thing in nature, and freshen in us the
sense that this thing is beautiful. That is another example of
what poetry in general does for us ; it fills us with pleasure by
recalling to us beautiful things and experit ie"^, and leads us
to notice beauty which may have been unnoticed litogether, or
may have become less impressive through fa. liliarity.

W}uit other example of this same thing Jiave tve in the poem '{
The suggestion of the beauty of sunset and e^ ,^ning in lines 5-8.

" Translucent " (line 5) — meaiiing ?- ^an you readl another

word with similar meaning 'i Transparent. —Is tliere any reason
why ^Hranshtcent" is preferable here 'if 1st. It is less common-
place, and hence free from the prosaic associations of
"transparent;" 2nd. ''translucent" draws attention rather
to the medium itself that transmits the light, to its lustre, etc. ;
" transparent " to the fact that other objects are visible
through it (See dictionary) ; evidently the former point is the

important one in this connection. To irhat does ^^ bathed"

belong? " Curtain." What is the exact force of " bathed ? "

It draws attention to the fact that the curtain is immersed in
light, i.e., that the light is abundantly and everywhere present.

Is there anything actnidly in nature which corresponds

to the ** curtain of translucent dexc'i" To the present writer
it seems not ; if this be the case, there is a defect here in the
poem.

Line 6. — "Flame." How is tJiis word more effect ire tJian
" sun f " It suggests the glow and the bright clouds of sunset.

Cj!

* H

Line 7.-
5

■" Host." What is the exact meaning of this u-ord ?

.^^,^:,-,^.,j-

METHODS IN TEACHING

Note its frequent use in the Bible, especially in connection
with the word Heaven. (See Concordance to the Bible).

Tho .attention of the senior pupils may be drawn
to this poem as an exempHHcation of the sort of
thin^^ poetry is fitted to do; to express in i.olodious
lan^ua^e an inspiring thought ; to bring us into
sym])athy with an idea, to open the mind by putting
us in the proper mood for its reception, ratlier than
to prove it, to force it upon us by argument ; to
suggest, to set us thinking and feeling, rather than
to state an idea dertnitely and completely.

The poem should be read aloud at the end of the
lesson and the pupils may be asked, as a written
exercise, to state in simple language of tiieir own, its
substantial meaninj>\

• ,1

LANCJUAGE TllAININC!.

CHAPTER 111.

LANUUAtiE TKAIMNG.

'The best niotliods of tniiniiig children in the art
of usinn- languai^e wi th ea s e, accuraey and clearness,
niight be expressed ni a few l>riet' sentences, but the
student of education, if oidy of nietliod in education,
needs to do nuich more than merely memorize a few
rules for his guidance in directin<^ the efforts of
youn*^ children to develop their powers of expression.
He needs to en(iuire what is really implied in the
terms, la)}(jaa<je and lavyuaye trainvnij ; to dis-
tinguish between the art of language, and the study
of language from the scientific point of view ; to
make a careful estimate of its educational import-
ance ; to consider the preparation on the part of the
teacher required for the w^ork of most effectively
training young cliildren in their motlier tongue, and
to study young children so as to understand the
extent and character of their language preparation
before entering school.

From the data gathered from the abovo named
sources, he should be able to deduce some general
principles for his guidance in the work, and to
decide up(3n the chief means to b(; employed in the.
schoolroom to accomplish his purposes.

WhatUil^^^i^d in Languag-e Training"?—

Langujt^^cri^jfilie art of expressing thought. Con-
sidered broadly, this applies to all modes of
expression, but in this connection we shall limit

V'M'

METHOD IN TEACHING.

',;

! -I

ourselves to tlie coiiHideration ol' expression l>y
means of words. The cultivation of lan^^uage power,
therel'orc, includes all that tends to develop the art
of usin^• words in ex[)ressin<,Mdeas; all the instruction
and practice which i^enerate educated skill in verbal
ex])ressi(jn. This part of the subject falls into two
divisions, oral and written expression. Written
expression is treated as a separate subject,
conipcjsition, so that we may a<;*ain limit our view
to oral expression of ideas. This clearly includes
primarily the development of ideas or of mental
power, and secondarily, a corresponding extension of
vocalnilarV; and of pcjwer to use words appropriately,
accuracy of pronunciation, correctness of syntax,
clearnei:s, force, beauty and fitness of ti<^ures ; in
other words all that <^oes to make lan<^ua<^e plain,
potent and pleasing.

The art of language, its practical use as an
insti'ument of thought-expression, must not be
confused with the scientific study of language as
grannnar, philology, etc. One may be a master of
the art of language who knows little or nothing of
grannnar and philology, that is of the scientific
aspect of language ; and similarly one may know
more grammar than has yet been written, and not be
able to spenk or write eitiier ejisily or correctly. (^
The most skilful carpenter may know nothing of the
chemistry and physics of the tools and materials he
uses: he has accjuired his skill through intelligent
practice ; similarly fclie champion athlete attains his
power and skill by judicious exercise and not by
studying anatomy and physiology. It is much tlie
same in language. Skill comes only through

LANGUAGE TRAININ(i.

ho
lio
nt

[is

practice, but the iiioro iiitcllii;('nc<' tlirrc is lu'lnnd
the practice the iiigher tlie (leort'c of [jcrtVctiiju
attainabh'.

The Importance of Lang^uag^e Training^— The

importance of traiiun;;' in one's niotlici" tongue niay
be clearly st.'en from tbi'ee points of view :

1. Tlie vclnl inn Itcfirccn /aiii/iKn/c ami f/miKjh^. —
It is often arjjfiKMl tbat thought and lanjiuaufe
iirc! insei)arable, and tins is pi'obaldy true enou<j:h
from a practical point of ^'i^'M^^iii^ -^ carcd'ul
study of the (piestion n nlhlM^ ^w tliat tbere may
be rudimentai-y thouobt, without any form of verbal
expression.* It sbould rather be said tbat without
verbal lan<jjua<j^e, thou<^bt nuist inevitably i*emain
rudimentary, in other words, tbat tbe f^rowtb of
lan^uawe power conditions tbe ^rowtb of thou<;bt
power. 'rbou<(bt is tbe sovereign and woi'ds bis
subjects. Tbe power and ran<;(' of iniluenci! c)f tbe
sovereij.;n depends upon tbe numbei- and character of
bis subjects. New territory can only be discovered,
explored, occupied and made a source of str i* ,tb
tbi"0U<»"b tbe services of tbe subji^cts, ^uide<l by a
strong and wise soverei<4-n. Eveiy new word added
to a vocabulary and broujjjbt into pi'oper active
relations witb tbe sovereio-n mind, becomes a
rc-inforcement to tbe wbole.

Between tbou^'bt and lanouage tbei'e is ai.so a
mutual inter-dependence of cbaracter as well as
of /rowtb in power. A person wbo tbinks clearly
and forcefully is likely to speak in tbe same way,
and one wbo seeks tbe clearest and strongest
expression of his tbounjbts will find his thou^dits

•u

i''

I ,.■

! I>

METHOD IN TEACHING,

become relatively clearer and stronn^or. On the
othci" lunwl confuHion in l.'in<jua<j:e is evi(l<'nce of
(•onl'iision in thon^ht, Ix'anty of lan;;na^e indicates
l)eanty in ideas and conceptions.

2. 7V/y' afUlfariifii nihif nf ht i)</(i<i(jc^ ifs im-
pnrhtiicc us (in i itsfnirnciif in Ihf (iffalrs of life. —
'l'hi'on<;li the three forms of verbal lan<^uaoe, speech,
reading and writine-, we exehan^^e thoughts and
ex[)reHs oui' feelin«4S and determinations. The more
skilful one is in the use of lantiuaife the more
etteetive does he makci tin; ex[)ression of his i<leas,
his emotions and his will. It is often remark«'d that
it is not HO much what oiu^ says as the way in which
he says It, that seenis to attract attention and exert
influence. This is, doubtless, measui'ably true in
eveiy d(»partm(Mit of lif<' wImm'c lanL;uaiL;'e is nnich
used ; in the councils of the nation, in the pulpit, at
t]»e ('(litor's or the t(;acher's desk, in the institute,
behind the counter, everywhere, he exerts most
influence who, with thnUL;ht power, has also culti-
vated th(; power of ex[)ression.

Tlien, too, ctdtivated lan<,nia<(e powei- is one of the
simplest and most connnonly read creileiitials ol*
e(lucation and refinement. An i^jnorant. man may
present a ;jjood a])j)earance and make a favorable
impi'ession, until his Hpeech " bewrayeth him," by
throwinii' off the <bsw:uise that w<'alth or men; social
HurroundintTH Inive enabled him to wear. lUit the
connnon toiler rises hin;her in our respect and esteem
the monn^nt we find him skilled in the use of o^ood
lan;:;uaue.

l\. Hk nal'ionni mul rucmJ I ntporlancr. — Throuj^h
its effects up(Hi the develo))ment of thought

LANGUAG?] TRAINING.

'.V

iiil
'in

and upon tlio personal inHuencc an«l material
prosperity of the individual lan<;ujif(e eonies to lia\e
a national si«^nitieance. It is e«'rtainly not a matter
of mere chance coincidence' that every <;reat nation
has d(;vi^lo])ed a ixi'<'at lanLfuaue suited to its needs
and its peculiar f^enius. There nnist he spontaneous
activity in the indivi<lual and in the nation to ^'ive
occasion for thou<^d»t an<l desire for expression — there
must he a measure of material prosj)ei'ity to ])rovid(»
the time and opp(n*tunity for the cultivation of
hij^h thought and expression ; hut when these
coriditions <;xist tln^y contiinially act and react one
upon another. Therefore, if one; would ti'uly ediicate
himself, if h(^ would j^oiin inlluetice and win esteem
amon^ his fellows, if lu^ would ])romote the hi^dier
life of his race he should strive to cultivate to the
utmost his power to use tlu^ mother toniL(Ue.

Prepapation of the Teacher- Om's lantruaoc is

es.sentially a \mrt of h'ins«'If. It is not something
that can he s(»cur<Ml in a few <lays and put on like a
new suit (>f clothes. It <rrows with him an<l tits him
as closely as his skin, and like his skin, too, it can
oidy he chanj^ed hy i^rowth throuLjh tim<\ as the old
i.s dis|»laced hy tlu' new ;^radually develo])e(l within.
If the conditions suri'oundin<r the tc'acher durintr
childhood and youth have heen favorahle to the
devt;loi)ment of ix<>'>d hahits of lan<rua<re Iw is
fortunate and there may he litth^ need of tho
displ acinic process; luit if the}' have heen unfavorahle,
as they fre(piently are, then hf must in/ike it a
special purpose to eontinuMlly srck the purtst fwmi
mii'it initrirnt liinLC<iM^^»' Ji^*»rt^» pi'oniote a healthy
j^rowth within, and he must apply vi;;()rous friction

•. f 1

METllOI) IN TEACHING.

I I

! I-

of self-criticism to wear away the old scale* of his//
bad lant^ua<;e hahits. It is n*«wtrtleploral>le, ami it
mM'iiis li'ijv;f^ly ine\'nisal)l<< Hmt wt— mniiy teachers are
continually repeatinj^, in school and out, the most
connnon and glaring examples of incorrect language.
The reason appears to be that they liave heard and
used these incorrect forms so frequently in childhood
that, in spite of better environments and more or less
good reading, the habit remains, and the language
sense is not shocked by forms of expression that to
the cultured ear are exceedingly discordant. \,

Every true teacher should \\\w^\i lit his ambition
to do his part to remove this reproa^i, should saturate
himsi^lf with good English, should in\'ite his intimate
friends to prove their friendship by fnijikly cluicking
his errors, and when errors are discovered to be a
part of his language habit, he should practice the
correct form aloud until his ear will promptly and
always rennnd him of that error, j ;

Hut to knov/ and use correct language is not. ^^^^^V
I sulficifuit, though it is tlie prtTnTf^Trtjuisite. jJSb^jp a/^
"^truly interesttMl in the cultivation of l.ingUMge powerT
to be able to inspire a love for good language and a
desire for improventont in that line of educationjff)
be prepared to select reading matter that is nlowt
helpful both for himself anrl his pupils, one mwst
have a feeling for English — a sensitive apprecia)
of the essential (pialities of good language. This/a
this alone, is "the spirit that giveth life" to <i1l
language teaching.

In everything that enters into the real being of
the pupils, the teacher's «»xample is more potent than
his precept, and this is lik(^ly to be true of his

LANGUAGE TRAINING.

''i^//

ire

ust

tod

ess

ige

on
ite
ite

' a
,lio
nd

ot^ ,ywuV

■'^«:

'1',

in
Is

tniininii" in lani-naire. If liis six'ecli is clear, cliaste,
easy and beautil'ul, it will nc^t fail to attract
imitation.

Preparation by the Pupil— When we considta*

the child of five or six years entering- school we find
that he has already nuide marvellous progress in tlie
cultivation of lan<,nia<:re power. In other words he
has laid ati educational foun<lat ion of two important
eh^nents.

First — He hns acfpiired a large amount of
knowledge relating to a wide range of subjects. The
growth of mental power is already well established.
The mind has such a stores of working material, and
has had such an amount of exercise, that it ni'tMls
only favorable conditions to insure contiinied vigor
of growth in power.

Seconfl — He has a measure of l.inguage power
that enables him to express his ideas, often crudely, it
is true, but with simple directness and pictuieHipie-
ness.

Between these two (^lenu'uts of his attaiinnents
there is necessarily a certain relation. While the
knowhidge will invariably be found in excess of the
power of expression, it will also be found as a
ireneral rule that those childien who have had best
opportunities for ac(juiring new i(Kwis, have also nwid<*
most progress in the development of huigunge pow* i ,

How has the little cliild, starting with nothing
but potentiality, ac(juired so nnich knowh'dge and
power (* His education has been largely undirected
and informal, but it has pi-occcded along natural

ines.

If a child were isolated he could not 1

educated, but through the aiediuui of seime

11 V.

i.fl

f iMi

I : !i

') 'ii

MPITHOD IN TEACHINO.

perception thoro has been constant contac^t between
the mind of the child .iiid the materia! worM al'.;ut
him. In an inlinite variety of ways thih h t8 bLOSi an
undesii^i ed contact, tlie result ol" mere i'nv!r<>Mnein.
tut just as }ippro])riat«; and eti'eetive in pfovokit)*;
mental activity. Then in tliousands of ways the
contact of mind witli the outside vvorh] lias l)eeii
directed by partuits, nurses, and companions.

The pi'oduction of vocal sounds by the cliild is
instinctive, but speech is an art acrpiired by imitatiois,
and at e'very stai^e in t)ie (hnelopment of lanfjuaj^e
pow(!r imitation is tlu> master a^ijent. The instinctive
cooin;^ and babl)lino- of (he buby <^5ves vocal power
and skill, so that after he has a few ihousand times
hi'ai'd th(^ word " Mama," and at tlie same times lie
has seeil his motlier's face, he learns to associate tlie
name and the face and to bal>ble " Mama." So he
early h^arns tin; name of tlie .](,jl>;, the cat, his iood
and drink, etc. WluMi the idea of action c<.meK to be
associated witli sounds litthi sentcuices are formed, as,
" Pa])a tinn."

Thus th<' ])rocesses cro on. Tin; world is all new
an<l fresh and int(irestin<^ to the little one, and
ov(Myb()dy lovers a little c* -'d, likes to show him
what seems to be new an«' r terestiuix and to talk
with him about tlu>m, and likes to hear him try to
expi'ess hinjsj'lf. Help, encoura;:;en»ent and j^uidance
are ever at his side. The child deliirhts toexercisti his
I ew power, lie cannot understand why \h' should
not tell about everythinjf hi» sees and hearR. Nay,
more, his lan<,nia^n' jiower becomes a playthin<]f to him
an<l conw's under the majL^ic spell of his ima^^ination,
just as tlu^ knotted rai,^ Ix^conuss a livin«^ baby, or the

'^m.

LAN(;UAGE TRAINING.

littl(3 stick • horse. He iiiaMui'acturcs the niDst
wojiiiert'nl slorit's, sniiictimes without :\ sliji<h)\v of
tiiitli, often with iiothinv" niorr. H\s jturcSiLs {M-.
Jihii'inerl at his <;ar'y <ie])!-avity, an^l eoi-hriiaMl in tlje
doctrine of inhorn sin in this ease; uatin<r two or
tliree (MMituries haek. To the chihl at this staur
these stories are no more lies than are. tlif ra;^ ltai>ies,
tho woo<h'n swo)«ls or thi^ mud pics.

As the child i;rows ohlcr and heconies more
ind('})endent, the encoui-a^'t'nicnt and lu'lp ari^
•gradually witlidiawn, and tlien^ is litth^ douht that
i-he I'atc of i^rowth of hoth kiM)wh'di;-e and cxpi-ession
steadily (h-eiincs (hiring edenientarv school life.

General Principles— Fiom the fore<^^oino- con-
siderations W(,' are ahlc to dr-rivc a frw o-enerai
fnndanu'ntal principles to ^nide ns in selcetinj^
materials and dccidin;^' npon the methods to Ix;
empl()3'ed in carryin*^ on the work of lanL;»iao;e
tiainini,^ in the schools.

pi. TIk'iw innsf })(> the iiioHt fiwonflth' <(»inl 'it'ian^
Jnr sf nil iihtf I Hi/ f/ioifi/hf. — -'I'he spontan<'ous desire
to tiX[)ress thoUL;hl is an essential condition of
tlw^ tjrowth of lann'ua^^e pow(!r, and witlt y<Min^
einldren at least this desire is maiidy induced by ' ;e
acquisition of new ideas. The ])Upils should he
continually occupied in fornnnj^ ch-ai- notions of
(»hjeets and snhjects of study, and this should he
followed hy the o])portunity of expressin<^ thesci
ideas with ease, clearness and accuracy. \

There is a, theory (piite ^^^'uerally !tccepl('d| amonj^
e(hicators at»d <>thers, that the iji-oat mM.sjters f)f
l'ln;^dish, oral or written, ha\t' nearly all llnid a
thor<jui;'h ti'aininj^^ in ancient das.sics. The \Teason

't,

l>\

METHOD IN TEACHING.

■I

HoeiuH obvious. An^ait from tlie influence of a
knowle<l{^e oi' the sources of so niucli of our language,
they have been tliorou^hly trained in En«,dish
throu^li tlie study of the chissics. Wliere the
teacliin^ has been ri<jflit the transhition of every
sentence has been an En^dish lanj(ua<^^e lesson. The
student worries throu<;h the original, vvorkin<jf out
the thouf^lit as })est lie can. When the thou<ifht
obtained is tolerably clear, tlui whole mind is
concentrated in an effort to put that thoui,dit into
the best possible Enjijlish.

Applied to the teaching,' of otlier subjects this
is preci.sely the principle we ur^^e as fundamental in
the trainin*;; in En<^lish. Direct the study of tlu;
pupils in appropriate literature, in nature study, in
form and numlun-, etc. ; when they have obtaincnl new
tliou<j;ht8 let them express them in the best En^dish
they can command. Where a series of tlioughts are
related tliey should find expression in more or less
connecti.'d lan^uatje. AmericK.i schools have recently
luMMi tloo(h^d with lanj^ua<;(* books, tlie main idea of
which is to get pupils to use certain words in
sentences, and consefpiei^tly teachers and ])Upils have
wasted much ^ime and have <^rown disgustecl with
tlie.se so called " lan<;uage lessons." (iood tijachiuji;*
must ever be directed in evolvin<( thou<^ht which
naturally seeks expression. This is essentially the
initial step in all lanj^ua^j^e training.
^ 2 'iftcvf >7'ij/7(/ nc (J(hhI rnodi'ls. — If the learner
in his iifFortp i > express thought has constantly
))€»fore him goo'^ snodels of language, his pra(;tiee
will teinl t*' clearness and correctness as well as
eane. The id al condition, of course, is tliat the child

LANGUAGE TRAINING.

should not liear or read any incorrect lanj^ua^e, but,
since, out of school, conditions frequently nmke
this inipossihle, it is all the more important that
teachers should make the school environment
especially helpful, j

The teacher's own lan<^uaL,a' is the first model ;
and whether it he for ^^ood or for ill, depends upon
its character. It has frecjuently heen observed that
some sli;^ht peculiarity of accent or pronunciation
on the part of the teacher gradually permeates the
whole school. Many other influences, though less
easily detected, are ecpially felt. H(jsides exercisin*^
the utmost care in the cultivation of his own
languajg^e, the attention paid to that of each child in
the school comes to have a connnon reciprocal
influence upon that of each of the others, whereas if
inaccurate and clumsy expressions frequently pass
uncorrected, the pupils usinn; such become veritable
stumblinu^ blocks to all the other memlters of the
school.

Then, too, the kind of matter read, especially if
read several tim(^s, becomes a most potent factor in
mouldinj^ the lan;;ua«,'e of the child. From this point
of view alone it is unfortunate that so many primary
reading books are filled with poor commonplace
sentences, designed especially for teaching the sounds
of letters, and lackin;.^ all the (elements of natural
interest and literary merit. Instruction in the
sounds of our letters is im])ortant and it will
probably always have its place in the teachin]L^ of
piimary rending, but just now it has a great deal
more than its own place. It is not everything in the
first two ycar.s' reading, and it is already bciu^

1 !■

Wi' 1

METHOD IN TEACHING.

> (

donionstrjitcd that tlit; sounds of tlic letters can be
tau^^lit just as successfully tliruu^li n^ood uppiopriate
litej'ature as tlir()U<^h the " cra/y <|uilt" lessons made
out oF a collection nt* words phonetically related.
The stories in the primary n^ach'rs, the supplemental^
reading matter, the memory selections, the hooks
read at home may all ha\'e a powerful influence upon
the thouiiht and humuMiie of the child and shcndd
thend'ore be the best lie can read.

I '\. There ttnisf he ahit inlanf t)pj)(jrt n h if 1/ for
praefice.-J-ln this connection as in many others, Me
have not «fone tar enouiih in the recounition of tlu;
law of educatioiiLth rough the self-acti\ ity of tin;
child./* From no selfish motive, but from example,
habit and a wrong idea of relative \alues, the
avera'fe teacher does from three-fourths lo nine-
tenths of all tlie recognized talking in the class room,
and leaves the other small fraction to be divided
among forty or fifty pu])ils. 'i'he littli^ child whose;
op[)oi'tunities for cultivating speech under the
jxuidanci? of the teacher are limited to a few stilte(l
and unrelated answers to (piestions, cannot be
(ixpect'd to make much progress in the growth of
language power. It wiM'ti as reasonable to expect a
child to develop a good physi(pie on an occasional
pinch of salt. It is (piite trut; the teaclnir's time is
limited and already more than occupied, but is it
occupied most economically for the children in this
matter of language training!' If we admit the
princij)le that^liere must be, not only abundant
op|)ortunity, but consid«'rable encouragement lo
practise, is it [)ossible that the utmost is being done
tu meet the retpuremeuta ^ \

\1^^.

LANGUAGE TUATNIN(;.

1 '^r

^«'

r
J

One of tlie greatest (liscoani^eiiu'nts to ])r()<;it>HS
in the <jjro\vtli of l{in;jfua<,fL' power, is iinsyinpHtlu'tic
criticism. Tlierc must be ciiticisni, or ratlu'r cor-
rection, but tliis may be done in sucli a way as either
to help or to hinder. It liindei-s when it makes
tlie learner self-conscious rej^anlinu^ his lan^uaj^e.
For example a father allowed his little hoy thirty
cents a week to use as he saw tit. Noticin«^ that he
was picking up some incorrect forms of speech,
probably among his playmates, he auTiounced that
the boy should foifeit one cent for every error in
language detected by his parents. At first the fines
amounted to only five or six cents a week, but in a
few weeks they increased to twenty or more, and in
a short time amount«Ml to more than the weekly
allowance, and even the sentences that were not
incorrect were frecpiently halting and uimatural.
For ease in talking the mind must hv, at ease.
Speech is fetterod by self -consciousness.

14. fjd ii<jnit(/(' tvdlnini/ niusf Ih' 'nil'niKih'hf
corrrldffd trifJt flic other suhjccfs of simhj. — In most
cases special l(^ss()ns in language, that is, Ics.sons
whose chief aim is the use of certain words, are
cojnparatively useless. This thought cainjot be too
strongly emphasized. ] If the study of i wiUir'arm^^Tir^ ^l^ h
and phenomcuia, of myths, legends, liistorical stories, 'j^T/Xl^
biographical sketches, of- li t eratui ». Trf— fai4*4, color
and number, does not stir the children with a desire

'^n\

MKTHOD IN TKACHING.

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not, as a rule, In any iiioasnn; HU[)ply tho need or
serve as a substitute.

If beFon; (leeidin<^ to teach a lesson teachers
would compel themselves to answer clearly tlie
(juestions, what is its purpose ^ how will the
j^rowth of a child be promoted by tlu^ jiroposed
lesson ? very numy so-called hin«;na<];e lessons
would " fall hack dead." The relation of lan;^Mni^^e
to thou<,dit renders it imperative that at every step
in every sta«^e the development of one should be
accompanied by a corresponding^ development of the
other.

The School Means of Language Training* and
How to Use Them —

1. Gonuersdfions. — One of the best means of
brin^in^ the home feelinj^ to the little stian^nn" in
the school room is to lead him into conversation,
and thus into s(!lf-for<ij(!tt'ulness. This is also
one of the simplest and njost natural means of
training in lanj^uaj,^' power. Lord Hacon has well
said " Certain it is that whosoever hath his mind
frauj^ht with many thou<,dits, his wits and undcjr-
standing do clarify and break up in comnnniicatin^
and discoursing with another ; he tosseth his
thouj^hts more easily, he marshaleth them more
onleily ; he seeth liow tlu^y look when turned into
words ; finally he waxetli wiser than himself; and
that more by an hour's discourse tluui by a day's
meditati<m/

The subjects for these conversations may Ije as
varied as the exp(n-i(Mices of tlie children, and should
be (b'awn from the incidents of the school room, the
play <jfround, the observations of the childnsn on the

LANOnAGE TRAINING.

l(!r-

hid
Iho

way to and from school, and in their hoiiicH, the
nhM,rart«'r.s in story and hioirraphy, tlu' infoiinal
h^sHonH in njann«'is and njor.ils and whatever is at
once intoH'stin^ and wholcsouje. In these exeicises
the chief <luty of the teacher is to encoiira«,'e the
n^ticent, to j^uidt' the line of conversation, and to
kindly h;ad to better ways of sayin<j thinj^^s.
Wh(>n lie j^oes heyond this to answer (juestions,
o'ive needed explanations, or correct misconceptions,
his own lanj^uage should he neither childish nor
technical.

2. Stories. — Ap])ro|)i*iate stories constitute one of
th<j very hest kinds of iiKJiital food for tlu; youn*;
child. In tlie first place th(;y stinnilate interest,
and the mere act of sustained int(;rest in appropriate
stories well told is tixcelhuit traininj^ in the hahit of
concentrated attention ; this in turn has a strouL*"
influence upon the formatio!i of the lan<^ua<re hahit,
(^specially if tlu; story is <^o()d enou^di to hear telling
several times. If, however, the children aie led to tell
the story in the hest way they can, the luMieticial
results in both thouL,dit and lan^uaj^e culture are
more than doubled. The; plan recommended by some
of the loading German educators of makinj^ rer^ular,
daily, systematic story-t(;lling a part of the
curriculum durinjr the fiist two or thre<; years
seems to be based upon recognized psychological
principles.

Every primary teacher should be .a good story-
teller. If the faculty is not natural it can be
cultivated. In junior classes telling is vastly better
than reading a story. When the children have
acquired considerable power as readers, the distinctly
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Curporation

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(716) 872-4503

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METHOD IN TEACHING.

new words kIiouIcI be placed upon the blackboard and
tlieii" nieanin*^ and pronunciation tau^lit.

No one sliould be exempt from taking part in the
repnxluction of these stories, because those who need
the exercise most will be likely to form habits of
inattention if they get the idea that they may
be (excused from their part in reproducing the stories.
In the early stages of school life it may be wise to
let the best story-tellers do more of this work than
the others because the backward ones may gain more
by listening than by their own halting, blundering,
discouraorinjj: efibrts.

At first, questions may, if necessary, be asked to
recall and coiniect the salient points of the story, but
as soon as possil)le the reproduction should be given
without question, hint or suggestion. At all stages
care should be taken that the reproduction be
as truthful as possible. Imagination has a true and
beautiful place in child life, but it is not in the
reproduction of a story.

It is said that when Lord Macaulay was a little
boy his father made it a practice to tell him a story
every night and to require the child to reproduce it
as well as lie couM. Gradually the stories selected
were longer and more substantial in character, and
still later stories were read to him, or the boy read
for himself, but always there had to be the
reproduction aiming at fulness, accuracy, ease and
clearness of expression. As the boy's powers grew
the nature of the subjects was gradually changed,
and biographies, historical sketches, essays and poems
were dealt with in a similar way. Is it any wondor
the man who had liad such training became a master

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Th

LANGUAGE TRAINING.

id
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of English, or that lie could reproduce a book after a
siiijile readiuL'i'

8. Uhject Lessons, — As a source of new ideas
there is nothing Ijetter for young children than the
study of objects, especially natural objects, or what is
now known as nature study; and it follows that what
provokes new ideas also calls for new language.
This study should lead to scrutinizing ol)servation,
hence to exact and detinite ideas and these will seek
expression in precise language. The old idea of
object lessons as an opportunity foi- giving the child
immense (juantities of gathered information about all
sorts of manufactured articles and foreign products
has done nuich harm to this impoitant i)hase
of elementary education.

r The true aim is the development of the child's
powers through exercise upon these objects. Hence,
again, the ciuef work of the teacher is to act as a
guide, to stimulate and direct this self-activity of the
child. I This, of course, can best be done by careful
questioning, and the teacher should, as a rule, do ])ut
little of tlie answering. Fre({uently what the pupils
cannot answ^er to-day may well be left over till
another day, to be taken home and discussed out of
school. Sometimes a good mind-awak<'ning (piestion
can be kept as a live issue for a week or more. Let
the teaclier direct, sustain and intennify the
investigations, lead the pupils to discover the errors
in their conclusions, but in eveiy good way
encourage them to tell what they observe and

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ils should be asked and

oncouraged to bring to tlie school suitable objects for

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METHOD IN TEACHING.

study, and every school should have a cabinet in
which to place such as can be preserved.

4. Pictures. — Related to object lessons, especially
when considered as a means of developing language
power, is the study of pictures. These may be the
pictures of animals or other objects used to give some
idea of the things themselves, or they may be works
of art, valuable for what they represent artistically.
Next to the study of objects children like pictures,
and this is a guarantee of interest and attention, and
an additional reason for their use.

The best pictures available should be used. The
style of drawing, the coloring, the acts represented,
the motive of the artist, the dress and personal
appearance of the persons shown, all form elements
in that unconscious education we so often disregard.

For very elementary work the teacher, if she has
the skill, may make suggestive sketches upon the
blackboard or upon large sheets of paper, or lacking
the skill to sketch, she may find large paper stencils
a helpful substitute.

Be sure that all have a good view of the picture,
then by carefully prepared questions lead the pupils
to :

(1). Tell what is represented in the picture.

(2). Describe each prominent figure.

(8). Explain the relation of the different figures to
one another, or to some central figure.

(4). Suggest a title for a story to be inferred from
the picture.

(5). Compose an original story for which the
picture would be a suitable illustration.

(6). Interpret the lesson of the picture.

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LANGUAGE TRAINING.

5. Reading and Literature Lessons. — If the
subject matter of the readinj^ books be of the riglit
character and be treated in the riglit way, these
lessons should exert a great influence upon the
development of the child's language power. In both
thought and diction the matter should be some what
above the learner that he may be constantly looking
upward, reaching upward, and growing upward.
The thoughts of the passage should be freely and
fully discussed, and reproduced by the pupils. His
power to express what he has read is the only true
test of the pupil's grasp of the thought, and of his
preparation for oral reading. It would be well if
during the first two years there were much more of
this reproduction test of the child's power to get
thought through silent reading, and much less
striving after oral reading before children have
sufficient power of word recognition. Paraphrasing,
of either prose or poetry, is an admirable exercise, and
though the child's expression may fall far below the
model studied, it will be continually influenced by it.
While the questioning upon a passage goes into
matters of detail, the reproduction should aim at
connected fulness.

Henry Clay has left us this record : " I owe my
success in life to one single fact, namely : At the age
of twenty-seven I commenced, and continued for
years, the process of daily reading and speaking
upon the contents of some historical or scientific
book. These off-hand (efforts were made sometimes
in a cornfield, at others in the forest, and not
unfre<[uently in some distant })arn, with the horse
and the ox for my auditors. It is to this early

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METHOD IN TEACHING.

practice in tlie ^reat art of all arts, that I am
iriflebted for the primary and leading impulses that
stimulated me forward, and shaped and moulded my
whole subsequent destiny."

6. Memorizing. — The memorizing of some of the
gems of literature in prose and poetry, not only
tills the mind of the child with best thoughts of the
world's highest thinkers, but furnishes strong,
beautiful, perpetual elements in the unconscious
development of language power.

Composition — In the discussion of oral language
training what has been said about Mie importance of
the work, the preparation on the part of the teacher
and of the pupil, the fundamental principles involved
and the means to be used, applies with equal force to
training i^i written language. The training in speech
should constitute a general preparation for the
written work and in most, if not all, of the elementary
composition oral discussions should precede and
prepare for the written exercise. Meantime the two
lines of training will more and more diverge and each
will become a more or less distinct art involving
special conditions and requirements.

For several reasons composition is usually con-
sidered a difficult art to teach. -

First. — It is connnonly thought that ability to
write well is a special gift, akin to that of the
nmsical composer, and doubtless the masters of the
literary art are specially endowed, but it is probably
e(|ually tiuc tluit most of these literary artists have
realized their endowment only through much patient
study and [)ra('tice and by this means anytme may
attain a fair den'ree of skill.

LANGUAGE TRAINING.

» I.

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Second, — Comparatively \'v\v persons, in seliool <>i'
out, are willing- to spend tlie necessary time and laboi"
in tliorou^li preparation of tlie suV)ject matter of an
essay, to say nothing of tlie necessity for persistent
and painstaking practice in expressing their thoughts
upon the prepared theme. Usually those who succeed
in ac(piiring power and skill in any art are so fond
of it that they enjoy the practice, but strong, patient
purpose may take the place of, nay, may usually do
much more than simple fondness for the art.

Third. — In large classes the task of revising pupils'
exercises, seems to make it impossible to providi; as
much practice as is desirable. This will be dealt
with under " marking exercises."

General Sugfg^estions—

1. Preliinlnary Work. — Where it is found in a
particular school, whether with primary or advanced
pupils, that the necessary foundation in oral train-
ing has not been laid, at least some time should be
taken to correct the omission. Written expression
is more difficult than oral, and the early training
should not impress the pupil as difficult.

2. Interest. — In written as in oral training there
can be no genuine growth in language power without
a spontaneous desire for expression arising from the
ac(iuisition of new ideas. It is therefore a prime
essential that pupils should be stimulated to a lively
interest in the subjects upon which they are expected
to write. Without this the work will be a mere
imposed task to be disposed of with the least p(jssible
effort; but where there is even a small measure of
love for the work there will be at least a correspond-
ing measure of art, and of growth in power.

Ill )'!

METHOD IN TEACHING.

i !1

3. Choice of subjects. — Much care sliould ha
exercised in t)ie choice of subjects. Tlie teaclier
should alwrys decide for junior pupils and usually for
tlie more advanced, but the tastes and state of
preparation of the pupils should always be considered.
One writes best upon those subjects witli which lie is
most familiar, though a child is not likely to choose
such subjects for himself. He will think it too
connnonplace until he has learned how much more
easily he can write uj^on it, and how much more
satisfactory he can make the result. Foi* the
elementary classes reproduction of stories and of the
ideas developed in nature study will be found most
interestini^ and helpful. In higher classes the regular
subjects of study should furnish much interesting
material.

4. Plannintj tlie essay. — There must be training
in organizing one's ideas preparatory to written
expression, that is, pupils must learn with wliat
and how to begin, how to wovk um the most effective
arrangement of the main ideas .md finally how to
conclude. This kind of training .should lead to the
formation of the habit of making outlines or skeleton
plans before begiiniing to write, without which
orderly and intelligent work seems impossible.

5. The elements of composition. — From the first it
should be a constant aim to develop clear ideas of the
elements of expression.

(a). The sentence, what it nuist, and what it may
inclmle ; how its limits nmst be indicated.

(b). What constitutes a pai'agraph, the purpose in
so dividing the essay, different ways of beginning
and ending, and how paragraphs should be indicated.

LANGUAGE TRAINING.

Revision by the Pupils — When, tlu-ou^rli prnctice,
pupils have jjjained considerable power and facility in
composition and are able to criticise the syntax and
rhetoric as well as the mechanical parts of their work,
they should be led to improve their own essays by
revisiujt^ them two or tlu*ee times before submitting
them to the teacher for examination. Then aftev
receiving the teacher's criticisms and suggestions they
should try again as often as the interest can l)e kept
up. In this way the pupil works constantly to exci'l
his former self. He has the satisfaction of seeing his
first crude production improve under his own effort.
He becomes conscious of his own power. He works
with care. The rules for punctuating and the laws
of syntax become vital principles wlien he finds them
necessary to the clear and complete expression of his
thoughts.

Marking" Pupils' Exercises — To do anything like

justice to the criticism and marking of pupils' essays
necessarily involves a large amount of arduous labor.
How can this work be reduced, and how can the
essential remainder be rendered most effective ?

First. — It should be borne in mind that spelling,
the use of capital letters, and ordinary punctua-
tion are matters of habit. Errors in these can be
in a very large measure prevented by careful
attention to tlie formation of right habits at the
beginning. To those who appreciate the import-
ance of directing the activities of children in right
lines and so foiining right habits, it will be reeogni/ecl
as vastly easier to train pupils to avoid n^aking
mistakes than to afterwards correct errors that
have become habitual. Those who neglect the

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METHOD IN TEACHTNG.

ounce of preventative nvv sure to need tlie pound
of cure.

Second. — It is not always desirable that the
learner's attention should be called to his written
errors. This su^^estion must be used with <liscretion;
carried too far it contradicts the first. The power to
write with ease can only come through nuich practice,
and this is the prime condition of progress. Much
correction by another is almost sure to discourage
and repress the very spontaneity so essential to
genuine self expression.

Third. — At as early a time as possible lead pupils
to revise their own exercises before handing them in.
As often as once a week one written exercise from
each pupil should be examined with care and
returned. But most schools should provide for daily
practice in written work. In that case it will be
sufficient to mark a part of the papers each day,
giving special attention to the backward or careless
pupils, but care should be taken that none feel
neglected.

Fourth. — (i). For primary classes : —

(a). Mark exercises with colored ink or pencil.

(b). Strike out misspelled words and write correct
forms plainly.

(c). Substitute caj^itals for small letters.

(d). Where the wrong form of a verb or other
word is used mark w.f.

(e). Strike out sentences of bad construction.

(ii). For more advanced pupils : —

(a). Use marginal notes to characterize passages
as good, bad ; strong, weak ; clear, muddled ; etc.

(b). Do not locate definitely errors in punctuation,

LANGUAGE TRAINING.

capitalization, spelling, ^ranunar, rlictoi'ie, etc., but
indicate in the margin ])y hucIi syni})ols as p, c, s, g, r,
and re((uire pupils to correct.

(c). The attention of the whole class may be
called to prevailing errors.

(d). Sentences and paragraphs illustrating the
contrasts referred to in (a) should sometimes be
placed upon tlie board and pupils led to note tlie
difference.

(e). When an exercise lias l)een found imperfect in
even a few minor points it should be re-written.

(f). By noting from time to time the common
examples in false syntax the teacher will collect
valuable material for training in correct idioms.

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METHOD IN TEACHING.

i r

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CHAPTER IV

In onlcr to d

ENCJLISll (jIllAMMAl
iscuHS the

value ul* Euirlish Grainiuar

as a Hcliuol study, it will bo well at the outset
to understaiul its scope and object. It has been
defined as " the act of speaking- and writing- the
En^'lish languai^^e with pi-opriety." " Hut for <^ood
reasons this traditionary view has, by competent
scholars, been rejected as false." Dr. Fitch say;,, that
whoever tries to teach or learn iii'aniniar as an art is
doomed to disappointment. Prof. Whitney writes in
these terms : " that the leading object of the study of
English grannnar is to teach the correct use of
English, is, in my view, an error, and one which is
gradually becoming removed, giving way to the
sounder opinion that grannnar is the reflective study
of language for a variety of purposes, of which
correctness in writing is oidy one and a secondary or
subordinate one."

" The traditionary English grammar," says
Hinsdale, " was created not by an original enquiry
concernino- the nature of the Enulish lanj»'uai»:e, but
by imitating Latin Grannnar." The wide dissimi-
larity between the structure of the English language
and that of the Latin renders any application of the
grammar of the one to the other almost useless, hence
the failui'e in the past to obtain good results from
this branch of instruction. And so great has been
the disappointment of teachers in not realizing the

ENGLISH GRAMMAR.

practical end as enil)0(liefl in tlie old drflnilion, that
they now call For the aholition oi* t' • suhjoct from
the cuiTicuhnn of school studies. Hut such demands
proceed from a grave misconception of the sphere of
the subject.

Eno^lish Gi-annnar is not the (trf of writing the
English language with propriety; it is not an art at
all. " It is a Hcieiice and as such it was considered
by the ancient Greeks." It is the science of
language, and since the unit of thought is the
sentence, it may be defined as the science of the
sentence. As such it is limited to " Etymology, or
the doctrine of words, and to Syntax, or the doctrine
of sentences."

Having determined its nature and field let us
examine its v^alue as a study. The study of grammar
has a high dlf^ciplinary value, besides having a
'practical value strong enough of itself to ensure its
continuance on the curriculum of school work.

Disciplinary Value— 1. Grammar deals with the
analysis of words and sentences, with a view to their
being arranged into classes on the basis of similarity
in relation. " This involves the analytico -synthetic
or inductive exercise of mind. In this process there
is obviously a peculiar training of the powers of
observation, working not only upon the forms of
words, idioms and sentences, but upon the realities
behind them, verbal distinctions, meanings and
relations."

2. There is also involved a vigorous exercise of
the logical powers — analysis, comparison, abstraction
and inference. " Intellectual processes are developed
by studying the relations of objects external and

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METHOD IN TEACHING.

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I; !

internal. From an educational standpoint the study
of the latter is much more important than that of
the former." It is only when the mind disregards
the sensuous elements of presentations and grasps
the deeper abstract relationships that it is introduced
to the sphere of scientific thinking. Now grammar
deals with the relations of thoughts and ideas as
expressed in the sentence, the comprehension of
which can ' suit only from the student's performing
the mental processes carried on by the originator of
the thought. This work on the part of the student
is rendered the more necessary in English by the
fact that its language is uninflected ; " the words do
not, as in Latin (by their forms), serve as guideposts
to indicate the thought." " But, since thought
relations in English are largely dependent upon the
position of the words and the spirit of the passage as
compared with the more mechanical languages, its
grammar is peculiarly valuable as a discipline." On
this Prof. Greene makes this very pertinent
statement: — As a sentence is the expression of a
thought, and as the elements of a sentence are
expressions for the elements of thought, the j)iipil
who is taught to separate a sentence into its elements
'IS learn imj to analyse thought, and consequently to
think.

3. The intellectual discipline afforded by the
study of grammar bears, in common with all other
studies when rightly conducted, indirectly upon
moral discipline. On this Prof. Laurie remarks,
" moral discipline is the habituating of the will, the
dominant function in a human being, to overcome
the difficulties of a temptation to stray from what is

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ENGLISH GRAMMAR.

.seen and affirmed to be tlie riglit path. But it is tlie
same will v\liicL I call upon for energizing activity
when I present the mind of a boy witli the
intellectual difficulties of formal studies and call upon
hvn to overcome these. There are not two wills in
man. The effort, then, which all formal studies
demand of the young that they may overcome
intellectual difficulties is not merely intellectual but
moral, in its effects on character."

Value for Practical Use— 1st. It enables the

pupil to apprehend with greater precision, the
meaning of what he reads. The student who has,
through the use of examples, thoroughly grasped the
loirical relations of the elements of a sentence
possesses the power to interpret not only short
sentences whose order, for metrical or other reasons,
has been changed, but also long and intricate
sentences, whose difficulty consists in their com-
plexity.

2nd. It enables a pupil to express, with greater
intelligibility, his own experiences and thoughts.
Thought and language are so interdependent that
after a certain well-marked stage, an advance in the
one is necessarily accompanied by a corresponding
progress in the other. So that any training that
enables the pupil to analyse thought, and there-
fore to think, must indirectly assist him in liis
composition.

What Herbert Spencer writes concerning Rhetoric
is applicable to Grammar. " Some practical result
may be expected from a familiarity with principles ;
the endeavor to conform with laws will tell, though
slowly ; and if in no otlier way, yet as facilitating

I : '

METHOD IN TEACHING.

' •?

revision, a knowledge of the thing to be achieved, — a
clear knowledge of what is accuracy and what is
inaccuracy cannot fail to be of service."

When to be Taught— It is a fundamental
principle in Pedagogy that subject matter and
method should be accommodated to the condition of
the pupil's mind. To present to a child a subject
that calls for the exercise of mental powers not yet
developed, is not only useless but positively harmful.
The study of Grammar demands the exercise of
a highly analytic function with which a child
in the formative language period is unable to
respond. Grammar study therefore, should be
postponed until the growing powers of the child
enable him to apprehend the relations involved in
the sentence and the functions of its component
elements. This will defer the study of grammar to
the fifth school year, or to speak in terms of our
grade system, the Senior Third Book grade.

It is advisable, how^ever, at an earlier period, to
direct the attention of the pupils to the essentials of
a sentence, subject and predicate, for the purpose of
correcting errors in their sentence composition.

What to be Taught — After teaching the
essential elements of the sentence, there will follow
regular exercise in the more minute analysis of
language — the classification of words composing the
sentence. The follow^ing order is suggestive : —

A. Units of the sentence.

1. Essential elements ; verb, noun.

2. Modifiers ; adjective, adverb.

3. Unit equivalents; pronoun, phrase, clause.

4. Connectives ; preposition, conjunction.

ENGLISH GRAMMAR.

-a

ise.

B. CoiiipariHoii and classiticatioii ot* the syntac-
tical relations existing between the sentence units.

C. Sentence forms and values.

D. Subclassiiication of parts of speech.

E. Inflection ; genei*al study of the purpose of
inflection as exhibited in the parts of speech followed
by detailed study under each part of speecli. The
following order is suggested : —

1. Number in noun, pronoun, verb.

2. Gender in noun, pronoun.

3. Case in noun, pronoun.

4. Tense in verb.

5. Person in pronoun, verb.

6. Comparison in adjective, adverb.

7. Mood in verb.

Method — In all departments of instruction the
end determines the means employed for its accom-
plishment. The chief end in teaching grammar is
discipline rather than knowledge, the development of
mental power rather than the ac({uiring of language
facts. Exercise is the law of growth ; development
of mental power is conditioned upon the exercise of
the activities involved. Grannnar deals with the
principles underlying the use of language. These
]jrinciples are broad generalizations induced from the
careful observation of the particulars and facts of
language. To be of value as a discipline, the pupils
must be led to analyse these facts and make the
inductions for themselves. By this means observa-
tion is quickened, and a scientiHc trend given to the
pupil's thought.

No text book should be used by the pupils before
the seventh school year, that is the Senior IV grade ;

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METHODS IN TEACHING.

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(

and even here there is no absolute necessity for its
use. Suitable passages from the reader, methodically
arranged, are superior to isolated examples from a
text book. Where a text is used, the greatest care
must be exercised that the pupils do not cease
original investigation to accept the ready made
definitions and principles of tlie G]"ammar author.

A few remarks will now be added dealing more
particularly with method in relation to the sub-
divisions of the preceding section. Division A
comprises the general classification and definition of
the sentence elements. The basis of this classification
and definition is function, and not form. To
determine the class to which a word belongs will
require the pupil to study the meaning of the
sentence that the part contributed by each word to
the upbuilding of this meaning will be clearly
apprehended. From several sentences the words
performing similar functions are selected, and, on the
basis of this similarity, grouped together and a
common designation assigned to tliem. The method
liere employed is evidently the ivductive.

No apology need be offered for the position of
phrase and clause in A. All the functions possible
to these elements have previously been studied in
noun, verb, adjective and adverb. And since
function, not form or structure, here, is the guiding
principle, a knowledge of the conjunction and
preposition may be postponed until these unit
equivalents have been studied at least in a general
way.

The method in B is similar to that employed in
A. To some extent it is a review of A, but differs

ENGLISH GRAMMAR.

of
Ae
lin
Ice

In
Is

from it in being more abstract. It serves as a
summary to the preceding work, being a generali-
zation of the relations involved among the classified
elements. Exercise of this kind affords rare training
of the power of analysis, and enables the pupil,
quickly and correctly, to assign to any unit its logical
value in the sentence.

In C, we have classification of sentences. The
basis of this grouping is form or composition.
The pupil is here introduced to the study of the
more complex units of thought ; but having already
studied the logical values of clauses, this exercise will
present no difficulty.

D introduces the subclassification of the parts
of speech. The mental activities employed in
this exercise are similar to those used in A; but
the basis of this classification is different. While in
the former it is function, in this it is significance, or
relation, according as the words to be classified are
notional or relational. On the basis of significance
will be classified, nouns, verbs, adjectives and
adverbs ; on the basis of relation, pronouns, preposi-
tions and conjunctions. Upon the accuracy of the
classification and the precision of the dc "^nition of
the classes, will depend the value of this department
of grammar. No thoughtless work may be allowed
and the very common habit of inducing generaliza-
tions from too few particulars must be carefully
guarded against.

Inflection is another subject that demands
thoughtful treatment. Nice discrimination of the
meanings and uses of inflected forms and their
substitutes conduces to clearness of stv)^ir;^^{^^3i^i^i^

/^ '-civ V.^tevveo»l3,

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100

METHODS liS TKACHINCi.

study ot* these difiereiiees afto'Tls tlie student a very

! -i

if i

profitable ineiital exercise,

luHection marks

runction and g-oiieral sio-nification. When pupils
have learned through pi-actiio to distin<»ui.sh these,
they are in a position to study the changes of form
(hjpendent thereon. In the se(\uence in grannnar,
therefoi'e, inflection should follow the deh'nitions.
Since inflection engages the mind in activities
similar to those employed in r;?assification and
definition, it should be taugiit, as they, inductively.

Limited space restricts the writer to the few type
lessons which follow. These, however, illustrate in
detail all the principles above outlined.

Subject and Predicate

Introduction.

1. Ask the pupils to name objects in the room,
such as desk, beL". cup.

2. Ask them to make statements about each of

these objects.

Devchrpnicnt.

1. Write one of these statements on blackboard.

The bell rings.

2. Ask the cImss to read the words that stand for
that about which the statement is made.

8. Underline this part.

4. Ask pupils to read the part used to state
something about the bell.

5. Doubly underline this part: The hell lil^Gii.

6. What is the use of the first part of this
statement ?

Ans. — It names the thing about which the
statement is made.

ate

lis

ENGLISH GRAMMAR.

101

What is tlio use of tlie second part ol' this
statement ?

Ans. — It is used to state st)niethinL;- about the
tliin<4' named in the first part.

7. Ask the pupils for other statements ahout
persons or things, and write them on hiaekltoard as
they are given. Tlien recjuire the chiss, in answer to
questions as above, to read each of tlie two parts into
whicli each statement is divided, and <;ive its use.

8. The teclniical tc" is, subject and predicate, are
now given to tlie pupils by telling them that the part
of a statement used to name the thini»- about which
the statement is made is called the subject, and that
the part of a statement used to state something about
the thing named in the subject is called the
predicate.

9. The pupils will now be asked to give the
subject and predicate of each of the statements on
the blackboard.

10. The pupils will now be led to form simj)h^
definitions of subject and predicate, based on the
charactei'istic ("unction of each. These definitions are
written on blackboard, and pujjils drilKnl on them,

Praotici 1 1 Exercises.

1. Statements are written on the blackboard and
pupils are required to name and underline the subject
and predicate of each.

2. Statements given orally are divided into
subject and predicate.

3. Pupils compose statements and analyse tlu^.m
as above.

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102 METHODS IN TEACHING.

The Noun

Introduchon.

1. Prescint an object to the pupils and ask them to
name it. Write the name on the blackboard. Make
use of other objects in the same way and thus lead
the pupils to distinguish an object from the word
used to name it.

2. Drill on the use of words.

Development.

1. Ask the class to give the names of persons,
places and things, and as they are given write them
on the blackboard, as, —

Mary, Hamilton, ball,

Tom, Toronto, lamp,

Henry, Oakville, chalk,

John, Lindsay, window.

2. Ask the class to make statements about each of
these, as, —

Mary sings. The ball rolls.

Tom runs. The lamp gives light.

Henry walked home. The chalk makes dust.

Hamilton is a city.

Toronto has many people.

Oakville is on Lake Ontario.

3. What are these (pointing to the words) we
have written on the blackboard ?

Ans. — Words.

What is the use of the word "Mary" in the first
statement ?

Ans. — It is used as the name of a person.

What is the use of the word "Tom," "Henry," etc.?

ENGLISH GRAMMAR.

103

4. In what are these words alike ?

Ans. — They are the names of persons.

What is the use of the word " ball" in the fourth
sentence ?

Ans. — It is used as the name of a thincj.

By similar questions lead pupils to state the
uses of the words, " lamp," " chalk," " Hamilton,"
" Toronto," etc.

NAMES

. A . ,

Names of persons. Names of jdaces.
Mary, Hamilton,

Tom, Toronto,

Henry, Oak vi lie,

Names of thinris.
ball,
chalk,
lamp.

4. In what are all these words alike ?
Ans. — They are words used as names.

Technical Terms.

The pupils are now told that words used as names

are called Nouns.

Definition.

After the pupils have been familiarized with the
use of the term through pointing out and naming the
Nouns in the sentences written, they are now asked
to frame a simple definition of a Noun, found'^d on
its prominent characteristic as presented. A Ncnn
is a word in a sentence used as a name.

Practical Exercises.

1. Write sentences on the blackboard and have
classes select all the Nouns.

2. Require pupils to name the Nouns in statements
of their own composition.

8. Require pupils to select and write out the
Nouns from sentences in the Reader.

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104

METHODS IN TEACHING.

The Verb

IntvDil uctli>n.

1. Ask class to make Heiitcnct's nsino- such sub-
jects as "tlie SUM," "Jolni," " the slate," etc.

2. Ah ^^^-^ - are given liave pupils analyse them
into subje^. ^nd predicate.

Develojwiev t.

1. Into what two parts may every sentence be
divided ?

2. Do the words " the sun " form a sentence ?
Ans. — No.

What leads you to think they do not ?
Ans. — They do not contain a predicate.

3. By using an additional word form a sentence
with them.

Ans. — The sun shines.

4. In this sentence what is stated about the sun ?
What is the word particularly used to do this ?

Ans.— *' Shines."

5. Make statements from the following by adding
words as above.

The cat ....
The dog ....
The boy ....
The large book .
The teacher . . .
Ans. — The cat jumps.
The dog barks.
The boy laughs.
The large book is on the floor.
The teacher stands at his desk

. . on the floor,
at his desk.

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ENGLISH CUAMMAR.

105

6. What words have bt'cii added ^.

Alls. — "Jumps," "Ijarks," "lau^dis," "is" and
" staiKlfs."

7. How <lid th(3 addition of thuHo words afi'cct tlie
original j^roups of words ?

Ans. — They made statements ol* them.

8. Then in wliat respect are the words, "jumps,"
"barks," "laughs," "is" and "stands" alike?

Ans. — They make statements when added to the
words which, of themselves, do not make statements.

Tcchnicdl Term.
Words, used as tliese, are called Verbs.

Definition.

The pupils are now called on to give a simple
definition of a Verb, as : A Verb is a word used in a
sentence to state something.

ExerciHes.

1. Tlie pupils are asked to name and underline
the Verbs in sentences on the blackboard.

2. Pupils give sentences on various subjects and
name the Verb in each case.

3. Pupils point out the Verbs in sentences in the
Reader.

The Adjective

Introduction. .

1. Briefly review the noun emphasizing the
distinction between the thing and its name as in a
former lesson.

2. Ask for examples of nouns.

106

METHODS IN TEACHING.

(

Dc/velopiiu'T) t.

Write on the blackboard senteiiceH Hiich as the
following:

1. Desks are in schools.

2. Books are on shelves.

3. Bees live in hives.

4. Children enjoy summer.

What desks are named in the first sentence ?

Ans. — No particular kind ; any kind.

What schools are named in first sentence ?

Ans. — Any schoo)s.

To what books and shelves will the names "books"
and "shelves" of second sentence apply ?

Ans. — To any books and shelves.

Similar questions will be put concerninjr " bees,"
" hives," '' children," and " summer," of sentences 3
and 4.

3. In what respect are the nouns "desk," "schools,"
"books," "shelves," "bees," "hives," "children" and
"summer" alike ?

Ans. — They are names that will apply to any
object or objects in the world of that name.

Single desks are in Hamilton schools.
Large books are on deep shelves.
Tame bees live in wooden hives.
Canadian children enjoy Indian summer.

4. To what does the word "desks" apply when we
say " single desks" ?

Ans. — To those desks only at which one pupil sits.
To what does the word "schools" apply when we
say "Hamilton schools?"

Ans. — To only those schools situated in Hamilton.

ENGLISH GRAMMAR.

107

Similar (iiu\stion8 are put concerning " books,"
"sl'^^lvoH," "bees," "hives," "children" and "sunuiier,"
as used in si^cond set of sentences.

5. The pupils an^ now led throut^h coniparinj^ the
nieanin<^ot' tlu; names "desks," "schools," etc., of 1st set,
with the meaning;- of the same names in the second
set, to see that the application of the nanrcs is
lessened or limited in second group.

6. Read the words used above to limit the
application of "desks," "schools," "books," "shelves,"
"bees," "hives," "children" and "summer."

Ans.— "Single," "Hamilton," "large," "deep,"
"tame," "wooden," "Canadian" and "Indian."

7. What then is the use here of the words "single,"
" Hamilton," "large," etc.?

Ans. — The words are used to limit the application
of nouns.

This answer is written on the blackboard.

8. In the sentence, " Many soldiers are killed in
battle every year," name the words that are used to
limit the application of a noun.

Ans. — " Many" and "every."

Suppose we say : " All soldiers are killed in battle
every year." How is the application of the noun
"soldiers" affected?

Ans. — It is enlarged or extended.

What word does this ?

Ans.— "All."

The same effect may be shown in the case of "every."

9. What is the use of the words "all" and "every?"
Ans. — These words are used to enlarge or extend

the application of the nouns "soldiers" and "year.''
This is now written on the blackboard.

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lOS

METHODS IN TEACHING.

10. Tlie teacher now explains to the chxss that
when the application of a noun is limited or extended
we say that its application is modified.

11. Read from these sentences every word used to
modify a noun.

Small troes sometimes grow lar^e apples.

Tall trees from little acorns grow.

Mary's mother was a clever woman.

Every pupil should do good work at all times.

Technical Term.

A word that modifies the application of a noun is

an Adjective.

Exercises.

1. Name all the Adjectives used in the sentences in
this lesson and name the nouns modified in each case.

2. The pupils are required to form sentences on
various subjects named by the teacher, using
Adjunctives.

3. The pupils point out tlie Adjectives in sen-
tences from the Reader, and name the nouns they
modify.

Note. — The folio wino- blackboard work will facili-
tate the generalization in above lesson, while at the
same time it sununarizes the pupils' conclusions at
each step.

1. Words used to limit
the application of a noun.
"Single," "Hamilton," "large,"

Noun I " deep," " tame," " wooden,"

Modifiers. 1 "Canadian," "Indian."

2. Words used to extend
the application of a noun.

^" All," "every."

Adjectives.

ENGLISH GRAMMAR.

109

The Adverb

Note. — To develop the conception of ;in adverb as
a word used to nK)dit'y a verb, adjective or otlier
adverb, will i'e([nire at least three lessons. The first
should show its function as niodifyint^ the appli-
cation of a verb; the second, its function as
nK)difyin<^ the application of an adjective; and tlie
third, its function as modifying the application of an
adverb. Only tlie first lesson will be outlined here.

Introdaction.
Ask class for sentences on given subjects, in
which adjectives will be used. Question them on the
use of these adjectives.

Development.

1. Write sentences on the blackboard as: —

The little girls sew neatly.
The young lady sings sweetly.
The postn^an comes often.
The sun shines brightly to-day.
The white snow falls silently.

2. Separate each of above into subject and
predicate.

Name all tlie adjectives used in these sentences.

3. What is the use of the adjective " little," in
sentence 1 ?

Ans. — It modifies the application of noun "girls."
What is the use of the adjectives " young" and
"white?"

4. Name the verb in first sentence.
What action is expressed by this verb ?

What are we told concerning this action of the
girls ?

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1 1

110

METHODS IN TEACHING.

Ans. — It is said that the action of sewing is done
neatly.

What word is here used to «how this ?

Ans.—" Neatly."

What is the use of the word " neatly ?"

Ans. — It is used to show how the action is
performed.

Suppose the sentence read " The little girls sew."
What might this mean concerning the sewing ?

Ans. — It might mean that they sew well, or
poorly, or anyway.

But in the sentence as written, what is the
application of the action sewing ?

Ans. — It applies to neat sewing.

What is it that effects this change in the appli-
cation of " sewing."

Ans. — The word " neatly."

What then is the use of this word " neatly ?"

Ans. — It modifies or changes the application of
the verb "sew."

5. Similar questions are asked concerning the use
of the words " sweetly," " often," " to-day " and
" silently," of succeeding sentences, leading pupils to
the conclusion that these words are used to modify
the application of the verbs in their respective
sentences.

6. In what respect are these words "neatly,"
"sweetly," "often," "to-day" and "silently," alike.

Ans. — They all modify the application of verbs.

Technical Teiin.

The pupils are now told that words used to
modify the application of verbs are called Adverbs.

ENGLISH GRAMMAR.

Ill

Exercises.

1. Other sentences are given orally or written on
the blackboard, and pupils are asked to name the
Adverbs and state their uses.

2. The pupils are given unfinished sentences and
are rec^uired to supply Adverbs.

3. Pupils are required to name Adverbs from
sentences in Reader and explain their function.

The Pronoun

Introduction.

Place sentences on the blackboard and call upon

the class to point out the nouns aad state their
function.

Developr)ient.

1. Ask a pupil of the class to perform an action
involving another pupil, e.g.,

Ask John to lend James his knife.
Now call upon a pupil to state what has been
done.

Ans. — John lent James a knife.
John, you state what you did.
Aus. — I lent him a knife.

2. Write these sentences on the blackboard :

1. John lent James a knife.

2. I lent him a knife.

What is the action expressed in sentence 1 ?
Ans. — Lending a knife.
Who performed the action ?
Ans. — John.

How did John state tnis action performed by
him ?

Ans. — I lent, etc.

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112 Ml^yrHODS IN TEACHING.

To whom (H(l ho refer when he .said I y
Ans. — To John.

What w ord luioht he hav(^ used instead of " I ? "
Ans. — The word Jolin.
What part of speecli is John ?
Ans. — It is a noun.

Then " I " is used instead of wliat part of speecli ?
8. Siniihirly treat the word "him" of second
sentence.

4. Ask James to state what was done.
Ans. — He lent me a knife.

Deal with the words " he " and " me " of this
sentence as with similar words above.

5. After these and other similar words are dealt
with and the pupils well drilled on their function,
the class will be asked to state in what particular
these words are alike. Each is used in a sentence to
take the place of a noun.

Technical Term.
The class is now told that each of these words is
called a Pronoun.

Definition.
The pupils are now asked to frame a simple
definition of a Pronoun based on the common
characteristic observed in the words studied.

Exerciseii!.

1. Sentences are given orally or are written on
i,\e blackboard, and pupils are asked to substitute
Pronouns where possible.

2. Skeleton sentences nre written and pupils are
required to fill out with Pronouns.

3. Pupils point out the Pronouns found in
sentences in Reader.

ENGLISH GRAMMAR.

113

this

on
Itute

are

The Phrase

Introduction.

Review through sentences on the blackboard the
functions of words and their si^eeclipartship.

Development.

1. Write such a sentence on the bhickboard as:

He sprang hastily from his grassy couch.

Question to bring out the function of " hastily "
and of " grassy."

What is the subject of this statement ?

What action is asserted of this subject ?

Ans. — The action of springing

What is the use of the word " hastily ? "

Ans. — It is used to show how the action was per-
formed.

(It limits the application of the word " sprang.")

What part of speech is the word " liastily ? "

Ans. — It is an adverb.

See if you can express the idea contained -in
"hastily" in another way. If pupils cannot the
teacher w

expr

tily

sprang
What expression

in haste, etc.

lave we used inst'^id of " has-

Ans.— " In haste."

What is the use of the words " in haste " as used

here ?

Ans. — They are used to show how the action
performed.

was

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114

METHODS IN TEACHING.

To what single word is this group of words " in
haste " equivalent ?

What part of speech is hastily ?

Then to what part of speech is this group of
words equivalent ?

Ans. — An adverb.

2. Deal similarly w4th the word " grassy " leading
the pupils to see that the words " of grass " do duty
for or are equivalent to the single word " grassy."

He sprang in haste from his couch of grass.

3. Now place on the blackboard such sentences as:

The house on yonder hill is sold.

The boy ran to his home.

My door opens to the child of want.

Question concerning the function of each of
underlined expressions, drawing from pupils that
they are respectively equivalent to a single part of
speech.

4. Ask the class to read the expressions,

" in haste."
• " of grass."

** on yonder hill."
" to his home."
" to the child."
"of want."

Let pupils test these as to whether they are
statements.

The fact that not one of these expressions is a
statement will be discovered and the reason given,
that none of these contain a subject and predicate.

5. Now lead the pupils to gather together the

'!*]

ENGLISH GRAMMAR.

115

a
)ii,

Ihe

facts learned, the points in wliich all these
expressions are alike.

These will be written on the blackboard as ob-
tained,

1. Each is a group of* words.

2. Each does not contain a subject and

predicate.

3. Each is equivalent to a single part of

speech.

Technical Tet'7)i.

The class is now informed that a group of words
not containing a subject and predicate and equivalent
to a single part of speech is called a Phrase.

Definition.

The pupils will now define a Phrase and this
definition will be written on the bhickboard and class
drilled on it.

Exercises.

1. Sentences involving Phrases will bo given and
pupils asked to name the:^T and give their functions.

2. Skeleton sentences given with blanks to be
filled in with Phrases.

3. Phrases in text of readers to be named and
functions given.

Note. — This should be followed by a lesson on
classification of Phrases on the basis of function.

The Clause

Introduction.

From sentences written on the blackboard review
word functions.

.if

; Till I

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116

METHODS IN TEACHING,

DcvelopTYient.

1. Teacher writes on the blackboard such a
sentence as,

A feeble man cannot carry a heavy load.

What is the subject ?

Wliat is the use of the word " feeble ? "

Ans. — It is used to show the kind of man.

What part of speech is feeble ?

Now exjjress the idea contained in " feeble " by
the use of several words as, A man wlio is feeble, etc.

What words are here used instead of the word
"feeble?"

If then this j^roup of words exactly expresses the
meaning of " feeble," to what part of i^.peech must it
be equivalent ?

It must be equivalent to an adjective.

2. Other examples are written on the blackboard
as, —

(1). The place where they lived knows them no
more.

(2). They trimmed their lamps as the sun went
down.

(3). The man who was sick is now well.

(4). He said that you told him.

(5). That he did it is not true.

What is the subject of the first sentence ?

What is the use of " whei^they lived ? " ; l,

Ans. — It is used to limit " place."

What part of s"^eech is " place ? "

Ans. — It is a noan.

To what part of speech then must " whcH they
lived " be equivalent ? ^

Ans. — To an adjective.

ENGLISH GRAMMAR.

117

8. The other examples will be similarly dealt
with, and the expressions under consideration written
on the blackboard as, —

" Who is feeble."

" Where they lived."

" As the sun went down. "

" Who was sick."

" Tliat you told him."

" That he did it."

4. By questions the class is led to see that each
of above collections of words contains both a subject
and predicate.

5. At the dictation of -the chxss the facts thus
learned will be written on the blackboard as,

1. Each is a group of words.

2. Each contains both a subject and a

predicate.

3. Each is equivalent to a single part of

speech.

Definition and examples will follow as in former

places.

The Preposition

Introduction.

Develop the notion of relation by pbicing a book
or other object in different positions relative to the
desk. Re(iuire the pupils to express these relations
between the book and the desk by means of
sentences.

Developvient.

Teacher writes such sentences on the blackboard
as the following :

1. The book lies on the desk.

2. The book is held under the desk.

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If
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118 METHODS IN TEACHING.

3. The box r(^sta on tlie table.

4. The boy lives in the city.

5. The girl in the school is wanted.

6. John is proficient in his studies.

7. The bo}'^ ran into the house.

8. The child ran to her.

1. Where does the book lie ? What word here
expresses the relation between the table and the
lying of the book ?

Ans. — The word " on." Read sentence 2.

Where is the book represented as being held ?
What word here expresses the relation between the
desk and the holding of the book ?

Ans. — The word " under."

Similar questions will be asked concerning the
relations expressed by " on," " in," " into " and " to," in
the other sentences.

2. Next, through questions, lead the class to see
that each relation word joins or attaches a noun or
its equivalent to some other word in the sentence.

8. Ask the pupils to state the facts thus far
learned about these words ; and as these are given
tabulate them on the blackboard thus,

' 1. Each joins a noun or its
equivalent to some other word in
the sentence.

2. Each shows the relation
between the notions expressed
.by these words.

Technical Term.

The class is now told that such relation words
are called Prepositions.

Relation words.

ENGLISH GRAMMAR.

119

Dcfinifion aiid Practical Krercm's.

The cbiHS should now be reijuired to frame a
(letinitioi) based upon the common characteristics
discovered in the Prepositions studied.

This definition will be written on the blackboard.
Practical exercises will follow as in other plans.

\'i

J!,

its
in

on
;ed

nds

The Conjunction

Introdttction.

Review the sentence. Lead the pupils to
understand the use of the terms " connecting " and
"joining" by reference to the cars of a train.

Development.

1. Write such .sentences on the blackboard as,

John came to school.
Mary came to school.

The pupils are asked to read them and finally to
express these two thoughts in a shorter way, as : —

John and Marv came to school.

2. Call the attention of the pupils to the way in
which this change has been brought about, viz., by
joining the nouns " John " and " Mary " by the word
"and."

3. Other examples of a similar nature t re given
and pupils are asked to combine the nouns as above.

4. The attention of the class is directed to the
function of the word " and."

5. Other examples of a similar nature are given
and pupils are asked to combine them by use of the
words " and," " or."

120

METHODS IN TEACHING.

6. The joining worfls used in these examples are
named and their connnon function in the sentence
stated l)y tlie pupils. This is written on the
blackboard.

The words " and " and " or " are used to join
words.

7. Sentences are now written on the blackboard,
as,

Willie was present in the morning'-.

James was absent.

John attended the exhibition in Toronto.

Henry did not attend.

He was too busy.

The pupils are asked to combine them.

Their attention is now drawn to the words by
wliich they have made the combinations and to the
fact that they have joined together statements.

8. After a number of other examples have been
treated as those above, the class will be led to state
in what these words are alike. They are used to
join statements.

Technical Term.

Pupils a (^ told that words used to join to<;ether
words or siatements are called Conjunctions.

Definition and exercises as in other plans will
follow.

Ppopep and Common Nouns

Introduction.

Review the noun, securing examples from the

pupils.

Development.

I. Let pupils give, in sentences, nouns as names

ler

ill

idividnal or Particular

Class Names.

Names.

boy,

Harry,

iron,

John,

man.

Hamilton,

city.

Mary,

map,

Europe.

5. In what respect are the words in first column
(as used in above sentences) alike ?
Ans. — 1. They are names.

2. They are the names of classes.

■ t»ir

ENGLISH GRAMMAR.

121

of thin<^s, places, persons and animals, sucli as boy,
Harry, iron, man, city, John, Hamilton, Mary, map,
salt, Europe, knil'e, Toronto, Canada, money, chalk.

2. Suppose I express the desire, that a boy shut
the door, who would perform the act ? In this wa}
lead pupils to see that the noun " boy " denotes any
boy.

8. How does the word " Harry " ditter from the
word " boy " in application ?

Ans. — Harry refers to a particular boy, while
" boy " refers to any boy.

What name do we use to designate a number of
things of tlie same sort placed together.

Ans. — A group or class.

4. Let pupils name all the nouns in sentences
above, used like "boy" to denote a class or group,
also those used like "John" to denote a particular
individual.

The teacher writes these in columns as they are
given by pupils as follows :

■|

■:'i '

122

METHODS IN TEACHING.

Technical Terms.

The teacher now tells the class that a noun used
as the name of a class of objects is called a Common
(class) Noun.

The pupils are led to generalize from second
column, as in 5 above. The teacher then gives
them the term " Proper Noun " as applicable to the
names in this column.

Definitions,

The pupils are now asked to frame a simple defini-
tion of a Common and of a Proper noun. These may
be written on the blackboard, and pupils drilled.

Exercises.

1. Ask pupils for examples in sentences of Com-
mon nouns ; of Proper nouns.

2. Let pupils classify the nouns found in
lessons in Reader.

^Transitive and Intransitive Verbs

Introduction.
Review the function of the Verb.

Develojymenf.

1. Write such sentences on blackboard as: —

The bov hit his brother.

John made a kite.

James sent a letter to his mother.

Mary mended her dress.

Bears eat berries.

*Tho autlior Is indcbtod to P;incipal MatMiiiiK. of Hamilton, for
HUgRestioiiK on this plan.

used
mon

3ond
;ives
» the

fini-
may

om-

for

ENGLISH GRAMMAR. 128

2. Name the verb in each sentence.

Name the subject of eacli of these verbs.

What is asserted of " V)oy " in first sentence ?

Name the action.

What would be the effect of closing this sentence
with the word " hit," as '* The boy hit "

Ans. — The sense would not be complete.

What then completes the sense of these words in
first sentence?

Ans, — The words " his brother."

Against what is the action of striking- directed in
fii'st sentence ?

(Who or what receives the action of striking?)

In what relation does " boy " stand to " striking?"

Ans. — " Boy " represents the doer of the action.

In what relation does "brother" stand to
" striking ? "

Ans. — " Brotlier" represents the one that receives
the action of striking (the one against whom the
action is directed).

8. Deal similarly with the verbs, subjects, and
objects in remaining sentences.

4. What have we learned concerning these verbs ?
The answers should be tabulated as follows : —

1. Each verb (as used here) is incouiph^te.

2. Each verb represents an action as pass-

ing over from the subject or doer to
some one or someiliin''' as receiver.

5. Now let pupils contrast the verb uses in such
sentences as : —

The man fell.
The wonwin faints.
The l)oy sings, etc.
with the verb uses in sentences above.

4
1 ■

'ui

124

METHODS IN TEACHING.

The pupils are led to see that the verbs here
do not represent actions as directed against any
person or thing.

Technical Terms.

The pupils are now informed that verbs of the
first class are called Transitive (action passing over),
and that verbs of second class are called Intransitive
(not transitive).

They should also be told that the noun or its
equivalent representing that against which the action
is directed is called the object (something in the way
of the action) of the verb.

Definitions and exercises as in other plans.

Classification of Adverbs

Introduction.

Through sentences on the blackboard review the
function of the adverb.

Developmient.

The teacher writes sentences on the blackboard,
as : —

i The book was placed there.

2. James ran forward.

3. The man lives here.

4. Tlie house stands yonder.

2. Name the verb in each of these sentences.

What is the use of the word "there" in first
sentence ?

Ans. — It is used to indicate where the book
nas placed.

To what word is it related ?

To what class of words does it belong ?

ENGLISH GRAMMAR.

125

the

irst
look

What is the use of "here," "forward," "yonder."
What part of speech is each ?
3. In what respect are all these adverbs alike ?
Ans. — They all indicate place.

Technical Term.
The teacher informs the class that such adverbs
are called adverbs oi 'place.

Development.

1. Teacher writes such sentences on the black-
board as: —

1. The boy returned then.

2. He lived there formerly.

3. She seldom visits them.

4. They always use it.

5. They often play.

2. B}:^ means of questions pupils will be led to
name the actions or states expressed by the verbs,
also to o'ive the uses of the adverbs "then,"
"formerly," "seldom," ''always" and "often."

3. In what respect are these adverbs alike ?
Ans. — They all express time.

Technical term is now ^iven as in case of adverbs
of place.

Third and fourth development : —

Deal similarly with adverbs of .nanner and of
degree.

Definition of each class and exercises as in other
plans.

^Relative Pronoun

Note. — The plan presupposes a knowledge on the
part of the pupils of the parts of speech with their

I .(.:

ili..:

*The author is indebted to S. A. Morgan, B.A., B. Paod., of the
Hamilton [Collegiate Institute, for suggestions in this plan.

! i

126

METHODS IN TEACHING.

phrase and clause ecjuivalents, also of the personal
demonstrative and interro<(ative pronouns.

Introduction.

Short review of the pronoun, conjunction and
adjective functions.

Developrnent.

1. Teacher writes on the blackboard such a
sentence as follows : —

Honest men are trusted.

What is the use of the word " honest ? "

2. Men who are honest are trusted.
Wiiat now performs this function ?

How does it differ from the former adjective ?
Ans. — It is a clause, while the other is a single
word.

3. Name tlie subject and predicate of this clause.
What word may be substituted for this suV)ject ?
Ans. — The word " men."

What then is the grammatical value of ** who ? "
Ans. — It is a pronoun standinjr for " men."

4. Is this pronoun personal ? Why not ?
Is it demonstrative ? Why not ?

Is it interrogative ? Why not ?

5. What is the value of the clause in which the
pronoun " who " appears ?

To what does this clause relate ?
Ans. — It relates to the noun " men."
By what is it related ?

Ans. — It is related to the noun " men " by the
pronoun " who."

For what does this pronoun stand ?

ENGLLSH GRAMMAR.

127

Ans. — For the noun " men " to which it relates
the adjective clause.

6. In the following examples pick out similar
pronouns, indicating the noun to which each refers,
also the clause related to it by this noun.

The boy who was sick is now well.
The knife that was lost is now found.
The book which you gave me is at home.
This is the house tliat Jack built.

7. In what particulars do you find these words
to agree ?

Ans. — 1. They are all pronouns.

2. They each refer to a noun in another

clause.

3. Each relates to its noun, an adjective

clause.

:1:

7 1

:'i,

Technical Term.

Teacher now informs the pupils that such words
are called Relative Pronouns, and that the noun to
which it refers is called its antecedent.

the

Dsfinition.

The pupils are now required to combine tliese
facts into a connected definition.

Exercises.

1. Sentences are given and pupils are required to
name Relative Pronouns and antecedents.

2. Pupils will change adjectives or adjective
phrases into clauses introduced by Relatives.

3. Pupils will name the Relatives and their ante-
cedents found in sentences in the Reader.

I V,i

128

METHODS IN TEACHING.

Number in Nouns

Introduction.
Briefly review the Noun.

Development

1. Let several pupils give statements about
objects and write on the blackboard such as are

useful.

1. The window is easily broken.

2. Books are on the desks.

3. Pencils lie on the table.

4. A ruler is useful for measuring.

5. A boy enjoys football.

6. Girls play the piano.

2. Name tlie nouns used in these statements.
Ans.— " Books," " desks," " pencils," "table," "ruler,"

etc.

3. How many objects are referred to by the word
" window ? "

Ans. — One object.

To how many objects does the word "books" refer ?

Ans. — To more than one.

Name all those nouns in above sentences used to
indicate one object.

Name all those nouns meaning more than one
thing.

The teacher writes these in two columns as

follows :

One thing. More tJian one thing.
window, pencils,

table, etc. girls, etc.

ENGLISH GRAMMAR.

129

4. Suppose we wish to speak of more than one
window, what word should we use ?

Ans. — " Windows."

Deal similarly with the other nouns in the
columns, having pupils use the nouns in each case in
a sentence. The opposite columns are now filled out,
each noun representing one thing having in opposite
column its other form representing more than one.

5. Compare the forms of the nouns in first column
with those in second column. The slight difference
in form will be noted by the class. Why are these
forms different ?

Ans. — To denote one or more than one of the
things for which the noun stands.

■j 1

1 ,:•

^il

refer ?
id to

one

Is as

Technical Term.

The pupils are now told that this change in the
form of the noun to denote one or more than one
object is called miinher.

Definition.

The pupils will be required to frame a simple
definition of number which will be written on the
blackboard and class drilled on it.

Singular and Plural

Introduction.

Review the lesson on Number.

Call upon class to give names of objects nidicating
one tiling, and names indicating more than one thing.

In each case be careful to have the pupil use the
name in a sentence.

< I

130

METHODS IN TEACHING.

Development.

1. Teacher writes these names in cohimns as they

are given, the pupils dictating the column in which

they are to be put.

Plural.
Singular. Nouns denoting more than one

Norms denoting one thing, thing.

book, books,

boy, boys,

crirl.

iris.

men,

squirrels,

mice,

desks,

pencils.

in'

man,

squirrel,

mouse,

desk,

pencil,

2. In what respect are the words in first column
alike ?

Ans. — They are names denoting one thing.
In what respect are the words in second column
alike ?

Technical Terms,

3. The teacher now informs the class that the
form of a noun used to denote one thino^ is called the
singular number, and that the form used to denote
more than one thing is called the plural number.

Definitions.

The pupils will be required to frame simple
definitions of smgular number and plural number.
These will be written on the blackboard and pupils
drilled on them.

^ '

ENGLISH GRAMMAR.

131

i they
which

han one

Exercises.

1. Pupils will form stateineiits in which nouns in
the siuixular number are used.

2. Pupils will ^ve the plurals of these nouns and
use them in statements.

3. Sentences are given with blanks to l)e tilled in
with singular and plural forms.

4. Pupils will name the nouns in Reader and till
in what number each is, also give the corresponding
singular or plural form.

'i'i

column

lat the
led the
[denote

[simple
imber.
1 pupils

^Gender

Introduction.

The teacher will write on the board,

" The boy ate an apple."
" The girl ate an apple."

What is the only difference you see in these
sentences ?

In the first the word " boy " is used, in the second
the word " girl."

How many kinds of persons are represented by the
words " boy '' and " girl ? "

"One."

If pupils should say " two " write such sentences
on the blackboard as : A dog ate a piece of meat, a
cat ate a piece of meat, and institute a comparison
with the sentences first given.

Why then have we used two different words in
speaking of two persons or things of the same kind ?

*The author is indebted to Mi„ E. T. Young, Vice-Principal of
Central School, Hamilton, for this plan.

■■fl

132

METHODS IN TEACHING.

Because there is a difference between the objects
themselves.

Have chiss write two sentences making statements
about another pair of objects which differ just as boy
and girl differ.

" The man walked a mile."

" The woman rested half an hour," etc.

At this point it will be necessary for the teacher
to explain that this difference between the objects is
a difference of sex.

Of what sex is a boy ?

If answer is not forthcoming teacher must tell.

Question similarly for the term " female sex."

Development

Write on the board the following sentences :

1. The man ran faster than the woman.

2. The sister lost her brother.

3. The girl gave the boy an apple.

Class selects from these sentences the pairs of
nouns which denote the male and the female of each
kind of object referred to.

man,

boy,

brother,

woman,

girl,

sister.

At this point the teacher should drill thoroughly
on sex, male, female, using for that purpose the
sentences just written on the board.

In the sentences on the board, how did we dis-
tinguish between the male and the female ?

By the use of different nouns, one for the male
and another for the female.

! !

^yaBJJiWJ»JiHri3*.^

ENGLISH GRAMMAR.

133

ughly

le the

le dis-
inale

Why was it necessary to use the dift'erent nouns
in the first sentence ?

To sliow that we had in mind a difference of sex.

Teclinical Term and Definition.

The teacher will here state that this chaufre in
nouns is called gender, and immediately ask for a
written definition of gender from each member of the
class.

Definition — Gender is a change in nouns to denote
whether they are the names of objects of the male or
of the female sex.

Teacher will state that the noun denoting an
object of the male sex is said to be of the niascidine
gender and that denoting an object of the female sex
of the feminine gender.

Exercises.

1. The teacher will add such sentences as the
following to those already written on the black-
board : —

The lion killed the goat.

The Count killed the lioness.

The man-servant chased the she-goat.

The Countess rewarded the maid-servant.
Class will write in a column the nouns of the
masculine gender ; also those of the feminine gender
in a column beside it, each feminine opposite its
corresponding masculine.

2. Masculine and feminine nouns are given and
pupils are asked to give the corresponding gender
noun.

3. Gender nouns to be selected from the Reader
and classified as masculine and feminine.

■;•'+

134

METHODS IN TEACHING.

Note. — If tlu^ teacher desires to I'etain tlie term
neuter j^endei', the first step in his phm should be to
classify objects into sex objects and sexless objects
and apply the term neuter gender to nouns denoting
sexless objects.

Case

Note. — Case may be defined either as form or
relation. The latter is chosen for this plan. When
the former conception is preferred, it will be found
more convenient to teach it from the pronoun in
which three case forms occur. Application may then
be made to the noun.

Introduction.

Review the function of noun and of pronoun.

DevelopTYient.

1. Teacher writes such sentences on the black-
board as the following :

1. John loves his mother.

2. John's mother loves him.

3. The mother loves John.

4. The mother's boy loves her.

5. He loves her.

6. She loves him.

2. Name the action asserted in each sentence.
What is the action asserted in first sentence ?
Ans. — Loves.

What is the relation of John to the action of
loving ?

Ans. — John represents the doer or subject of the
action.

In what relation is " mother " of the second
sentence to the action of loving ?

ENGLISH GRAMMAR.

135

t •

■^"'1

Ans. — "Mother" represents the subject or doer of
the action.

Name those words in above sentences that repre-
sent tlie doer of the action.

Ans.— "John," "Mother," "boy," "he," "slie."

To what classes of words do tliese belong ?

Ans. — "John," "mother" and "boy" are nouns ;
" lie " and " she " are pronouns.

3. The pupils are now told that nouns and
pronouns used to represent the subject of an action
are said to be in the subject ive relation.

4. In what relation does " mother " of first sen-
tence stand to the action of loving ?

Ans. — "Mother" represents the one receiving the
action.

It represents the one against whom the action
is directed.

Name each word in above sentences, representing
that against which the action is directed.

Ans.— "Him," "John," "her," "her," "him."

5. Teacher explains that the thing or person
against which the action is directed is called the
object of the action, and that th« noun or pronoun
representing this person or thing is called the object
of the action word or verb.

In what relation is the noun or pronoun where it
stands as the subject of the verb ?

Ans. — It stands in the subjective relation. Then
what would be an appropriate name by which to
designate the relation of a noun or pronoun used as
tlie object of the verb ?

Ans. — The objective relation.

• '.

.. rtM

136

METHODS IN TEACHING.

6. In the sentence John's dog can swim. With
what word is " John's " connected in sense ?

Ans. — With the word " dog."

In what relation does John stand to dog ?

Ans. — John is the owner of the dog.

7. Teacher now explains that this relation is one
of possession and that the noun " John's " is said to
be in the 2>osHessive relation to the noun " dog."

8. Name all the words in above sentences used in
the possessive relation.

Ans.—" John's," " mother's," " his."

9. The following summary on the blackboard will
aid the pupils : —

Subjective relation. Objective relation. Possessive relation.
John. John, John's,

mother, mother, mother's,

boy, his.

he, him,

she, her,

10. Examples will follow and pupils will be asked
U' state the relations of the nouns and pronouns as
above to the other words with which they are
connected in sense.

Technical Term.

The teacher now explains that this relation of
nouns and pronouns is called case.

Definition.
The pupils will now frame a definition of case
and this will be written on the blackboard.

I i!

ENGLISH GRAMMAR.

137

With

IS one
laid to

laed in

rd will

ition .

asked
uns as

lion

1' case

Tense

Introduction.

Through conversation with the class brinfij out the
three divisions of time and the fact that action must
be either in the present, the past or the future.

Development.

1. Ask a pupil to come forward and perform some
action as the taking of a book. As the pupil
performs the action have him state what he is doing.

I take the book.

This is written on the blackboard.

2. What action is asserted here ?
Ans. — The action of taking.

At what time is this action performed ?

Ans. — It is being performed at the present time.

Use other illustrations of similar nature, drawing
from the class in each case that the verb expresses
action at present time.

3. Now suppose that you wish to state that John
performed this action yesterday or an hour ago what
would you say ? ^

Ans. — John took the book.
John will now tell us what he did.
I took the book.

What is the action here expressed ?
When is this action represented as taking place ?
Ans. — It is represented as taking place in past
time.

4. Now compare the statements. What form of
verb did John use in first statement ? In second

■ 1

i '■<

ill

138

METHODS IN TEACHING.

statement ? Are these alike ? Then why did he
chaut^e the form of the verb ?

Ans. — To denote a change in tlie time of the
action.

Other examples of verbs in past time forms are
given and the class familiarized with the necessity
for a change in form to denote a change in the time
of the action.

5. Now, suppose you wish to state that the action
of taking will take place to-morrow or next week,
how will you express it, John ?

Ans. — I shall take the book.

What verb form have you used here ?

Ans.—" Shall take."

Is this form the same as you have used in either
of the two cases above ?

Why have you used a form different from eitiier
of those above ?

Ans, — That the action may be represented as
being performed at a future time.

Other examples are given as abov^e.

6. These statements are now written side by side
as, — I take the book. I took the book. I shall take
the book. How many different forms of the verb
liave been used in these sentences ? Wliy has the
form of the verb been chano:ed ?

Ans. — To denote a change in the time of the

action.

Technical Tervi.

The class is now told that this change in the form
of the verb to denote a difference in the time of an
action is called fcntie.

Definition and practical exercises will follow.

ENGLISH GEAMMAR.

139

"i\

■ '.M

V side
take
verb

8 the

Comparison of Adjectives

Introduction.
Review adjectives of quality.

Bevelojpnient.

1. Have pupils compare sticks of different lengths,
objects of different weights, pupils of different
heights, etc. etc.

What can you say of this stick as to length ?

Ans. — It is a short stick.

What can you say of this other one as to its
length ?

Ans. — It is a short stick.

What (juality represented by the adjective
" short " belongs to both of the sticks ?

Ans. — The quality of shortness.

How do these sticks compare as to sliortness ?

Ans. — This stick is shorter than that one.

Which of these sticks possess in a greater degree
the quality of shortness ?

2. The teacher displays a stick still shorter and
liolds it beside the others already examined.

Now what can be said of this stick as to its
length, in comparison with the others ?

Ans. — This stick is the shortest of the three.

3. Similarly secure from the pupils such sentences
as, —

It is a long stick.
This is a louixer stick.
That is the longest stick.
This is a heav}^ weight.
That is heavier.

■;il"

■ 1 ■

[•if-

••tl

' ::'!

^41-

140

METHODS IN TEACHING.

A tall boy.
A taller boy.
The tallest boy.

Name the adjectives used in all the sentences
above that are used to express the quality of the
object.

The teacher will write these as fjiven, in three
columns as follows : —

short shorter shortest

long longer longest

heavy heavier heaviest.

5. In what respect are all these words alike ?
Ans. — Each is used to rr ^resent some quality of

the object represented by the noun.

Why do we use the adjectives " shorter " " longer "
" heavier " and " taller," instead of the adjectives
"short," " long," " heavy" and " tall," in the sentences
above ?

Because we wish to represent the object in each
case as possessing the quality in a greater degree.

6. Similar questions will be put respecting the
forms " shortest," " longest," " heaviest" and " tallest."

7. How then have we represented the diflference
in the degree of the quality possessed by the objects ?

Ans. — By a change in the form of the adjective.

Technical Terr)i.

Teacher ex^^iins that the change in the form of
an adjective to denote a difference in the degree of
the quality is called comparison, and that each form
is called a degree in the coinjmrisov. The names of
these steps or degrees are given and written over
their respective colunnis.

ENGLISH GRAMMAR.

141

I ...

in of

ie of

form

}S of

)ver

Definition and exercises will follow as in other
plans.

Note. — This lesson should be followed by one on
the uses of the degree forms, and the method? of
indicating the Comparative and Superlative degrees.

Mood

Introduction.

Briefly review definitions of statement and verb,

also inflections of the verb for tense, person and

number.

Development.

1. The teacher writ ss on the blackboard.

1. John studies his lessons.

2. John, study your lessons.

3. If John study diligently he will recover

some lost time.

L. Name the verb in each of these sentences.

What is the action expressed in each case ?

Who is represented as the doer of the action in
each sentence ?

What would you call this group of words spoken
to John ?

Ans. — It is a command.

How then is the assertion to be viewed in the
2nd sentence ?

Ans. — It is to be viewed as a command.

3. By comparison of sentence one and three, lead
tile class to see that in sentence one the assertion is
viewed as the declaration of a fact, while in sentence
three it i:^ viewed as doubtful (a- conditional.

4. Other examples are given and pupils asked to
state the manner of viewing the assertion.

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METHODS IN TEACHING.

5. How is this difference in the manner of
viewing the assertion indicated ?

Ans. — By a variation in the form of a verb.

Tecltniccd Temi.

The teacher informs tlie class that tliis variation
in the verb to sliow a difference in the maniier of
viewing the assertion is called mood

Definition and exercises as in other plans.

Note. — This lesson will be followed by one on
eacli of the moods.

Infinitive

Introduction.

Write on the blackboard the sentences : —

1. John runs home.

2. The girls walk to school.

3. If he runs he will be warm.

The pupils are called on to read the sentences, to
name the actions and finally to note the various
limitations of number, time, etc., placed upon these
actions.

The class is then in position to see that these are
limited ' forms. F"om this the word finite may be
easily developed by referring to the word " finis," at
the end of a book. " Finis " means end or limit.

Development.

1. Place on blackboard the sentences :

(a). To run makes John warm.

(b). Girls like to walk.

(c). Walking is good exercise.

2. What are the verbs in these
"Makes," "like." "is."

s ntences ?

ENGLISH GRAMMAR.

143

3. Name other action words in these sentences.
"To run ;" "to walk ;" "walking."

4. Lead pupils to see that these latter words have
no limitations placed upon them.

Generalization.

There are certain forms (verb) which express the
action in a general way, with no limitation as to
number, person, time or mood.

Technical Term.

Each of these forms is called an Intinitive,
(opposed to finite).

Definition.

Derive from class a simple definition of an
infinitive. (An infinitive is a verb form not limited
as to number, person, etc.).

Practical Exercises.

1. Place sentences on blackboard containing finite
and intinitive forms and have pupils name and
distinguish them.

2. Have pupils originate examples in statement
forms.

The Participle
Introduction.

Review briefly the characteristic functions of (a)
Adjective, (b) Verb. This may be done through
such examples as : —

(1) The Jiigh fence fell.

(2) The man was innocent.

(*1) All animals defend their young.
(4) They mounted him on a white horse.
Note. — It is advisable, at first, to use in (b)
Transitive Verbs.

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144

METHODS IN TEACHING.

Development.

(1) We saw the man leading the child.

(2) He kept us waiting for a long time.

(3) Tired by his long walk, he lay down.

(4) The man guarding the tower was killed.

1. Read the first sentence. What is its subject ?
Its predicate ? What is the relation of " leading ? "

Ans. — It is related to " man."
What is its use in relation to " man ? "
Ans. — " Leading " describes " man,"
What part of speech is " man ? "
Then " leading " performs the function of what
part of speech ?

Ans. — That of an adjective.

2. What does " leading " express ?
Ans. — Action.

Against whom is this action directed ?

Ans. — Against the child.

Now write on blackboard the following sentence :

The man is leading the child.

In this sentence what is the verb ?

What is the relation of the word " child ? "

Ans. — The word " child " is the object of the
verb " is leading."

Is there any difference in the relation of " child "
in this sentence and " child " in (1) above ^

Ans. — There is not.

Then what is the relation of "child" in (1) above ?

Ans. — " Child " is the object of " leading."

In this sentence the word " leading " is tlien
used like what part of speech ?

ser
th(
an
th(

pla

»>

the
Ihild "

)ove

tlien

ENGLISH GRAMMAR.

145

Ans. — It is used like a verb.

In what respect ?

Ans. — In that it takes an object.

3. Now what have we learned about the uses of
the word " leading ? "

Ans. — It is used like an adjective to modify the
noun " man," and it is used like a verb in that it
takes the noun " child " as an object.

4. In a similar manner deal with

waiting,

" tired " and " guarding " in the other sentences.

Generalization.

In what respects are the words " leading,"
•' waiting," " tired " and " guarding " in above sen-
tences alike '.

Ans.: —

1. They are used as adjectives to modify nouns

or their equivalents.

2. They are used like verbs in that they take

objects or are governed by adverbial
modifiers.
These facts should be written on the blackboard.

Technical Term.

Pupils are now told that words which, in the
sentence, perform the function of adjectives while at
the same time they partake of the nature of the verb
are called Participles, (participating in the nature of
the adjective and of the verb).

Definition and practical exercises as in other
plans.

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METHODS IN TEACHING.

CHAPTER V.

READING.

First comes good reading. ... The value of good reading
aloud has never been recognized. Good reading is the first
training of the beginner, the last crowning excellence and
consummate perfection of the finished master of all perfected
culture. All skill of heart, of head, of lips, is summed up
in the charmed sound of noble utterance. — Thring.

At the outHot it is important to distinguish
between reading as a mode of attention, — silent
reading, — and reading as a mode of expression
usually spoken of as reading aloud.

The former is similar to listening to speech, the
latter involves this and adds to it, telling what is
heard.

So far as the first, that is silent reading, goes,
there is no difference between it and reading aloud.
The first is simply thought-getting, the second is
thought-getting plus thought-giving. Reading deals
directly with thought ; there is no such thing as
reading words. Hence it would be well that a
certain connnon exercise called reading, which
is mere word-pronouncing, should be given a
different name. It may be granted that the
utterance of words arranged in sentences sometimes
conveys to the pronouncer a hazy idea of the
thoughts by the sub-conscious hearing of his own
monotones and even that some people when reading
to themselves seem to find it necessary to whisper or

READING.

147

goes,

laloud.

111(1 is

deals

[ig as

lat a

^hich

|en a

the

Itimes

the

own

iding

ler ov

vocalize tlie words ; tliese facts Hhislrfitc tlx' tenacity
of liabit an<l the coiiscc^uciit iiiipoitanee of starting in
the right way.

Tlie liabit of saying words arranged in sentences
dissociated from thought, wlietlier reading so calU'd,
or repeating definitions, is one of the most pernicious
that a pupil can form. Let no exercise be caUed
reading, not even in the first lesson of the Primer
that does not depend on attention to tlie thought
symbolized by the words of the sentence. It is of
much importance that, from the first, both teacher
and taught should clearly distinguish between
Readimj and Pronowncimj Words.

Those who have perse veringly tried to teach
reading by imitation and rule admit that the results
are transitory and (Th^appointing. Listen to children
engrossed with their games. Their pronunciation
and composition may be very defective, but their
inflections and emphases are well-nigh perfect.
Nature thus teaches that the direct path to correct
expression is by attention to the thouglit. Col.
Parker maintains that teaching reading consists
entirely in the presentation on the part of the teacher
of the conditions for the functioning of words.
There is no doubt that attention to thouo-ht must be
the basis of an}^ rational method of teaching reading

Several methods of teaching reading to beginners
have been devised and practised but we have not yet
reached a concensus as to which is the best. The
reason is that the personality of the teacher counts
for so much. Sympathy, interest, intelligence, dili-
gence, earnestness, as well as confidence in the method
used, each and all, count as factors in producing the

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148

METHODS IN TEACHING.

;

n^Hult. Till! syiupatliotic, <lili^(!iit tciacher of youu^
children using an ini'iuior method will always sur])ass
the spiritless teacher using tlic superior one.

Clearly, cliildi'cn inight learn to read as they
learned to hear and speak, not by pi'aetising the
analysis of words and the synthesis of their sounds
but b^'' efforts upon words as wholes and combina-
tions of words. They learn a few words, slowly at
first, by oft-repeated efforts, then short sent(!nces, and
later, words and sentences rapidly by unconscious
inductions and generalizations. Such efforts, at
first, and mainly throughout, are due to the impulse
of thought and the desire to communicate thought.
This is essentially true notwithstanding that so much
of the chattering of young children is to gratify the
pleasure of exercising their newly found faculty of
speech.

Words, spoken or written, are symbols capable of
arousing the appropriate mental activities whether
the stimulus acts through the ear or through the eye.
It is an open question whether the learning of a
wor<l requires a greater number of aural or visual
stimuli. In addition to the difficulties arising from
the irregularities of English spelling, there are
obvious physical reasons why learning to read and
to express thought by writing takes more time and
labor than to know spoken words and to speak.
Were it not for these difficulties a deaf-mute child of
five or six years of age might acquire the knowledge
and use of as large a vocabulary as that possessed
by a normal child of the same age.

In a period of tw^o or three years most children
learn to speak their thoughts by the hear-and-say

READING.

149

ledge

messed

ildren
d-say

method, and in a like or somewhat l)riefer time tlioy
might, on attaining school-ages learn to read hy the
look-and-say method.

It is not proposed here to describe in detail all
the different methods of teaching reading to
beginners. It is enough to say that in the Word
method the beginner starts with the word as a
whole; in the Sentence method with the sentence; in
the Alphabetic method he learns the names of the
letters ; then he begins to spell by letter-names and
pronounce words, e.g., " double-you-a-jee, wag ; " in
the phonetic method he learns a phone for a different
character for each different sound in the language,
and spells the phones to suggest the word (in W. L.
Robinson's phonetic alphabet there are sixty-five and
in Sir Isaac Pitman's thirty-six characters) ; in the
phonic method he learns the sounds of the unaltered
letters of the English alphabet and their combina-
tions and synthesizes the sounds to make the word.

The special advantage of the Word method is that
the start is easy and can be made interesting ; its
disadvantage is that the learner takes a long time to
reach the inductions which enable him to recognize
new words. The advantage of the Sentence method
is that the reading is intelligent ; its disadvantage is
that of the Word method in an increased degree.
The advantage of the Alphabetic method is that it
lays the lightest tax of any method on the energy
and ingenuity of the teacher and is therefore suited
to the lazy or unresourceful ; it has tlie dis-
advantage of the former methods an<l is almost
invariably — although not necessarily — followed by
monotonous, thoughtless reading. The advantage of

150

METHODS IN TEACHING.

i V

the Phonic and Phonetic methods is thcat they make
the recognition of new words easy and rapid ; their
limitations arise from tlie incompleteness and
rediin lancy of the alphabet and the irregularities
of English orthography.

By each and all of these methods the learner
acquires the ability to recognize new words by
similar analytic-synthetic processes. By the Word
and Sentence methods, and to some extent by the
Alphabetic method the child attempting to pronounce
new words combines elements which lie has learned
as the result of many unconscious analyses. The
child taught for example by the Alphabetic method
says " double-you -a-ess, tvas" '' double-you-a- jee,
tvag," etc., etc., and learns by-and-by the adjustment
of his vocal organs necessary to utter the first sound
in the new word ivigicavi by its association with the
utterance " double-you," and later, by its association
with the visual stimulus. The greater the similarity
between the name of a letter and its sound the fewer
repetitions are required to establish association
between them.

A fair measure of the efficiency of a method of
teaching primary reading, i.e., tlie mechanical-mental
stage, is the time and effort required to take a
beginner from the start until he can readily discover
a thought within the range of his knowledge or
experie?ice written or printed in words that are
nearly or quite regular in their spelling, some of the
forms of which are new to him. For the test let a
sentence in large ])rint be selected from a book or
let one be improvised and written on the bhickboard.
Take for example : — " Nate Gar-land is coming from

READING.

151

Fre-niont to vis-it his cous-in Carl Brisc. Carl says
that Nate will teach us how the boys in Fre-inont
play pris-on-er's base." An average pupil, six years
of age, receiving three ten-minute lessons a day
ivlth appropriate seat (vork, can be taught in from
sixty to ninety school-days to read so that he will be
able after silently studying an exercise like the
above for from two to five minutes, to turn
his back to the blackl)oard and tell what the
sentences say, provided that the names are familiar
or that his memory can retain them. This week
(in October) to a class of little children in a rural
school, who took their first lessons in April (pre-
ceding) and hence had been at school less than
ninety days, the following test in word-recognition
was given. Four names — Bertha Carter, Farhhill,
London, No-vein-her, were written in a column on
the blackboard and the class directed to make up a
story using these words. In less than two minutes
one little fellow stepped up to the examiner and in
tones so low as not to be heard by his class-mates
said — "Bertha Carter lives in Parkhill; she is going to
London to visit somebody in November." The only
word of whe four that they had previously seen, so
the teacher averred, was London.

Two hundred times a year for over twenty years
the writer has had the opportunity of observing the
methods of teaching reading practised by many
different teachers, ami of testing the results of these
methods. Me proposes here U) discuss and describe
the nu^thod which has [)r()du(*ed the best results he
has seen. 11' it lias to have a iianu^ it may be caljeil
the Inductive-Phonic method. While agreeing with

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111

152

METHODS IN TEACHING.

Dr. Stanley Hall tliat there is "no one and only
orthodox way of teaching reading, the greatest and
hardest of all the arts in which ear, mouth, eye and
hand must each in turn train the others to automatic
perfection," yet he contends that every successful
teacher of the subject m;,st have some way whose
steps are related and whose processes are suited to
the child-mind.

The aim of the instructor of beginners in reading
should be the natural, oral expression of thought
apprehended l:>y the child from his (the child's) own
silent reading of the sentence. The process from the
first and throughout should enlist the learner's
interest and can easily be made to do so.

Children at the proper stage become as nmch
inteiested in the discovery of words, or of pronounce-
able combinations of letters that are not words, by
the synthesis of their phonic elements, as they can
be in any other ex(;rcise connected with reading by
any method. The interest of the very beginners
can be most easily' eidistisd in real words, such as
cat, dog, cdiidfj, doll, etc. This is one reason for
starting by the Word method. Another reason for
so starting is that by^ a judiciously selected list of
words the teacher can present the alphabet to the
young learners in such a way that without telling
them the sound of a single letter they can by their
own induction, directed by the t(!achei', discovei* the
sound of each and every one of them by the process
to be illustrated pirsently, an«l hence almost from
the first assist in fui'thering their own progress.

Flow shall the first word be taui^ht ^ This
(question raises another — what shall the first word

tl
tl

I 4

ers

for

()!•
of
he

'ir
Hie

'HS
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READING.

153

be? Those who liave started with cat, rnf and hat,
each under a picture, can corroborate the criticism
that these words too closely resendjle each other
to be suitable for a first lesson by the ./ord method.
A graver evil is the presence and position of the
pictures. They are not needed to give the child
a concept of the things for which the words stand
and their presence begets a tendency to look outside
of the word rather than at the form of the word
itself for suggestion as to what the word is. Such
pictures would obviously be helpful to deaf-mutes
and to foreigners wlio are learning at once the form
and signification of words. They are of service to
other children if used, as will be shown later in
connection with the " Key-list."

Almost any familiar word will «lo to start with.*
Candy is as suitable as any other. Write it on the
blackboard, preferably in vertical script, with letters
separated. Tell the child that the woi-d is candy.
Do not waste time asking the child such (juestions a^
" What would you like to find in your stocking at
Christmas," in the liope that in the list he niay
mention candy. More than half the time of niany
a reading lesson has been lost in a worse than useless
circundocutory "development" of words. Writi^
the word again, write it smaller, write it larger,
write it largei* still, writ«^ it very large, write it very
small. The learner will observe you closely an<l
will say candy every time it is written. Writer
several other words, — the learner will tell \'<>n which

*Kxpericiico proves the iiuwiHdoni of (H)ntliiiiiK the optMiiiiK h'ssons to
words of not more tliaii tliioo hitters. The more HtrikiiiK lln' rontmsl in
the form of words the more easily bcKinnors loiini tlieiu by Aw Word
niothod.

154

METHODS IN TEACHING.

are candy and which are not candy. Have tlie
child take the crayon and ^nide liis hand in writing
the word. Tliis is not to teach writing, but to
train liini in observing and comparing word forms.
If tlie word lias been written with the letters
separate have him take the pointer and show you
what letter to write first, then next, and so on. To
take to his seat give him an envelope or a little box
with a score or more slips or tablets each bearing
a word — underlined that he may know the bottom
from the top — several of which have the word candy
written on them. Direct him to pick out all the
slips that *' say " candy and place them in a row,
then to find any others that seem to be alike and to
lay such in rows by themselves.

At his second lesson review nt)}dy and similarly
teach another word, waggon, for example. Have
him point out a letter in iraggon that h^ does
not see in candy, and a letter that seems the same
in both words ; neither name nor sound of the letter
is mentioned, attention is called to form only. Give
him seat- work as before.

At the third lesson review the two words taught
and teach another, for example, cat. With cat and
candy in favorable position for comparison give him
practice in pointing out similarities and differences
in form. Continue seat-work on the lines proposed
above. Don't distract attention by telling stories
about cats, waggons, etc. A serious and common
fault is di\'erting children's attention from the real
])oint of the lesson not only l)y lomidabout "develop-
ment " of words already referred to, but also !)y
anecdotes that happen to have a sort of verbal

READING.

155

ion
•a

)al

relevancy to the lesson. These stories, etc., intended
to direct attention to the lesson, but generally
divertin<ij it, have value in connection with the
language lessons, but are out of place and worse
than a waste of time when one is teaching word
recognition.

The power gained in learning to recognize
quickly several easily contrasted words, such as the
examples given, (pialifies the learner for the acqui-
sition of a number of words which we shall call
a key-list. These, each teacher will, according to
circumstances, select to suit the class of learners.
One is given here for illustration: Oaf, dofj, hen,
pig, nitty, rat, lid, box, sun, fan, web, jug, lath,
.ship, king, chick, vest. These contain all the letters
used in Part I. Other things being equal, such as
the suitability of the words, the shorter the list, the
better. Som^ teachers say they find initial
consonants (easier for beginners to separate from
the words than final ones ; others say they have
better success with final consonants. Teachers who
use one class pretty exclusively would require a
longer list of key-words than those who use initial
and final consonants indifferently.

As each word is taught it is given an abiding
place on the key-list chart, — a strip of heavy paper
may be used of about eight by thirty-two inches, or
sixteen inches sfjuare — and an outline picture added
after each. Instead of drawing them, pictures cut
out of old papci's may be gummed on the chart. For
largi^ classes the ki'y-words should be written on a
hirger chart or on a blackl)oard.

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METHODS IN TEACHING.

cat.

ilo(j.

hen.

pig.

miuj.

rat.

thl.

Ih>x.

sti n.

fan.

awl}.

J^'U-

lath.

sh I p.

llvij.

hid'

rest.

READING.

157

For reasons already stated tlie picture is added to
each word <tfter it is taiii(lit. Tlie pictures are put
there for the benefit of those pupils wlio may liave
been absent on the days when some of the words were
taught and to make the words instantly available as
a phonic key for reference by all the pupils of
the class. It is not necessary that the whole list
should be learned by the Word method before it is
used for its specific purposes, as described hereafter.

Concurrent with the foregoing exercises in learn-
ing words by the Word method the pupils receive
training in oral phonics. Devote a minute or two
at every lesson to such training. Begin by requiring
the synthesis of the sounds of easy words such as
coWy shoe, clutlk, sheep, knife, mouth, nose, sky, slate,
cheese. The teacher may ask the child to tell what
is in his closed hand. The child doesn't know.
T will tell you," says the teacher, " it is a n -i — f."
If the child cannot synthesize tl^e three separate
sounds, try him with two ni — f or n — if. Not much
ingenuity on the teacher's part is needed to teach a
child to combine any two or three assimilable sounds.
The blackboard is not used in these exercises.

Long-vowel words are the easiest to begin with.
When the sounds of words like the examples given
above can be synthesized proceed to short-vowel
ones such as cat, dog, Jwn, pin, etc.

As a second step in oral phonics the teacher
vocalizes the sounds, the child imitates and then
combines them. The teacher should aim at purity of
phonic enunciation on the part of the pupil. Some
teachers are unsuccessful solely on account of the
incorrectness of their phonic analysis. When

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158

METHODS IN TEACHING.

> 'I

I r

analyzing' pen for oxample, they say pch-ch r tili.
They might as wull spell tlie word by tlie ohl
alphabetic method. The most common impurity —
not by any means the only one — in phonic analysis
is the kind of aspiration referred to above. Taking
a few lessons in Pitman's phonography will prove of
much assistance to the teacher of phonics.

In the third stage the pupil will analyze the
words used in the first set of exercises in response to
the teacher's dictation. He should proceed to the
separation of, at least, the initial and final con-
sonants. It is not desirable to detain him in oral
work until he can separate the short vowel sounds
in, for example, such difficult words as ^n?!, hen.

The foregoing work in words and oral phonics,
which may be accomplished in a week or ten days,
prepares the learner to begin " written phonics."
To illustrate how this can be done successfully take
the word (fo(j which the child knows when he sees it
written in separated letters on the blackboard. When
he hears the word ilo(j he can tell the first sound, or
the last one. With pointer in hand he can show the
first letter and as he knows the first sound he can at
once correctly answer the usual question — " What
does that letter ' say ? ' " He can also find the sound
of (J and in like manner discover by his own easily
made inductions the sounds of all the other con-
sonants in the key-list. Using this list give such
practice as, " Wliat does this letter say ; what, that?"
and so on. Then direct the learner to point to the
letter that says te', to the one that says se; to the one
that says ?, etc. Throughout Part I. and even in
the first reading of Part II. there is nothing gained,

READING.

159

, '-m

but on tlie contrary often serious liind ranee, in
speakin<^ of the individual letters by tlieir ordinary
names or any otlier designation tlian their normal
sounds as used in the key -list.

The t' aching of the short v /els presents some
difficulty and various devices h'>\e been adopted to
overcome it. Sometimes they are taught like the
consonants from analysis, but the difficulty lies in
obtaining pure vocalization. One method of sur-
mounting it is by treating the short vowel and its
secjuent consonant as a digraph. Exercises for
practice may be written on the blackboard thus :

c-at

;i-(;rv

h-en

P-|^^

m-ug

Oti

etc.

The drilling is conducted in vertical and then in
liorizontal lines and finally promiscuously. If you
point (*) to im for example and the child hesitates
then point to ??i, if he hesitates still direct him to
show you that letter in the key-list, which should be
hanging convenient for reference. He tells you at
once what it says there. Impress the sound on his
memory. Go back to im ; if he does not know it
now point out pig, then ig, then im. Thus he learns
how he can find out for himself what these
combinations of letters sound and he can, while at
his seat, practise columns containing review and new
combinations and be prepared to pronounce them

(*) In all these written word and letter exercises it is an excellent
practice to use two pointers to delimit precisely the letter or combina-
tion of letters you wish the child to sound.

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METHODS IN TEACHING.

readily when lie comes to his class. Some very
successful teachers in phonic-spelling exercises
recjuire the child, when he is not ready at once to
pronounce the digraph, to prolong the short vowel
sound until he lecalls what the sequent consonant
says so as to make the vowel sound coalesce with
that.

Different children vary greatly in the rapidity
with which they can learn to discover the sound of a
letter from its use in a known word. A certain
little girl was not at all a prodigy who, taught in the
manner here described, told her mother on the
evening of her first day's practice in phonic discovery
that she had learned all the letters in that day.
There is usually something wrong with the teaching
if it is found necessary to tell the learner the sound
of a letter. Some of the advantages of teaching the
letters by this inductive-phonic method are that
children learn them quickly, their interest is easily
maintained by the excitement of discovery, their
minds receive a useful kind of training, and they are
at once put in position to help themselves and so to
do more than mere review work at seats. Indeed,
the difference in the progress of classes taught by
different users of this method seems to be measured
by their skill and diligence in assigning appropriate
seat work.

The child began oral phonics by synthesizing the
sounds pronounced by the teacher. One or two
intermediate steps followed bridging that exercise
with its converse which qualified him to associate
appropriate sounds with their corresponding signs in
words that had been learned by the Word method.

READING.

161

the
itwo
Icise
bate
Is in

Lod.

He is now rea<ly to synthesize the phonic elements of
written words. Knowinj^ r at he can discover by
referring, if necessarj'-, to his key-list h-nt, in-at, l-<tf,
<L-at, f-at, etc. ; kno\vin<^ <f-<>U he can discover 1-(>(J,
^-'\<y. f-^V, etc.

The teaclier will now prepare or determine upon
a graded series of phonic exercises. He may use and
enlarge the lists in the text-book taking those in
Lessons 7, 8, 9, 13, 14, etc., to the end of the OnUrio
Primer, or he may follow the order in which the
consonants are taken in his key-list, or he may devise
a series which he thinks better than either. He
must determine how far he will carry these phonic
exercises before he begins sentence reading.

He may begin work on the sentence when his
pupils can easily recognize three-letter combinations
or he may delay it until they can readily synthesize
four or five- letter combinations. I have seen a class
that had not done any reading, working with evident
pleasure on a column of combinations including cain,
gran, hrust, clatih, shark. A, e, i, <> and it were called
*' the starters." The column may or may not have
been studied at seats. The pupils as called stepped to
the board and with a pointer in each hand started
with the digraph formed of the vowel and ita secpient,
pointed out and pronounced «8, ii.sf, ra,st, J>rusf ; <tsh,
lash, clash, etc. The teacher similarly pointed and
marked off the more difficult combinations, the pupils
answering as called upon and for review, simul-
taneously.

Successful teachers vary with respect to the
extent to which they carry these phonic exercises
before reading is begun but if a good foundation of
11

■ m

'hi

■ i

I I

102

METHODS IN TEACHING.

ready \vorcl-ruco;^intioii he lai<l tlic pro^n-oss in
reading is very rapid. Suiiiu of them ^o .so far tliat
the pupils can readily pronounce any rej^ular word in
Part I. or indeed ahnost any combination of four or
five phonetically compatil)le letters. Up to that stage
the exercise nearest reading which they had practised
was, by way of language lessons, composing sentences
containing specified words.

But whether reading be begun at so advanced or
at an earlier stage, this principle should be most
scrupulously observed that the child must recognize
every word in the sentence and then, after silently
construing the words, read the sentence, that is, tell
in natural tone and expression the thought that the
sentence has told him. One day a child after study-
ing the sentence — " The big pig is in the gar-den " —
raised his hand to imply that he could read it. He
said (piite earnestly, " The pig is rootin' up things in
the garden." His experience probably tilled out the
mental picture suggested by the words. That was
reading. Had he said "the-big-pig-is-in-the-gar-
den" in measured monotones he would have been
pronouncing words, but not reading in any sense.

In anticipation of the first reading lesson some
teachers teach, by the Word method, a few phrases
such as a cat, the cat, my eat, a do(j, the dog, I see,
etc., as though these were words of two syllables.
The common habit of saying tJi uh cat is as disagree-
able and incorrect as tJte cat.

Assuming that the first reading lesson is to be
given on the sentence, — A cat is in the man's hat, —
the teacher says to the child, " Do you know every
word in this sentence ? " The child does. " Is it

./.^KflMdi^MllailUMiteMMUaii^^

* I '

READING.

163

Is.

al)()ut a (lo^- :* " IMio child — " No; it is about a eat."
" Wliero was tlu; eat lyin}.? ^ ' AiiHwer — " In a luit."
" In whose liat i* " Answer — " In tlie man's liat. " Or
the teacher may tell the child to take the two point-
ers and show the words that tell where the cat was
lyin^, wliile one of the other pupils in the class may
be recjuired to read the words so pointed out ; or the
curtain* is slipped over the sentence and the teacher
j^eta the pupils to tell what the sentence says.

The next sentence may be — " The man has a cat
on his arm." " Do you know every word in this
story ? " asks the teacher. The sounds in kvih may
have to be synthesized aloud. " Now can 3'ou tell
me wliat the story says T' The child may need
assistance. If so, lie is to be aided by questioninjj,- as
before ; if ot, the curtain may be slipped over the sen-
tence or the child may look at the teacher. He may
say, " The man is canying a cat on his arm." The
word ('(iri'jjliig is not in the sentence, but no matter.
We are at i^atc/i/?(/ now, nnd reading first and fore-
most is attention to the ^.lought. Enough that the
child lias combined the words, found the thought and
expressed it naturally. Let it be distinctly under-
stood and invariably acted upon, that whenever
words arranged in a sentence are submitted to a
learner it is for the purpovse of training him first in
thought-getting and second in thought-expressing.
Heianever, ')w^^'e/•, to be permitted to proceed, saying,
''The-man-has-a-cat-on-his-arm." In these sentences
the voice is not to articulate the words until the mind

1' )•■

;*i;

* Many teachers have a wire streich \ along the top of the black-
board on which they suspend by rings yard or two of thin curtain.
This curtain is used in various blackboaii' ijsercises.

i i

164

METHODS IN TEACHING.

through the eye Iijih (Withered tliem into or()U[)s tliat
to tln' chiM liave soiiie seiiHe.

It is not for inl' )nnatioii that tlie child is reading
now ; he is carried on l)y the i)leaHur(! derived from
tlu! exercise of liis increasing power to discovei* tlie
tlioughts synd)()li/ed in tlie sentences. Those who
urg(! eidistnient of interest ])y using desirt; to express
intrnisic tliought could not deny tliat tin; mere dis-
covery of thought in a. commonphice sentence such as
" N<'(l hit till' </()(/ nv tin' tnick iritli <t Ih(J stick," is suffi-
ciently int(M'esting if they witnessed the atiimated (^ye
and (expostulating hand emphasizing tlie exclamation
— " IMease sir, I know what it says; I know it, let me
tell!"

AJthough many commorj words are not spelled
strictly phonetically, yet these do not offer formidable
«li<Hculty to the child taught b}'' the method outlined
here. In the blackboard lessons a few diacjitical
<levices may l)e intr<)duce«l such as drawing a light
lime through silent letters and slui'rin<{ combinations
of lettei'S representing single sounds, ('.<j., breath.

In exercises for phonic synthesis it is advisable to
adhere to normal combinations, but when irregular
words occur in sentences some of the elemetits of the
word antl the; context usually enable the child to
sui'mise them. In a stoiy of a dog and a cat it was
related that '' Fvrd fnit tlinn luith in ti t(ut</-j/(ni." A
child, tiying to rcead it, said, "I know all the woids
but I cannot read it." She was pi'onouiicing lioth
with the short sound of «^ On being asked to tell
what it seenuMl to say she made the attempt and tln.'n,
suiiling, said. " (). I know now what it says," and
interpreted it cori'ectly. When words so iri'egular as

}ir

1 10

UiH

Ids

\fh

-11

las

READING.

165

knife. V()}i(jlt and th<>tr occur it is Ix'st to anticipate
the difficulty and tell the child at once what to call
tlieni.

Under present circumstances hy tlie method of
teacliin_i( i-c^adin^* outlined liere, the hlackhoard or
charts made hy the teacher will he used almost
exclusively for the foundation woi'k. In the first
place traininL"- in word recognition proceeds so far
l)efore readin<^ is attempted tlnit wIkmi wordsairan^'ed
in sentences are suhmitted, the efforts of tlie yoini»(
learner are taxed to recotniize not the words but the
tlumoht tliat the words tell. Thus, reading from tlie
first is Tjatural and int(^lli<,^'nt. Secondly, separation
is effected between the learnintr of a sound and the
leariiin^f of a siirn for tin; souikI ; each acquisition is
applied and perfected in tuiii. Sui-e and rai)id
pi'ofrress in word recognition by the ])honic method is
foun«led on tlie child's power to synthesize ih«' sounds
syml)olized by the letters. In the third i)]a('e, letter
n.imino; is avoided. Not infre(|uently a visitor mij^dit

Teacher — '" What

I ear

•1

letter
does ./<7' si

sucn a coii()(|uy as this

that

(^hi!d-"./

Teacher -"What

'I'he child then n'ives the sound of f/
as heard in (jet. Tlui l)ei»inner"s pi-o^n-ess will be
retardcMl if with each letter a?-e established two
associations— name and sound — particularly when
the name is the better or<rani/(!d of the two.

Even though the blackboard Im- the only " read-

nur book" for the first two mnnths it is i

H'cessar\'

that the readin;;' lessons as w«'ll as tli»' phonic exer-
cises be n^i'aded. The teacher ma\' wi'ite a series <>f

readintf lessons

<hort

«dit

interest ill!'' stories,

ori«;inal, (jr culled from every available source, on

166

MP]THODS IN TEACHING.

I !

charts (slieots of wrapping or lieavy priiitinj^-papcr),
but it is conveniimt and fairly satisfactory to choose
from the primer, omittiiijj; the first six and thi^ 11th
and 12th lessons.

Transition from script to print will be made
befoi'e promotion to Part II. of tlie First RejuUir.
It is more easily made from vertical than from slant
script. To make the transition use the authorized
printed tablets and be<^in witli practice in plionic
spell ini^. I.e., sound in<,^ the letters and pronouncing
the words. A wcu'k's practice will (pialify the class
to read as (easily in print as in scrij)t. (Jo throuf^h
the tablets readinj^^ several of tliem a day, always
keeping in mind that readinjj^ is tliought-getting and
thought-expression. Then take tlie book (Part I.)
and beginning at the 1 8th li^sson read it througli,
wliich, if propel' seat- work on it be assigned, can be
<lone at the rate of two or three pages a day.

The learner is now ready I'or pi'omotion to
I'art n. lb' eim read well eno\igh to enjoy a story
suitable to his ag«' printe(l in easy and mostly
regulai' words ; perha[)s he can also write it so
legil)ly that he can I'ead it from his slate or exercise
book, lie has waste*! no time in letter naming or
oral spelling by lettei's. He may have concepts of
number up to e'ight or ten, and his exercise book
may be tilled with attempts at writing words
and sentences and interpreting them by pictures. I
have known some teachers make much use of this
exercise as a seat occupjilion. At the close of a
lesson in Part 1. tlie\ would write a b'W review
.sentence.^ './/., the doll is sit ting on th«' bench
with its back to the wall, lor the class to read

READING.

167

silently at scats and tlicn interpret hy «lrawinj^
pictures. Children at tliis sta^'e shov; less lu'sitation
to attempt such illustrations than older pupils vvlio
have not heen accustomed to this work.

Tlie work in Part II. need not take lonn^ to
descril)e. Usinj^ the autliori/ed hool run rapidly
tlirouirh it, readin*^ o-dy a sentence or two in eacli
lesson, but paying speci>d attention to tlio exercises
in plionics. The class well tauglit in Part I. can go
to the lOth lesson at the rate ot four or five lessons a
(hiy. The lengtliening oi' the sliort vowel by the
final (' mute may be taken up in two or three lessons,
and the five vowels dealt with together. Lengthen-
ing <> and r by doubling them is easily taught. An
easy way to teach the long vowels represented by
ai and a//, (ti(\ en, ru\ ir and //, (xt, <><•, (tl, on, oj/' and
(>//, is ))y a key-list written on^ a chart and a picture
added after each in a manner similar to the list
given for Part I. For this purpose the following
list has been used with success :

i)r

oi
.k

lis
a
w
•h
id

. »

1(38

ZiiJ-ZiKJ'

//(>/

'.>'.

IxHff.

(fin'cn

pad.

/'"//•

^((/r.

/fv//:

/)<'*''.

METHODS IN TWACHTNG.

*l\i

u...

>-V*v. w»ww>v.<

^) w.

hoilf.

Inn'.

l-C(i n

liousp.

i-inr.

ri'<K(\

Ikh/.

READTNO.

169

(II

HaviiiiT nnicwod the T>horicF of t'ijo book in this
maimer tli*^ h'iinu'r i.-i prepar -l to reluii; io the
beirinniujjf oF it and rejid tlie lessons -t iiis ^eat. !!(;
Ci 1 make out nearly all the woi 1.^ a;i«« will hy his
own study '-f the lesson he prr lai'ee! to Miiswer
(juestions on the suhjeet matter v>r lo show the?
sentence that an*<\vers the (juestion, and tlien read it
if re(|uii'ed to do so. His proL;ress will he at the !at(;
of two or three ])aL!;es a day; th(» poetry will Im'
omitted until tlui next readin<^. As a seat exercise
he transcribes part ol* his lessons, care bein^ taken to
have him form the habit of writinj^ tl)oufj)its. Some
pupils in tlieii' transcrij)tions do not even wi'itt;
words as such, but transfei- oroups of lettei-s without
mentally pronounciuji^r iii<'m. Obviouslj^ such occu-
pation aids neithei* i-eadini^ nor spelling. Tiansci'i])-
tion should always he done with so much care as
constantly to improve the writin^j.

le woi*

to tl

w comi)leti(>?; n

►i' ti

li'

seon*

readinj^ of Part 11. has been i'«'peaiedly ac((/ni[)lishe(l
in from sixty to tu^dity scho ;! d lys «ii<l it represents
a dcjL^ree of proticiency in "i adiiJif that iwis l)een
accepted as (|ualitication for |)r'omotion tn tin See«)n<l
Header, l^ut important woi i if» rj.'jidinjjj rejuains to
be (h)ne b(»fore !»i'omotion. Hitherto thereadinjx has
l)een stron^^ly emphasi/e(l nw the side of attention <»r
thou«i[)it«^ettin}^, not for the puipo.se of inci'easinj;
knowK'(|<^e hut to lay the tbundation of that pi-ocess
of detinin^j, inte!'])i"etin^- and eon.struin^'' wliicli I >r.
Hinsdale calls the basic element in all readiiii;. Al
til* next readil!<;' of (he hook nltention will lie
st l'oil|L;'ly direetecj towards r./'^;/V'.s',' /n^>.

if tl

le yout .i^ leaiMiei- can rec;»Mni/e we^ids easny

«*!■

Ilf I

It ^f

I
it.

«>

170

METHODS IN TEACHIN(;.

and lias fonned tho habit of f^athciiii^ tlu'in with thu
eye and then voealiziiii,^ tlicin not as so many s(;parate
words Imt as ji^'roups of relate*! words, siicli reading
will ho int('lli<i^ent and intelli^'-ihlc; and yet it may be
greatly deficient in ivspect to expression. Now is
tile time to lay the Foundation for expressive readin<ij.
The voice is flexible, tiie sul)ject matter is within the
child's experience. Thou«ifht and feelin<:j will prompt
the suitable kind of emphasis and inflection but these
require i"einforcin<j; and the l(;arner must be made
conscious of their value and mode of producti(jn.
" Imitat(^ me" should be the last resoit of the teacher
who aims to str(^n<^then or refine tlie (pialities of liis
pupil's vocal expression. One may imitatt^ without
tliou<j^ht or reason. The chief n^liance shouhl be
placed on judicious (piestionin*;. Ueferriu}^ for illus-
tration to the first lesson of Part II. the ])upil reads:
" Fred and Will are «^^oinf( to tlu^ pond." Teacher —
"Who did you say are i^oin^ T' Answer — '' Fmi
and WiHy Teaclier — "Head it ajjjain so that every-
one will know who are <,'oin<^." Teacher — " Goin<;
wlierc r' Answer — "To the jutiniy Teacher —
" Read it a^jjain, brin^innr the boys and the pond bL'fore
our notice. " Second sentence : " '^riiey both are fond
of tisliing." " Wliat new thin;^; is told us here/"
Answer — "That the boys ///'' //.sA /////." " Read it to
make the sentence tell that." Thinl sentence:
" F»"ed's rod is so long that it bends as he ho]<ls it in
his hand." "What do<'s this sentence ti'll us?"
Answer -' Thai l<'i'ed s rod is a long one. ' " How
longr' Answer ' Tlialil l»ends." " Read tin- sentences
to make it say so plainly." I'upil reads: " Kred's
rod i8A<(v liHKj that it hetuU us he holds it in his hand."

:r :
in
?"
>\v

READING.

171

In like niannor tlie other sentences of the paraij^nipli
are examined and practised and finally the whole
para«^raph is read. Not every paraj^raph is treated
thus thoi'ou^hly, but some part of every lesson is
devoted to the rational impi'ovement of expression.

Most of the lessons in the hook are suited to train
pupils to read expressively. A few, (.(/., No.s. 8 and
14, are of little value, hence the advisability of takin;^
up some lessons more thoroujjjldy than otliers. This
remark applies with special force to the pieces in
verse. Some of them, rj/., " Baby-bye,"' " Lady
Moon," " What does Hiidie say," and " They Didn't
Think," are well worth careful teaching. The voice
should respond to the rhythm without bein^ cai'ried
off by it. Skip the rhyminm' lessons that you cannot
prevent the children from reading in a swinging
sing-song.

In the prose less(jns avoid depriving the children
of tlie pleasure of finding out the story. 'I'he assign-
ment of a new lesson as sometimes done consists
mainly in telling the children what they should be
left to discover. This deprives tliem of a real
pleasure and robs them of the opportunity of deriving
from the lesson its highest value.

Th«' lessons ill vei'se should be taken up with a
somewhat diff<'rent pui'posc from the pi'ose ones, or
rather with an additional purpose. The pioper
ttiaching of one of them should make such an impres-
sion on the child's mind as would pronipt him to say,
" Oh, mother, we h.id a beautiful irsson to <lay ; Irt
mi' mid it to you!" Teach the piree so that its

thet

le (il

lality

wil

ii)nr!M \\\ some oti'riM

I'l

< >

child's sense of beauty. One way to do this, is, in

172

METHODS IN TEACHING.

1 1

assinrnin^ it, to read it in your very best manner
while tlie cliildren watcli you and listen to you.
Read it again wlrile they follow the lines on their
books. Read it so that they will know the thought
and feiil the beauty. Discuss with them the })eauti-
ful th(jughts and the beautiful expressions. Lead
them by <|U('stioning to see tlie main thought in each
stan/a and to note the relation and arrangement of
these thoughts. Explain difficult words and phrases.
It may be well to read it for them again and then to
liave them read it not only by stanzas in turn lait
also facing the class read the whole poem. Finally,
when they understand the poem and like it have
them memoi'i/e it.

When memorizing is assigned it is not enough to
say " (»et so many lines off by heart for to-morrow."
Insti'uct them how to memorize and occasionally
devote; a recitation period to this instruction.
Connnence with an easy exercise, r.g., "The darling
littlt^ gi'"b' P'^-i^^' •'^'^- I^ this l(;sson has been taught
as described above; tin; pupils will have noted the
repetition of the <{uestion Jind will easily learn its
variations. The answers naturally follow the
variations in the (|uestions. Having fixed that the
1st stanza pictmes the secliKj of her sweet face ; the
2nd the hcurinij of her pleasant voice ; the 3rd the
kiHHciii;/ of her pure thoughts and acts the
memorizing may then be completed in five minutes.
Again in the poem "What does little l)irdi(; say?"
page 43, the black l)oard should be usecl to show the
parallelism l)etween r»ii'<lit> Mud l>aby. Whe!» that is
neatly done the memorizing will scarcely recpiii'e an
etlbrt. In like manner in every piece worth

*^^

1(5

ill

READING.

173

meinorizinfj th(; toaclior can find sonic means of
lt'HHenin<^ tlui profitlcsH drndi^^cry that too ot'tt'ii
attends th(i exorcise known as learning hy heart hut
wliicli often lias very little heorl in it.

The mind receives, retains and recalls (recollects).
Repeated recollecting secures retention. It is
therefore necessary to occupy part of the time
devoted to memory w^ork to recollectin*^ — writing or
reciting poems previously memorized. Memorize
only the best, and review them several times. These
poems in the memory may be likened* to pretty
paintings hung round the parlor ; if they are worth
putting there they are worth keeping free from dust
and cob-webs.

Dictation and oral spelling will be added to
transcription in this the final reading of Fart II.

Recapitulation

Part L

Oral phonic synthesis

by children ;
Oral imitation by chil-
dren ;
Oral analysis by chil-
dren ;
Phonic analysis of key words and association of

letters with their sounds ;
Phonic synthesis of the sounds of written (or printed)
letters aiming at proficiency in pron(Juneing
coml)inations of letters ;
Reading, i.e., cognition of thoughts from written or
printed words arranged in st^itences.

Easy words by . word-
method ;

Key words
method ;

bv word-

111

^m$

'li

174

METHODS IN TEACHINCi.

>i I

I • '

rt '

l\irl II. i)f the, First Reader.

(tt). l*IionicH of iHMnainiii^^ consonants, of two-Jind-
three-consonMiit combinations, and of tho
lon^ vowels.
(/>). RcadinjGf the book for practice in appl^'ing
the instruction un<lor (a), and for continued
practice in thouglit discovery.
^rranscri})tion.
(r). ll(!adin<;- tlie prose* lessons i'or pivictiei? in
(expression.
lleadinH- ])()etry :
Men»ori/in<^ ;
Dictation and oral spellin<;\

The Second Reader — TIk^ principles and practices
a|)i)lied to the teachin<;- of th(i final reading of Part
II. oT the First Book are ap[)lical)le and appropriate
to the work in this grade. \S, a child leaves the
Second Reader with a monotonous, inexpressive
habit of reading, the probability is great, that lie will
never become a good oral reacler.

I'he incentive to read for information begins to
appear now. The learner is ceasing to feel ])leasure
in merely cognizing thoughts in the sentences he
reads, but he is beginning to enjoy reading as a
means of extending his knowledge or leading him
into new fields of imagination. He revels in tlic
fairy lands of the nursery classics.

As intei'est in the subject matter increases the
teacher should give correspondingly increased
attention to vocal expression. Gradually he sliould
intioduce exercises to train the pupil in the

READINC;.

175

DO
•('
le

a
In

conscious use oF nic'ins timt (Miluincc tlic foir*' jind
IjL'iiuty of his uttcriinct'. To <lo this well n'(|uin's
skill on the part of the teacher. One day at recess a
teacher and an inspector were discussing- this suhjeet
when it happened that a hoy said to another at some
distance, " Frank, are you <lone with that knife yet ?
I want to use it myself now." Tlie words were
written on tlie board and the hoy called to read them
hut the teacher was unahle to f^et tlie propriety and
fj^i'ce of the expression which the boy had used under
the impulse of intrinsic thou;j,ht. The boy realized
that he was not rtMidin<^ it as he had spoken it, but
he lacked the skill in the conscious control of his
or<^ans to produce the desired effects.

Good oral reading is a very complex art. It
depends first on ^ood silent readin«jj which involves
the art of interpretin<^ symbols capable of layini;"
before the reader's mind the author's thou<(ht, feeling
and purpose ; and second, on an extensive training-
in tlie use and control of the powc^rs of vocal
expression. From this sta<^e forward the .somewhat
mechanical translation of symbol into spoken .sound
will be subordinated to the clarification of the insi<rht
into the author's meaning, later called literature, and
to training in vocal interpretation or elocution.

The latter sub-division, while so largely de-
pendent on thought, nevertheless has an important
and complex mechanical side. All its elements
cannot be taught togethei , they should not be
taught at haphazard, but the teacher's plan should
previse a judicious arrangement of the.se elements,
giving special attention to one at a time, choosing
les.sons to multiply examples of it, and dwelling on it

li; :•

( h

IMAGE EVALUATrON
TEST TARGET (MT-3)

1.0

I.I

2.5

1.8

1.25 1.4 1.6

-• 6"

/^^i

Photographic

Sciences
Corporation

^N^

^ \ '^\

33 WEST MAIN STREET

WEBSTER, N.Y. 14580

(716) 87'}-4S03

176

METHODS IN TEACHING.

until it bcicorncs incorporate<l witli tlio reading habits
of tlie learner, who, while led onward and upward to
the nior<' and more difficult is ever carrying along
with him the fruits of his previous efforts.

This is not the place to write a treatise on
elocution, but it is proposed to show by a few
examples how the teacher's knowledge of that
subject, acquired as a part of his academic education
may be applied in the teaching of oral reading to
intermediate classes.

Every paragraph, sentence and even part of a
sentence, being a group of related words, has a core
or central idea. By a species of analysis in the silent
reading or as a result of the teacher's questioning,
the reader determines this central idea. The
recognition of that determination in the oral reading
is called emphasis. How emphasis, while it would
yet be premature to use the term, can be taught by
judicious questioning, has been already illustrated in
the final reading of the 1st lesson in Part II. of the
First Book. A class in the Second Reader is
prepared to appreciate the value of emphasis, and to
learn how to strengthen or otherwise modify it at
will. With the purpose of showing the value of
emphasis by Force, and for practising it, the teacher
will prepare a few blackboard exercises. The
following will serve as examples : —

1. Did you wheel to London yesterday ? No ;

I walked.

2. Did you wheel to London yesterday ? No ;

my sister did.

3. Did you wheel to London yesterday ? No ;

I went to Parkhill.

READING.

177

iV IS

id to
it at
le of
Lcher
The

No;

4. Did you wheel to London yesterday ? No ;

I went on Saturday.

5. Did you wheel to London yesterday ? No.
This lesson may be recited in a variety of ways

after it has been studied a few minutes by the class.
The teacher may read, " Did you wheel to London
yesterday ? " and require the class to infer from
the answers which (juestion lie read : or he may
require the pupils to read the question from the
answer — "No; I went on Saturday;" or the pupils
may be called on by twos — one to read the question,
the other, the corresponding answer ; finally each
pupil in turn will read all the (questions and their
respective answers. Deal similarly with the next
exercise : —

1. Who made that noise ? He broke my slate.

2. What did he do ? He broke my slate.

3. What did he break ? He broke my slate.

4. Whose slate did he break ? He broke my slate.
In the foregoing exercises no underlining, or

other clue than the meaning, should indicate the
emphatic word.

As another kind of exercise, have the pupils tell
the circumstances under which each of the following
readings would be appropriate : —

L Tluif little girl a<lds (juickly.

2. That llffle girl adds ([uickly.

3. That little (firl adds (|uickly.

4. That little girl ndds (juickly.

5. That little girl adds qalc/dj/.

6. That little girl adds quickly.

Deal similarly with the sentence, " The sweet
odor rises from that white Hower." Indeed, it is
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METHODS IN TEACHING.

easy to multiply examples for exercise in varying
the meaning according to the varied emphasis by
Force, and thereby illustrating that the correct
reading of a sentence may re(i[uire not only the
understanding of what precedes it, but also in many
cases of what comes after it. After practising such
selected examples, specially suitable lessons may be
chosen, ^^^., "The Idle Boy," "Who Stole the Bird's
Nest," "No Crown for Me," "Tonnny and the
Crow." (!)•

Another kind of emphasis — that of Time — was
partly illustrated on page 170. It is of more
frequent employment, but to use consciously requires
more careful discrimination, than emphasis by Force.
Raymond, in " The Oi'ator's Manual," lays it down
as a fundamental rule, that the relative time
apportioned to a word indicates the mind's measure-
ment of it, i.e., the speaker's judgment as to the
amount of importance that it conveys. It is easily
applicable to words with long vowel sounds and
prolongable consonants, and it contributes largely to
that quality of light and shade necessary to make
oral reading agreeable as well as intelligible. As an
example take the first paragraph of Lessson XII.,
Second Reader.

I wonder if any of us ever saw tJtis little girl. She
did not mean to be a naughty girl, m she loved her
father and mother, and would have been very sorry to
disobey them. She wished to do well but she did
not carry o u t her good wishes. When told to do any-
thing, or to go anywhere, she would say .

The general rule is t'.iat the new or distinctive

(1) Ontario Second Reader, pp. 12, 27, 47, 76, respectively.

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170

She

her

did

Ave

idea is einpliatic unless when a word is immediately
repeated for emphasis. In the second sentence it
would be wrong to emphasize the first " slie ; " tlie
new ideas are introduced by the words "mean,"
'* naughty," " sorry " and " disobey," and these are
not all of e(i[ual emphatic value. The ju<licious
teacher would not expound the rule and by direct
application of it hope to get the learner to read the
sentence well, but he would revert the learner's
attention to the sentence, that, owing to appreciation
of the thought probably in conseciuence of judicious
questioning, had been well read, in order to make the
reader conscious of his art. From such I'epeated
examinations he can gradually deduce the rule.

Emphasis by slides of the voice, or Inflection,
may be made the subject of special instruction in the
advanced second class, but it has difficulties that will
not be mastered below the high school. True, a
child in the primer can understand what is meant by
raising, maintaining or lowering the voice, and can
consciously use appropriate slides in reading such
sentences as, " Have you learned your lesson yet ? "
" What is the title of it ? " He would under the
impulse of his own thought say, " Will yoit come to
our' place with m6 or shall V go to your' place with

you

He could distinofuish the meanintr if he

were asked the questions : " Is your lesson about
su-gar or cotton' ? " " Is your lesson about sfigar or
cot'-ton?" Yet these would be difficult enouLdi
exercises for the Thii'd class to read. It wcmld be a
well-taught senior Fourth class that could deduce
the generalization that negative ideas take the
rising inflection and positive ideas the falling one.

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tiii

Enon((h liuH been stated to sliow that tlie
elements ov (jualitieH of vocal expression, although
properly receiving prominent attention, one at a
time, cannot l)e completed in turn, one making way
for another. The efficient teacher of oral readin<»;
must be well accpiainted with the whole subject of
elocution, he must be able to present along pedagogi-
cal lines the sections of each division of the subject
adapted to the capacity and attairnnents of the
respective classes. It is all the better that he is
himself a good elocutionist if he avoids the danger
line of relying too much on imitation. There are
worse ways than that. " I give " said a teacher,
" ten marks for perfect reading, six for pronunciation
and four for minding the stop?)." But according to
our definition this "perfect reading" was not
reading at all.

Limits of space forbid the treatment of pitch,
tone, movement, vocal gymnastics, etc., Init there
are two elements so appplicable to the reading of
junior sses and so important throughout that they
deserve special notice. These are imitative modu-
lation and articulati(m.

Young pupils easily see the value and appro-
priateness of imitative modulation, and delight to
practise it. Tlie sounds of a surprisingly large
number of words seem to harmonize with their
meanings. Children are (juick to perceive this fact
when their attention has been called to it a few
times. They may be easily shown the effect of the
r's, in the stan/a ;

oj-j-i^aai&aiiEii.

)Y0-

heir

I'act

tew

Ithe

READING. 181

I'll make a terrible scarecrow, {ijrim,

With threateninj; arms and with hrietlinj^ head,

And up in the tree I'll fasten him,
To frighten them half to death, he said.

lie fashioned a scarecrow all tattered and torn—
Oh, 'twas a horrible thing to see !

They will vie with eaeli other in pronouncing
tcri'ihlc, (jrlm, hrisflimj, frigliffu and horrlhle, to
make the sound enforce the nieanino-. J)r, Corson
tliinks it not improbable that Sliakespeare voiced his
language as he composed, so appropriate is the sound
of the words to the thought they symbolize. We
believe he is (juite right, as the plays abound in
examples of such appropriateness. If a person be
reading Macbeth, silently, on coming to the
description of the witches' caldron, the impulse
to read the lines aloud and by explosive articulation
to imitate the boiling pot will be well-nigh irresistible.

Double, double toil and trouble.
Fire burn and caldron bubble.

The Second Reader furnishes numerous examples
for imitative modulation in, " Who Stole the Bird's
Nest," " Good Night and Good Morning," " Robert of
Lincoln " and " The Lazy Frog," but the best lesson
in the whole series for this kind of exercise is,
" The Story of a Drop of Water," pp. 144-15L

Articulation. — Not reading only, but all other
recitations should be marked by insistence upon
distinct articulation.

Articulation exercises suited to the advancement
of the classes may be written on the blackboard or

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METHODS IN TEACHING.

rlictated to be written by tlie pupils for sul).se(juent
reading. Some types oi* exercises are : —

1. Combinations of consonants difficult to
articulate, e.g.,

sphere. bursts. rhythm,

length. posts. precincts, etc.

breadth. elm.

2. Words of which a consonant, vowel, or syllable
is liable to be dropped, c.y., —

I'eijj'lar for reoular.

rev'i'ent " reverent,

partic'lai- " particular,

hist'ry " history,

etc.

3. Additions or substitutions of sounds, e.g., —

chimley for chinniey

drownded " drowned.

Toosday " Tuesday,

heith " height,

etc.

4. Dropping final sub- vocals and aspirates, (\g., —

fren's for friends,

ac's " acts.

and.

askin'

etc.

asking.

5. Indistinct separation of like sounds coming

together,-

whole lot.

fresh sheet.

till late and till eight.

an ice-cold drink and a nice cold drink.

etc.

READING.

183

6 Provincialisms used by pupils and the juiiib-
liug toi^ether of words in conunon phrases, —

as idear for idea,
niebbe for may be, etc.

A prevalent error — that the sole use of oral
reading is to communicate thought to others — has
stamped itself on our e<bicational practice. Much of
the finest poetry as well as impassioned prose has to
be vocalized to l)e properly appreciated. The thought
or the emotion is richly eidianced by the effort of
giving it appropriate utterance and hence the cultiva-
tion of the readino- voice becomes a means to a noble
end. Dr. Corson rightly places a high value on that
early attunement of the sympathies to good literature
which begets an inw^ard impulsion to vocalize what-
ever one sj)ecially enjoys in his reading. Indeed, he
places so high a value on reading aloud that he
affirms, presupposing the re(iuisite vocal cultivation
on the part of the student, that in literary examina-
tions, a sufficiently qualified examiner could ari-ive
at a more certain estimate of what a student has
appropriated both intellectually and spiritually of a
literary product by requiring him to read it aloud
than he could arrive at through any amount of
catechizing.^

As the teaching of literature is the subject of
another chajjter its important bearings on the
reading-lesson will he but briefly referred to here.
Much that passes under the name of litei-ature in the
junior and intermediate classes is not properly named,

1 Corson's The Voice and Spiritual Education, p. 55. This little
book is well vorth careful reading.

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METHODS IN TEACHING.

('.(/., i]\v 111, 're (lotiniii<jj of words and plirasi's some-
tiiiic's called " meanings." ])(3Hinn(^ i.s, however, an
important part of the instruction in readin*,^ and
jijives the teacher opportunity to exercise tact and
skill. Of the common methods in vo<(ue the worst is
indicating a list of words of which dictionary defini-
tions are to be written and then memorized. As a
usual exercise a certain class had written and
memorized such definitions of the assigned words in
the lesson on page 122 ol' the Third Reader. One of
the words was cleave in the line — " Tis because they
cleave unto a familiar, favorite few." The definition
learned was " To divide by force." On being asked
to write an original sentence using the word cleave,
one girl wrote, " She cannot cleave her sum." Pages
could easily be filled with accounts of similarly
useless and ridiculous results of a rather prevalent
way of teaching (?) " meanings." Where practicable,
the context in which a word is used should be studied
to disclose its meaning. When it is not possible to
discover the meaning from the context the teacher
will have to decide whether to refer the pupils to the
dictionary or to explain the word himself. The
dictionary is a necessary book and every pupil in the
Third Class and upwards should receive instruction
in its proper use, not only to discriminate among
definitions, but also to interpret diacritical marks
and contractions.

In illustration of some of these principles and
suggestions take the lesson in the Third Reader : " A
Wet Sheet and a Flowing Sea "

READING.

185

A WET {^IlEET AND A FLOWING SEA.

Allan Cnnninghdm.

A wet sheet and a flowing sea,

A wind that follows fast,
And fills the white and rustling sail,

And bends the gallant mast ;
And l)ends the gallant mast, my boya,

While, like the eagle free.
Away the good ship flies, and leaves

Old England on the lee !

" O for a soft and gentle wind I "

I heard a fair one cry ;
But give to me the snoring breeze

And white waves heaving high ;
And white wav -s heaving high, my boys.

The good ship tight and free, —
The world of waters is our home,

And merry men are we.

There's tempest in yon hor id moon,

And lightning in yon cloi •
And hark the music, marii ^b

The wind is piping loud !
The wind is piping loud, my boys,

The lightning flashes free, —
While the hollow oak our palace is.

Our heritage the sea.

The teacher's spirited reading ot* this short poem
will cause the pupils to admire it. The movement,
music of its language, and sentiment will win their
favor. But there are terms in it that land boys will
not understand or will misinterpret. The beauty of
the piece is enhanced by weaving it around distinct

. • •'

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I .

and correct

imao'es.

Therefore before the oral

186

METHODS IN TEACHINa.

I'oadinj; is ])r;i('tis(Ml souk; (IcHiiiiio; \v<jrl\ should be
(lone, [n this (•oinit'ctioii it is wortliy ol* rciujirk that
pupils may ^^riisj) tlie tiiou^ht or synipatluzo witli the
emotion in a passai^e coutaininfic words that tliey
cannot define or do not understand, and per conti'a,
th(!y may undei'stand oi* he able to define every word
in a passai^e and yet fail to o^rasp tlu; thought of the
whole. The sentiuice is the unit of meanini^. Pupils
are prtitt}' certain to suppost^ that "sheet" means a
sail, hence they ai'e not likely to search for its
nieanino', indeed, looking- up the word in the
dictionary may confirm their erron(ious supposition.
This is, therefore, an example of a word that the
teacher should explain. He should tell what the
sheet is and try to draw from the pupils, if possible,
the effect of its beinf^ wet. After the explanation the
unabri(l<4'ed dictionary mio-ht be consulted with profit.
In like nianner " flowing sea," " horned moon,"
" piping loud," " hollow oak," and " heritage " should
be explained or developed. The efficient teacher
guards against doing for the pupils what they can be
got to do for themselves, hence he lefers them to the
dictionary for " gallant mast," ' lee," " tempest,"
" mariners," rnd " palace," and requires them to
define by studying the context — " my boys," " fair
one," " heaving," and " music." Of course the context
has to be kept in view throughout, whether the
assistance in defining be from the dictionary or any
other source. This rule is most emphatic. For
example, one dictionary defines " palace " as " the
residence of a sovereign ; any magnificent building."
The chief value to the pupil from the study of this
word is the exercise afforded in reaching the

READING

187

coiiclnsioii tlint it is tin' kini^HiiK'Ss of the sailor in
the situfitioii drscribt'd I'atlicr than tlu' iiiaii'iiitii't'iicc
of the <^(j()(.l .ship that makes his lioine on the wave
a palace.

No rule can be prescribed for determining^ the
extent to which verbal explanation should precede the
oral i-eadino" of a lesson. Excessive verbal dissection
ot* a piece of literature usually oives aversion to it
rather than affection for it. An elocutionist before
an audience would seem ridiculous if he interp(>late(l
verbal explanations as he proceeded with his reading-.
He relies, or should rely, on his voice to interpret
what is not conveyed on the surface by the words.
"A susceptible reader," says Dr. Corson, "on the
first reading of a poem or an impassioned prose com-
position, will be more or less immediately responsive
to the key-note of the composition. An increased
familiarity will finally bring this key-note fully
home to his feelings or as fully as may be ; and if
he has made the articulating thought his own,
he is prepared to interpret the composition to the ears
of others."

To get the best results from the lesson under
notice, which, it must be remembered, is poetry, and
therefore In some respects should receive different
treatment from a prose lesson, the teacher's reading
or the pupils' practice and study will come
immediately after such explanations as are necessary,
to clear the ground of misconception or total
obscurity. The best practice for the pupils will be
oral, and that usually has to be done at home. In
such a lesson as this it is far more important that a
pupil should leave it with a love for it even though

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METHODS IN TEACHING.

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Si i

he cannot explain all the tenns used in it, than
that he should leave it able to define every word,
but careless whether iie ever sees or hears the poem

again.

The dragging in of every verbal relevancy is
another prevalent fault. To illustrate, I ([uote part
of an exaniir.ation paper based on this lesson : 1.
Tell what you know of i^ llan Cun-^'nghani. 2. What
sea was meant? 8. Why is England called ohH
4. What is the cause of lightning ? 5. Spell and
define homonyms of .svr, Ice^ our and /((h'. Is it too
much to say that not one of these ([uestions should
occupy any attention whatever in the teaching of
this lesson. Suitable questions, as a rule, are
answerable solely from a searching study of the
text.

A less prevalent, though not less serious fault, is
a disposition to seai'ch for and dwell upon flaws in
statement or construction. Dwelling on such
questions as whether the shore in the case was on
the lee, and criticizing the association of the horned
moon with the tempest, i'epels the pupils instead of
attracting them.

The treatment of the lesson, on the contrary,
should be constructive. It should aim at stimulatino;
the imagination to create a succession of pictures, —
first, the good ship fleeing before the wind ; second,
a vessel heaving higti on the white-crested waves ;
and third, a palace on the boundless water amid the
grandeur of lightning and storm, — and at the further
exercise and cultivation of the esthetic sense by
attention to the suitability of the language and tlie
melody of the composition.

READING.

189

are

the

Now we como to the fault most common of all,
viz., pil'ng Pelioii upon an Ossa of defining an«l
explanation, making ho much prepai'ation to read
that no time is left to do the rivtdinuf. If tlie
teaching of reading n.>ist be one-sided, let it err on
that of too much practice at the expense of explana-
tion. There should be plenty of spirited practice, at
home if not at school, (*) in giving vocal expression
to the thoughts and emotions the lessons are
intended to convey, and that with conscious, daily
increasing r<;gr.rd to tiie elemen'^s of time, pitch,
(juality and force.

The culmination of the defining, explaining, silent
reading, constructive criticism, and mental imaging
is this reading aloud by the pupils. A short poem
like this may be read througliout by several members
of the class during the recitation period, the others
all receiving an opportunity to read some part. On
the side of elocution, selected parts should receive
special attention. For example in : —

" O for a soft and gentle wind !
I heard a fair one cry ;
But give to me the snoring ])reeze
And white waves heaving high,"

the teacher will take advantage of the excellent
opportunity the quatrain offers for imitative modula-
tion in "soft," "gentle," and "snoring;" for emphasis
by tinie in "soft," "fail'," "snoring" and "white
waves heaving high:" for emphasis by force in
"fair one" and "me;" and for varying force,

* I have pieen a class practising? in summer weather under the shade
of a tree near the open school window.

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METHODS IN TEACHING.

liH

■i

movement and pitch in each of which (jualities the
second line varies from the first and from the otlier
two. At this staije the elocutionary elements
themselves and not the names would receive
attention.

In poetry correctly read, a measured flow is heard
which distinguishes it from prose. That measured
flow must not be confused with a chanting sin^-song
utterance easily and often acquired. Poetry is better
read as so much prose than in the latter manner.
Correct pronunciation and accent nmst not be
sacrificed to eke out a poet's limping measures or
defective rhymes.

The school Readers will, of course, be the main
reliance for the subject-matter of the reading-lessons.
It is fortunately, now, as easy as it is desirable, to
obtain an adequate supply of suitable supplementary
reading. But it should not be overlooked that every
text-book in the school is to some extent a reading-
book. The proper assignment of a lesson in history,
foL' example, consists largely in directions for or
assistance in the reading of the prescribed pages of
the text-book.

To sum up. — An intelligent application of the
principles set forth in the first part of this chapter on
the lines of the inductive-phonic method duly infused
with energy, diligence, and sympathy will carry the
class quickly and pleasantly through the mechanical-
mental introduction to roadinji;. To the pedam)irics of
the succeecling part the teacher sliould bring a good
academic training in literature and elocution. His
success will be largely measurable by the extent to
which his pupils are taught to appropriate the

^ed

of
)(]
is
to

READING.

191

author's thought and feeling by tliat species of
analysis, construing and discrimination going on as
silent reading, and by the way in which he seizes and
builds upon the natural impulses to give the suitable
qualities of vocal expression to what they know and
feel.

In conclusion we quote the standard directions
given to his students by Prof Monroe, Dean of Boston
University School of Oratory :

1. Sf<in(l or sit in a good position. Body upright,
chest expanded, shoulders thrown back, head erect.

2. Hold tlw hook properly. Support the book in
the left hand, \\\t\\ three fingers beneath it, the thundj
and the little finger extended above to keep the leaves
down, elbow free from the body, and forearm elevated
at an angle of thirty to forty-five degrees.

3. Breathe before tlte liuiys are empty of air, and
before necessity or fatigue forces the lungs to inspire
too great a volume at once.

4. Keep the eye and mind in advance of the
tongue. That is, look ahead on the page, and
see and understand clearly what you are going to
say, before you speak.

5. Think the thouf/hts avd feel tJte e))i<}ti.o))s.
Unless this is done the reading will be as profitless
to the reader, as it is dry, mechanical and meaning-
less to the hearer.

6. Be in earnest. Always throw yourself into the
spirit of what you read and try to do youi- l)est.

7. Make yourself heard, uialerstood and fell . Do
this without overstraining the voice or [)itehing its
tones too high.

8. Listen to others. Strictly attend while others

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192

METHODS IN TEACHING.

are readiiif^ ; try to see wlierein they do well that
you may make their merits your own.

9. Study the, Rcaduxj-kxson. — Prepare your
reading exercise as carefully as you would for a
recitation in any other subject. The productions of
the great masters of thought and expression cannot
be read properly without much study.

GEOGRAPHY.

193

11 that

your

for a.

ions of

cannot

t^ll

CHAPTER VI.

GEOGRAPHY. — PART I.

Though eminent educationists have done much in
recent years to spread abroad true ideas of the real
nature of Geography and of the right methods of
teaching it, yet it is but too evident that a great
discrepancy is commonly found l)ct\veen such
principles and the ordinary practice of the schools.
Too frequently has its scope been confined to location
and statistics, with elaborate map drawing as its
great display and long lists of empty names as its
chief result, — to the utter disgust of the child and the
dwarfing of his intellectual faculties.

Chief among the causes that have prevented a
more intelligent treatment of this subject may be
mentioned (1) The lack of a right conception of its
nature and purposes ; (2) Too great a dependence
upon text- books, as well for the order as for the
substance of the lessons ; (3) The pressure of exami-
nations, leading to the crannning of those facts and
names judged likely to be asked for; (4) The
dwelling upon unimportant details so that the main
principles are lost sight of.

The purpose of this brief sketch is to offer,
especially to such teachers of junior classes as aim at
something better than mere memory work, some aid
in raising this subject to a higher plane, making it
at the same time both educative and practical.
13

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METHODS IN TEACHING.

Scope and Aim — On account of its more or less
intimate connection with Geology, Botany and otlier
sciences it is not easy to define strictly the scope of
this subject. But the following quotation from Geikie
gives a pretty comprehensive view of its extent and
purpose : " It seeks to present a distinct and
luminous picture of man's surroundings — the earth
he walks upon, the air he breathes, the waters that
fertilise his fields, the ocean that bears him from
continent to continent, the living things that minister
to his enjoyment alike on land and sea. It selects from
the various sciences .... those facts and conclusions
which bear most closely upon the well-being of man,
or which enable us most clearly to comprehend the
general plan of the marvellous creation wherein we
form a part. It is the special function of Geography
to direct our attention .... to the «.ver changing
phenomena that surround us and infiue.^ce our daily
life ; to increase our knowledge of the country we
live in, and thence to trace analogies and contrasts
among the aspects of nature in other regions of the
globe. Geography compares the topography of one
continent with that of another, dwelling upon the
fundamental elements of each, and showing how
they have affected the distribution and development
of the human population .... Connecting the end-
less diversity of local detail with human history.
Geography notes how largely it has influenced the
progress of human events, how, for example, it has
directed the migration of peoples, guided or arrested
the tide of con(iuest, moulded national character, or
given its own coloring to national mythology and
literature. Gee graphy further contrasts the climates

GEOGRAPHY.

195

of the i;'l()h(3, calls attention to tlie varyin^jj pliases of
plant and animal life by whicli they are accompanied,
and traces tlxeir intiiience upon the march of dis-
covery, and the spread of civilization and commerce."

Observation the Foundation— Assumino, then,

tliat our object is not to teach tlie surfaces of maps,
(which for the pupil bear little relation to the reality),
but instead to build up a clear conception of the
earth's surface and its relation to man, how ! .all we
proceed ? It must be evident that if the child cannot
see and understand what comes under his own eyes,
he can form no adequate conception of what is
distant and unseen. But "Every school district is a
world in miniature, i'or it repeats the structure and
story of its life in pictures so vivid and lan<^uage so
simple that every child may see and read." It is all
important then that the stai'ting point shall be that
district with which a child is familiar, and that the
knowledge be gained by himself direct from nature
and not through books. Tlie method here advocated
may be thus sunnned up : — observe, express, reason.

To carrj^ out this plan it is best to begin almost
at the very outset of the children's school life, and
wdtli subjects not generally recognized as intimately
connected with Geograpliy. The chief purpose
should be to train pupils to observe clearly and
thoroughly. The facts thereby gained may be of
but secondary importance ; but it is the p<mrr to
observe that should be aimed at, and the /ntblt of
observ^ation that should be cultivated.

The earliest lessons on the familiar things in and
about the school, theii- home and the innnediate
vicinity, will of necessity be somewhat superficial and

196

METHODS IN TEACHING.

disconnected, only the most elementary and obvious
facts bein^ asked for. When the limit of the
children's knowledge has been reached, the whole
should be given in coiniected form, the teacher
adding such new facts as he deems necessary to a
clear understanding of the subject an<l within the
easy grasp of the pupils. But there must be no
attempt to force them to see through the teacher's
eyes, — rather should he follow their line of thought
than attempt to lead them. What a child discovers
for himself, is many times more valuable than if got
through hearing or reading. The questions should
be so framed that to answer them the child must
have see/i and noted something. This is a great
stimulus to examine things closely, and notably
encourages some pupils wdio may not shine in other
studies. Constant repetition and i-e vision are
necessary until the class has thoroughly mastered
these fundamental notions. Yet these review^s should
never be identical in form with the first lessons.
New aspects of old facts give clearer insight and
greatly aid in fixing them in the memory. Provided
a teacher is thoroughly familiar with this subject, all
forms of land or water should suggest numberless
questions, — comparisons, differences, causes, effects, etc.

Advantages of Rural Schools— Schools in the

country are the most advantageously situated
for this work. The>*e, the natural appearance
of land surfaces, little changed by man's action,
offers the best opportunities for the study of
hills, valle^/s, plains, streams, watersheds and the
circulation of watei' over the land. I'he tilled fields,
the neglected connnon and the woods afford v.M-ied

GEOGRAPHY.

197

[ction,
ly of
II the

(iclds,
nried

(3x;iinplc.s oi* vegetation; while (liffereiit types of
aiiinuil life can l)e .seei> in tlieir natural habitat.

VV^itii such abundance of material for stimulating
observation and reasoning, it needs only that the
school should tui'n the child's attention to these
things to have him appreciate nature through liis
own senses and not as described in the dry pages of
a text-book. The " Barefoot Boy " should more
commonly realize Whittier's conception ; for when

Hand iu hand with her he walks,
Face to face with her he talks,

then indeed " Nature answers all he asks."

Course in Tovm Schools— In towns, attention

will naturally be dii'ected more strongly to the
humanistic side, but all the forms of land and
water within each reach should be carefully studied.
The earliest lessons might well include visits to the
markets to note what farmers offer for sale ; the
chief local industries, — raw materials, process of
manufacture, disposition of the finished product ; the
public buildings with their location and purpose ; the
railways, — freight carried to and from town, direction
of road, neighboring places on the line, other means
of locomotion ; building materials, where got, how
prepared, etc., etc. There should be a series of lessons
on the common food-plants, e.g., wheat, corn, rice,
coffee, etc. ; on the materials used for clothing, e.g.,
wool, silk, cotton, etc. ; on the life and work of
farmers, miners, lumbermen, sailors, etc.

But even in towns there is fair opportunity for
observing natural phenomena. The various forms of
water, — mist, fog, clouds, snow, ice, hail, dew, etc., —

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198

METHODS IN TEACHING.

may be seen ; Jind tlieir causes and effects explained
wlien tlie pupils have lieen properly prepared, 'i'he
rising- and settin^^ of the sun, the varyini;- len<^th of
night and day, lieat and cold, the 2)0siti()n of the sun
in the sky, the changes in th<' "^'um's asp(;ct, the
direction and force of win<ls, .i. uroad expanse of
the sky dotted with bright stars and their movement
across the heavens, the appearance of tlie Great Zeal-
and location of the North Star, etc., etc., — all may be
noted in the town nearly as well as in the country.
The varying seasons should be remarked, as spring
with lengthening daylight, increasing warmth, the
opening of buds, the n;turn of birds, and reappearance
of animals, — in a word, the awakening to new life of
much that was dormant during the cold season. In
a later stage of the course the causes producing such
changes will be developed, if possible from the pupils
themselves.

And with earnest, resourceful teachers much can
be done even in towns to study plant and animal life.
Parks and gardens offer much material ; flower beds
and window boxes may be planted and cared for
by the pupils ; grass or flax seed may be sown in
wet cotton or a sponge ; a sweet-potato vine may
be grown in a glass of water, etc. Simple experiments
will show the differences in vegetation caused by
light, heat, moisture and soils. Types of several
forms of animal life are easily within reach, and are
of much interest if rightly studied. The wonderful
changes that a caterpillar undergoes should arouse
the intelligent curiosity of any class. It is not
intended that the teacher should be a botanist or a
biologist to conduct such teaching successfully, but

GEOGRAPHY.

199

'■ i»

: !
■ 1,

can
life,
beds
for
n in
may
nents

i by

eral

I are

erful

rouse

not

or a

, but

only that he shoul*] have some pei'sonal ac(|uniiitanee
witlj the subjects of liis lessons, and not base Ids
teaching wliolly on books.

Cultivate the Imag^ination — In connection
witli observing, the power to ima<ijine sliould
be carefully cultivated, for the purpose of this
teaching is not chiefly to make familiar the land
and water forms, the plant and animal life of the
district, but rather that, by appreciatin<^ what thus
falls under his own eyes, the child may be enabled to
picture the j^reat world beyond his small hori/on.
This he can do only through his imagination, which
is not a creative process, but only a working up of
old experiences into new. Our concepts of the earth
depend, then, upon what we have seen and under-
stood of that part which has come within our view.
As the pupil's field of observation mast neces-
sarily be very limited and his examination of it
rather imperfect, he must rely chiefl}'^ upon the work
of others and their presentation of it, for his know-
ledge of the vast world, — hence one great reason for
developing imagination at this stage. When the
familiar brook and meadow have been studied, the
teacher should endeavor by pictures, oral description,
and other means of illustration, to have his pupils
imagine, e.g., the great Mississippi, whose type they
have just examined. Similarly the neighboring hills
are used to build up ideas of the Alps, while a field
of sand on a hot and windy summer's day may
suggest the great Sf^hara, and the pond of a few acres
broaden out into Lake Ontario.

IllustratiOLS of Method— Within the narrow^
limits of this sk' Lch it w^ould not be possible to give

(

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200

METHODS IN TEACHING.

full (Retails as to tlic carrying out of tlii.s inetli(j(l.
The varying eonditioiiH ot* each locality mufst lai'^ely
detei'uiinc the order, and to a certain extent, the
treatment of the .subjects. But even a few imperfect
illustrations may be of some service.

If the weather has suggested " rain " as an
appropriate lesson for the day, even the youngest
pupils may be asked what rain is, where it comea from,
its appearance in falling, on what kind of days it
comes, what becomes of the part falling on the soft
ground, that falling on the hard road or path, the
appearance of the grass and plants after showers, etc.
When they have acquired more information the
subject is again taken up and they may study what
became of the water that sank into the earth, its use
to plants, how it again reaches the surface, where it
then goes, etc., etc., to lead to an understanding of the
circulation of water over the earth's surface. At a
later stage they might be questioned as to what
becomes of the water when wet things dry, under
what conditions drying is most rapid, where the
water goes when boiled away in a kettle, under what
circumstances they can " see their breath," the
moisture on a pitcher of cold water in a warm room,
the " frost " on window panes, in cold weather, etc.
Thus, gradually, they may be led to grasp the wonder-
ful circulation of water between the earth and the
air and its dependence upon the sun's power.

The neighboring brooks and streams should be
studied with particular care, to understand the action
of running water and why the land is organized into
slopes. The pupils should find out where the water
comes from, where it goes to, why it runs in a

r,E(XJUAl'HV.

201

ter
a

paitic'ular direction, wlicrc its coui-sc is swiftest and
where slowest, witli reasons: the ap[)eMi'ane«' ot' the
l)anks and hottoni ; wliether it is earryin;^ down
gravel, sand, or mud, and which of these prevails and
why, in a certain part of its course ; liow it appears
after a lieavy rain or nu'ltin(^ snow ; where it
is eating" away its hanks and the cause ; whether it
spreads silt over the land ; where it lias formed pools
and the reason ; what effect on its course an obstruc-
tion or a hard hank has ; what is the life in its stream
or alonu' its banks, etc., etc. From the sticks or loi^s
floated on its surface they will see its carrying
capacity, and if water wheels are f(jund along its
course they will have a demonstration of its powei"
to move machinery. How shall we compare the
ideas of running water gained from such teaching
with what they learn from the useless repeating of
the definition, "A river is a stream of water running-
through or over the land," when even the meaning of
" stream " is not known ?

Direction — In determining direction by the sun,
neither the east nor the west should be the point of
beginning, both because the position of the rising or
the setting sun varies from day to day and because
the opportunities for such observations are not
favorable during a good part of the year. But the
direction of the sun at noon is always the same, and
the time for observing is opportune. An upright
post four to six feet long, fixed in an open part of
the ground, should have the length and the
direction of its shadow marked by the children
at, say, nine o'clock, noon, and four o'clock. The
relation between the length and direction of the

'! ■

'■[•

202

METHODS IN TEACHING.

sluidovv and tlie positioii of the sun should be clearly
seen. The length and the direction of shadows cast
by tele^rapli poles, trees, persons, etc., should be
noted, until the pupils can readily infer that at noon
the shadows are shortest and point always in one
direction. Tiie names "south" and "north" may then
be <^iven. Either in the yard or on the school- room
lloor a due north and south line should be drawn,
with another at right angles to fix east and west.
There should be many exercises, varied and repeated,
until the pupils can readily determine the directions
of places and objects from one another. Later on,
they should learn how to tell direction by the north
stai' and by the mariner's compass.

Measuring^ Time ; Chang-e of Seasons— Obser-
vations of the sun's apparent course should be
continued, to show how time is measured and on
what the change of seasons depends. The measuie-
ments of the post's shadow should now be as exact
as possible and should be recorded at intervals of
about a fortnight. The children will watch with
gi'eat interest the gradual lengthening of the noon
shadow from the sunnner solstice until it attains its
greatest length at the winter solstice, and then its
shortening: till it attain reaches the exact measure-
ment recorded on the 21st of June of the preceding
year, when it once more starts to lengthen. The
precise length reached at the time of the fiill and of
the spring equinox should be noted and compared, as
also the hour of the rising and the setting of th' sun
then and at regular intervals throughout the year.
The characteristic features of each season should be
duly remarked, as winter with its short daylight, its

GEOGRAPHY.

203

cold and snow, the aViscnct' of vetretable and much
animal life, etc., etc. They may thus be led to
appreciate vvliat we mean by day and year, and how
each comes to be a standard measurement of time.
Even from their own short experience they can
readily recall that day has followed day, sea.son
fol^;v/ed season, and year followed year, and will
understand that the same ceaseless succession took
place in the past and will probably continue in the
future. The important matter is to have them
connect such succession with the position of the sun
in the heavens, and then, but not till then, should be
unfolded to them the wonderful truth that this earth
is b;:'.t a great ball constantly spinning on itself and
iXoinof around the sun. Time and effort should be
spent and all simple means of illustration employed
to make clear this great step in the child's progress
which conflicts so much with liis early impressions.

Estimating' Size and Distance — The junior

grades should be taught not only to determine
relative position but as well to estimate relative
distance and size. In dealin"; with the larger
divisions of the world, the figures used have
little meaning for children because the terms are
practically unfamiliar. How can it help them to
conceive the greatness of the Mississippi to say that
it is four thousand two hundred miles long, if
"thousand" and "miles" are to them but empty
words ? But the distance between two well-known
points, say in their walk to school, should enable
them to appreciate " mile." Many will have gone to
places some miles distant, say, to a town ten miles
away. Sucli a unit would be of service when dealing

]

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204

METHODS IN TEACHING.

I ■' 1^

with large areas or distances by 1\ ivincr the class
observe how small it is relatively. To estimate how
long it would take a railway train of average speed
to cross North America at its widest part would
appeal more forcibly than to give its distance in
miles, especially to those who have travelled by
train. Should there be a familiar hill re(|uiring say
twenty minutes to climb, this might be made the
unit, and pupils will better realize the great height
of some mountains if told that it takes days to reach
their summits, or that their tops stretch higher than
the clouds they see, rather than to state their height in
feet or miles. When the size of other towns or cities is
to be given, their own should be made the standard ;
other counties and countries should be compared or
contrasted with their own. Instead of giving dry
and often meaningless figures use familiar units
whenever possible, and also make appeals to the
eye by simple diagrams.

Subjects of Study — Lack of space prevents any
but a brief reference to other subjects of study. But
some consideration should be given to locomotion by
water and by land, the advantages of each, which
was earlier; the reasons for the location of railroads,
either on account of the nature of the surface, or the
centres of population ; the condition of communities
to which access is obtained by roads alone, by roads
and by rail, or by roads, by rail and by waterways.
Some attention should be given to the distribution of
population in the vicinity, — how the numbers and
grouping of the villages and towns are dependent
upon the fertility of the land, the richness of the
mineral deposits, or the advantages for commerce,

i u

'■ iV

GEOGRAPHY.

205

manufacturing, etc. Some simple ideas should be
gained of industries and commerce, and whatever
industries the district may be noted for should
receive special consideration. These observations,
which later would lead to an intelligent under-
standing of climate, should not be neglected,
especially as the simpler parts of the subject are
very attractive to children. Differences in tempera-
ture, how indicated by the thermometer, their
dependence on the sun, winds, elevation, etc., might
well be considered in so far at legist as they can be
judged from local conditions. In some schools it is
the practice to have pupils mark the readings of the
thermometer at stated liours, and a record is kept of
the year's temperature. The construction of the
thermometer should be explained when the pupils
are prepared to receive it. The number of bright
and of rainy days might be noted, with the
prevalence of each during the different seasons ; the
amount of rainfall might also be estimated if
convenient. The direction and velocity of the winds
might be remarked, noticing from what quarters
come the warm winds, the cold winds, those that
bring rain or snow, etc. Atmospheric pressure is a
difficult subject, and along with a full treatment of
climate, may well be reserved for a more advanced
stage.

Excursions and Field Lessons are of great value,

though often difficult to carr}^ out successfully. Yet
on holidays or outside of school hours it could
probably be arranged to have the pupils, in cla.ss or
groups, view^ from a hill-top, or other commanding
point, the surrounding country. The hills, streams.

!:i

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206

METHODS IN TEACHING.

V. \

lakes, islands, roads, etc., would be observed, and
described in sinij^le lan^ua«;e, their directions and
distances estimated, their names given, and so far as
may be, their relations studied. The main and lesser
divides could be traced, noting whether vague as on a
plain or sharply defined as on the crest of a ridge ;
the slopes leading from these divides to the streams
examined as to whether they are gentle or abrupt,
long or short, smooth or rough, etc. Attention might
also be directed to the arrangement of the streams
and the drainage areas, the size of the streams and
the area of the surface drained, etc. Such a " bird's
eye " view is woi'th more than maps, models or mere
descriptions, if the teacher knows how to use it.

Denudation — The slow wearing down of the land
surfaces should be studied in the action of r^iin, frost,
brooks, etc., in breaking up or carrying down to lower
levels, — the active movement on steep slopes, the slower
rate on flat surfaces, on which the waste accumulates
often to a considerable depth. The slight wasting
during dry summer or steady winter weather, the
great activity during rains and in spring and fall
when thawing and freezing rapidly alternate, will be
remarked. The great (quantity of waste borne along
by ma^^v streams, especially during flood times, and
the action of ponds and lakes in allowing the waste
to settle and discharging the water purified ; the
growth of deltas in favcr-able places, — all should be
noticed. In time pupils will understand that all
soil is but waste from the great store house of the
rocks, resting on its way to the ocean. It nuiy be
advisable to ofier suggestions and ex[)lanations in
regard to many geographic forms, if it can be done

■t I

■I^

GEOGRAPHY.

207

so as to convince pupils of their essentially simple
character. At a later stage they should fully
appreciate the fact that the present; geographic
features have not always existed in this fonn, but
that they are the result of long-acting processes, and
are being constantly modified. The older treatment
of this subject was empirical, exercising the memory
but not the reason ; the later teaching is more
rational, for geographic foi'ms when understood are
more easily retained in the memory than when
meaningless.

Modellings — Pupils should not only examine all
surface forms in their neighborhood, but it is equally
important that they should represent th.em. The
educational maxim that " there is no impi'ession
without expression " applies here with especial force.
The expression by language, moulding, drawing oi*
by all these means, leads to greater clearness in
observing, for, in the endeavor to combine and
represent his mental images, the pupil (juickly
recognizes the limitations of his knowledge. Though
moulding or modelling is not so easily provided for
or so generally used as is drawing, yet the earnest,
resourceful teacher could readily find means if only
he recognized the great value of the work in
representing form and relief. It is not intended that
nature should thus be taught, for a child should,
whenever possible, get his ideas from the real hill,
the field or the stream, and so have true pictures of
these ; the sand model is onl}^ a means of reproducing
his perception of the reality, and is laid aside as soon
as pup'ls have clear ideas of forms, and can imagine
them in other relations than those seen by the eye.

i,V^

208

METHODS IN TEACHING.

^ V

The earliest lessons may aim at emphasizing but one
chief feature, e.r/., a neighboring hill ; but gradually
the representation may include additional features.
If suitable pictures or diagrams are at hand for
illustration, the pupils may model other topographical
features not found in the district. It is decidedly
better to reach conceptions in this way rather than
by the rote learning of definitions.

When the teacher uses the sand or moulding
board his work should always be done in view of
the pupils, largely by their aid and subject to their
criticism. Time and effort should not be wasted in
striving for perfection, though fair accuracy should
be aimed at. If possible the school district should
be represented in relief in some more stable material
than sand. From the school as a centre, all points of
interest in the vicinity should have their distances
and directions determined by the pupils, and the
map be built up part by part during six or eight
weeks. In this or other models the vertical scale
should not be unduly exaggerated or a false impres-
sion will be given.

Maps and Map Drawing— Of great value in this
subject is the ability to read maps well, for a good
map shows the chief geographic features and their
relations more clearly than would pages of
description ; and undoubtedly the best way of learning
to read maps is to begin by making them. In
schools where drawing has been intelligently taught
through a study of objects and by the aid of the
board, the beginnings of this subject will present
little difficulty. Probably it is best to start with a
plan of the school room, showing the four walls and

GEOGRAPHY.

209

the position of the doors and windows. In
subseqr<^nt attempts further details may be added,
while the cale is varied. All measurements should
be made by the class and then reduced to the scale
chosen. Later efforts should show the schoolhouse
and grounds. Then the district, which has already
been represented in a model, should be mapped on
the board. In this way the two means of
representing geographical features are associated
from the outset. The signs used should be those
found in the best maps. Thus taught, each sign
readily recalls a clear, because familiar, concept ; after
some practice pupils will be able to interpret map
language readily and to form a fair mental picture of
the country so portrayed.

The same principles should govern throughout
the course. The first maps of a continent should, if
possible, be drawn from a raised model, so that pupils
should all along associate outline with relief. They
should be led to see that coast lines show the limits
where the continental slopes rise above the level of
the ocean, and that the same slopes are contin :od
below the level of its waters. In such maps no effort
should be wasted on details, but all attention should
be centred on the outline and general proportions.
The first maps of North America, for instance, should
show but few coast irregularities ; it would suffice to
mark only Hudson Bay, Florida, Gulf of Mexico
and Alaska. Later on, further details may be added.

Contrary to the usual practice, the early maps

should occupy less time in their drawing than would

the later ones, both because there is less detail and

because the whole attention should be given to grasp

it; i-

11 ;

iifi.

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210

METHODS IN TEACHING.

iHi

i -I

.! :f

and to express the (jeiwral proportions. With the

relief map in clear view of all, as many as can be so

acconnnodated take places at the board ; the others

work on papei* at their seats. At a word of command

all start, and the sketching is limited to about half a

minute. After criticism the maps are erased and

other trials made, until a creditable sketch can be

produced by the majority, within the time limit.

Subsequent lessons should review the work already

done and add such further details as are of

importance. When one country or continent has

thus been treated, the others should be studied by

comparison with it and with one another as to form,

area, coasts, etc. In connection with this work the

teacher should ask su<^gestive questions, which may

be answered from the map, e.g., In what direction is

the continent longest ? Where is it broadest ? What

is its general shape ? Compare as to outline and

size with others previously learned. How does the

greatest length compare with the greatest breadth ?

Which coast line is the longest, the shortest ? Which

coast is the most regular ? the most broken ? Give

the chief indentations in the order of size, etc.

There should be frequent practice in sketching
without the model, to see what the pupils can
accurately reproduce from memory as evidence of
their real knowledge of outline, surface, productions,
location of cities, etc.

The chief value of this branch o our subject is
its employment as a means rather than an end. The
production of beautiful and elaborate maps, merely
for the sake of appearance, but with little regard to
the means used, is to be strongly discouraged, as

GEOGRAPHY.

211

■ 'i

the
)c so
:hers
iiand
alf a

and
m be
limit,
•eady
•e of
■j has
id by
form,
k tlie
L may
tion is
IWhat
and
3s the
adth?
kVhich
Give

tching
s can
ce of

ctions,

|)ject is
The

lerely
iard to

ed, as

bein^ of little educational worth. The great aim
should be to lead the children to acquire correct ideas
of tlie surface under consideration, and to express
such concepts in a clear and simple form. But this
cannot be done when the maps are traced tlirough
thin paper, or when instruments and elaborate
construction lines are used, for then all attention is
fixed on producing an exact copy, rather than on
studying the form and relations of the original. But
when the pupil makes his own discoveries of the
relative length and directions of coast lines, of the
trend of the watersheds, etc., such knowledge is of
value, not only in that particular instance, but
also to stimulate to a close examination of other land
forms.

Except when the general shape and boundaries
are to be studied, the use of the prepared outline map
is often advisable, economizing time and effort, and
giving an accurate foundation for the special matters
to be considered. Some such maps are left to show
clearly but one particular subject, e.g., vegetation,
others grow from day to day as the study proceeds.
Such exercises are not to be carelessly cast aside, but
carefully kept, — the pupil thus having in a clear and
striking form the record of muvih of his work in this
subject.

For teaching purposes the common wall map is of
but little value. Instead the teacher may use
stencils, or better, practise rapid and correct sketching
on the board, the pupils filling in their own maps as
he proceeds. Some of the maps most frequently used
may be outlined in dark paint on the boards, or if
these are small, on linen or heavy paper. By means

212

METHODS IN TEACHING.

of simple diagniins on lar^e .shf^ets of mjinilla {)ap(3r,
many .strikino- illustrations of various facts can be
pres(;ntod in a eleai- and impressive foi'm,- -relative
areas, density and distribution of population, extent
and value of the chief productions, the amount and
kind of exports to or imports from different coun-
tries, etc.

The County — Before entering on a wide field it
may be advisable to make imaginary journeys to
districts beyond the immediate neighborhood of the
school but yet moi-e or less known to the children.
If a good map is available the county might become
the subject of study. Such trips could be made by
following the course of the roads, the railways or the
streams. There should be nothing in the nature of
tasks to be mechanically learned by heart, but
instead the pupils should be encouraged and directed
to discover what the map may reveal or to contribute
facts gained by themselves. The course of the
streams should be observed, and they may be
followed upwards to their sources and downwards to
their outlets, their area of drainage determined and
the watersheds located. The general configuration
of the surface, the nature of the soil, the means of
communication, the dependence of the products and
the industries upon the character of the surface, etc.,
should all be carefully studied. There should be a
judging of areas, direction and distances, a comparison
of valley with valley, stream with stream, etc.

When the school district and its environments
have been carefully studied, the scattered and
isolated facts thus gained should be collected and
classified in order that their significance and mutual

GEOGRAPHY.

213

aper,

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utive
xtent
:, and
coun-

eld it
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ildren.
ecome
ide by
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ure of
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ay be
irds to
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ans of
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nments
)d and
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mutual

relationsliip may be clearly perceived. It is a correct
pedai^^o^ic principle that facts should be seen and
understood first as facts, before examining their
causes and effects. While the surface and other
geographic features of the district have been studied
cliiefly as so many unrelated facts, the numerous
dependent rehitions existing among them should now
be enquired into and made as clear as possible. In
the early stages of study, pupils do not readily
perceive the relations of things to one another ; they
more readily grasp the resemblances but must be
trained to detect the differences as well. It would be
unwise at first to point out reasons, and unwise at any
stage to deduce general laws from too few data. It is
only by the comparison of several streams, noting
their points of agreement and eliminating their
accidental differences, that pupils will be able to
understand rivers as a class. They will have studied
the formation of clouds, their movement by winds,
the fall of rain, the welling up of springs, the flow of
the water down slopes to the sea, before their
wonderful connection and their dependence upon the
sun's power are grasped. Reasoning is the last ot
the three steps yet in many respects the most
important, for without it ^^e could not apply what
we have learned.

Country or Continent ?— In determining the
next step after the district and its environments, mere
nearness in space should not count, but instead what is
the simplest and most related to the preceding study.
If the pupils have gained from observation true ideas
of slopes and of their relations, they should be able to
imagine other land areas made up of like forms, — the

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METHODS IN TEACHING.

clearness of the picture depending largely upon the
simple or the complex airangement of the slopes.
On account of the detail involved, the adjoining
county or one's province is more difficult to imagine
than is a whole continent. The frame work of North
America, for instance, is verj^ simple, being made up
of two great land masses, each having two slopes,
with a great central plain and four great river
basins. The continents, then, may be taken up when
local geography has been exhausted ; first our own,
then, in the order of their simplicity of structure,
South America, Asia, Europe and Africa. This
study should centre chiefiy on relief, — the great
slopes and their arrangement relative to rainfall,
drainage and heat.

Topics in Studying^ a Country

1. Position, etc.

/- 1. Latitude, longitude, hemisphere.
I 2. Boundaries.

2. Pliysical
features.

1. Highlands

"i 3. General form.
I, 4. Size, absolute and comparative.

f f Ranges.

I Direction.

1. Mountains. < Slopes.

Heights.

V Volcanoes,

2. Plateaus, extent, [etc.
elevation, effects, etc.

/I. Causes.
12. Effects.

3. Deserts.

2. Lowlands.
l3. Draw profile.

1. Watersheds.

3. Drainage.

2. Rivers.

3. Lakes.

r 1. Source and outlet.

I 2. Direction, with reason.

I 3. Size and use.

I 4. Branches.

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215

[etc.

4. Climate.

I. Causes.

Products

and
Commerce.

7. Life.

[ 1. Latitude.

2. Elevation.

3. Mountains.

4. Slope.

5. Winds.
0. Moisture.

^ 7. Currents.
2. Peculiarities.
^ .*S. Healthfulness.

Chief productions in order of importance.
Localities where found ; preparation, use.
Leading exports, where sent, routes.
Leading imports, where got, routes.
Great commercial centres and facilities for
trade.

' 1. Vegetable.

2. Animal.
( Races, population, occupations.

3. Human. \ Language, civilization, customs,
i Government. [religion.

8. Political Divisions.

9. Striking characteristics.

10. Comparisons with our own and other countries
already learned.

In the foregoing table an attempt is made to give
in due order the topics in studying a country. It is
believed that the general arrangement is a good one,
though in some particulars it may be departed from
at the teacher's discretion. The following outline of
the study of our continent is based only in part on
this order.

North America — An irregular triangular prism ;
simple shape due to few centres of uplifting, chiefly
two. On west, the Cordilleras, of complex structure,
several parallel with some cross ranges, supporting
lofty plateau, gradually rising from 800 feet in north
to 8,000 feet in Mexico, in places a thousand miles in
width ; now less than half the uplifted mass
remaining, present denudation slow as rainfall

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METHODS IN TEACHING.

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decreased ; volcanoes at north and south. On east,
the Appalacliian system, irom Newfoundland to
Alabama; several ranges, generally parallel, lower
and less well-detined than Cordilleras, and farther
from coast, no volcanoes; some ranges old and greatly
worn down ; others (e.g., Alleghanies,) of recent
formation. Between these two systems lies great
Central Plain, from Arctic Ocean to Gulf of Mexico,
with scarcely a break ; its area of arable land the
largest of any continent. The Laurentian a third
system, probably oldest land in continent, now much
worn down, the waste has built up much of eastern
district, difficult to trace trend of some of its ranges ;
now of but sliglit geographical influence.

On inner side slopes from two great highlands
very gradual, Mississippi marks meeting place ;
arrangement of great land masses sends most of rain-
fall into great central plain ; Height of Land and
Great Divide determine its flow north or south.
General land mass but little broken, compare with
Africa, with Europe ; effects ? Hudson Bay and Gulf
of Mexico conspicuous features, probably remnants
of original central ocean. On northeast, numerous
islands, separated by sounds, generally level, probably
pirts of -mainland sunk beneath sea, form much
changed by ice action ; great mineral wealth, suitable
soil, great natural advantages for connnerce, but
rendered useless by cold ; fossil remains prove
climate once mucli milder. Greenland, true form not
known ; except strip along south all covei'cd with ice,
thousands of feet thick, renuiant of great ice age.
Irregularities of east coast prt)bably old, water- worn
valleys, further deej^ened by ice, and depressed below

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GEOGRAPHY.

217

ocean. From New York to mouth ot Rio Grande
a fringe of small islands foi'med by wave action along
gently sloping coast, protect mainland. Coral islands
for about two hundred miles along Florida coast ;
southern mainland here of same formation and still
growing south ; effect on Gulf Stream ? West
Indies and Aleutians different from others ; appar-
ently sununits of growing mountain ranges, many
volcanic. Numerous deep, irregular bays, along
southeast coast, probably formed by rivers when land
was higher, then valleys lowered below ocean, now
filling with silt.

Drainag^e — Four chief river basins, the Mackenzie,
the third in size, the chief into the Arctic, valley but
little known on account of great cold, apparently re-
sembles that of Mississippi ; stream freezes to bottom,
thaws first towards south, causing floods and very
irregular course in north ; fed by many great lakes ;
of little use for commerce. But sliglit separation be-
tween valleys of Nelson and Mississippi ; with but little
portaging one can pass in a canoe at high water from
one to another. St. Lawrence the second in importance;
with possible exception of Nile the greatest lake-fed
river ; very steady flow ; not descend by gentle
declivity but by series of rapids or falls liaving great
level stretches between ; scarcely a trace of sediment
and so but little cutting power and no delta.

Except Amazon, Mississi])pi has greatest length of
water navigable Tor larger vessels; ti'averses territoiy
with great differences of climate and rainfall, carries
much nnid, fre(|Uently changes bed, Icvcts r('(|uired
some hundreds of miles From mouth, outlet by
several streams, delta steadily extending.

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METHODS IN TEACHING.

The wliole continent is particularly well watered,
and streams so situated as to be of great service to
commerce. Africa lias moi-e large streams, but
within tropics and with great rapids. Asia has more
navigable waters, but several empty into the Arctic.
South America has about enual facilities but mostly in
tropics with little variety of productions. The great
number and area of fresh water lakes, a special
feature unequalled in any other continent, resulting
chiefly from glacial action ; Great Salt Lake an
exception.

Forests — When settled by Europeans, forests very
continuous except in Mississippi valley. Appalach-
ians hold flnest forests of broad -leaved trees in world,
but have also coniferous trees, " in no other spot of the
temperate zone are the timber trees so varied or so
useful," one of leading exporf^s to Europe. North-
ward the number and the varieties decrease, north of
St. Lawrence the firs predominate, but farther up
cold stunts growth. Our Pacific forests begin v/here
rainfall is moderate, thence towards north increase
in number and area covered, latt^' decreasing from
cold, but reaching a tliousand miles fartlie^' tlian on
east coast ; mainly cone-bearing, some species sequoia
and redwood among largest in world, but few
remaining. The palms and palmettos, the Cyprus and
live oak, worthy of notice.

The prairies probably once forest clad, but repeated
burning of undei'growth and dry grass gradually
destroyc^d tre(\s.

rpi

riie prairies, a charactei'istic feature, covered
with coarse grass, and varieties of flowers, formerly
feeding great herds of buflalo and deer, the abundance

GEOGRAPHY.

219

of which kept aborigines as wandering hunters ;
rapid settlement of continent largely due to their easy
tillage and great fertility.

Climate — All sorts from polar to tropical as land
stretches from 10° to 80° ; greater variety than in
any other continent except Asia; four chief divisions,
— frozen north, one-fourth of continent ; arid region of
Cordilleras, about one-fifth ; tropical climate of
extreme south ; and great central region of medium
temperature and rainfall. No protecting mountains
at north to keep off Arctic winds, hence changes of
temperature great and often abrupt ; colder than
Europe in same latitude, east colder than west, why ?
(jrulf of Mexico a more important climatic factor than
Atlantic or Pacific ; much evaporation from great heat,
prevailing winds carry the moist warm air far into
interior, influence felt probably up to Great Lakes.
Rainfall pretty evenly distributed over habitable
portion, only about one-twentieth of continent really
arid, irrigation employed. No extensive deserts as
found in other continents, amount of rainfall in
proportion to surface exceeded only in South
America and Europe. Small area of perpetual ice and
snow relative to other polar divisions, but Greenland
is greatest known district of glaciers, its icebergs
sometimes of several cubic miles may float a
thousand miles south ; effect on climate ? A great part
of coast subject to cold water currents, felt less on
west as but narrow openinir from Arctic ; Gulf

op
Stream chief counteracting agency

? effects?

couri

Japan current aids on west ; the west coast wanner
and moister than east. Except Europe, North

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METHODS IN TEACHING.

America best suited by climate and general build to
serve for highest development of human race.

Soils, of three classes, glacial deposits cover much
of northern part, all that district once occupied by
ice fields, not of great fertility but lasting ; farther
south, derived chiefly from underlying rocks, of
different degrees of fertility, the limestone area being
the most fruitful ; the third are alluvial terraces
resulting from overflow of rivers, the richest of all.
The alkali plains in the west are the result of
lessened rainfall.

The vegfetation is very rich and of wonderful
variety ; besides maize, the potato and tomato, which
are indigenous, all grains, fruits and roots known in
the old world before America was discovered, thrive
well in one region or another. While the polar
regions sustain only stunted trees, lichens and mosses,
the south furnishes the banana, sugar cane, palms
and bamboos, and the intermediate temperate
regions produce cotton, tobacco, rice and all sorts of
food grains in great abundance.

Minerals — No other continent afl'ords as great
variety or richness of mineral products. There are
three chief mineral belts corresponding generally to
three chief mountain systems ; that of Appalachians
most explored, that of Laurentians but imperfectly
known, while in Cordilleras there exists a greater
and more varied litore of mineral wealth (except fuel)
than is found in any equally large area in the world.
The coal fields of Appalachians, the most important,
being easily accessible and extensively woi-ked : the
anthracite, produced in Central Pennsylvania, beds
not over five hundred square miles in area but

',i:jiiiai£^&iiiiuaAiii^jcm.i,-jsi.

GEOGRAPHY.

221

:f. II

usually very thick. Coal Ht'l<ls of coutiueut
ori<.;iually much more extensive but became stripped
away by st'a and glacial ice. Abundance of copper
in nearly pure state about Lake Superior ; iron is
widely distributed and extensively mined. In
southern Appalachian region a peculiar advantage
exists in coal and lime being found close to the iron.
Oil and gas, resulting from the decay of animals and
plants, exist in several though probably limited
districts.

Commercial Advantages— In civilized communi-
ties it is of the highest importance to liave ready
access to the markets of the world for the necessary
interchange of products. The location of our conti-
nent is most favorable for trade with the great
commercial and manufacturing peoples of Western
Europe, and through the Mediterranean with a portion
of Asia. The Pacific offers easy connnunication with
Eastern Asia and Australasia. The ice-bound condi-
tion of the north and northeast coasts shuts them off'
from much connection w^ith the rest of the world ;
the shallowness of Hudson Bay is another obstacle.
If water communication between the two oceans can
be effected at the Isthmus of Pannma, it will be a
great aid to commerce. Ours is the great food-
exporting continent, sending to the populous countries
of Europe their chief supplies of grain and meat.

In so extensive a territory the necessity for
suitable internal communication is as important as
the means for trading abroad. One great advantage
both for domestic and foreign commerce is the great
extent of coast line and the numerous well-situated
harbors. The system of internal waterways afibrds

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METHODS IN TEACHING.

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great facilities for trade ; the Mississippi is the most
important, provichno-, witliits tributaries, 85,000 miles
of nav^igable waterways. The St. Lawrence and the
Great Lakes furnish an excellent water route from
the Atlantic to the very heart of the continent for a
very large volume of trade. Though the Mexican
peninsula has no great rivers, the country is in no
part far from the coast. The Gulf of Mexico and the
Caribbean Sea are of great commercial advantage by
their position, affording, in connection with the
Mississippi, ready communication from the great
central plain to South America and the Antilles — one
of the largest and most fertile groups of islands in the
world.

The gradual slopes of the nterior permit the easy
construction of railroads, for even the Cordilleras are
more easily crossed through passes than are the great
chains of the old world. The wonderful variety of
products in different parts of the continent furnishes
abundant material for trade, domestic and foreign.

There is excellent provision for cheap and
abundant power for manufacturing, not only from
the great supply of fuel advantageously located,
but also from the numerous streams having a
considerable fall. The lake-fed streams of the north-
east and towards the southern part of the Appalachians
furnish a steady supply. There are few, if any,
districts providing a larger and cheaper supply of
power, and this region is likely to be the seat of still
greater manufacturing industries, especially as the
food supply is cheap and abundant.

Miscellaneous — To arouse interest and awaken
sympathy it may be well to have *Jie juniors study

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GEOCxRAPHY.

223

aken
;tudy

cljiM life ill various countries. As a rule, chiMreii
(Icliglit in lu'arinj^' about the homes, games, food,
dress and manner of living of those whose life
presents a great contrast to their own. Illustrations,
models, reading etc., may be freely used, so that they
may have a vivid picture of the Indian boy, with his
canoe, bow and arrows, of their little Eiskimo friend
clad in furs and living in a house of snow, etc. The
dwelling on trivial matters, or those merely
entertaining, should liowever be carefully avoided
throughout the course; in all cases the aim should be
important and the matter of value.

For convenience, definitions are grouped together
at the beginning in most text books, but good
teaching requires that they be taken up only as
the subject demands, and if possible, be both
discovered and framed by the pupils. If necessary,
the teacher may suggest a better form, but he should
remember that, as children are not critics of words,
exactness of language does not necessarily imply
clearness of thought, — which latter is the point to be
aimed at. The real purpose of definitions is not to
make mere parrots, but instead to develop perception,
description and generalization.

A good sized globe, properly mounted, is
indispensable, and should be continually referred to
in order to correct wrong impressions likely to result
from flat maps.

Aids for Teaching— There should be a cabinet
of collections furnished largely by the pupils,
to illustrate grains, woods, Ici'ves, animal or
insect life, articles of manufacture in their raw
and finished state, etc. Too often these things

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224

METHODS IN TEACHING.

are mere names to the pupil. It is of ^reat
importance also to interest the pupils in making a
collection of pictures, showing scenery, noted cities
or buildings, houses, dress, productions, etc., etc. ;
arrange these by countries or subjects. Similarly,
clippings from magazines or papers may be collected
and kept in scrapbooks, properly classified. In the
higher grades a geographical magazine should be
subscribed for and other means taken so that obsolete
or incorrect geography be not taught. It is essential
to the most successful teaching to have pupils read
suitable books of travel and use the information to
expand and illustrate many of the lessons. Should
the school lack a library of its own, some interesting
books might be got from the public library. But it
cannot be said that your teaching is the best unless
you have stimulated the pupils to study for
themselves, and in every way encouraged such
efforts. It is advisable also to have some good
works of reference for the use of teacher and pupils
alike.

Text Books — Much of the unsatisfactory showing
in this subject has resulted from a slavish dependence
upon the text book. Not only was the matter of the
book treated with religious reverence by being taught
in its entirety, neither added to nor departed from,
but the precise order of arrangement was also
scrupulously followed. It needs but little considera-
tion to show that while convenience dictates a certain
order for text book arrangement, the best order
for teaching is often a very different one. It
is best to use no text book until pupils come to the
study of particular countries, and then it should

GEOGRAPHY.

225

f^reat
ing a
cities
etc. ;
ilarly,
lected
[n the
Id be
(solete
lential
3 read
ion to
should
■esting
But it
unless
Y for
such
good
pupils

Lowing
adence
of the
aught
i from,
IS also
sidera-
sertain
order
le. It
to the
should

be used rather for the purposes of review thati of
actual learning. But the books used by the child
should be more than mere tabulated lists of countries
and capitals, rivers, mountains, exports, etc., which
is all that some manuals now contain.

Useless Details — A common fault which should
be carefully guarded against is the giving of too
many details of relief, outline, location, products, etc.,
and often without any connection between tliem.
Teach only such forms and facts as are necessary
to a proper grasp of the subject, and not as unrelated
units, but as parts of a great wliole. Can we cut
down to fifty the list of cities to be remembered ?
The great commercial centres number less than that.
Show the use of the atlas and gazetteer and spare the
wearying effort to load the memory with, useless
details. Assist pupils to discover the influences
affecting the growth of great cities, and the
commercial relations of such cities to the surrounding
district, and they will have more important know-
ledge than the exact size and location of the chief
cities of the world.

Teacher's Qualifications — Accepting as trub
these views of the scope and aims of Geography,
it is evident that not every one is qualified
to teach it properly. An essential condition of
success is a thorough, intelligent study of the
subject to grasp its great principles and their
relation. A wide range of reading is necessary, to
have full and accurate information, with a large store
of illustrations drawn from many sources. Above
all, the teacher should have such a practical
knowledge of his subject as mere reading cannot
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METHODS IN TEACHING.

^ive unless aided by reflection and personal
observation. Thus eijuipped, he may free himself
from the slavery to text books as well as from the
bondage of tradition and habit, and shape iiis course
according to the spec^ il needs of his class and his own
individuality.

The subjoined list of books will be found
serviceable ; the writer has drawn freely on several of
them.

Pupils' Books

Seven Little Sisters. Each and All. Stories Mother
Naturo told her Children. — Andrew's.

Little Lucy's Wonderful Globe. — Yonge.
The World by the Fireside.— iCir/>i/.
Madam How and Lady Why. — Kingsley.
Little Folks in Feathers and Fur. — Miller.
Two Years before the Mast. — Dana.
What Darwin Saw.

Our World Reader. No. 1. No. 2.— Hall.
Footprints of Travel. — Ballon.
Geographical Readers, various sets.

Teacher's Books

The Teaching of Geography. — Geikie.
How to Study Geography. — Parker.
Child and Nature.— i^rj/e.
A New Comparative Geography. — Meikeljohn.
Comparative Geography. — Hitter.

Earth and Man. Common School Geography. — Guyot.
I'hysiography. — Huxley.
Physical Geography. — Tarr.

Story of our Continent. Man and Nature in America, —
Shaler.

Methods and Aids in Geography. — King.
Methods of Teaching Geography. — Crocker.
The Realm of Nature.

MATTTEMATTOAL OEOaRAPHY.

227

9 lot.

ica. —

CHAPTER VI.

(Qntthmed.)
GKOGRAI^nV. — PART II. — (MATHEMATICAL).

I. The Shape of the Earth— For the best results
in these lessons, the teacher should be provided with
a globe without lines of any kind upon it ; for, one of
the main purposes of the lessons is to show why
certain lines are placed where they are apon a
globe.

1. Make a dot on the surface of the globe and
let a pupil start from this dot and continue in the
same direction until the finger or pointer returns to
the starting point.

Let another make the same experiment on the
desk ; another on the blackboard.

Then inform the class that a few hundred years
ago people thought our earth flat, like the table or
the blackboard. Ask what people in those days
would naturally regard as the fate of one who
ventured too far out on the ocean's surface. Then
ask why we no longer fear such results. All are
doubtless familiar with the fact that the earth has
been circumnavigated.

As a matter of interast, ask for the name of the
first circumnavigator. If they do not know, give an
outline of the voyage and the change of view it
brought about.

Now repeat the three experiments with which
the lesson was introduced, and see if all realize what

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METHODS IN TEACHING.

1 (earing the circumnavigation of the earth has on its
wliajie.

2. Phico a toy boat behind the globe and
gradually raise it, keeping the body of the boat in
contact with the globe. Let the pupils tell what
parts they see first, wdiat parts next, until the boat
is in full view.

Repeat and let the class tell why the larger
part of the boat is not seen first. What shuts it out
of view ? Try the experiment on lloor or desk when
all parts are visible all the time.

Next appeal to the experience of the child.
What has he seen first with a real boat on the earth's
surface ? I'hen let the class state the conclusion
regarding the shape of the earth, to which this fact
would lead. The class should then be trained to
draw a diagram illustrati7ig this fact.

Showing Rotuxuity of the Earth.

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3. Stick three pins of equal length upright and
in line on the desk or on some other convenient
plane surface. Let pupils notice that the tops are
in line. Stick the same pins not very far apart and
in line on the surface of the globe. When the eye
looks from the top of the first to the top of the
third, the top of the second seems higher on account
of the curvature of the globe. Now by placing three

'Siig-iaiaaiiilTMHii;1i,T;iaKiMrr«;;^i<a»^.

MATHEMATICAL GEOGRAPHY.

229

poles of oqiial len<^th vertically in a straight line at
coriHiderahle distancen apart on a level beach or plain
it has been found that the tcjp of the second, as in
the case of the <;lobe, is higher. Let class draw
conclusion and then practise the diagram.

•'vi

and
ent
are
and
eye
the
)unt
iree

Fig 2. The Cubvatuuk ok thk Kaktii.

4. Let the pupils observe the shape of the
shadow cast by a circular plate on a wall, a black-
board or a floor. They will notice that the shadow
varies from a slraio-ht line when the edge of the
plate is towards the source of light, to a circle when
the plate is held perpendicular to the direction of the
rays of light. Afterwards, try the sphere and the
class will notice that the shadow is uniformly
circular.

See how many of the class have observed an
eclipse of the moon, and tind what is their recollection
of the shape of the shadow cast by the earth. Since
the shadow has always been observed to be circular,
they will, with the lesson of the circular plate and
the globe fresh in the memory, draw the conclusion
regarding the shape of the earth.

5. Take the globe again, and place vertically on it
a pin or piece of wood, to represent a man. How
much of the globe can he see ? The class can be led
to the conclusion that the limit of vision is formed
by what we call tangents to the earth's surface from

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METHODS IN TEACHING.

the point of vision, and therefore the line between
tlie visible and the invisible is a circle (Horizon).
Let the pupils look about thein when outside and
see how on the earth's surface we have a similar
circular boundary line. A j^ood diagram is helpful
here, as it shows why one sees a greater distance
when in an elevatec position. Bearing of this fact

""■''^ ■■' at the ioJ> vj
a,

EMLARGKMKNT OK .'ORIZON BY ASC'ENDINCJ A MILL.

on the shape cf the eartli? There are other proofs
which do not ler.'i themselves so readily to
elementary treatment and yet are most convincing.
They may be given in outline to the older classes.
Two of these are : —

(j. The weight of a body is practically the same
at all points on tlie earth's surface, though slight
variations are observed on the tops of high
mountains, and even at the sea level in ditl'erent
latitudes, on account of tlie bulging out of the t^arth
at those points. Tluui, the conclusion : — Since a
spliere is the only solid on which all points on th(i
surface are equally distant from the centre, the earth
is spherical in form.

MATHEMATICAL GEOGRAPHY.

231

Mlt
•th

a
ho
•til

7. The pendulum really furnishes us with the
most delicate test of the g'eneral sphericity of the
earth, and the slight departures therefrom. The
diameter at tlie equator is thus found to be about
26^ miles greater than the polar diameter.

II. The Size of the Earth— Teach the division
of circles into quadrants and the sub-division of the
right angles so formed into degrees.

By cutting an apple or orange through the centre,
lead to the conclusion that the section of a sphere
through its centre gives a circle. The arcs on the
circumference subtending ecjual angles will at once
be seen to be equal. Hence, if an arc of one degree
can be calculated, the circumference is obtained by
simple multiplication. (Give the results.)

To make the size of the earth clearer to the
chUd's mind construct simple problems, such as, "If
a train travelling one mile per minute could journey
around the earth, how long would the journey
occupy ? "

III. The Motions of the Earth— Introduce the
subject by bringing out the fact that we may easily
be mistaken regarding motion. Some of the class
have, doubtless, been in a train, and on looking out of
the window have been convinced that the " other
train " or the earth was visiV)ly moving, while they
were at rest, but at last realized that it was their own
train which was in motion. What child has not
noticed that tlie moon sometimes seems to be
hurrying through the fleecy clouds? May we not,
then, be mistaken also about the jj-lobr on which we
live, which seems so fixed and innn')vable ?

First, then, convince the class that simicthlwj

llf:

ill

u'^n.

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232

METHODS IN TEACHING.

.17

must move. Ask the class where they look for the
sun in the morning and where in the evening. Can
they explain the apparent change of position in any
other way than by saying that the sun moves ? To
reach an answer, perform an experiment.

Take John and James to represent the sun and
the earth, respectively. Let James (Earth) remain
fixed while John (Sun) moves in a circle about him,
coming into sight on James' left (sunrise), continue
till directly in front (noon), then on till he disappears
from James' view on the right (sunset).

Next repeat the experiment with John (sun) fixed
and James slowly revolving on his heel from right to
left. The same succession of sunrise, noon, sunset
will follow. Repeat with two globes.

Which of these two ways of producing these
results is the more likely in the case of the earth and
the sun ? Either the sun, moon and stars move
through millions of miles about the earth every day
or the earth revolves on its axis. The distance of
some of the stars is so inconceivably great that the
former is impossible.

Bring out the fact, that since the sun seems to
move from east to west, the earth must revolve in the
opposite direction.

2. Arrange the globe so that it can be rotated
rapidly, or better, have a small grindstone. When
the rotation increases sufficiently drops of water are
thrown from the surface in the direction in which
the body /n rotniinij. Tell the class that the eai'th
does a pi'ecisely similar thing. A stone dropperl
down a deep mine or a cliff' always falls a little cant
of a vertical line, in other words, is thrown east by
the earth's rotation.

MATHEMATICAL GEOGRAPHY.

233

I'KOOF OK EAKTll'8 KOTATION.

If the earth moved as fast, comparatively, as the
grindstone, tlie motion of the stone would be
horizontal from the top of the cliif (ae). If the
earth did not revolve at all the stone would fall
vertically (ac). As the rate of revolution is sk)W it

falls between these
two and nearer the
perpendicular (ad).

Focault's experi-
ment has made the
rotatory motion of
the earth visible.
For a description of
this see Jackson's
Astronomical Geo-
graphy (Ginn 61 Co.),
or Lockyer's Elementary Astronomy.

Some of the more Evident Results of the
Earth's Revolution—

1. Day and night. Have a lighted candle or lamp
and let the pupils observe on how large a part of the
globe the light from either will shine. So in the
case of our world — one-half will be enlightened.
Follow a point during a complete i-evolution and
observe how long it is in darkness. The darkness
is simply the shadow of the earth.

2. Use the globe to lead the class to see that in a
sphere <ft rest no points on its surface are
distinguishable^ from (jther points. N(5Xt maik with
chalk several "points" on the sui'facr of the globe
and revolve it. What is the nature of the path in
which each [)oint moves ^ Let the class note the
varying sizes of the circles described by the various

i^:

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: V.

234

METHODS IN TSACHING.

V ■

points. Wliere arc the points that travel fastest ?
(EquatorY Slowest ? There are two which are
i-eally a,t rest, (Poles). The line joining them (Axis).
The definitions Vvoiild readily follow from this treat-
ment, e.g., '* In a revolving sphere there are two points
on the surface which are at rest. These are the Poles."

"The line joining these is called the axis," etc.
Just here a little more light can be thrown on the
bulging out of the earth at the e(|uator. 'ict some
boy take a pailful of water and whirl it i:i a vertical
circle. The class will see that some force acts on
the water when the pail is at its highest point to
prevent it falling out (centrifugal). Since the earth
at the equator revolves mo»"e rapidly it is acted upon
most strongly by this same force and so bulged out
while a corresponding flattening occurs at the poles.

The Yearly Motion of the Earth— Place some
objec^ in the centre of the table to represent the sun,
and let the globe, representing the earth, revolve with
its axis perpendicular to the table, but with no
motion about the sun.

The class can be led to see that in that case the
length of day and night, as well as of the seasons,
would be constant at the same point throughout the
year.

Next cause the globe to revolve on its axis but
with the axis inclined away from the pevDendicular,
yet with no motion about the sun. The pupils will
observe that under such conditions part of the globe
would be in continual darkness and part in perpetual
sunshine, contrary to the facts observed in the case of
the earth. C/an any motion be suggested that would
agree with the known facts ^ Choose some point in

.tiiii£®!>ffiist*3V-tAi3if!;;ill>l4VlT*»'*

,u.fiiim.i.,mami

MATHEMATICAL GEOGRAPHY.

235

the

but

the room corresponding to the North Star. Cause
the ^lobe to revolve on its axis, witli the North Pole
pointing- towards the fixed point, and at the same
time let the globe move about the representation of
the sun.

If the globe is made of tin and a lamp used to
represent the sun, this part of the subject can be
made much clearer, as the contrast between the part
illuminated and that in the shadow is much more
decided.

Teach the seasons wholly by questioning as the
globe revolves on its axis, and moves very slo v^ly
about the " sun."

Pictures of the earth, (I) at the vernal equinox,
(II) at the summer solstice, (III) at the autumnal
ecjuinox, and (IV) at the winter solstice, which can be
seen in any geography, will resist in teaching the
seasons.

From experience the pupils know that in winter
the days are shortest, and hence the sun's rays act
for a comparatively short time each day.

The following diagram shows also the weakening
of the effects of the sun's rays by their
distribution over a greater surface.
Rays falling vertically, as at A B, ai'c
distributed over twice as great an area
when falling oblicjuely, as at C D. a| | ] ■ — |B

Let several members of the class
in succession describe the distribution of
light and heat on the earth's surfjice in /

the different positions dui'ing its jouiMiey

round tlu; sun, r.

Just

now

y
/

part about the North po'e is in darkness

OMLlyl'K KAYS.

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236

METHODS IN TEACHING.

day after day, (revolution after revolution), the
part about the south pole is in sunshine, while
the sun's rays are shining* vertically about
here." This describes the state of affairs about
Christmas, and will serve to make clear to them the
kind of Christmas weather experienced, say in
Australia.

They may be told that by observation it has been
determined that the greatest distance the sun's rays
ever fall short of, or beyond the poles is 23" 28' and
this is therefore the measure of the inclination of the
earth's axis to the perpendicular. This it is plso
whicli fixes the position of the Arctic and the
Antarctic circles, which are the circles bounding
those parts of the earth which are alternately in
darkness and in light for a considerable period.

Let some member of the class take a piece of
chalk and hold it steadily at some point on the line
between the illuminated part and the part in the
shadow, and then revolve the globe. If the globe is
in the position of the earth on Dec. 22nd, the chalk
will trace the line representing the Arctic circle. So
for the Antarctic circle,

Introduce the last pair of parallels by a talk on
shadows. At what time of day are shadows longest?
Is there any shadow with us at mid-day ? Is the
mid-day shadow longer or shorter in sunnner than in
winter f It is most interesting to drive a pole into
the earth firmly, to re<juire the pupils to mark the posi-
tion of the end of the shadow at different hours of the
day and then to join those points ])y a curve. They
will observe by keeping this up weekly for two or
three months that the shadows at mid-day lengthen

MATHEMATICAL GEOGRAPHY.

237

in winter and shorten in summer. Under what
condition would there be no shadow at mid-day ?
Is it ever so with us ? Where can this occur ?
Try the ^lobe again in its course round the lamp.
Pupils can (roughly) point out how far north the
sun's rays are vertical, and may then be told the
exact distance (in degrees). This fixes the position
of the tropics, and incidentally gives the meaning of
the solstices. The class is now ready to be taught
the meaning and extent of zones, with their names
and characteristics. The position of poles, axis,
equator, tropics, and Arctic and Antarctic circles
were, as has been seen, determined by (1) The
revolution of the earth, and (2) The inclination of
the axis to the plane of the orbit. In measuring
distances north or south of the equator, it can be
made clear that all circles through the poles at right
angles to the equator are of equal length and
therefore the choice of one has been determined by
mutual consent of the nations. Give its position
and drill on globe and map on the determination of
longtitude east and west, latitude north and south.

Well constructed diagrams are almost indispens-
able. Let pupils represent all the above positions of
the earth at the various seasons of the year.

Let a member of the class show the points on
the globe where it is noon at the time while the
globe is held in proper position. This collection
of points forms a meridian. How long before these
points have noon again ? It has been agreed to
place lines of this kind on the globe so that their
noon-time shall be one hour apart. How many will
there be ( What about the comparative lengths of

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238

METHODS IN TEACHING.

the.se meridians ? Then liow will degrees of
longitude compare in diii'erent parts of the earth's
surface ? How many degrees between two adjacent
meridians ?

By cutting apples or other bodies of similar form
teach the distinction between great circles (those
with the centre of the object as their centres) and
small circles, (which have not that point as centre).
What small circles have been drawn on the globe ^
(Parallels of Latitude). If these circles vary in size,
and yet are divided into 360 equal parts, compare
the lengths of a d<^gree on different parallels.

What is the greatest number of degrees north or
south you can go (Latitude) ? East or west,
(Longitude) ?

Perhaps the most difficult point in elementary
maUiematical geography is the teaching of the
ecliptic. The following diagram shows one very
effective method.

;i ^' *

ILLUSTRATION OF THE PLANK OF THE ECLIPTIC.

The surface of the water represents the plane of
the earth's motion. The ellipse in which the earth's
yearly motion is completed is the ecliptic. The

MATHEMATICAL GEOGRAPHY.

239

fliagmm also makes clear that the inooii's path does
not lie in the same plane, and that all eclipses must
occur while the moon is passing through the plane of
the earth's orbit. The objects may easily be placed
so as to make clear the conditions that produce an
eclipse of the sun and an eclipse of the moon.

• fv

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'It

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¥.

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240

METHODS IN TEACHING.

CHAPTER VII.

HISTORY.

■i < !

i >

. i

Before undertcaking to do aii}^ scliool work, it is
of prime importance that the teacher slionld clearly
settle in his own mind the answers to three
questions : —

(1) What is to be taught ? (2) Why this should
be taught ? (3) Hov^ it is to be done ?

It is the purpose of this chapter to attempt
answers to each of these questions so far as the
subject of history is concerned.

I. Why should History be Taught ? 1 . Uses. —
History reveals the past life of a people and so
imparts facts which are of use everywhere.

(a) They are of use in enabling one to understand
literature. The newspapers, magazines, and gener.,,i
literature are written for the man of general
intelligence. To be ignorant of the great facts of
history is to confess that one is lacking in general
intelligence, and is thus cut off from understanding
much that is written and talked about.

(b) As history teaches the deeds and habits of
men and the results of their actions, it supplies
valuable lessons of conduc^j. It is hence, as Carlyle
says, " Philosophy teaching by example." In this
way history may be said to be the window of the
soul, looking out upon the deeds of humanity. Thus
it makes one experienced and old without the

HISTORY.

241

c, it is

clearly

three

should

ttempt
as the

Uses. —
md so

irstand
rener.^i
reneral
icts of
general
inding

)its of
ipplies
Jarlyle
11 this
I of the
Thus
it the

troublesome lessons in the one ease and the i,n'ey
hairs and wrinkles in the other.

2. Disciplinary Values. — History has great value
as a subject for training the mind.

(a) It exercises the memory. This is true of all
history teaching, even when taught improperly as it
often is, but when a correct use of the laws of
association is made, it is unrivalled for giving
legitimate exercise to the memory.

(b) History constantly calls into exercise the
powers of imagination. Unless the scenes of the
past are made to stand out clearly in the mind of the
learner, much so-called history teaching must be a
mere saying of words — a parrot exercise. It is in
this connection that vivid descriptions, apt illustra-
tions and constant appeals to things within the
experience of the child are so valuable.

(c) As all facts are more or less complex, and so
need to be analyzed to be fully understood, history is
one of the best school subjects for indirectly
teaching the importance of getting a clear view of
the causes of events and their effects by analyzing
these, noting how each operated in its own proper
direction, with its own degree of strength, and how
all concurred to produce the general result. It is no
easy matter to measure the forces that influence
human conduct, and determine the course of events,
but in the attempt to do this the student soon finds
ample practice in analyzing events, thus history
disciplines the mind in analysis.

(d) History presents evidence to be weighed ;
events ind characters must be constantly compared,
contrasted or balanced, hence the judgment or

:.■!»

'HI

242

METHODS IN TEACHING.

critical wide ol' the inind receive ample exercise in
the Htiuly of this subject.

(e) JudL^ineiit may even pass into reasoninpf
wlien premises are hiid down, inferences are drawn
and causes are searched out. In one sense history
may be regarded as the sokition of a series of
problems, types of which may be conveniently stated
as follows: — (1) Given certain moral, religious, social,
physical, or other forces, what effects may be
expected to result? (2) Given some condition of
human society or some event, how is it to be
accounted for ?

(f) By appealing to our sympathies and by
gratifying our curiosity, history attracts us.
Naturally we are curious to know what manner of
men our ancestors were, whence they came, how they
lived, what they believed, how they were governed,
so when taught properly, history is so fascinating to
a young mind that it arouses interest, awakens
curiosity, induces attention, and so helps to form
habits of concentration and attention.

3. Value for Moral Culture. — The subject of
history is the doings of human beings. When these
are treated as such and not as mere names, its
lessons induce moral behavior. The men who
make history become models whom the learners
unconsciously imitate. How many British boys
have been inspired by the example of a James Watt
or a George Stephenson, or American boys by that
of a George Washington or a Benjamin Franklin ?

Its lessons induce a spirit of optimism and beget
confidence in the ultimate triumph of right and
goodness. The learner, little by little, looks more

-'-'■«*^"^''--- V, -t^***!^

irT Swi i tt at t^

ct of
these
!S, its

who
brners

boys
Watt

that

I beget

and

HISTORY.

248

and mow npon tlie })ri^ht side; of tilings and the
riglit side of people. He iec()<;ni/.es the gooihiess
and ort'atness of otlier a;jjes ,ind otlier peoples, lience
a healthy spirit of humility is Ix^j^otten in him, and
thus its lessons correct the insular narrowness of a
Briton ov the spread -ea<j;leis'n of an American orator.

4. Value fi)r fr'uchmij patriotism. — As history
teaches what others have done and suffered for us,
our national pride is constantly stimidated and
feelini^s of patriotic zeal are constantly calle<l forth.
History thus becomes one of the best, perhaps the
only means, at the disposal of the teacher to
inculcate patriotism. Nowhere else can patriotism
so well feed her fires as at the altar of history.

5. Vidiie for lanijtuKja ivork. — As history
furnishes many apt phrases, c.r/.,as brave as Leonidas,
as just as Aristides, as stern as Cato, as generous as
Philip Sydney, and gives ample practice in both oral
and written composition, it gives most valuable
training in the powers of expression. In the practice
of prose narrative and in supplying topics for
composition, history stands unrivalled among school
subjects.

II. What to Teach— 1. Fads. So nuich is said
to-day about the uselessness of teaching facts that it is
well to remind teachers that there can be no lessons
drawn from history without a knowledge of the facts
upon which these are based. While facts alone do
not make history, there can be no " philosophy of
history " without them. It is true that there is
history only when the facts are elaborated, condjined,
and brought into their proper relationships. But for
beginners history must necessarily be largely a study

' 'm\

244

METHODS IN TEACHING,

of facts. Tlicst! sliouid relate botli to the (loinestic
and tlui f()j"eiL;ii history. In tlie f(n'iner chiss such
facts as rehite to the progi'ess of the people in arts,
science, conniierce, etc., as well as to manners and
customs, civil struj^g-les, etc., should be taught. The
latter class will necessitate the teachinj.^^ of foreign
wars, tr<;aties, etc.

2. Teach cliar act eristic facts onlji. These are such
as mark the age, the epoch or man. l^etails and
connectinij: links should be tilled in at leisure or on a
second discussion of the subject, (gathering these
details should be the work of the pupil.

Those who hav(! only a limited knowledge of
history and so cannot discern the relative importance
of various events (historical perspective), violate this
suggestion in one or other of two ways:

(a) They teach facts which are not characteristic,
and so create a false impression, oi*

(b) They teach characteristic facts but so combine
them as to teach them in disproportion.

8. TcacJi h(0(/raph I/. A nation is a collection of
units. The more prominent of these should be
taught. 'IMie gi'eat valu(^ of such biographies is their
attractiveness. C^hildren take nmch monj interest in
actual men and women than in the facts of sociology.
Another advantage of bi()gra|)hicnl teaching is its
unity, as well as its convenience as a nucleus for
incidental teaching on a nundu'r of other points.
E\'ami)l(!s of such tcjudiing may be found in the
bi()grai)liies of C(>lund)us, .IjuMpies Cai'tier, C'lianip'ain,
Lii Salle, Frontenac, Wolfe, Montcalm, W'm. L.
Mackenzie, («eoi-ge l>ro\\n. J. A. Ma(d)onald. Kgerton
Kyiirson, and others in Canadian history; and iji

HISTORY.

245

DllltS.

)'iaiii,
. L.

'itnii

il in

Alfred, Becket, Lnn<j^ton, Simon do Mont fort, Chaucer,
Warwick, Francis Drake, Sliakcspeaic, Cronnvell.
]\Iarl)x)roii(;li, tlie IMtls, Watt, Steplienson, and others
in Enn^lisli history.

4. Teach (lutes. Some knowledi^e of dates is
ahsohitely essential to an intelli^'ent com})rehension
of history, (/hronolooy is called the handmaid of
histor}'. However, all dates are not to he leanKnl.
Those only which mark eras or epochs should he
taught at first. When the event is tau«^ht, explained
and illustrated, the <late will be so associated with
it that its remend)rance is easy. The date should be
learned through the event, and never the event
through the date.

5. Te((cJt civics. As the children should be made
accjuainted with the society of which they will soon
be memliers, with the civil duti(\s which they will
have to fulfil, with the institutions they will have to
support and strengtlu^n, they nmst receiv(; insti'uction
in civics, which ma}' ])e defined as the scic^nce that
treats of citizenship and of the relations between
citizens and the government.

Although this iscouiparatively new in our schools,
the idea is not new. At th(^ begiiniing of tlie century
Talleyrand demanded, " A new catecliism which
should make known the natui'e .nd rerpiirenwuts of
the constitution, since men were to live under its
laws and defend it at the peril of their lives." In
French, Swedish and Swiss schools there is a well
defined programme of this work. For our ( )ntai'io
schools a course in civics should deal with such
subjects as the following: —

: M

! 1

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lil'

246

mp:thods in teaching.

(1) Government:

(a) Different forms of — Monaroliical, Aristo-

cratic, Democratic, etc.

(b) Brandies of tlie Government — Lef^nslative,

Executive, Judicial.

(2) Legislative brancli:

(a) Governor-General and Lieutenant-Gov-

ernor, their duties, appointment, etc.

(b) Senate, its composition, duties, powers, etc.

Asseml)ly, their composition, duties,
powers, etc.

(3) Executive branch :

The members, how appointed, their duties, etc.

(4) Judicial branch:

The need of law; how j^ood citizens honor the
law; judges, courts, etc.

(5) The Municipal System of Ontario.

(6) The citizen — his obhgations, his rights, etc.
III. How to Teach History— 1. TmcJi thronf/h

interoM. — As one of the main purposes of teaching
this subject is to induce an active interest in the
• 'veryday affairs of life and hence to make intelligent
readers, this subji^ct is to be so taught as to excite
the liveliest interest of the pupil. This can be <lone
by the teacher who has a wide knowledge of the
subject and is himself really interested in liis work.
History is not a subject that can be taught by
everyone who calls himself a teacher. To teach it
successfully requires even gri'ater prepai'ation than
suffices to teach other subjects with fail" efficiency.
In making this pi'epjiration, the necessary reading
sliould not be confined to the so-called histories.

HISTORY.

247

Poets, and especially the writers of the historical
novel, often furnish very vivid pictures and very
correct accounts of the life-history of a people. The
teacher should make an extensive use of these and
the ballad, not only in his own preparation but also in
his recommendation of what books the pupils should
read.

2. Teach (mdly at first. — The voice of the teacher
is necessary to arouse the pupil to effort, to excite his
sympathy and to create an intei'est in the work, so
the lessons at first should be oral. Tlius also the
teacher is enabled to adapt his matter to the needs
of the class, and can pass over the unimportant while
dwelling on the important. But soon the text-book
should supplement the oral work for there is danger
in merely entertaining the pupil while making the
work interesting and animated. To prevent incom-
plete, unsystematic teaching, books should be used
from the fourth form onward.

At the same time the evils attending oral work
may be minimized by close questioning during the
lesson, and at its close pupils should be recjuired to
stand and give as complete an account as possible of
each part of the lesson. This is preferable to having
many short trite ({uestions answered. Pupils should
also be required to write out the h'sson, either in
answer to (questions asked on it or as a composition.
This should be done before the lesson has time to
become so dinnned as to be largely forgotten. With
carefully framed (piestions, it will often be an
advantage to allow the pupil to use his text book, or
notes.

8. Teach history and not a text book, — Tg do this

i!l

248

METHODS IN TEACHING.

I i'

the teaclier must know his history. His knowled^o
must be far wider than is to be ^ot from the study
of au ordinary school history. The teacher who
possesses thi.s knowledge will not be likely to
reproduce the text book and nothing more. He will
be in a position to give a simple narrative of deeds
and events, and a glowing description of persons and
their doings. His history teaching will never be a
mere recital of names and dates.

4. Teach through the medium oj biography luhen
possible. — Biography is one of the most interesting
and ennobling of studies for children. Fires of
enthusiasm are lighted in their minds by the lives of
great men, and unconsciously they are influenced by
the lessons of such lives.

5. Teach so as to connect the new with the old. —
Care should be taken to connect the new with
circumstances and conditions that are now known
and familiar to the pupils. In doing this the
narrative should be so objective that events are not
only spoken about but become experiences to them
by the natural processes of thought. Many teachers
still are content to have their pupils repeat, parrot-
like, such expressions as " Alfred came to the throne
in A.D. 871," when the children know nothing of a
throne, or coming to a throne, or of A.D. 871. Such
work must result in a permanent disl'ke for this
subject and must inevitably defeat the purpose for
which this subject is being taught.

6. Teach by making use of the self-activity of the
jmpil. — The pupil must be more than merely
receptive. He must be active in reproducing both
orally and in writing what he has learned as well as

HISTORY.

249

tlie thout^ht produced by it. Heiico the importance
ol' haviii;^ the child make diagrams, charts, etc.,
ilhistratinu the lesson and of ]iavin<r him use his
jud<;iiient and reasoninj; powers in reachinjjj con-
clusions.

7. Teach, hy covipari'^on (iivJ confrasf. — When
possible, the pupil should compare similar and
contrast dis8ii.:<iiar actions and persons. Doing this
regularly causes him to find much more in history
than a mere remembering of facts. This compels
hiui to use his judgment as well as indirectly teaches
him to associate any effect with its proper cause.

8. Teach throiajh VToper associatiovs. — Connect
liistory, geography and chronology everywliere,
show how the history of a country is attected by its
geography. Show how its geography influences the
national character of the people. When speaking of
St. Petersburg refer to Peter the Great and his work
in making modern Russia ; when Arabia comes up in
geography refer to Mahomet, the Hegeira, etc.

9. Teach hy bringing the study of history into
organic (connection with the study of language. — No
subject is better adapted to advance the real study
of language than history. The connection between
language and history can readily be made as
follows : —

(a) Use the historical topics as subjects of
composition.

(b) Read for the class fre(juently well written
descriptions, not mere manuals.

(c) Have recitations of patriotic poems and
ballads such as : — This Canada of Ours (G. W.
Johnson); God Bless Canada (I)ewart): A Ballad for

250

METHODS IN TEACHING.

Brave Women (Mair); The Plains of Ahralian*,
(Saiinster) ; The Chai'«jje of th(! Lii>ht Krioade,
(Tennyson); \Vi-(!ck ol* tlie White Sliip (Henwms);
E(linl»nr<ili after Plodden (Aytoun); Tlie Arnia<hi,
( Macau hiy), etc.

10. Tcjtcli hy Ink) nil (ufranffff/c of some
occur re ace of (jenernl interest to the jmjiUs or
nrlij/iltorJfood. — A lioliday or an election should be
used to niak(^ clear the object of the holiday, tlie
nec(!ssity of ehjctions, how they are held, etc. On the
last school day before May 24th, may be discussed
such ((uestions as the extent of the British Empire,
its developuient and resources, the relations of
Canada to it, the unity of the empire, the Hajv and
its significance, etc. On a similar occasi(jn before
Dominion day, a lesson should be given to tlie school
on the e.\tent of Canada, its resources, its conniiercial
advanta<jjes, its f^overnment, the advantajjjes of being
a Canadian, etc.

An electioi; in the neighborhood is a tine
opportunity of tt^iching children the meaning of the
ballot, how to mar'-: a ballot, etc. A good plan is to
hold an election in school with the pupils as the
vot(M's. One of the pupils is appointed returning
orticer, another a deputy n^turning officer, another
poll clerk, othei-s scrutineers, etc.

The visit of the assessoi- or tax collector, a case
b(d'ore a m{lgistl'at(^ the annujil repairing of the roads,
etc., may b(» used to make clear the nature of our
nnniicipal and provincial governuient. '^Fhe work
should be very largely conducted by (piestions
These may be viv(Mi one <lay and the ans\v<M's taken
the ne.xt. In case there is troul)le in answering a

HISTORY

251

(|uostioii, a coinmittee may Ix' appointed to ascertain
the answer and report. With a (piestion or two
propounded regularly, and a few minutes — not more
than ten — taken to <liscuss the answers each day,
j^^reat interest may be arouscMl as well as intelHf]r('nt
observation and incjuiry set on foot. Such (piestions
as the foUowino- will soon make the pupils intelli^rent
and interested re<(iirding some of the common thin<^s
about them: — Who is the assessor? What does he
do ? Who appoints him ? For how lon^ is he
appointed? For how much is your father's property
assessed ? Wliat is the paper called on which the
names of the people and the values of their property
are placed? Can one ol^jectto his assessment? How
can he do this? If a mistak(^ has bt^en made how is
it rectih'ed ? What is "real" pioperty ? Wliat is
'• personal " property ? et^

IV. Stagres in Teacningf History— From the

state of development of the pupil the teachint^ of
history falls naturally into three stao-es.

1. First ,sf(t(jr — t/tf picture and story stdgr. This
is adapted to the youngest pupils in our schools.
There is to Ix^ no formal teaching of history but now
the way should be prepared for later instruction of a
systematic kind. Lessons dealin<( with the men of
the past — how they lived, dressed and travelled —
narratives of personal adventure — deeds of heroism —
stories be^nmnn*^ with "once upon a time," etc. Tlu^
leai'nin^^ of facts is of very secondary impoi-tance,
henci^ no attempt should be made to have absti'acts of
the teachin«i; remend)ered.

2. Second stdifc — the i nfnnndthfn sltnjr. 'I'his is
the stage when the pupil has to acquire a clear and

.Hi

252

METHODS IN TEACHING.

■I' ■!

■ *, ■

woll-onlonMl outline of the most important facts.
TIh3S(3 slionld !)(' i;i'(Mip(Ml under leadin*;* events rather
than clironologically, ('.(/., in Canadian Instory, the
discovery and exploi'ation of Canada, the j^overnment
of New France, the stru<jj^les between tlie French and
Britisli colonies for supremacy, etc. Minor points
which have little bearing upon the general story
should l)e omitted. The treatment of what is given
should be full rnd realistic, and the teaching nnist be
definite and C( "ei\v — vividness alone will not do.
The facts nuist o ^o associated that they may l)e
recalled with readniess w.id certainty.

-3. Third sf<(</e — fhr jx^i'^od or epoch sfage. — As
the general secjuence of the more important facts is
now known, the teacher may begin with any period
as e.g., the Dominion of Canada since Confederation,
tlie age of Victoria, the Stuart period, etc. What has
been previously learned will form the basis of the
new work. The facts should be cemented into a
clear and consistent wliole, so that any subsecjucnt
accjuisitions may be related to the whole, and thus
find their own natural place in the period. It is in
this stage especially that the pupil will be recpiired
to exercise his judgment and reason upon the facts as
they are presented to his mind

V. Methods of Teaching: History— 1. Chnmo-
lo(ji('<(l Method. — This discusses the events as they
follow in time, whether they are connected or not.

2. Topicid MetJiod. — The leading events in the
life and development of a nation during the period to
be studied are selected, and the history of each is
pursued consecutively, without reference to other
events, except in so far as these have a direct influence

HISTORY.

253

upon the one under consideration. The period is
tlius studied under such headings as wars, the
growth of constitutional h'berty, tlie pro<;ress of the
people in arts, the power of the church, etc. Tliis is
tlie nietliod reconnnended for the tliird sta^a'.

3. Tlie Am d 11 1 lad Method. — This method takes a
fact as it is and stej) by step proceeds backwards
until a bejyjinnint^ is reached. It ben^ins with the
eft'ect and searclies out the cause. It proceeds from
the consecjuent to the antecedent.

4. 'The Sj/)dhetir(d Method. — This method is just
tlie reverse of the Analytical. It be< *.is with the
cause and works towards the effect. ] proceeds
from tlie antecedent to the consequent. It is
chronological in its nature.

From the fore^oinj^ it is seen that a topical
method must be analytical, so far as ^he whole period
or epoch is concerned. Whereas, the treatment of
any given topic may be either analytical or
synthetical.

VI. Difficulties in Teachings History—]. Dtffi-

fulti/ from the ii<dure of the .suhject. — The subject
demands from the teacher wide reading. He must
be, as Bacon says, a "full" man. Mucli experience
and sound judgment are also necessary to make a
proper selection of facts.

2. iJijficidtt/ from mahifdinhuj priq)er historical
perspective. — The leading events and the great actors
in these should be at the front. Th<; unimpoi-tant,
both in events and actors, should l)e kept in the
background — this is often diflicult to do, csjxH'ially
for the person of narrow reading.

3. Dijjicidt}j fnnic the te((cher. — The teacher must

t I

254

METHODS TN TEACH TNG.

possess <j;()od dcsci'iptive powers. He must h(^ apt at
illustration, skilful in conipai'ison, l)e possessed of a
o-ood voice. These will enable him to vitalize his
events and characters.

4. Difficulty from the luck nf experience in the
pupil. — For the ])upils, hist<jry is a strange mixture
of the simple an«l the complex, of the easy and the
difficult. They easily comprehend a part. Other
parts require maturer ndnds than theirs.

5. JJilfJciilti/ from tlie iilnise of t/ie inemory. —
There is a strong tendency to overwork tlu^ memory.
Very oft<ni this mental power is called up(^n to play
the part of tlie jmck-horse in carrying things wliich
liave neither been understood nor digested.

VII Mistakes in Teaching* History— 1. Mintoke
in nniiKj tlie text fxxiL —It is a mistake to assign tlie
lesson in the book before giving an outline of it in
the class.

2. Mistake from- lutring no settled scheme. — The
teaclier has no clear idea what should be attempted,
Ikjw much detail should be given, where he should
finish, etc.

S. Mistake from nnsuitahle matter. — It is a
mistake to attempt to teach matters which are
entirely beyond the range of experience of the child.
When such is done, allusions are made which are not
understood, terms are given whicii have no meaning,
etc., hence the pupil is confused and soon acquires a
dislike for the entire subject.

4. Mistake from neijlect of 1 list or i cat perspective.
— It is a mistake to teach as if all events art' of equal
importance.

5. Mistake from insajf.clent 2)i'<p"i'<^ttion. — It is

HISTORY.

255

IS a
are

!hild.

le not

ning,

Ires a

't ive.
M]ual

lit is

a mistake not to prepari' eacli lesson tliorouj^lily.
Even if the teaclier is an extensive rea<ler and a
careful thinker, he requires this careful preparation
to prevent obscurity and staleness.

6. Mistake from nut usuhj proper appliances, —
It is a mistake not to use the blackboard, maps,
charts and pictures to illustrate the lesson, and thus
appeal to th«^ eye as well as to the (»ar.

7. Mistake from, nsimj fhr lueuion/ irnpvoperl ij.
— It is a mistake to permit unintelligible cram, or to
teach as though general impressions alone were
needed. Without a clear apprehension of facts
history is practically valueless.

8. Mistake from infrodacinu critical donl^ts. —
It is a mistake to tell a story and then proceed to
show that probably this or that part is false. Such
criticism is unsuited to young children.

9. Mistake from i^nsufficient questiiniing nr
im^p roper review. — It is a mistakp not to (piestion
thoroughly at the time of the lesson. This compels
the ])upil to give that mental concentration to the
work which is apt to be wanting when he knows
that he is not to be thus (juestioned. Reviews
should be so frequent that the second impressions
must occur before the first have vanished, to produce
any effect. Questions and reviews are the tw^o main
means of insuring cleai' and definite concepts.

VIII. Sug^gestions— 1. Enthusiasm and a love
of histitrij ((re necessar}/. — As the end of teaching
history in school is chiefiy to induce a love of the
subject and there})y promote subso(pient I'eading on
the part of the pupil, to teach successfully the teacher
must be enthusiastic over it. As in all other school

' 1'

256

METHODS IN TEACHING,

.subjects, tlii.s i.s a cuso of " like teachor like pupil."
This earnestness and enthusiasm can be ac(|uire(l by
careful study, extensive reading and much reflection
and discussion.

2. Maps, sketches, charts, pictures, etc. — Sketch
routes of travel and journeys of exploration. Draw
plans of places, and the position of contending armies
using crayons of different colors. Show pictures
illustratinfr the dress, ornaments and habitations of
the people ; their pursuits, manufactures and
commerce ; the architecture of the times, etc.

3. Historical perspective should he preserved. —
In connection with any period, epoch, or reign, there
is always some event round which the others
circulate, towards which they gravitate, and from
which they radiate. This should be selected and
carefully taught.

4. Use the comparative method. — From the time
the subject of history is seriously taken up, (second
stage) the tracing of analogies is not only useful in
itself, but is especially valuable in teaching this
subject. One series of events is often the best aid to
understanding another. The comparison of the two
is one of the best means to make clear both. In this
way a period known, aids in the study of a new one ;
the present helps in understanding the past. Only
thus can the past be made interesting and real to the
child.

5. Procedure in an ordinary lesson. — The usual
method should be that of an oral lesson. The
teacher must tell the story as if he had been an
eye-witness with sufficient fullness for the pupil to
Sfet clear and accurate notions, and with such

HISTORY.

257

ime

econcl

ul in

this

lid to

two

this

one ;

Only

the

emphasis and reiteration as are necessary to its htiinj^
retained. The lesson must be a living reality.
There must be no vagueness, no wandering aimhissly
hither and thither. At convenient points, the
narration should stop and the pupils be required to
recapitulate what has been gone over and a concise,
well ordered summary of what is essential should be
placed upon the blackboard. During 'ihe recital use
should be made of the maps, sketches, charts, and
pictures already referred to.

6. The use of the text hook. — The chief use of the
text book is to give definiteness to the impressions
made during the oral lesson, as well as to enable the
work to be reviewed as often as necessary. With
pupils having text books the lesson may be
conveniently brought at least three umes before their
minds as follows : —

(a) When the lesson is first outlined orally by the
teacher.

(b) When the pupils, on a subsequent day, ore
questioned closely and carefully upon the previous
lesson.

In a rural school this review may be conducted by
the class answering in writing questions which the
teacher takes a moment to give before he begins to
teach another class. The first part of the history
lesson would thus be the reading by tlie pupils of
their written answers to these questions.

7. Use supplementury rew lings. — As one of the
main purposes of teaching history is to induce
children to read, and as this is largely a matter of

258

METHODS IN TEACHING.

1;?

■

.4 '

liking and hiibit, the toaelier should IVecjUcntly road
vivid descriptionH of nu'ii and thin«ijs. (No^'s shoul*!
be kept of where .such may lie found). This will tend
to excite the dt^sire for fiu'ther rea<lin<j. Halhids and
poems illustrating parts of the history und<'r
discussion should be not only read but also learned.

The historical novel such as Conan Doyle's "Micah
Clarke" or "The White Company," Scott's "Ivanhoe"
or " The Talisman," Kingsley's "Westward Ho" or
" Hereward," Henty's books, etc., may be reconnnended
to be read by the pupil himself. Supplementary
Readers, such as those prepared b}' Chambers oi*
Collins or Blackie, may be purchased by the trustees
for use in the school. Such means will do much to
impart a liking for the reading of history.

IX. Lesson Plans — As a miide to beginners in
drawing up a lesson plan, one is here submitted. The
necessary headings are purposely omitte(l and only
the kiody of the plan is presented. Each tcachci"
should fix in his mind as clearly as possible what he
means to teach and how he intends to doit. Wlien
an outline of each of these is systematically ai'ranged
the result is a lesson plan. When possible, and in
liistory it is always possible, the plan should be
divided into two j)arts called "Matter" and
" Method." The matter should show cleai'lv what is
to be taught under each heading and itof fhc hnn/htgs
alnnr. These headings can n(!ver show what the
teacher intends to impart. This should be stated
clearly, not only in history ))lans but in those for all
subjects.

y rcufl
slioiiltl

11 tulKl

ds ami
uiulor

lied.
Mi call

inlioe"

" or

1 ended
eiitiiry
ers or
rustees
lucli to

icrs in
The
] only
jiclicr
lat he
When
•Jinked
nd in
lid he
and
hat. is
kI i infK
it tiie
stated
foi* all

HISTORY.

Mag^na Charta

259

Mattkk.

Mktikui

I. Intn.liiition. Previous otlorts of the

Barons to secure themselves ajj^ainst
oppression. Charter of Henry I.

II. Cirnininfiinri's irh irh U-l to Ihi'iJhdrd'r.

1. The al>U8es of the Feudal System.

2. The exactions of the reign of Rich-

ard I.

.'{. ()pprossi(jn of John. His character.
The Ukss of Normandy. His
submission to the l*opo.

<.^>ueation on the termn
of this Charter.

1. Kxplain and illus-

trate.

2. (Question pupils as

to the causes of
these.
.'{. Kxplain and illus-
trate eacli of
these.

III. M<<ni« III! ii-hici, tin' Vlimlrr ii'ds

1. Council of llarons held at St. |

Aloan's during .John's ah.sence.
His return and revenge.

2. Confederacy of P.arons formed at .>

St. Paul's, 12i;{. Charter of
Henry I. read.

.'». .lohn renews his cruelly and op- ;{.
pression. C(»nfederates meet at
St. Kdmundshury, 1214. .lohn
attempts to detach the flerj^'y
from the confederacy. Failure.

4. .lohn compelled to Hi<,'n the -^reat
charier at Itunnimodo, 1210.

Kxplain and notice
the union of
spiritual a n d
temporal lords.

Kxplain the sig-
nificance of this.

Kxplain and illus-
trate I'ach.

4. Point out on map.

Ill
1:

i:i^

lil

260

METHODS IN TEACHING.

Mag^na Charta—Continued

Mattkh.

Mkthoi*

IV. Fionsinnn of the Charfer.

1. Abuses of Feudal System were 1.

rediessed,

2. Royal prerogatives wore restrained. 2.

3. A fair adininiHtration of the Law .S.

was secured.

4. The liberty and property of the 4.

subject were protected.

V. Ejf't'cts of M(iiin<t CInuld upon tlw

Notion.

1. Resistance to despotic rule was

encouraged.

2, The love of liberty was strength- '>

ened.

Ex{)lain and show
how.

(^)ue.stion and ex-
plain.

Refer to the fact
that the Charter
was ratified
t h i r t y-s even
times down to
the second year
of Henry VI.

= i

!^1

ARITHMETIC.

261

CHAPTER VIII.

show

year

AUlTllMKTir.

The cliapter on this Hui>j('ct, us oriirinaliy prepju'orl,
cont.'iincrl a full discussioM of th(» value and uses ot*
arithmetic, tlie origin of ninn])er, the stajjjes of tlu^
nieasui'ing pj'ocess, the unity of the sul)jeet, the
elements — quant ity-unit-and-numher — enterin*^ into
a complete idea of num])er, the natui'e and rdatioji
of the operations, and the d<!velopment of the activity
involved in giving numerical valuation to (piantity.
Limitation of space, howevei', compelled the writer
to omit the theoretical part.

It is intended, in a short time, to place befoi'c the
profession the conn)let(^ work in which 'IMieoi*y and
Operations will he logically and p.sychol<\i;i('ally
treated.

Primary Number Nund»er arises through the
proper adjustnient of the mind's activity in dealing
with ({uantity. How stnise material becomes
(|uantitie«l, how (pianlity becomes valuated, how
objects when presented arouse forces and determine
the directions of the fun<lamental activity, what
forces tend to obstruct and counteract this activity,
and how the miiul rises from the [M'l'ccption of
related things to a conception of tin* j'elation, are all
importa?it nuei.tions for th • t<'ac}ier.

Discrimination and relation are involvrd iti all
number from the Hxing of an indefinite vague

■I

:i:i

* ■' I

' I

262

METHODS IN TEACHING.

(jiiaiitity to tlio most complex valuation '>f Hm:
sjimo.

(/ounting Is the l'uii<laiii«'iitMl njM'rMlioH in
ai"itliiiiotic. Tlie otliL'i" o[)oiati(jns arc (lovices tor
speed l)y UHJiio- mcmorizod resiilts instead of ^oing
over th(^ same modes' of measurement each time.

The hi<^her steps are dependent on the elementary
process, hui what is implied in the countinj^ sta<(es is
made explicit in multiplication and division, and
definitely notated in fractions.

Numlx')' then should ho treated jvs resulting- from
measurement, the process l»y which the mind makes
the va<rue whole definite.

A j)ropcr method recoi;nizinL;" tin; nature of mnnbcr
will hai-moni/c suhject and .nental action. '

1'her(i are four nu'tlnxls of t«"U'hin<^ primary
aritlnnetic, (1) Syndx*! Method, (2) ()hie(;ti'.r
Grube Method, (:^) Constructive Method, (4) llela-
tive Ma«;nitude Method.

In the orij^inal these were fully discussed <«ud
compai'ed ill the li<jjht of the psycholo<:^y ofnumlter.

The Constructive Metiiod is the one advised in
this hook. It is i-atioiial ; mai- . .d is present I ; the
])U})ils make the indefinite ipiantity definite by
<liscriminatin^% relatin*;" and nund)erin^' the parts
chosen as measurers.

When the material is psyehically woi'ked upon the
necessary })rere( I ujsites of time and space accompany
the normal activity, and numlter ideas become focal
in consciousness.

'■ This method expands the mind demandini;' the
repetition of activiti«s and takin;;; advantai^t^ of
dawci'inr interest in ev«'ry kind o^' value; it relies

!!..■

ARITHMETIC.

263

and

UjMJii tlio t'onnalion of luihits of ac(ioii oj- ilotinite
iiM'iital [)o\vurs, ,i!id seciuvs meujory of factN as a
})ro(luct of spontaneous activity. This nii'tliod,
lelyin;; im the niind'H own activity of partin*; and
wholin^' — its natural functions — secuijs a continual
support and reinforcement from an internal interest
which is at once the condition and the pjoduct of
the mind's vijijorous action. " — " Fsi/rhohij/i/ of

To Teach the Numbers from 1 to 10— Use

kinder<;art»'n sticks or cubes, and test the pupil's
knoNvh'd<^e of his one. two, etc.

Workinj^ fi"om within a. whole, let the pupil
separate t^roups into parts and comhine them, and
mm; that he r<ico^ni/.es a whole as made up of parts,
and that the parts make a whoi«'. Hy exercises in
countin<^^ive an idea of an indetinite whole throut^h
th<^ relating of the parts.

Pupils may count sini^de thini^^s witliout knowing
the nund)er involved in the n:imes, hut this is a
stron;;' starting- point.

(Jive id'jas of more or les.s and compai'e groups l^r^
show that the more or less depends upon the " how-
many."

(live constructive exercis«'s re(jui) iiia- a certain
"how many" to i-nahle j)upils to ti.\ the indefinite
whole hy looking to the pai'ts.

Hegin with two. Pu])il knows 2 as 2 "ones." H(^
will re.iuire! to develop the numhor *2 as 2 "one
ohjeets," 2 "one groups," etc., and hy this means
develop the idea that 2, \\, etc., are twice, thrice,
titc.,a certain 'thing-unit' used to measuie the whole.

Proceed in this way with the numhera fr<jm 1 to

b« >

264

METHODS IN TEACHING.

10, nui] teaeh tlio same ])y steps similar to those
outlined in teaching "eight." Make haste .slowly.

To Teach Eight— First supply pupils with 16
kindergarten sticks, 8 white, and 8 red.

Let them find a "two" (the (pialitative differ-
ence, color, will suggest a division).

Let them place the red group to one side.

Pupils, in dealing with the parts — say of eight —
to gain an idea of eight, lose sight of the whole when
the attention is on the parts. A pupil will take the
group eight (unknown eight to the pupil) and divide
it into two parts. He will tell you there are two
fours, but he will forget from where the two fours
came. Let him, therefore, keep the red group before
him, so that the analysed facts in the working group
can be referred to the red, or standard group without
an act of synthesis with the '"orking group.

The pupil will construct to bring out the following
facts wliich should be recorded on the blackboard.

nn. fiA.fi^l.mA.AAAA.AAA.
DAI, aAA,0Al.llllllll.

Judicious questioning wnll bring out the number

etc.

element in t!ie above.

Now vepi'^sent these facts in • • •
the foriii r.f niuii her pictures, as # # #

Shov thai f h< dots stand for any unit.

QuesHon o?s flie nund)er i)icture. How many
fours ? How many twos ? Cover a part ; how many
are co'. ere<l / Draw a line through the dots. How

manv ai/ove

the 1

ine

How

man'

bel

iii

ARITHMETIC.

265

etc.

Now i^ive tlie iwiine " t'i<^ht " to tlic «;• roup, and
vvriU' the .syiiihol on the l)lackl>oar<l. TIhii indicate
tlie facts discovered in N, as 4 and 4 = 8, etc

Leave out parts, as 8 is 4 and what ? 5 and wliat
make 8 ?

Give exercises in countinir out groups of eit^ht.
Then we can have one 8, two 8's, etc.

Let pupils niuasurc distance witli an ineli
measure, and put a chalk mark at the l)e<^inning and
end of each eight. Vary the units.

Secure practice from related experience.

Bring out that 4 and 4 make 8, and that 4 is
used as a unit twice to measure 8. Let pupils see
that if we count up 8 in twos, that 2 is the unit, and
that 4 shows how many counts of 2 we make.

Give tlie idea, name and symhol. Make use of
the idea to master it and by practical problems bring-
about familiarity through use.

Give practice with numbers thus: —

What number witli seven makes 8? with one
makes 8 ? with six makes 8^ with two makes 8? etc.

How many fours in 8 ^ twos ? ones {

Give seat work.

After the numbers from ouv to ten are taught, or
as each is developed, place on cardboard as follows: —

• • • • L) U U L)

= 8 = eight.

• • • • n u n [J

Supplement with easy problems, and let pupils
work up problems from their own expenene*'.

Notation and Numeration If (Ih; nund)ers from

one to ten have been taught as above, the pupil will
liave little ditKculty with notation. Write ten

I. r

■ i

I. '

'■ i! ,

266

METHODS IN TEACHING.

0, 10, 20, :{o, 40, 50, m, 7(), ho, jm)

1, 11, 21, ;u, 41, ni, (ji, 71, HI, 91

2, 12, 22, :i2, 42, 52, «2, 72, H2, S)2

;i, i;{, 2;i, 'X\, 4;i, r.;{, (;.*{, 7;i, h.'^, <»;{

4, 14. 24, U, 44, 54, (14, 74, H4, M4

5, 15, 25, .'{5, 45, 55, (i5, 75, H5, !>5

(), 10, 2<;, ;{(), 4<), 5(;, ho, 70, ho, <>o

7, 17, 27, ;i7, 47, 57, 07, 77, H7, !>7

H, IH, 2H, ;W, 4H, 5H, OH, 78, HH, «>H

t>, l!>, 2J), ;«), 4i), 5«>, 0<>, 7*.>, HI), W

as 1 toil and 0; two tons, as 2 tons and 0. Write
thuH: — I ten, 2 tens, 8 t»?n.s, 4 tens, 5 tens, 6 tens,
7 tens, «S tens, 9 tens, 10 tens. Anain ms:— 10, 20,
ao, 40, 50, 60, 70, 80, 00, 100.

Read above as 1 ten, 2 tens, etc.

Now 1 ten and 1 unit, 11 ; 2 tens and 2 units, 22,
etc.

All the num-
bers from 1 to
})}) may he put
into tlui form of
a table as shown
in the scjuare.

Tlie names
may now l>e
j^'iven. Some,
as eleven and twelve may ])e ^iven eai'lier.

Give pupils practice in buildini,^ the numbers with
sticks. Eleven and twelve are named.

Contrast and explain the others in this way —
three (8), thirteen (bS), and thirty (80); four (4),
fourteen il4), and forty (40).

This will j^ive sij^niitieance to the names and
enable ])Upils to hvo, the law by wln'cli nunibers aie
named. The notiition, fiom 100 to 1,000, may be
similarly dev(;loped.

(live praictice in decomposition. Show tlutt 105
also indicates absent tens, and that 120 indicates
absent units.

Use devices for fixing the place of the tens, units
and hundreds, as : —

ARITHMETIC.

267

Hox

n|- ti

and

When the pupil has (rrasped tho principh; of phice
vahie in small numbers, he will have no ditliculty in
un(lersian<lin<^ it when extended.

Hy this method of teaehin<; notation, numeration
is learned at tin? same time.

Drill pui)ils on readinti^, writinj^ and evolvintj^
numhers in the al)ov(! tahles until they are entirely
familiar with them.

S(^parat(! numbers into numerical jx^i'iods^ and let
pupils name and remend)er tlu^m.

See that this eonvc^ntional part of the sultjrct is
thoi*ou«i;hly taught and many dilliculties \\\ the simple
rules will be removed.

Familiarity with 10, our fixed basis of notation,
will furnish a key to apparent diHieulti<'s. The
pupils i^iasj) that nund)ers {greater than t«Mi Jire
expressed in terms of ten and nuist be so thou<^ht of
and operate<l with. Tlu^y will be led to recognize
the law : — Eveiy figure placed one place to the left
reju'esents ten tinu's its value in that first place.

If primary innnb(?r teaching is ('arri<'d out
according to the prec(Mling suggestions, and elemen-
tary notation and numeration properly co-ordinated
therewith, there will be little difficulty with the
languag*! of luimber. The significance of the digits
and the noughts is known. The puj)il knows that
ten iniits make a new unit of m<'asure ; he will
readily extend tins to the higher ten unit, etc.

. ,1'j

1-1

268

METHODS IN TEACHING.

Diill of c()Ui*s(! iiinst be <nven in icadiii!

aiH

wi-Hin^ imnihcrs in order (liat (lir pupil may iiimKMli-
iitiily stale the miinl)ur and its unit, and also nutate
any named derived (juantity.

Tlie significance of the ten digits in i-epn3sentin<jf
numbers of any ma;^nitude should 1)0 pointed out.
Nund)ers from 1 to 9 are expressed ])y one di^it ;
from 10 to 99 l)y two di<,n'ts, each representin<ij a
particular unit, 'i'his may l»e extended to thousnn<ls,

(!tC.

The idea of nann'no- (^roups l)y tlie use of previous
names should be impressed. The binding' to<^et]ier
of ten as one ten, the ten tens as a one huncb'ed, etc.,
by a thread of thou<^lit will sui^i^^est uniformity.
Few characters and place value j^ive rise to the unity
of th(i notation system.

The Four Simple Rules— All calculations are
bascul on the fundamental operations, addition,
subtraction, multiplication and division, and the
pupil should become thorou<jfhly ac(juainted with
these fundamental process(^s if he is to master the art
of arithmetic, for theory alone will i^ive neither
rapidity noi- accuracy in calculatini;-.

Nu!nber develojjs the thought power : the
opei'ations enable the student to use mnnbers in
detininijj \'alued (juantities in many convenient ways.

This part of arithmetic develops the power of
attention, accuracy in thought and expression, and
.sliould receive its ])rop<)rtion of time in the school
room. Constant and wcill directed practice is
necessary in order that the pupil can make use of
arithmetic outside of the school room.

Our system of notation, the symbols, and signs of

^mta^.:

ARITHMETIC.

269

opt'ration, toniwil statt'inents of tlic operations ami
ai'itliiMftical pruccH.soH, all ten<l to rt'iidur tho sul)j(!ct
obscuro ; and too much attention cainiot be devoted
to the representative side of the thou^dit expressed in
these complex forms.

Do not attempt to teach the four simple rules
simultaneously. All the operations are lo»;ieally
implied in countinj^, but they should not all be forced
into conscious recognition at a time when the pupil is
masterinn^ the I'orm and expression of simpler
notions.

Many of the facts brouf^ht out in teachin«(
primary number imply the four sim})le rules, but
there should be no explicit statements of tlie formal
processes.

Addition — When we measure (piantity with a
unit we i»'et number and call this (juantity derived or
mejisured ; and the numbei- is tlie measure of the
(juantity in terms of the unit. We can measure in
succession a number of ([Uantities, derived from the
.same unit, and find tlie total nund)er of times this
unit is repeated. Since this measuring }»y hand
would be tedious and sometimes impossible, we
operate with the numbers which rei)resent the
measurements, by memorizin*,^ a table of tlie
com})inaiions that are found in the numbers from
one to ten. These results can be easily extended to
liundreds and thousands.

Addition is the operation oi' ('ond)ininj^ »,!ie
numbers that measure the parts of a (piantity in
terms of a certain unit in ord(;r to Hntl tlu; number
tliat expresses the a<^(^rt^jj;;ate measure «)!' the whole
measured quantity in terms of the same unit.

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IMAGE EVALUATION
TEST TARGET (MT-3)

1.0

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2.5

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1.8

1.25 1.4

1.6

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6" —

►

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Photographic

Sciences

Corporation

23 WEST MAIN STREET

WEBSTER, N.Y. M.fSO

(716) 872-4303

•1'

270

METHODS IN TEACHING.

The following coiiibi nations should be memorized
and practice given in addition in order to Jipply the
table. This order will be found advantageous.

, .11111111
y^) 1234 5 678

... 2 2 2 2 2 2
W .'J 4 5 7 9

/ ■. »o o o o
V^),6 7 8

... 5 4 8 2 1
vn 5 7 8 !)

. . 3 8 ;3 ;i 3

V) 4 5 8 9

^, fJ 6 6

W 7 8 9

2 3 4 (i 7 8 9

2 3 4 () 7 8 9

..4444

(/) 5 7 8 9

7 7 8

8 9 9

(^')

(^)

These combinations are the foundation of all the
operations and they should be thoroughly mastered
so that the pupil can give them rapidly and
accurately, in any order as 4-f-7 = ll, 7 + 4 = 11, 11 =
7 + 4,11 = 4 + 7."

In time the emphasis may be placed upon the
reverse process and the subtraction ta])le learned
thus: 11-4 = 7, 11-7 = 4;

Questions in addition may be set giving practice
in the new combinations, and at the same time
reviewing those already learned.

Examples. — (a) Practice in tens by using 7 + 3.
Arrange and add vertically, 3 + 8 + 7 + 4 + 6 + 7+3 +
54.5^_7_|.3 + 34-7 + 4 + 6 + 5 + 5 + 7 + 3. (b) Practice
in 4 + 5, 3385 + 8992 + 9556 + 5228 + 2939 + 0255 +
2323 + 2963 + 5759 + 7637 + 3896 + 7236.

A full complete set of addition (luestions dealing
with the combinations has been necessarily omitted.

If the above results are arranged vertically and
added it will be found that no addition is required
that has not been learned, although the specific object
is practice on 7 + 3, and 5 + 4.

See that the pupil uses the addition table in
practice in addition.

The work should accordingly be graded and
systematically developed until the pupil has

jIF'^y^g^Jill;** tStfWP"!**^ ™*f,Ti^r^^ 1

le 111

ARITHMETIC.

271

thoroughly maHtered and applied all the combina-
tions giv^en above, and can add accurately and
silently. Addition may be divided into two cases.

i. Addition of numbers in which tlie sum of any
column is less than ten.

ii. Addition of numbers in which the sum of any
column may exceed nine units of that order.

Easy exercises should be given in the first case
until pupils become familiar with the formal process.
Measuring should also be emphasized. Show the
necessity for the operation.

Casp. //.—Example.— Add 347,965 and 821.
Writing vertically 347= 300+ 40+7

f)C5= 900+ 60+ 5

821= 800+ 20+ 1

Adding we get 2000 + 120 + 13

= 20h+ 12t+]3u
= 20h + (lh + 2t) + (lt + 3u)
= 21h + 3t + 3u
= 2100 + 30 + 3
= 2133
The above will appear simple in class work, and
the pupils will soon discover the canying process,
more especially if this part of the work is varied.
Then the work may be shortened. Each sum will be
analysed when added.

Subtraction — Sul)traction is the inverse of
addition and the genesis of division, just as addition
is the genesis of multiplication.

Subtraction is the operation of finding a number
which is the measure of the difference l)etween two
derived quantities expressed in the .same unit. We
work for the number and apply it as a measure of

;■, i

272

METHODS IN TEACHING.

the difference. Now review and emphasize the sum
and parts in addition tables.

There are two cases of subtraction.

i. When the figure of each order in the minuend
is greater than the figure in the subtrahend.

ii. When the figure in the minuend with the
exception of the first to the left may be less than the
figure of the same order in the subtrahend.

Some practical measurements should now be given
to lead up to the necessity for subtraction.

Pupils should also be led to see the advantage of
operating with the remembered results thus doing
away with counting.

Case /.—Example.— From $458 take $123.

We are required to find the number that will
define the difference when $123 are taken from $458.

Writing thus Irl we have eight units — 3 units = 5
units; 5 tens — 2 tens = 3 tens; 4 hundreds — 1
hundred = 3 hundreds. The difference is $335.

Considerable practice should be given in examples
of this kind until the pupil becomes familiar with the
nature of subtraction.

Case II. — Either of two methods may be used.
The process may or may not be explained, but
proper teaching demands that the pupil should have
some reason for what he does.

(a) The Method of Decomposition. — Example. —
From 834 take 375.

834 = 8h+ 3t+ 4u = 800+ 30+ 4 = 834

= 7h-hl3t4- 4u = 7004-130+ 4 = 834

= 7h + 12t + 14u = 700 + 120 + 14 = 834

375 = 3h+ 7t+ 5u = 3O0+ 70+ 5 = 375

Difference = 4h + 5t+ Pu = 400+ 50+ 9 = 459

w^mn-^'^m:^-'^^. ■s^sfti

\^X^*'<^-r «.,-.7 ^ -f. ^ i, *-'W-»<*' •<i3S:^7~7TST'""

le sum

inuend

th the
an the

given

;age of
doing

it will
1 S458.
lits = 5
eds — 1

amples
ith the

> used,
d, but
d have

iple. —

i = 834
I = 884
I = 834
5 = 375

) = 459

ARITHMETIC.

27?

X
X
X
X

This method gives excellent practice in the
comparison of units.

The formal step may follow exercises like the
above.

(b) Tlir Method of Equal Additions. — The teacher
should, first by presenting the necessary truths, show
the fundamental axiom upon which this method is
based.

First present dots to represent
the numerical value of any mea-
sured quantity. A = 6 and B = 4.
The difference is seen to be 2.
Then increase by adding equal
numerical valuations as shown by the crosses.
Through perception of this kind the pupil will gain
a conception of the truth " that adding the same
quantity to each does not alter the difference;" also:
*' that if the same measured quantity be added to two
unequal measured quantities the difference will
remain the same."

Example.— From 834 take 375.
Adding 10 units to 4 we have 14 units — 5 units
= 9 units.

We must add a ten to the 7 tens = 8 tens. Now
add one hundred = 10 tens to the 3 tens = 13 tens — 8
tens = 5 tens.

We must now add 1 hundred to the 3 hundred =
4 hundred ; 8 hundred — 4 hundred = 4 hundred.
Difference = 459.

Here 5 and what make up (10 + 4) = 9. Since we
added to the top line we must add 1 ten to 7 = 8 tens.
18

!l' ■;

I::

Ihi

274

METHODS IN TEACHING.

'riicn rS tons and wluit make (10 + 3) tens = 5 tons.
Sinco wo added I hundred to niiiniond we must add
1 hundred to the 8 hundreds = 4 hundreds. Then 4
hundred and what make 8 hundreds = 4 hundreds.

The remainder is 459.

(d) IVte Complementary Method. — Example. —
From 834 take 375. If,

Here we subtract from ten each time and add the
difference to the minuend digit (10 — 5) + 4 = 9. We
add 1 ten as before to the 7 = 8, (10-8) + 3 = 5.
Again add 1 hundred = 4. Remainder = 459.

A comparison of these methods is a good exercise
in " method."

Multiplication — Multiplication may be shown in
its relation to addition when the exact quantitative
value of the unit is not considered. It may be
shown to be a short form of addition by finding the
sum of addends numerically equal to one another,
and numbering them. As 5 apples + 5 apples + 5
apples = 3x5 ap^' ^s = 1 5 apples.

When, however, the multiplicand is regarded as a
derived measured quantity in terms of a standard
unit, and the multiplier (times of repetition) shows
the ratio of this unit to the quantity to be deter-
mined in terms of the prime unit of measure in the
multiplicand, a higher stage of the evolution of
number is represented as 5 ft. X 3.

In this stage of measurement we repeat a derived ^
quantity a number of times as a unit, and then
by multiplication we define the total measured
(quantity in terms of the prime unit of measure from
which the unit-multiplicand is derived. By the
operation of multiplication we find a single measure

■I!

3^?««ie^'B^^^Sj*^V.^<i^wift^^-::

'.--^VWn^f*"-*

5 tons,
list add
Then 4
mdreds.

mple. —

add the
9. We
+ 3 = 5.

Bxercise

lown in
titative
nay be
ing the
mother,
pies + 5

led as a
tandard
) shows
3 deter-
3 in the
tion of

derived
id then
easured
re from
By the
neasure

ARITHMETIC.

275

(number) that gives th(^ same (lorived (piantity in
terms ol* tlio prime unit vvliich <loriv('s the muUi[)lo
unit. By multiplying together the numbers which
represent the measure ot* the derived unit and its
times of repetition, we also substitute the prinu^ unit,
and the product of the numbers measures the same
quantity in terms of that prime unit.

The multiplier states the times of repetition of
the unit-multiplicand. The operation of multiplica-
tion does not repeat it. We multiply, obtain the
product of the numbers, then use this new number to
define the same measured (juantity in terms of the
prime unit deriving the multiple unit — the multi-
plicand.

Nature of Multiplication— Find the cost of 5
yds. of cloth at $3 per yard.

Here the derived unit of measure is $3, and this
is to be repeated 5 times to give the measured
quantity of money to be valued in the unit $1.

If now we find the product of the number 3
which measures the derived unit by the number 5
which gives the times of repetition of the derived
unit, we obtain a number which values the quantity
5 yds. cloth in terms of the prime unit $1 . • . 5 times
$3 = $15.

The quantity of money is the same in each case,
but the unit changes from one $3 to one $1 ; hence
the niiviber varies as the measure of tlte <lerived
^tnit $3, i,e., the number which values the quantity
in terms of the prime unit is 3 times the number
which values the same (juantity with the $3 unit.
The measure (5) that values the yards is now used

f ■

276

METHODS IN TEACHING.

with 3 by the oporation of multiplication to value
the clotli ill tci'iMs of the unit $1.

Steps in Multiplication Develop the idea of
tiui(3S — Add li ft. till 36 ft. is the sum.

Emphasize the times of repetition.

Consider times in relation to tiie 3 ft. Then
develop the number 12 as measuring 36 ft. in terms
of the unit, now derived unit, 3 ft.

Now this nuit of measure with the number 12
denotes the quantity, 86 ft.

When " times of repetition " is developed and the
derived unit in its relation to the number of times of
repetition is understood, the defining process may be
shown to depend on the memory of the products of
the number that measures the derived unit, and
the number that gives its times of repetition in
measuring the quantity to be more definitely
uefined.

The pupils will see the necessity for memorizing
a set of products collected and arranged as tables.

How to Teach the Tables— Derive a unit of
measure, say 2 ft. and repeat it 2, 3, to 12 times, and
find the sum in each case.

Pupils should first build all the tables from actual
measurements, them memorize them. 2, 8, 4, 5, 10
and 11 times seem to form an easy group on account
of certain recurrences, and the appearance of certain
mnemonics; 6, 7, 8, 9 and twelve are more difficult.
It should be pointed out that a portion of each is
already learned, and liere the " Law of Commutation"
should be developed.

'^^f7:•^^■?

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ARITHMETIC.

277

) value
lea of

Then

I terms

iber 12

and the
imes of
may be
iucts of
it, and
tion in
sfinitely

lorizing
)les.

unit of
Qes, and

II actual
4, 5, 10
account

certain
difficult.

each is
iitation"

Example 8x4
r • • I

4x3 By intuitioMK.

• • • 9

This shows that 8 times 4 times a unit ec^uals 4
times 8 times a unit= 12 times a unit.

Use should be made of this law in operations, thus
avoiding incongruities arising from using the multi-
plicand as a repeated quantitative unit.

Multiplication may be divided into two cases.

i. When the multiplier does not exceed 12.

ii. When the multiplier exceeds 12.

Case I. — Lead up by easy examples, such as 4-|-4
-1-4 + 4-1-4 = 4x5 = 20, to show the shortened form
and give such examples as, 2X2, 22x2,222x2 to
lead up to the formal process.

Example 4632 x 4,

Decompose thus
(a) 4000x4 = 16000
600x4= 2400
80x4= 120

2x4= ^ ?

"^632x4=18528

(b) 4000 + 600 + 80 + 2

1 6000 -h 2400 + 120 + 8

Th.

2
4

1 6'l^b

24H

12t

2Th + 41i

Ui + 2t

18Th

(d) Final form.

4682
4

TS52S

1 1

278

METHODS IN TEACHING.

Cane II. — Buforc proceeding witli this step, the
pupil should feel the necessity for the new process.
He has exhausted his multipliers to 12. Present the
truth by dots that 13 times a number = 12 + 1, 11 + 2,
or 10 + 3 times the number. The pupil will be led to
see that 10 times + 3 times a number is 13 times the
number. The reason for selecting 10 and 3 will also
be seen.

Example. — 132 x 13. We require 10 times and 3
times 132. Adding these, will give 13 times 132.

Final form.

(a) 132 X 3= 396
132x10=1320

132x 13 = 1716

(b) 132
13

396 = 132 X 3
132(0) = 132x10

396
132

1716

1716 = 132x13

Show the truth by dots that 20 times a number
equal 2 x 10 times a number, then give exercises with
10, 20, 30, 40 etc., as multipliers. Then use 23, 33,
etc., and extend the principle to hundreds.

Introduce examples with noughts and give
practice in the use of factors.

Show also by dots that 2 times 10 times a number
is 20 times the number.

Division — When we measure a derived quantity
as 15 ft. by the unit whose measure is 3 ft. we obtain
a number which gives the times of repetition of the
unit and which also defines the relation of the unit to
the measured (juantitj^^ 15 ft.

Division enables us to operate with the numbers
that represent these measurements, and we find that
the value of a measured quantity in terms of another

SISi.

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'it) ».": '■'■;\',-mi «;r'''J. ' < -'

ARITHMETIC.

279

step, the

r process.

•esent the

1,11 + 2,

be led to

times tlie

will also

les and 3
J 132.

brm.
c) 132
13

396
132

1716

number
ises with
23, 33,

nd give

number

quantity
e obtain
n of the
e unit to

lumbers
ind that
another

measured quantity" is obtained by dividin*:; Uie
measure of tlie derived (piantity by the measure of
the derived unit. Division thus reverses or undoes
multiplication.

The ratio and the measured quantity may be
given to find the measuring unit, as divide $15 among
3 boys, how many $s will each get ?

Here we ask what number applied to the unit
"one dollar" to form a measuring unit for $15 will
give the number 3 ? By operating with 15 and 3 we
get the co-factor 5. Then 5 applied to the unit $1
gives $5 the measuring unit. This is the amount for
each boy.

In either case we operate with the numbers and
interpret the result; according to the measuring
demand. In either case we can show the relation of
division to subtraction by successive subtractions.

The operations in division may be divided into
two cases.

i. When the divisor does not exceed 12.

ii. When the divisor exceeds 12.

Give some exercises to lead up to tlivision and
connect with multiplication.

Using the tables the pupils will soon see the
converse of them, as the process depends on what was
done in multiplication.

Multiplication. Division.

3x5 = 15 15-i-3 = 5

4x6 = 24 24-^4 = 6

7x8 = 56 56-f7 = 8

Use the multiplication products to introduce the
formal step 2 |^ 3 | J^ 7 |^ 8 | 72 1 2 1 144

{ • • • •

( ■»

ii'.
I '1.

III:

Ill

280

METHODS IN TEACHING.

A<(alii, in such examples as the followin<^, the

pupils will see the result without the use of new

tables. 2 1 44 2(444 41888 ,

I I . I . etc.

22 ' 222 ' 222 '
When the tens figure will not contain the divisor
evenly then separate as follows : —

216-i-2=:2 i 200 + 10 + 6

100 + 5 + 3 = 108

Use numbers from 1 to 12 by the formal method.

The so called " Long Method " of short division
will not seem necessary if the implied inverse of
multiplication which is now made explicit in division
is thoroughly understood. The long method of short
division may be used to relate the old and new when
" long division " is introduced.

Case I. — Divide 816 by 6. Decompose the
dividend to show multiples of 6 thus : —

6 1600 + 180 + 36
100+ 30+ 6

Express shortly thus : —

6 1 816 Explanation : 6 is contained in 8 one

136 time and 2 over. This 2 makes 20 of

the next lower order which with the 1 make 21.

Now 6 is contained in 21, 3 times and 3 over.
This 3 makes 30 of the next lower order which with
the 6 makes 36. Lastly 6 is contained in 36, 6
times.

Since the product and remainder are obtained
mentally, this method is called " Short Division."

Case II. (When the divisor is greater than 12.)

This process of division may be shown to be the
exact converse of multiplication just as in the smaller

AElITliMETIC.

281

in^, the
of new

) divisor

method,
division
^erse of
division
of short
!W when

Dse the

8 one
s 20 of
ake 21.
3 over,
ch with
Q 36, 6

)btained

}>
m.

I 12.)

be the

smaller

examples whe)i using the tables we found that 4-f 2
= 2, was tho converse of 2 x 2 = 4.

Suppf^^e we wish to divide by 13.

i. We might build a table and carry on the
divisions as before, but, as many larger numbers will
occur, it is best to introduce the new method at
once.

ii. As we have seen, division is the inverse of
multiplication ; multiply 132 by 13, i.e. :

Multiply 100 + 30 + 2 by 13 = 100 X 13 = 1300

13 30x13= 390
2x13= 26

1300 + 390 + 26

Now divide 1716 by 13.
1716 less 100x13 = 1716-1300 = 416
416 " 30x13= 416- 390= 26
26 " 2x13= 26- 26=

1716 less (100 + 30 + 2) 13 =
Again: 13 1 1300 + 390 + 26

132x13 = 1716

100+ 30+ 2 = 132.

Again : Let it be required to divide 1716 by 13.
From 1716 subtract 13x100 = 1716-1300 = 416 re-
mainder after 100 subtractions.
From 416 subtract 13 x 30 = 416 - 390 = 26 remainder

after 30 subtractions.
From 26 subtract 13 x 2 = 26 - 26 = remainder after
2 subtractions.
Hence there have been 132 subti'aetions in all, or
the quotient of 1 716 by 13 is 1 32.

This principle of subtractions may now Ih3 stated
in tabular form as follows :

r;'

tl!

;

i'ji

'H .

282

METHODS TN TEACHING.

(a) 13J 1716 I 100 + 30 + 2 (6) 13j 1716 | 132

1300

416

390

The pupils will soon adopt tlie formal pr -ess and
extend to larger numbers.

Practice should be given in the use of the trial
divisor and trial dividend.

The pupils should frequently build a table of
1, 2, 3 — 9 times, the divisor.

Division by factors, and finding the correct
remainder :

Example.— Divide 48362 by 42.

One pair of co-factors is 6x7. Hence divide
first by 6 and this quotient by 7.
6 1 48362
7 8060 = 2 units remain and 8060 (sixes) as quotient.

1151 = 3 sixes remain and 1151 (forty twos) as
quotient.

. • . the remainder = 3 X 6 + 2 = 20.

Again : Divide 39265 by 105. The factors are
3x5x7.
3139265

5 1 13088=1 (unit) remains and 13088 (threes) as
quotient.
7 I 2617 =3 (throes) remain and 2617 (fifteens) as
quotient.
373 =() (fifte(Mis) remain and 373 times (one

- 100.

hun<lred and five) as ((Uotient.
Remainder = 1 + ( 3 X 3) + (6 X 1 5) = 1 + 9 + 90

132

OSS and

he trial

able of

correct

divide

uotient.
wos) as

ors are

I'ees) as
[3ens) as
ics (one
4-9 + 90

ARITHMETIC.

283

Pupils may now deduce the rule for findini^ tlie
correct remainder.

Proofs, short methods, and arithmetical terms
connected with the simple rules should now be
systematically dealt with. Th terms, addend, etc.,
should be inductively developed, but no formal
definition should be demanded.

The idea is to furnish the pupil with a language
which to him has meaning.

Compound Quantities — When a quantity has
been measured by, r.nd written in terin.s of units
irregularly derived from one another, but which are
so related that each of the larger is measured by the
unit next smaller than itself we call the quantity a
" compound quantity."

The operation by means of which we can change
the unit value of these compound quantities is called
"reduction."

Pupils should make their own measurements,
first deriving these aggregates and then expressing
them in terms of a single unit of lower or higher
value. They will soon discover a reason for
reduction.

The need for adding, subtracting, multiplying and
dividing will be felt when the stage of measurement
and operations are related.

The operations used in defining those measure-
ments are called the " Compound Rules."

The calculations arising from these quantities are
very essential. The pupil should study the rules
for the fact knowledge! ncc^'ssjiry in ])r;ietical life.
In tlie sinq)le rules we are dealing with (|U}intities
formed by one regular denomination (ten) and having

' I, !

• :'.

> t

r--

284

METHODS IN TEACHING.

a value dependent on the position of the digits
expressing the numbers.

We have a number value indicated by the symbol
and a local value known by the relative position of
the symbol. In 234 we have 200 + 30 + 4 = 2 (10)" +
3(10) + 4. This shows the 10 times increase in value
as we go to the left.

Compound Quantities : — In compound cjuantities
there are two elements to consider, the relation of
the measuring unit, and the ten ratio in the number.
The operations in consequence are called " com-
pound."

In measuring quantity such as extension, linear,
superficial, cubical measure, capacity, weight, time,
angularity, and value, we use standard conventional
units, but they bear no definite relative value to each
other. They are for the most part irregular and
variable.

Considerable practice should be given in this
department of the work. Attention should be givon
to the varying unit. The number element will be
seen to depend on the same measuring process
already mentioned — quantity-unit-number.

Develop objectively the units and associate the
measuring value of the unit with the name. Each
unit that can be conveniently developed in the
school room should be taught objectively. The units
should be used in actual experience in measuring,
weighing, counting, etc.

Bring out the relative value of the pint, quart,
gallon, peck and buslicl. Use the actual measures.
Secure a lai'iic box of line sawdust for Mk; school
room. . Let pupils make lists of things measured.

ARITHMETIC.

285

) dibits

symbol
dtion of

1 (10)" +
in value

uintities

atioii of

number.

" com-

[, linear,
it, time,
entional
! to each
lar and

in this

3e givon

will be

process

ate the

Each

in the

'lie units

;asuring,

t, quart,
leasures.
e Kcliool
leasured,

weighed, counted, etc. Deal with the actual quanti-
ties.

Give, as ffir as possible, detinite ideas of linear
units ami apply them directly in measuring. Also
give definite ideas of surface, square inch and its
relation to a square foot. ' Then develop scjuare
measure (two dimensions) from linear measure (one
dimension), and cubic measure (three dimensions)
from linear and square measure.

Use exact units and drawings, until terms used
are charged with meaning.

Give simple problems with one denomination to
impress the fact that these quantities can be defined
more accurately by operating with the numbers that
value them.

Pupils should measure quantity ; establish the
ratio, build the table, write it neatly, and then
memorize it ; but in memorizing no set order should
be used exclusively.

Reduction — changing unit value — will now
follow, showing that quantities derived by using
certain units may be derived by using one or various
units in the same scale. The number depending on
a unit will of course vary, but the quantity will
remain the same.

Pupils should have practice in deriving ({uantity
with different units.

Let pupils measure a quantity 3 gallons, again
12 quarts, again 24 pints. Such experience will lead
up to reduction, and show the reason for the process.

Reduction will be seen as the operation that
changes the number value of a quantity when the
unit of measure changes.

^»

t I

'1 ''

i I!
i

i II

286

METHODS IN TEACHING.

The teacher, having led the pupils to comprehend
the number, will now develop and make cleai" the
operations, addition, subtraction, niultijjlication and
division, in the use of these numbers.

The order is, first derive numbers from quantity,
then bring about the facility by using the numbers
in the operations.

Reduction may be formally treated as indicated
by the following examples.

The two kinds of reduction — reduction descending
valuing a measured quantity in terms of a lower
unit, and reduction ascending, valuing a measured
(juantity in terms of a greater unit — are inverse
processes, either of which may bo used to verify the
other. In the first we operate with the numl)ers by
multiplying ; in the second by dividing.

Let it be required to change 12 yards 2 feet 9
inches to inches. We here find it convenient to
illusti'ate once more the " Law of Commutation."

= # # # Suppose each line to repre-

= • • • sent 1 yard = 3 feet as shown

= # • • by dots.

= • • • Thus we see that 4 yards =

3 times 4 times 1 foot = 4 times 3 times 1 foot.

Hence by this law either factor may be used as
multiplier, i.e., 4x3(1 foot) or 3 x 4 (1 foot).

12 yds. 2 ft. 9 in. As there are 3 feet in 1 yard,
3 in 12 yards there are 12x3

(1 foot) or 3 X 12 (1 foot), (Law
of Commutation).
= 36 feet ; 36 feet + 2 feet = 38
feet.

38 feet
12
465 inches

ARITHMETIC.

287

[ihend
r the
11 and

intity,
mbers

icated

nding^
lower
asured
n verse
iV the
jers by

feet 9
ent to

repre-
shown

ards =
ised as

I yard,
12x3
(Law

et = 38

12 1 632 i nches

-8 inches

3 52-

17—1 foot

Aixain : in I foot there are 12 inclies ' in 3S
feet tliere are 38x12 (1 incli) or 12x38 (I inch)--
456 indies and 456 inches + 9 inches = 465 inches
/ ^ 12 yards, 2 feet, 9 inches = 465 inches.

Let it be required to change 632 inches to yards,
feet, and inches.

Since there are 12 inches in
1 foot, there will be as many
feet in 632 as 12 is contained in
632. 632-f 12 = 52 (feet) and 8
inches remaining. Again : since there are 3 feet in
1 yard, there will be as many yards in 52 feet as
there are times 3 feet in 52 feet ; 52 feet -^3 feet = 17
times 1 yard, and 1 foot remaining. Hence 632
inches = 17 yards, 1 foot, 8 inches.

These operations may be compared with the
notation system in the operations called the four
simple rules.

Compound Addition

H T U

6 7 3 (h) 6 7 3 {<•)
4 3 4 4 3

7 8 5 7 8 5

(a)

HTU

1892 17,18,12 18, 9,2

From previous knowledge the pupil can readily
and accurately add such questions as (a). By
separating the columns as in (b) the pupil makes
more definite the process that has been in use in (a).
He obtains as sum 17H, 18T, 12U.

He now makes explicit the ten ratio and 12 units
are seen as It and 2u. The 2 numbering the units is
placed under the units column and the ten added

',i

4^.-,

288

METHODS IN TEACHING.

with tlie tens, making 10. This is again seen as 1
hundred and 9 tens. The 9 tens are placed under
the tens column and the hundred with the hundreds,
making 18 hundred.

The result is now expressed in the customary
form as in (c).

The pupil will now be in a position to extend this
knowledge to compound addition, and can relate the
old and new, attending particularly? to the varying
ratio, the chief new element.

Derive by actual measurements the quantities
3 yards, 1 foot, 4 inches ; 2 yards, 2 feet, 7 inches,
and 4 yards, 1 foot, 8 inches. Now define the whole
quantity by adding, then measure again to verify the
result.

(d) yds. ft. in.

3 14
2 2 7

4 18

(e) yds. ft. in.

3 1 4
2 2 7

4 18

9 4 19

10 2 7

Note that as in simple addition, quantities
expressed in the same unit value are placed in the
same column.

In (d) we first add as in (h) obtaining 9 yards, 4
feet, 19 inches as in (d).

The pupils know that 19 inches = 1 foot, 7 inches.
We then have 5 feet = 1 yard, 2 feet. Again, 9 yards
and 1 yard = 10 yards. The sum is now shown as
in (e).

The other operations may be similarly related to
the remaining simple rules, and the new point in

^<J*:«f-V-')''??y'!5^fj*!??t^.'^S!"'--n

ARITHMETIC.

289

n as 1

under

ndreds,

toraary

md this
late the
varying

lantities

inches,

e whole

srify the

uantities
d in the

yards, 4

7 inches.
I, 9 yards
}hown as

related to
point in

each of the compound rules emphasized and developed
by the pupil.

Greatest Common Measure — If tlie measuring
idea has been carried out, the relation of the unit to
the thing measured will be familiar to the pupil.
The unit will be looked upon as the measurer.

There will now be an opportunity for giving
special attention to exact measurement by measuring
measured quantities with a measured unit. The way
is thus prepared for " Greatest Common Measure "
and " Least Common Multiple."

By actual measurement, let the pupils derive
with a measured unit certain measured (juantities.
By this actual measuring process the terms, measure,
" multiple," " common measure," " common multiple,"
" greatest common measure," " greatest common
factor or divisor," " least common multiple," sub-
multiple, prime factor, and composite factor, can be
educed.

The formal process may then be introduced.

Let the pupils derive 15 feet with the foot unit,
also derive 3 feet, 5 feet.

Let them now measure 15 feet with the 3 ft. unit,
and the 5 ft. unit (a higher stage of measurement,
because a derived quantity 15 feet is measured by a
derived quantity 3 feet, or 5 feet).

Lead the pupils to discover that the greatest
derived quantiuv that will exactly measure two or
more derived quantities is their greatest common
measure, and that the number defining this common
measure is the greatest common factor, or divisor of
the numbers that value or define the multiple
quantities.
19

■ ''I

'i:

290

METHODS IN TEACHING.

s ' >f

Suppose that 12 feet and 18 feet are two derived
quantities of which 12 and 18 are the number
values.

Now the derived (juantities 2 feet, 3 feet, 4 feet,
6 feet and 12 feet will exactly measure 12 feet, and
the derived quantities, 2 feet, 3 feet, 6 feet, 9 feet, and
18 feet, will exactly measure 18 feet; therefore the
numbers 2, 3, 4, 6 and 12 are divisors or factors of
12, and the numbers 2, 3, 6, 9 and 18, are divisors or
factors of 18.

Now 6 feet is seen to be the greatest common
measure of the qua">tities 12 feet and 18 feet. Also
6 is the greatest common divisor of the numbers 12
and 18 which value these quantities.

Lead the pupils to discover, that, in measuring
a derived quantity 15 feet by a derived unit of
measure 3 feet, or 5 feet, the 15, 3 and 5 are the
numorical values of the measured quantity and the
measuring units. Then establish the principle
that if one derived quantity exactly measures
another derived quantity, the number that defines
the unit of measure is a factor of the number that
measures or defines the multiple quantity, and, that
the number that defines the multiple quantity, is a
multiple of the number that measures or defines the
unit of measure.

After this has been clearly brought out, we can
perform the operations of multiplication and division
on the pure number symbols, knowing that they
represent relational values in the above measuring
process, and that in place of actual measurement we
may mentally perform the operations with the
numbers to the neglect of the measurement. Impress

^ .'itisn*^

derived
number

it, 4 feet,
[eet, and
feet, and
jfore the
actors of
visors or

common
et Also
mbers 12

Qeasuring
I unit of
5 are the
Y and the
principle
measures
at defines
nber that
, and, that
atity, is a
etines the

t, we can
d division
that they
measuring
remeut we
with the
Impress

ARITHMETIC.

291

that in openitin<T^ we imply the actual measurement
whicli may be stated wlien necessnry.

Working now with pure numhcrs as n.'presentiiig
the above measurements we may proceed to tind the
H.C.D. of numbers easily factored.

{(t) Factor Method. — Take the numbers 35 = 5 x 7
and 77 = 11x7.

The pupil sees that 7 is a factor of both and that
it is the H.C.D. He mu3t now translate this into
the measuring process ^ \ if a (juantity measured by
a unit = 77 times that unii, and another quantity
measured by the same unit gives 85 times that unit,
then the greatest common measure of these quantities
is 7 times the same unit.

(h) Formal Process. — By finding all the prime
factors of small numbers it is easy to find the C.F.'s
and H.C.F. of these numbers.

Take the numbers 16 and 24. The factors of 16
are 2, 4, 8 and 16 ; and of 24, 2, 3, 4, 6, 8, 12 and 24.
Hence 2, 4 and 8 are seen to be counnon factors and
8 the G.C.F.

60 = 2x2x3x5 = 22 x3x5 and 72 = 2x2x2x3
x3 = 23 x32

Let class note that, (1) factors must be prime,

(2) that the divisors and last quotient constitute all

(3) that their products give the original numbers ;
i.e., 23 X 32 ==72, and 22 x 3 x 5 = 60.

Discover the following: — The product of the
lowest powers of those factors which are common io
all, is the G.C.D.

4«

292

METHODS IN TEACHING.

(d) Loiii*' Mctliod. — The fundamental truth on
wliich this method depends may be placed before the
pupils in this way.

E A

: X c

Let AB and CD be two measured (|uantities in
terms of E.

Now E measures AB, CD, and also XD their
difference. It also measures AB + CD. It also
measures any number of times A B, any number of
times CD, any number of times their sum or
difference.

Hence the truths. If a measured quantity as a
unit measures two measured quantities derived from
the same unit as the unit of measure, then that
measured unit will measure the sum or difference of
the two (piantities or any multiple of any of them.

Also : — The number representing the value of the
measurina- unit will be a Common Factor of the sum
and difference of the numbers representing the value
of the two measured quantities or any multiple of
these quantities.

Introduce the " long method " by using 2 small
numbers say 83 and 72.

Divide as in iiie process until there is no
remainder.

We get 72, 6Q, 33, 30, 6, 3 from the operation.

It is seen that 3 will divide 6 and hence the

ruth on
3fore the

iitities in

KD their
It also

lumber of
sum or

itity as a
ived from
hen that

Eerence of
them,
luc of the
f the sum
the value
ultiple of

ig 2 small

ere is no

•ation.
hence the

ARTTflMKTIC.

298

others, since they are all mnltiph'S of .S. It is found
also to he tin; only iiunihrr that divides all witlujut
a reinniiider. Ifoiieo .'} is the II. (J.I), as may he easily
seen by resolvin*;' the nund)ers into their prime
factors.

" The truth explained and reason of the process
shown."

Take 144 - 48 x 8, and 240 = 48 x 5.

48 X 8
48x2

(48x1)

1
1

48x2
48x2

48 X 5 It is seen that 48 is a factor

48x8 of every dividend and re-
mainder. It is therefore com-
mon and from what has been
said can be easily shown to be
the H.C.D.

The truth established may now be illustrated by
pure numbers.

Take 85 = 7x5, and 84 = 7x12. From this we
can show 7 to be a factor of 85 ; 84 ; their sum ; their
difference, and any multiple of 85 or 84, or any
multiple of their sum or difference.

Suppose now we wish to find the H.C.D of 8149
and 26179. We are obliged to adopt some method
other than factoring. We use this long method.

" Divide the smaller into the larger and continue
until there is no remainder " (see text book). The
last divisor will be the H.C.D.

8149
2961

188
188

8
8
5
4

26179
25192

From this we see according to
the principle established that the
number rec^uired measures 47,
188, 940, 987, 2961, 25192, 8149
and 26179.

Now 47 is seen to br a factor of all these and
since it is the greatest fn^tor of itself and must

987
940

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)

294

METHODS IN TEACHING.

i :

(M)M(MiM tlic Wy.V. it rollowH that 47 is the ll.C.F.
ro((ui 1(3(1.

Spacij will not poiMiiit a mom d(itail(3(l Htateiiieiit.

Thr(io or morc! nuinbers may he simihirly dealt
with. Short, neat, compact methods ol' usin^ this
process should be given.

Least Common Multiple -Alter developing the
terms nmltiple, etc., the class will be prepared to find
the L.C.M. of two or more numbers.

Impress that one defined ([uantity is a multiple of
another defined ([uantity when that other (juantity
exactly measures it. Extend this measuring idea to
"common multiple" and "least common multiple."

It may be seen that some of the multiple (juanti-
ties of 2 feet, are 2 feet, 4 feet, 8 feet, 10 feet and 12
feet, and that some of the multiple rjuantities of 3
feet, are 8 feet, 6 feet, 9 feet, 12 feet.

The numbers 2, 4, C 8, 10 and 12 are multiples
of 2, and the numbers 3, 6, 9 and 12 are multiples of
3 ; 6 and 12 are common multiples, and 6 is the least
common multiple. The L.C.M. of numbers prime to
each other is their product.

To find the L.C.M. of 18, 24 and 30. Express
them in their prime factors.

18 = 2x3x3; 24 = 2x2x2x3; 30 = 2x3x5.
Then (2 x 3 x 3) x (2 x 2 x 2 x 3) x (2 x 3 x 5) = 12960 =
their product is seen to be a multiple of 18 because it
contains the prime factors of 18 ; also of 24 because
it contains the prime factors of 24 ; also of 30 because
it contains the prime factors of 30. Hence 12960 is
a common multiple. Now discover the L.C.M. of 18,
oO and ^2Jf. It is plain that (2 x 3 x 3) is a multiple
of 18, and that (2 X 3 x 3) X (2 x 2) is a multiple of

ARTTHMETTC.

295

. ll.O.F.

itcnieiit.
ly dealt
in^r this

nnjr the
d to find

iltiple of
(juantity
o' idea to
Itiple."
e quanti-
3t and 12
ties of 3

multiples

dtiples of

the least

prime to

Express

= 2x3x5.
= 12960 =
because it
14 because
K) because
3 12960 is
IM. of 18,
a multiple
lultiple of

24 as it contains all tlic prime fiM-tors of 24 ^ \
(2x3x3)x(2 X 2) is a comiiio!! multii)le of I.S and
24, and (2 x 3 x 3) x (2 x 2) x 5 Ih a nuilliple of 30
since it contains all the prime I'actoi's of 30. It is
therefore a conunon nudtipK^ of these three nniubers
and it must be the "least common multiple" because
the least number po.ssible of prime factors is taken to
produce it.

The L.C.M. of KS, 24 and 30 is therefore (2 x 3 x 3)
X(2x2)x5 = 360.

The formal method of finding- the L.C.M. may
now be given. (See text book).

Find the L.C.M. of 16, 30 and 36.

First find prime factors.

16 = 24 ;30 = 2x3x5;36 = 2'-' x 3^

The L.C.M must contain 2* x 3-' x 5 = 720, . • .
720 is the L.C.M.

We have the following rule : " The product of the
highest powers of all the factors that occur will be
the L. CM."

To find the L.C.M. o/396 and 814 (larger numbers)
396 = 22x18; 814 = 22x37.

The L.C.M. must contain 22 and 18, also 22 and
37, . • . the L.C.M. is 22 x 18 x 37. That is 396 x 37
= L.C.M. But 37 = 814

By substitution 396 x 814 = L.C.M.

Since 22 is the H.C.F. we have the foUowin";
formula '^gs = L.C.M. where A and B represent two
measured quantities and D their G.C.M.

This method may now be extended to three or
more numbers. Give practice problems to secure

■?• '. J

296

METHODS IN TEACHING.

1^ ;i

interest, rapidity and accuracy, in order to prepare
tlu! way for the use ot* H.C.]). and L.(y.M. in
fractions.

Recapitulate : Find H.C.D. and L.C.M. ot 16385
and 18018.

Resolve into prime factors. 16335 = 3^ x 5 x 11- ;
18018 = 2x3-' x7xllxl3.

From generalizations the H.C.F. is 3- x 11 and
the L.C.M. must contain 2 x 3^ x5x7xll2 x 13.

Hence the L.C.M. is 2x33 xSxTxll- x 13.

Fractions — The term fraction seems to be used
in a variety of ways as " one or more of the equal
parts of a unit," an unperformed division ; a ratio
between two quantities; a number indicating and
explicitly stating the measuring process by means of
which the number idea is developed in defining
quantity.

In the treatment of fractions, the continuity of
the measuring process giving rise to a higher
development through a uniform adjustment of
activity should be recognized.

The teacher who examines the nature of the
above statements will have no difficulty in deciding
on a method of tetiching the science and art of this
department of arithmetic.

If fractions are considered as parts of things, and
have only a qualitative meaning, if the ratio implied
is eliminated by concreting the unit, if the sub-unit
(fractional) is not compared with the prime unit, if
the terms of the fraction merely represent unper-
formed oper.itions, or if the thought power that this
stage of measure«nent demands is not developed.

SSpA

) prepare
L.CM. in

oi 16335

x5xll2 .

X 11 and

112 xl3.

xl3.

o be used
the equal
1 ; a ratio
iting and

means of
defining

:inuity of
higher
tment of

e of the
deciding
•t of this

ings, and
3 implied

sub-unit
e unit, if
unper-
that this

veloped,

ARITHMETIC.

297

fractional work fails to perform its true function a-^
a branch of arithmetic.

Concrete treatment may serve as an introduction
but the power oi iibstraction and generalization must
be increased by a proper development of the number
idea according' to the stasfe of mental evolution
demanded. The process ot* this stage of measure-
ment must ail abstract thinking. Ratioing by
comparing magnitudes should be prominent. There
should be a training in relating — the very essence of
fractions.

Fractions should be viewed as a continuation of
the early stages of making a vague whole definite by
finding the parts (analysis) and relating the parts
(synthesis).

The idea is the same in fractions. What was
implied — ratio — in counting became explicit in
multiplication and division ; and now in fractions it
is not only more explicitly brought out but it is more
adequately expressed by the notation of fractions.
The fraction idea involved in the early stages of
counting is now made more definite, and not only
should the teaching give the numbers designating the
terms of the fraction, but the modification of one
through the other.

What then is a fraction according to its use in
making definite this stage of measurement ?

An examination of ^ will show the complex idea
involved therein.

The pupil nmst first think 5 (say) then 0, then
the unit J, then the relation 11.

Tlie proper teaching of fractions should reinforce;
tlie pupil with liis past knowledge and power in

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298

METHODS IN TEACHING.

deriving- quantity, and onipliasize tlie ratio idea now
pioniinent, tliereby sustaining that continuity which
gives rise to the unity of the subject.

" A fraction may be considered as a convenient
notation for expressing quantity in terms of the
process wliich measures or defines it." — " Psychology
of Number." — McLellan cC' Deiuey.

A fraction is a number in which the unit of
measure is a definite part of some primary unit." —
" McLellan's Public Scliool Arithmetic."

" A fraction is one or more times the reciprocal of
an integer." — Grahami.

When a pupil in aggregating thinks explicitly 5
in terms of its own unit, it is an integer.

When he thinks the unit in terms of 5 it is a
fraction.

" How a fraction is derived according to the
measuring process as indicated by the notation."
Any unit may be used but the primary unit should
be a measured unit.

For convenience the linear foot is used.

B Let A B represent 1
foot.

Let C represent 1 inch

D, unmeasured, D2 =

D, now measured.

C —
D,-
D2

(unmeasured)
(measured)

By comparison, analysis and synthesis the pupil
derives a new sub-unit from the primary standard
unit and conceives its relation thereto. A new
demand is made in numbei'ing and unless these
standards of comparison are set up in the mind, the
work does not amount to more than " ciphering," and

ARITHMETIC.

299

> idea now
ity which

onvenient
ns of the
sychology

e unit of
y unit." —

jiprocal of

splicitly 5

5 it is a

ig to the
notation."
ait should

present 1

ent 1 inch
ed, D2 =
easured.

the pupil
standard
A new
ess these
mind, the
•iiig," and

the operations lead to a mere conjui-iiij;" witli
iiiinilxT.s.

AB= 12 obtained by a<ldini4 = 12 times 1 obtained
by multiplication (the times idea becoming promi-
nent).

The "one" is conceived to be one of the twelve
iV. His conception of this relation is the new
working product of the mind. The iV becomes a
sub-unit. There was a synthesis for the 12, an
analysis for the 1 and a conception of the relation
of the discriminated part — one — to the related parts
— a whole — of twelve ones. In applying this iV to
D we find it repeated 5 times = 5 times (the unit) ;
but since the sub-unit is a unit whose relation to the
primary unit from which it is derived is indicated
by iV, we notate or express the complete measure-
ment this way tV = 5 times the sub-unit whose
relation to the primary unit 1 foot and whose name
or denomination is indicated by the symbol 12. In
rV we have the following: 12 shows the number of
sub-units in the primary unit and names the sub-
unit as iV. It also implies the relation of the
primary unit to the sub-unit. The 5 shows the
times of repetition of the sub-unit in measuring the
quantity D and implies the relation D, to C, and
through the 12 shows the relation of the new
measured quantity D2 to the prime unit 1 foot.

This view of fractions demands a certain kind of
mental exercise. The mind is kept close to the
necessary truths whose beauty alone forms an
element of the ideal ; the known experience of to-day
is used in interpreting to-morrow's. Both number,
and definite (juantitative relations are presented.

i' III;'

■!(

riij

300

METHODS IN TEACHING.

Quantity and fractions arc not div^orce*!. Every symbol
and indicated ojxji'ation can be and should be translated
into meaning-. Accuracy and skill in manipulations
are not to be overlooked. Memory is not to be
burdened by arbitrary rules — " Invert the divisor."

The thinking faculty is invigorated, strengthened
and developed by orderly, consecutively, logically
arranged material, j^i'esented in such a way as to
cause a normal mental reaction demanded by this
Stage of measurement.

Teaching^ Fractions— The pupils are familiar
with the measuring idea, with number as a tool of
measurement, and are prepared to extend this mea-
suring idea.

In teaching fractions bring out the analysis of a
whole and the synthesis of the parts.

Draw attention to times of repetition of parts as
1 = 3 times J not merely 3 out of 4. Use equal
objects freely and give exercises in comparing
denominate quantities. Write tables reciprocally, I
yard = 3 feet ; 1 foot = J yard.

Increase power by deriving quantity from
environment. Refer symbols and operations fre-
quently to actual measurements before operating.

Let statements be illustrated and given afterwards
in clear, consistent, concise language.

Introduce lessons orally and when symbols can be
translated into measurements, i^ive clear written
statements of the work. Discover relations and use
numbers to express them.

Give plenty of practical problems and let pupils
freciuently construct problems for themselves. Use
shortest methods and avoid stereotyped solutions.

ARITHMETIC.

801

J symbol
'iiisl{it<^d
iiilatiouH
t to be
nsor."
igthened
lotjjically
y as to
by this

familiar

tool of

(lis mea-

f^-sis of a

parts as
e equal
nparing
)cally, 1

^ from
•ns fre-
ing.
srwarrls

can be
written
ind use

pupils

. Use
t)ns.

1st Lesson in Fractions— Fold kindergarten
paper (4 inch squares) to give an idea of the parts of
a quantity without a physical analysis.

Use measures, quart, etc., to give an idea of equal
parts.

By using lines, and measuring, develop equal
parts, notation, and terms.

Let pupils draw 5 lines, each 1 foot long and
measure them with 1, 2, 3, 4 and 6 inch measures.
Discover the equal parts in each, and what part (the
relation) each is to the whole.

Express these parts as 1 out of 2, etc., and name
them as one half, etc. Introduce the notation \, etc.

Show l = 5 = ;i=i = ! = H,etc., and ^ = J = il= A=H, etc.

Develop meaning of numerator and denominator,
ioj> one names = nuinher of 2^<(rts taken = numerator ;
bottom one numbers and names parts in the prime
unit = denominator.

" A fraction is a number in which the unit of
measure is a definite part of some primary unit of the
same kind."

" The denominator shows into how many parts
the primary unit is divided to give the direct unit of
measure. It also names the parts."

" The numerator shows the number of them that
measures the quantity. — McLellan and, Ames.

Let ABCD be a definitely measured
quantity.

Divide and color with chalk.
Conq)are, group and relate l)y
diagram J of 1 = J ; I of \ = \\ I of j =
I; i of i = A; J of i\> = ;.'•>.

By the use of diagrams intrinsic interest attaclies
to the operations, and variety is secured.

1 i

]K ■ :i

I . I

802

METHODS IN TEACHING.

Steps in Fpactions— Development of the idea
and terms of a fraction ; development of certain
fundamental truths giving rise to rules of operation.

Operations : — Reduction, addition, subtraction,
multiplication and division.

Quantity may be derived by measuring with
prime, multiple, fractional, and combined units.

If the unit changes the number defining the same
quantity will accordingly vary.

By actual measurement and the presentation of the
implied relations, the pupils will conceive the truths
which give rise to the following principles of operation.

The operation which changes the unit of derived
quantities without altering their value is called
"Reduction."

We have the following reductions :

A whole number to a fraction ; a fraction to a
whole number; a fraction from higher to a lower
unit value ; a fraction from a lower to a higher unit
value ; mixed numbers to improper fractions ;
improper fractions to mixed numbers ; fractions to a
common unit value , fractions to a common number
value (same numerators) fractions to a higher unit
value ; a set of fractions to any unit value.

We reduce to define more definitely, or to aid in
performing the operations.

We have 6 important principles to some one of
which the rationale of every fractional process can
be traced. These principles should all be illustrated
by diagram and connected with (juantity as explained
in No. 1.

I. Measure any line AB by A of AB = 30 units,
by iV of AB = 10 units ; by i of AB = 5 units.

ARITHMETIC.

303

he idea

certain

peration.

I traction,

Qg with

its.

the same

on of the
le truths
peration.
t derived
is called

bion to a
a lower
^her unit
ractions ;
ions to a
L number
rher unit

to aid in

ne one of
)cess can
lustrated
explained

30 units,

Now take AC (say) A of AB = x% of AB = i of AB.
/ ^ A = T% = i ; that is 2 X 3 X 1 _ 2 X 1 _ ,

2x3x5~2x5 ~'

Cancelling the 2's and 3's we have i = 6 = 5:

From the measurement we find that if a unit
becomes i, i, etc., as great the number valuing the
same quantity becomes 3 times, 5 times, etc., as large.

The converse is true. Hence we have the
following principles of operation for reducing
fractions. " Multiplying, or dividing both numerator
and denominator of a fraction by the same number
leaves the value unaltered.".

The pupil should see the truth and see that his
operations must verify it.

Rules : (1) By multiplying the numerator by an
integer, we multiply the value of
the fraction by that number ; as

= 4;

24x2

= 2x4 = 8.

6 ' 6
(2) By dividing the numerator by an
integer we divide the value of the
fraction by that number ; as,
24^2

24 .

— =4;
6

= 4^2 = 2.

(3) By multiplying the denominator by
an integer we divide the value of
the fraction by that number ; as,

= 4

= 4-1-2 = 2.

6 6x2

(4) By dividing the denominator by an

integer we multiply the value of

the fraction by that number ; as,

51 = 4

24
6-r2

= 4x2 = 8.

(i;

304

METHODS IN TEACHING.

Reduction of Fractions— I. Reduco 5 tuet to

4ths. (Illustrate by line).

Operation.

1 foot = 4 units Explanation.— We

^ ' 5 ft. = 5 X 4 units = 20 units here wish to express

, \ 5 f t. = V ft. 5 feet in terms of

the vniit J foot.
Since 1 foot contains 4 units, 5 feet contain 5x4
units = 20 fourths = \".

II. Reduce 7^ to its lowest terms.

Operation
60 ^ 80x2 ^ 15x2x2 ^ 5x8x2x2 : Explanation :
72 86x2 18x2x2"'6x 8x2x2 —Fractions are

in their lowest

86x2 18x2x2

Since 7i = l

60 60^12 5 or 5x12

72 72-M2 6; .6x12

5; denomination
6 (greatest unit)
when the terms
are prime to each other.

Hence divide both terms by their H.C.F.

III. Reduce I to 15ths (lower denomination).

Operation.
1 = H Explanation. — i = A ; hence z =

i = To, therefore 4 times iV=rl; or the ratio of
1 = 4 times i-V = tI; 5ths to 15ths being 8, there are

3 times as many ISths as 5ths in
any number. Hence 1 = 3 times tV = H.

IV. Reduce 8 tt to an improper fraction.

Operation.

1 = f Explanation. — We her wish

to express the integral part
of the number in tiirms of
the fractional unit i and then

8 = 8xf =V

4J) 1^ rt 4 3

o^ ~f~ o^ '5

) tcet to

,tion.— Wc

to express

terms of

I foot.

itain 5x4

phination :
ictions are
leir lowest
mination
test unit)
the terms

ition).

hence i =

ratio of

there are

las 5ths in

lier wish
rral part
terms of
and then

ARITHMETIC.

305

combine it witli ,^ to mak(5 one Traction. Since in I
tliere are n, in S tliere are 8 times ',= '"; V' + ^ = V'.
V. Reduce V to a mixinl num])er.
Operation.

5 iiftlis=:l unit

1 tiftli = T, unit

47 tiftlis = 45H-2

= 9 prime + 2 sub-units = 9 -f -

= m

Explanation. —
Here we wisli to ex-
press the numl)er in
terms of the pi'imary
and derived sub-
unit. Since in any
nundjer there are h
as many "ones" as there are 5ths, in V tliere are 5 of
47 ones = 91

Addition and Subtraction— At this stao(^ tlie
pupils have the idea of a fraction ; the terms are
understood ; the notation is sio-niticant. They have
also gained power in deriving (juantity, in using
different units, in comparing- these units with tlie
primary unit, and in valuing the times of repetition
of these units. They have a knowledge of the
terminology in wdiich these stages of measurement
are expressed and they have gained skill and
accuracy in manipulating the symbols which express
the number values of these quantities.

Addition of fractions will present little difficulty.
The idea of aggregating — finding as a whole a
quantity made up of parts — may now be connected
with the pupil's past experience in simple addition.
Parts of a whole valued in different fractional units
are now to be aggregated.

Note connection with the simple rules.

t:l:

i ^■

306 METHODS IN TEACHING.

Steps in Addition of Fractions

(ct) I I 'i;{0) i, i g ; (c) J, I J ; (d) 13i, 2^.

In doalint^ with the operations in fractions the
numbers only will be used. Each number should be
derived from quantity, and the necessity and reason
for the particular operation determined by the pupils
before beginning to operate.

This should be done until every operation is
significant as a means of indicating or defining
certain modes of measurement.

(a) Find sum of f, 2, 2.

Operation.

£+S + 2=3 + 5 + 6

14
4

1 4

= i .

= 1 + t + t + I =1 + 1 + 1+1 =3s =31

(/;) Find sum of h, f , J, i^^.
Operation.

^ + 4 + 1 + ^ = ^ + ^^ + ^^ + ^"^:

= 8 + 12 + 10 + 7
16

3 7 ,

= ttt;

3 7 n Ti

T cr = J, in

Explanation: — A is
seen to be a measure
^f each of the units

h i> i> ^^^y ^^d as it is
a measure of the
equals, the number 16 which names and shows the
relation is a multiple of the numbers 2, 4 and 8
which define the other units. Now having valued
each of the above in terms of the unit iV we can
agfi^regate as in (a).

3tions the
should be
md reason
the pupils

eration is
r defining

= 3.1

ion: — 15 IS

a measure
the units

md as it is
! of the
shows the
, 4 and 8

ins: valued
iV we can

ARITHMETIC.

307

1 'J

r. 1 II
n = 1 ■-'

•2 7 2 4 I ;i

Ex[)liiiiation.

We tirst find a
unit that will ex-
actly measure J, J,
J. We find this
unit to be I'a, be-
cause 3, 4, 6, are factors of the number 12.

Hence the above can all be valued in terms of the
unit tV and can therefore be aggregated.

We now discover the following facts : (1) to add
we require the same unit, (2) the new unit is a
measure of the others, (3) its denominator is a
multiple of the other denominators, (4) the number
varies with the unit. (5) We conclude to use the first
muUiple of the denominators.

Hence the rule : To add fractions reduce them to

the same unit value by finding the L.C.M. of the

denominators and then adding the new numerators.

(d) Find the sum of 13J and 24

Operation.

13i4-24t = (13 + 24) + j4-|

'8-

= 37 + i + «
= 37+^+1
= 37i

Explanation. — Add
the numbers represent-
ing the primary unit
and proceed as before
with the fractional
numbers. Avoid when possible reducing mixed
fractions to improper fractions before performing the
operations — addition and subtraction.

Subtraction — Since addition implies subtraction,
the one being the inverse of the other, it will not be
necessary to go through a set of examples as in

308

METHODS IN TEACHING.

i':l

{nUlition. Tliese operations should not be separated.
They hIiouM l)e taii<;ljt hh correlative pliasc^s of the
same ineasurinj^ pr(jcess. The subtraction is implied
while the pupil is dealin*^ explicitly with addition.

As the pupil will make better progress with one
thing at a time, addition may first receive emphasis
until the process of changing to a common unit value
is comprehended.

Subtraction may then be taken up in the same
order as given in addition.

The subtraction of the numbers representing the
unit of measure will be easily connected with the
same operation, — subtraction — in the simple and
compound rules.

Multiplication and Division of Fractions— The
correlative phases of the same measuring process
should be observed in performing the operations of
multiplication, and division of fractions.

These operations present greater difficulty to the
pupil, than addition and subtraction of fractions, as
they involve a two-fold ratio expressed by the
numbers which measure the derived unit, multipli-
cand and the times of repetition ii. %e implied
measurement.

The object of multiplication is to bring out
explicitly the number of primary units that measure
an implied measurement expressed in terms of a
derived unit as ($i x J) implied measurement = by
multiplication I which applied to the prime unit =

H-

i '■'

separated.
isos of tlio

is implied
li ad<lition.
8 with one
3 emphasis

unit value

n the same

senting the
d with the
imple and

itions— The

ing process
aerations of

julty to the
Tactions, as
sed by the
t, multipli-
he implied

bring out
hat measure
terms of a
rement = by
rime unit =

ARITHMETIC. 809

Steps in Operation

(a) §x5;(6)6x§;(.')5X t;{d)[5ix2l
(a) Multiply § by 5.
Operation.

i. §x5=§-j-S + § + S + S =V = 3i.

Or,
ii. By diagram. ^ ^ ^ ^ Explana-

tion. — Since
the new num-
erator will
contain 10 units, 10 divisions are required.

Let ABCD = unity, i.e., it will contain 3 divisions.
Then A B K R = i of a unit and A B F H will
contain S of a unit. Also ABMN = 5x2 times J =
10 times J or V.

Or,
iii. *x 5 = 5 times 2 5x2

units "units
5x2 = 10 =V = 3J;

8 K F C

Explanation. — Re-
peat 5 times, the (2) in
the derived unit t ft.*
Then define the ([uan-

units units
tity by substituting the unit ;\.

■'^'Note — § ft. is considered a derived unit when it
is to be repeated. There is also a derived sub-unit
J ft. used in defining the derived quantity ii ft.

To show that J of any quantity = J of 8 times
the quantity.

Let A be any (|uantity
measured in terms of the
unit ]. A then (Mpials ]•
Let B, C, D, l)e each mea-
sured quantities equal to
A. Take BF, CG, DH = J

C
D

310

METHODS IN TEACHING.

r[4

of each. Now we see as a necessary truth that AK
= BF + CG + DH.

= I of each of the 3 equals B, C and D.
= 1 of S times A.
/,f of 1 = 1 of 3.
Show J of 1 = J of 3 by using numbers.

|ofl=iof3. Nowiof3 = iof¥
i ofV = | = Jof 1. /J of 3 = 1 of 1. •
(b) Multiply 6 by it.
Operation.

Explanation.— Since we operate
with the pure numbers represent-
ing measured quantity, we can
commute these factors, and hence

(i X ^ = 6 X 2 i^,,)
6x2

= 4

obtain the result 6x2

= 4.

Operation.
By diagram

A K

Explanation.

Draw A D and
divide it into 7
equal parts. Draw
AB at right angles
to AD, and equal to four of the equal parts. Complete
rectangle ABCD. Through each point of division
draw lines parallel. Then ABCD = unity ; AMND =
f of ABCD; AMLK=I AMND and AMRS = ? of
AMND = ? of f. Then AMRS is the required figure.
B^it AMRS contains 15 S([uaros and ABCD contains
28 H(|uares. ^ ' , AMRS = .rs of the whole / /i of J

Or,

ii. Using pure numbers, multiply f by J.

h that AK
;, C and D.

we operate
i represent-
,y, we can
, and hence

.nation.

A D and
it into 7
rts. Draw
ght angles

Complete
f division

AMND =
^RS = ? of
ired figure.
D contains

ARITHMETIC.

Operation,
f X 3 = V Explanation
5x3

1 fi

1 r>

too great so we take i of this

7x4

w rXf = M

Hence f x J =

^ X 3=r

e i of

5x3

311

is 4 times

tI.

7x4

To multiply f by | we must do to f
what is done to unity to get f. We must divide t
into 4 equal parts and take 3 of these parts. Each
part will be 5 and 3 of these 5x3

7x4

6_D

M C

Hence the rule :_?^^l^^L^i«_^.?^_^l^:_

Product of denominators.

To illustrate the " Law of Commutation " by
showing 5 of J = i of i

I. ABCD = unit; AEFD = tunit
and AEHG = \ of AEFD = \ of H of
ABCD = A of unit.

II. Again same unit ABMG = ^ of
unit, and AEHG = t of ABMG = ! of \ of ABCD = A
of unit.

The truth is direct.
id) Multiply 15f by 2*.

Operation.

15Jx2i =(15 + J)x(24-^); Explanation,

= 30 + ^ -f 10 + i =40 + S =i2; Separate both num-
bers into prime and
derived units and multiply first by the prime unit 2
and then by the derived^unit 1 Adding the result
we get 42.

Do not allow pupils to reduce at all times to
mixed numbers.

SI;

«. .

312

METHODS IN TEACHING.

: Vi,

T M

li'

li!

I i

n,'

prove

X r

8x5

4x7

(a) J X 4 = 8, since |x4 = 8x i x4;
(/>) f X 7 = 5, since ?x7 = 5xf x7.
Multiplying (a) and (h), / , ( J x 4) ( f x 7) = 3 X 5.
Divide through by 4x7.

' ' 4x7

Generally

Let J = factor A and ? = factor B.

/ 3 = 4A;5 = 7B.
Multiplying 8 x 5 = 4 x 7 x A x B.

. -.AB^^-^;
4x7'

But AB is the product of | x f

3 V 5 —

8x5
4x7

Generally -^x^ = ^- —
•^ b d bd

Division — When we measure a derived quantity

l)y a derived unit whose measure is prime to the

measure of the derived (juantity, we obtain a number

which is fractional.

By division we operate with these nuiabers

representing the measure of the unit and the whole

measured (|uantity and ol)tain a number which

expresses the ratio ol' the whole (quantity to the unit

of measure.

Example. — 1 'f feet measured by J feet. Reducing

we have 14 cii'hths bv 7 eio'hths — 14

units l»y 7 units. Wy division 14-r7

= 2 the ratio.

7) = 3x5.

ARITHMETIC.

quantity
le to the
I number

nuiabers
he whole
ler which
o the unit

Reducing
;htlis = l'4
ion 14-r7

313

The operation of division may also render implied
an explicit measurement thus reversing multiplica-
tion.

Steps in Division

Indicated Operation.

2^i

■I -^ 9

5i i-dh

Measurement.
(a) 2 ft. ~ «d by t ft unit.
(6) f ft. ^ «d by 2 ft. unit.

(d) 5i ft. ^ ^d by 3i ft. unit.

("^*^ equals measured).

The quotients from above, being pure numbers,

may be used as the divisors of the measures of the

dividend quantities, and the (juotients resulting will

be the numbers defining the derived units of measure.

(a) 2 ft ^ ed by i ft unit.

Operation.
2-f^ =ff -j-7 Explanation.

6 thirds -^ 2 thirds = 6 units -:- 2 units; — If we wish
6 units ^2 units = 3 . • . 2-=-:'i =3 to find the

I'atio of H feet
to 2 feet we operate with the numbers by dividing
the measure of the whole quantity by the measure of
the unit.

(6) t ft. ^ «d by 2 ft. unit.
Operation.

^ -=- 2 = I -f- ^ Explanation.

2 thirds -^(l thirds = 2 units -f 6 units ; — In place of
2 units -f-() iniits= H = .'j. Mie actol'mrji-

s n r in*:' we
mentally perform the opeivition ol" dixision i>y
dividing the measures as shown in the operatic^i.

I !■

:«'!!

jj ll

314

METHODS IN TEACHING.

Operation.
i-^% =i',-^j%, Explana-

9 twelfths -^ 8 twelfths = 9 units -^ 8 units ; tion.- This
9 units -I- 8 units = f = 1|. act of mea-

surement
can be mentally performed by operating with the
numbers that value the derived quantities. This
operation is division.
{d) 5i ft. " ed by 34 ft. unit.

Operation.
5i-f3i=V-fV Ex-

21 fourths ^14 fourths = 21 units -^ 14 units; plana-
21 units ^14 units = Ti = l*- tion. —

We can

perform the measurement of 5i feet with the unit 34
feet by operating with the numbers that value the
derived quantities. The operation is called division.

Analyze the following :

(a) 2^f; (6)1^2; (c)f^t;(cZ) 5i^34;

Example (a).
2-^^ Explanation. — J is contained in 1, 3 times

/ , in 2, 2x3 times ; this is twice too great
as we wish groups of 2 thirds.
2x3

Result

Example (h) f !- 2. Explanation. — 3 divided by 2 =
f but this is 4 times too great since we had
to divide not 3 by 2 but J by 2.

Result = , ^ ^ Since 'i of 1 = i of 3.
4x2.

Explana-
ion.-This
^ct of mea-
mrement
with the
3S. This

Ex-
plana-
tion. —
We can
le unit 82
value the
i division.

1, 3 times
too great

ed by 2 =
Ice we had

ARITHMETIC.

315

Example (c) f -^ I . Explanation. — J is contained in

1, 3 times ; in I it is contained I of 3 = . ;

but we wish groups of 2 thirds. Result =

3x3

4x2

Example (d)5k^Sh. Explanation.— 5 i ^ 3 i = V -i-

k Now in 1 we have h, 2 times, in V we

21 X 2
have — -. — ; but we wish groups of 7 halves.

Result =

21x2
Tx7 ■

The above may also be treated as the following

examples.

Divide I by f. This means I part of 5, since ? of

l=f of 5. Dividing by 5 we have^^ — — which we

4 X

see must be set right by multiplying by 7 since we

3x7
should have divided by f part of 5. Result = j — -

'r X D-

Again : Divide I by t- Reduce to the same unit
value, i.e., to the greatest common unit value. Then
3x7 . 4x5 3x7 . 4x5

we have

4x7
= 3x7

4x7

28 • 28
4x5

twenty-eights ' twenty-eights.
= 3x7 units -^ 4 x 5 units.
= 4x5 J 3x7= [ 3x7

4x5
To divide 1' by 5 is to find how many times f is
contained in t. Reduce to tlie stimo unit value, :f =
at J r = ^g 5

ill

IS = JiT

= 1

IV.

316

METHODS IN TEACHING.

I'M

Divide ? by }. This means to find what fraction
multiplied by t will give r.

Take the known = 6 |18_j_, \ 6 times Q = 18; / ,
Q = 8. ?

Hence we have 1 1 f

Rule : " To divide by a fraction is to multiply by
its reciprocal."

Proof of Rule. CS^ f = 3 x L
(1) 3 x4 = 3; (2), f x7 = 5;
multiply (1) by 7 = I X 4 X 7 = 3 X 7 ;
multiply (2)by4=f x7x4 = 5x4;
Jx4x7_3x7

Divide 1 by 2.

Generally

f x7x4 4x *"
3x7
4x5
c a

K?- =

■I!

b d b

Decimals— Decimals involve an element of
thought not deiranded in fractions. They have the
same elements of ratio, but there is this added
difficulty, that instead of being expressed by a
number, the denominator must be calculated mentally
by the pupil, from the number of decimal places
occupied in expressing the numerator. This is a
step further in complexity. It is therefore a mistake
to teach decimal fractions before vulgar fractions.
When the object is to place the whole theory of
numei'.'ition mikI notation of our decimal system
before the ])U])ils, th<^ unity of this department of
arithmetic can l»e moi'e fully related by treating
decimals first. The pupils have already learned

ARITHMETIC.

817

fraction

= 18; /.

Itiply by

jment of

have the

is added

ed by a

mentally

lal places

riiis is a

a mistake

fractions.

heory of

system

tment of

treating

learned

tluit the value of a di<^it depends on its unit and tliat
this unit is known by tlie position of the digit.

The pupil's idea of ,su])-unit ac((uir('d througli the
measuremeuts uxi)ressed by tractions will now be
combined with his knowledoe of notation and also
extended. The notation is an extension of the ten
ratio system, and hence the position indicates the
name of the sub-unit. Notati(m sliould now be
explicitly brought before the pupils. It should be
noted that every digit in the imit's place
retains its intrinsic value while every digit to the
left of the unit's place acquires a local value
according to its position. The units have their local
position and the number gives the measure expressed
by the particular unit. The ten times increase as
the digit moves to the left must be noted. Bring out
that the value of every digit in a system of decimal
fractions becomes ten times less or i\) as great as it
moves to the right.

By reduction of fractions the pupil will be able to
express, fractional quantities in terms of the sub-units
iV, r^TT, etc. The metre and Canadian coins may be
used as units in deriving quantity. These measure-
ments can be expressed as fractions in terms of the
above units. This new mode of expressing these
measurements will be easy and naturjil if the
notation is analyzed and made explicit. The pupils
should have considerable practice in writing fractions
in terms of the units tV, tK, etc., before using the
decimal system in expressing them.

With the following expression!^ the pupil is quite
familiar: 111-f ^^J-f rU -f ^U-

The increase and decrease by the ratio ten,

- 11

! I

ill

.If;

W i.

I
I j

f=i

P-

J 5,

318

METHODS IN TEACHING.

should be pointed out. The above equals 100 + 10 -f- 1

Introduce the decimal point to separate the whole
units from the sub-units and locate tenths, hun-
dredths, thousandths in their respective positions.
Then we have 100 + 10 -f-1. 111.

^.e. 100 = 1x100 .1 = 1 x tV = .V

10=1X10 .01 = 1 X Aj> = T*t7

1=1X1 .001 = 1 X TTo ff = tAtT

Now give names to the parts — integral and decimal.
A decimal will be seen as one whose unexpressed
denominator is ten or a power of ten. This unex-
pressed denominator is the new element to be
attended to and recognized.

It will be seen that this notation may be
extended to millionths, etc., as before it was extended
to millions, etc., a natural extension consistent with
the already familiar notation.

Reading and Writing" Decimals— Since decimals
are fractions expressed in this new form, considerable
practice should be given in reading and writing
der-imals in order that the pupil's knowledge of
nooation and fractions may be carried into this new
but related part of the subject.

Drill on the relative position. Note that the
number defining each unit must have its last digit
placed in the position of that unit.

Twenty-five units = 25 ; Twenty-five hundreds = 2500
Twenty-five tens = 250 ; Twenty-five tenths = 2.5
Two hundred and twenty-five hundredths = 2.25
Two thousand two hundred and twenty-five thou-
sandths =2.225.

'^f^f^Q^ij^j^*^K^^^^^^^^^k^^rir^^

^ii.-"<*';,^iJt.;

ARITHMETIC.

319

hio+i

i whole
i, hun-
)sitions.

decimal,
cpressed
is unex-

b to be

may be

ixtended

nt with

decimals

iderable

writing

edge of

this new

that the
ast digit

is = 2500

2.5
E.25
ve thou-

The first position to the right for tenths.
The second " " " hundredths.

The third " " " thousand tlis.

Dictate the number first as 2225, then when the
unit is named the point indicates the absolute value.

Never allow pupils to say " decimal one five " etc.
Read 15 one hundredths. Naming the unit decides
the position of the point.

Drill on reducing units to tenths, to hundredths,
to thousandths; hundredths to tenths, and thousandths
to hundredths and tenths, etc., until the pupil can
readily reduce up or down.

Bring out that .5 = .50 = .500; i.e., that adding
ciphers to the right of the decimal does not alter the
value and that the unit value changes, decreasing by
the tV ratio, and that the number defining the unit
necessarily increases ten-fold.

Special attention should be given to the expression
of decimal numbers in the hundredth's unit, thus
preparing the way for percentage. Give plenty of
exercise in reading and writing decimals. Vary the
exercises until all forms and expressions become
significant.

Addition and Subtraction— Very little new will
arise in the o.bove operations. Compare with the
simple rules. Emphasize that we can only aggregate,
or compare aggregates by adding or subtracting the
numbers that define measurements in terms of the
same unit. These two operations will be easily
understood.

Multiplication — Multiplication indicates a stage
of measurement. The unit — the multiplicand — and
the number — multiplier — indicate a measurement.

':1

I 'J

! i

320

METHODS IN TEACHING.

By inuUi|)lylii<:^ tlicse iniinbcrs we fiini tin.' value of
the inoasiinHl ((unntity in tci'iiis of the prime unit
from which the multi[)]iean(l is dci-ivecl. We operate
with the numbers to define the measurement. Pupils
will f^ain very little power by multiplying "decimals
by decimals." They should refer the numbers to the
(plan titles measured in terms of the decimals then
" multiplying decimals " will have some meaning.

Steps in Teaching Multiplication— (I) Multipli-
cation by 10, 100, etc. ; (2) a decimal by a whole
number ; (8) a whole number and a decimal by a
whole number ; (4) a decimal by a decimal.

Give drill in multiplication by (10) ten. Begin
with whole numbers. Educe that multiplying by 10,
100, etc., removes the digit one place, two places,
etc., to the left of the point and dividing by 10, 100,
etc., removes the digits one, two, etc., places to the
right of the point.

Two methods of multiplication may be used.
First Method. Multiply .3 by .7

reduce to fractions = A x tV = iVo
written in decimal form = .21.
Second Method. Multiply .3 by .7.

since 3x7 = 21
^ ' ^ .3x7 = 21 tenths = 2.1
but .3 should have been multiplied by 7
tenths ^ ' ^ the answer is ten times too great.
Hence i\ of 2. 1 = .21.
This second method assumes that pupils are
familiar with the *' ten ratio." It affords excellent
training in comparison owing to the change in unit.
The other steps can be similarly illustrated.

value of
iiiie unit
J operate
. Pupils
decimals
trs to the
lals then
ning.
Multipli-
a whole
lal by a

1. Begin
ng by 10,
o places,
/ 10, 100,
!es to the

ised.

7 21

= .21.

ied by 7
too great.

)upils are

excellent

ofe in unit.

ARITHMETIC.

321

The pupils should for the sake of facility discover
a ruh; for themr^elves and apply it in practice.

Division of Decimals— If the pu])il has learnt
the tenfold increase or decrease in multiplying or
dividing by ten and the corresponding change of
decimal point, he will have little difficulty in undoing
the work of multiplication.

Mistakes are more frequently made in division
than in any other part of the work. Pupils seem to
have difficulty in placing the decimal point in the
quotient. There are two reasons for this. The pupil
may not understand the measuring process giving
rise to division, or he may overlook the relation of
the units.

Example I. Divide .6 by .2.

It seems impossible to divide 6 tenths into 2
tenths equal parts, but it is quite legitimate to
measure 6 tenths by the unit of measure 2 tenths.
We g^t as a number 8 which defines the ratio of 2
tenths to 6 tenths. This is what we mean by
division at this stage.

Example II. Divide .6 by 2.

Here we wish to find what unit taken as a
measurer to measure 6 tenths will give the number 2.
We separate 6 tenths into two parts and find the
unit of measure 3 tenths = .3.

The first measurement suggests the idea of
changing to the same unit value ; the second suggests
reducing the divisor to a wholt number.

We have therefore two methods of teaching
division, (1) by reducing to the same unit value, (2)
by changing the divisor to a whole number.

Changing to the same unit value which emphasizes
21

'■I

.322

METHODS IN TEACHIN(i.

the comparing of units, has been l)ei'oi'e tlu; pupil in
the simple and compound rules and fractions. This
method is therefore a legitimate extension of what
the; pupil already knows. The other method depends
on a truth or princi2)le which ought to be place«l
before the pupils.

" If we increase the unit of measure and the
(piantity to be measured, in the same prcjportion the
relation remains the same."

To give a perception of the related elements of
number — unit — quantit}^ in order to lead to a
conception of the relation, place the necessary reality
before the pupils.

• • •

• • • •

• c

• • •

First present the dots as above the line C D.
Discover the reUition. Then present dots as above
and below C D. Discover the relation. The three
dots above the linT3 C D, and to the left of A B,
represent the numerical value of any measured quan-
tity to be used as a unit of measure ; the twelve dots
represent the numerical value of any measured
quantity to be measured by the unit to the left of A B.
Now double the dots in each case as above and below
C D, then it will be seen that the relation remains
unchanged.

Since this is a typical case, it holds good for all
cases. This is not induction, as only one case is

\ pupil in
iiH. Tliis
of wluit
1 depends
be placed

and the
jrtion the

3nients of
!ad to a
ly reality

-0

lino C D.
i as above
The three
:'t of A B,
ired quan-
^velve dots

measured
eft of A B.

and below
on remains

Dod for all
Qe case is

ARITHMETIC.

328

necessary as far as seein<^ the truth is concerned.
Hence we have the following; rule of operation, if
both divisor Mini dividend be iindtiplie(l i>y the same
number the (piotient is iK^t changed.
Sfrps in Jloisiuii of Decnmds —
{(t) A whole number ami a decimal, by a whole

nund)er.
(/>) A d(!cimal by a decimal.
{(•) A <lecimal by a whole nund)er. ,
First method :
Example I. — l)ivi<le (J. 4 by 5. Reduce both to
tenths = 6'4< tenths, by oO tenths. Now ()4
tenths contain 50 tenths once and 14 tenths
remain. This "one" isa whole nund)er in the
(piotient.
Proceed now, nniltiplyin^ each remainder by 10,
and regulate the (quotient accordin<^ly. The (piotient
= 1.28.

Example IL— Divide 2..56 by .0032. Reduce
both to ten-thousandths. We then have
25600 tenthousandths -i- 32 tenthousandths
/, 25600-^32 = 800.
Second method :
Example I. — Divide .64 by .5. Multiply both
by ten, to make the divisor a whole number.
We then have 6. 40^5 = 1. 28.
Example II.— Divide 2.56 by .0032. Multiply by
10,000. We then have 25,600 ^ 32 = 800.

Example III.— Divide .0032 by 1.6. Multiply by
10, to brino- the divisor to a whole lumdjor.
Thus we have .032-^16. Dividiii<;- we find
no units in the (|Uotient. Take down the
tenths we find no tenths in the quotient.

!•

824

METHODS IN TEACHING.

Take <lown tlie 3 Imndredtlis ; 16 will not
divide -S. hence we have no hundredths; but
8 hundredths and 2 thousands make 32
thousandths. Now 16 divides 32 thou-
sandths, giving 2 thousandths as (quotient.
Therefore the (quotient = .002.

Rchifion of Declniftls to Vulgar Fractions. — When
the pupils have become familiar with decimal notation
and can readily handle the four simple rules, they
may consider the conversion of decimals into common
fractions, and the conversion of common fractions
into decimal form. The conversion of decimals into
fractions will be ap] irent when the denominator is
substituted, which in the reading is implied, .275 is
read 275 thousandths = iWa. Reduce to its lowest
terms. No dilHculty will be experienced in convert-
ing pure decimals into fractions if plenty of intelligent
practice has been given in notation and numeration
of decimals.

Converting frach'ons into decimals, however,
requires more thought which, if properly directed,
wdll lead to a classification of fractions into 3 kinds, as
below^ ; (1) those wdiich give pure decimals; (2)
those which give pure recurring decimals ; (3) those
which give mixed recurring decimals.

To reduce I to a decimal.

7 Here we wish to <ret rid of 3 twos

"^ 2x2x2 ^Multiply by ten three times. Then
we have

7xlitxl0\10 _ 7x2x2x2x0x5x5 _ T^x .5x0x5 _ K75 _ g^^
2x2x2x10x10x1(1 2x2x2x10x10x10 loxloxio KHKi

Now for every time there is two or live as a factor
in the denominator, nudtiply both numerator and

1 will not
idtlis; but
make 82
82 thou-
s quotient.

IS. — When
il notation
fules, they
;o common
fractions
nmals into
ininator is
d. .275 is
its lowest
n convert-
intelligent
lumeration

however,
directed,
8 kinds, as
imals ; (2)
(8) those

of 8 twos,
les. Then

: .875

as a factor
jrator and

ARITHMETIC.

325

denominator by Um, since 2 and 5 an^ the only prime
ftictors of 10. But as ti^nths and liundrrdtlis hoM a
certain position in reference to tlu^ pc^int, the denom-
inator need not be written. Hence we see tht» reason
for "add nou*^lits and divide by tiie denominator."

Second method — Reduce ^ ; ^ of 1 = ^ of 7 has been
already proven.

Lead to a conception of this trutli by usin<^ (h)ts.
8 I 7.000 As 7 will not contain <S, reduce 7 units to
.875 tenths = 70 tenths ; dividin*^ 70 tenths into
8 parts we get 8 tenths and G tenths remaining -= (JO
hundredths ; dividing sixty lumdredtlis into 8 parts
we get 7 hundredtlis and 4 hundredths remaining =
40 thousandtlis. Dividing by 8 we get 5 thousandths.
/,i = .875.

To reduce § to a decimal.

By the first method we see that no numl)er of
nmltiplications by 10 would enable us to eliminate 8,
since it is not a factor of 10; hence we conclude that
§ cannot be converted into a decimal with a finite
number of digits.

I = .0666 = .6 a pure recurring decimal.

To reduce — to a decimal = '

14 7x2

Here we have 2 as one factor of the denominator.

Multiplying by 10 we get rid of 2. This will give I

digit in the quotit^nt that will not repeat. Since 7 is

not a factor of 10 we have the divisor again giving an

infinite number of diLnts.

8 8x1x10

= .2142857,

a mi.xed
decimal.

i'e('urrin<j

^ ^ 14 7x2x10

We have the following classification of frnctions
as reirards their I'elation to decimals.

^ k

' il

r-^

326

METHODS IN TEACHING.-

h'!

1. Fractions, whicli in tlieir lowest terms luivo in
their (Icnoiiiinators only the prime i'actois 2 or 5,
<^ivc a finite decimal.

2. Fractions whose denominators contain neither
2 nor 5, j^nve a pure recurring decimal.

3. Fractions wliich in their lowest terms have
other factors in denominator as well as 2 or 5, will
give mixed recurring decimals.

To convert a pure circulating decimal into a vul-
gar fraction :

Example — Change .27 to a vulgar fraction,
Multiply by 100. Pupils may discover the
reason for using 100. Then. 27 x 100 = 27.27
= 27 + .27. Take .27 from each .side and we
get .27x99 = 27. Divide each side by 99
we get .9.7 = U

To convert a mixed circulating decimal into a
vulgar fraction.

Example — Change .314 into a vulgar fraction.

Multiply by 1000.
(a) .3l4xl000 = 314.4 = 314 + .4.' Multiply by

100.
(/>) .314x100 = 31 +.4. Subtract (b) from (a);

900 times .314 = 283. , ' , .314 = ii;:i!

Other methods of reducing decimals to vulgar
fractions might also be given.

Percentag^e — Percentage should not be considered
as a totally new phase of arithmetic. At most it is
merely a special kind of measurement already devel-
oped in the treatment of fractions and decimals. The
pupil has really no new stage of measurement with
which to deal, but, on account of the nature of our

us have in
i-H 2 or 5,

ill neither

jrins have
1 or 5, will

nto a vul-

[• fraction,
scover the
100 = 27.27
ide and we
ide by 99

nal into a

ir fraction.

iiltiply by

from (a) ;

I'l

5 to vuli;ar

considered
; most it is
eady devel-
imals. The
ement with
.ture of our

ARITHMETIC.

327

system ot* commercial transactions, it is ruund conven-
ient to make calculations witli 100 as a standai'd.
Sf('j}s Id TcdchiiHj Pi'i'Ct'itf(i<jr.- — [. Show relation
to fractions and decimals. lU = .07 = 7 of the
hundred parts of a unit. The, business man
calls this 7 per cent, (to be developed as
follows) :
2. Develop the term per cent. %. \U of 200: .05 of
200, now 5 '/ of 200. This is seen to be the same
as the fractional and decimal treatment.
8. The pupil knows how to chani^e fractions to ecjual
ones of diflereiit unit value. (CJive practice in
this).

4. Have fractions changed to hundredths, and estab-

lish that this is a convenient <lenominator on
account of the special mode of measurement used
in business.

5. Put stress on the different ways of writing hun-

dredths. Jm, =.07 = 7 , a short way of stating
the first two. Give examples using the three
methods d. of 200, .07 of 200, 7% of 200. The
pupil will now see that his fractions and decimals
are chanii'eable to hundredths and that 7 / is a

o /o

statement of the other two in another form.

6. Convert such fractions as i, .1, ], \, /., etc., to

hundredths. Now write th<'m as decimals. Then
use them with the name / . Establish this rela-
tion well.

7. I[ave pupils solve the samequestion all three ways,

and point out that for ia})idity and brevity we
may select the one best snited to ouv pur[)ose.

Example —Find ( j = iV. = .25 = 25%) of .*648.

328

METHODS IN TEACHING.

8. Giv(i practice problems:

(<t) How iiiucli is 2% or 1200, of 200 feet, of 200

lbs., of 200, of 50, etc.
(h) 6% of certain quantities gives S36, 60 feet, 72

cents, flOOO, etc. Find the quantities.
(c) $12 is what % of $24 ? of $60 ? etc.
((/) Increase certain sums by 5%, 10%, 20%, etc.>

of themselves. What % then have we ?
(e) An increased sum ir. $104, 208, or 52 cents.
If the increase was 4%, find the sum ni first.
(/) Diminish $60, $80, etc., by 5%, 10%, etc., of

themselves.
(g) A sum diminished by 5%, 10% is $190, $380,

etc. Find the sum.
Vary the mode of solution. — Now give questions
involving three relations.

Example : — A number diminished by 25% of itself
is $60. Find the number when increased by 25%.
Establish that the relation of 60 to the required
quantity is 75 to 125, or 3 to 5. Now if $60 is
measured by 3 units, 5 units will be the measurer
of $100.

Give plenty of practice in this until pupil can
solve problems without too much analysis.

Pivrticiditr Application of Percentage. — The pupil
will now be familiar with the relation of percentage to
decimals and fractions, and will be able to apply his
knowledge of % to particular cases. The chief diffi-
culty will be to understand the nature of the tran-
sactions and the language of the problems.

Do not attempt to educe the technical terms used.
Develop the nature of the transactions but in-
struct in the terms. Simple names as rent for interest,

•L'L, ol' 200

60 feet, 72
,ities.

„ 20%, etc.,
e we ?
' 52 cents,
iin iil first.
)%, etc., of

a90, S380,
3 questions

% of itself

by 25%.

recjuired

if $60 is

measurer

pupil can

-The pupil
•centage to

apply his
chief diffi-

the tran-

rnis used.
IS but in-
r interest,

ARITHMETIC.

329

price for connnissioii, and lots for stock, may Ix- us(m1
until the nature of the transaction is understcM^d ;
then the technical terms should be '^'iven.

Give plenty of time, and vary the rates and
amounts in the same ti'ansactions.

The special application of % will come under the

following headings

5. Stock.

6. Taxes.

7. Duties.

8. Exchanirc

1. Profit and Loss.

2. Interest and Discount.

3. Commission.

4. Insurance.

9. Partnership.

Certain customs growing out of the " Law JMei'-
chant," such as "three days' grace," should be im-
pressed. A note drawn January 31st for one month
is by statute law due on thv^ last day of February.
The statute, however, recognizing the custom of the
"Law Merchant" legalizes the "three days' grace,"
originally a custom, and hence the day of maturity of
the note is March 3rd.

The teacher should carefully grade the exercises
in each of the above cases, and should not depend too
much on any text book.

i *•

fr:

itl

330

METHODS IN TEACHING.

CHAPTER IX.

DllAWING.

i .!

H 1

Introduction — Drawino- is expressino- knowledge
l)y incaiiH of a picture. All children liave the power
to tell, and delif(ht to tell what they know by means
of a dravvin<»:. The teacher should p-ive the child an
opportunity to draw by puttin<jj suitable materials in
his hands, and, possibly, by suoo-esting a suitable
subject. The subject should interest him and
therefore should be drawn from the child's environ-
uKiut. The skilful teacher can lead the cliild from
simple and crude representations to observe the form,
beauty and structure of thing's about him, and to
express his observations by a drawing.

The child, as soon as he comes to school, should
be made to feel that lie has power to picture objects
and is not dependent on the teacher for that power.
The teacher's duty is to direct him, and by
encouraging (piestions to lead him to discover liow he
may improve his representations. Too much must
not be expected from a child. All children can be
taught to draw, even if the attempts are at first crude.
It must not be expected that all will draw e([ually
well after the same amount of training. Such
uniformity is not expected in other subjects, and
should not be expected in drawing.

xpr

ession

by d

rawinii" is a union o

f tl

le min(

the hand and the medium. If the idea in the mind
is perfect, the hand, by practice, may be brought to the

DRAWING.

881

nowledge
the power
by means
3 child an
iterials "in
I suitable
liiin and
s en V iron -
hild from
I the form,
in, and to

3ol, should
ire objects
lat power,
and by
er how he
luch must
en can be
hrst crude,
iw ef[ually
vs Such
)jects, and

the mind,
n tlie mind
Uii'ht to the

same dcii-ret^ of i)erfection. Until rccontlv it wms
thought that di'awiui;' was a trick of tlic hand, ami
therefore uninterestin<r exercises in line drawini>-
formed the larger part of a course in drawing. Form
without thought will not interest. Perfect the
knowledge and give opportunities for expression by
means of a drawing.

A course in drawing should be influenced largely
by the locality, but generally it should include a
study of the actual form of objects, their appearance
and their beauty.

A study of the actual form of objects is the basis
of the constructive arts. The form of anything to be
constructed depends upon its use, and as several
forms i^iay possibly perform this function etjually
well, it will be desirable to select the most beaiUlfal
one.

The representation of the appearance of objects
on a flat surface depends upon certain principles that
can be learned only by observation of the ol)ject. A
stori/ may be told by a certain grouping of objects in
a picture. Pictures of recognized value should be
studied for the story they tell and for lunv it is told.

Objects may be made more pleasing by the

lication of co/o/*; bv the arranii-emeiit o^ decora five

appli

fonns, or by both ; the study of how form was
enhanced l)y the application of color and ornament in
the past is highly instructive.

The teacher should seldom interpret form for the
children, or in other words, draw. pictures for them.
The (juestion then arises — can the teacher who cannot
draw tccich drawinn; ^ The teacher is the i-uide, and
the children's source of inspiration, and unless he

332

METHODS IN TEACHING.

'■ M !

■ V n %

knows the course Ik; cannot fnlHl his (hity. A know-
IcMl^^e of tlic ditliculties to Im; overcome, the [jh^asures
to be enjoyed, and tlie results t'j be expected in a
course ol" drawing' cannot l)e ol>tained except by
<^oin<j^ over the course. Every teacher can learn
enough of the subject by a little application, to
teach it, but as in every other subject, the more one
knows of it, and of the mental processes by which it
is obtained, the ]>etter he is able to teach it.

The Value of the Type Forms— All piimary
teachino- begins with a study of objects familiar to
the child. He has observed by sight and touch many
objects before coming to school. His knowledge of
tliem is necessarily vague and indefinite in many
particulars, as may be noticed by his expression of
them in a drawing. To make his knowledge full,
complete, and exact it is necessary that he should
genei-alize and group the many obj(icts that have
come under his observation. If left to his own
resources, he may be able to refer these many
form-impressions to the standard types, but this is
very improbable. At this age the child must be
helped. The best way to help him is to place before
him, along with several miscellaneous objects, the
tj/pc that is the embodiment of all these miscellaneous
objects.

Suppose that we place before the child a number
of objects that may be referred to the splievo as their
type, such as an orange, a tennis ball, a baseball, a
marble, an apple, a •plum, a peach, etc. He has seen
these but he has very indefinitely noticed that they
are chjsely related to each other in FORM. By
reason of their different uses they stand apart and are

-~i

I i
) 'I

DRAWING.

883

A kiiow-

pk'.'l.SlUL'H

Aiid ill a
xcept by
an learn
jation, to
more one
r which it

piimary

iniiliar to

iicli many

wledgc of

in many

fe^sion of

edjxe full,

le should

lat have

his own

3e many

it this is

must be

,ce before

ects, the

ellaneous

I number
as their
iseball, a
has seen
hat they
RM. By
t and are

just so many isohited thinj^^s. Place amon^- tliom two
or three s])her('S of different sizes. Allow him to
handle and observe these objects. Ask him if they
are of the same shape. Get him to select the
'' rotnidast " ones; the next ''roundest'' and the next,
and so on. The child easily forms a se([Uence of
fornjs from the most spherical to the least. He is no
lon<;er bewildered. The objects possess a new
interest by reason of their relation to each other in
fo»'m. He recalls many other forms that are similar
in sliape and he notes resemblances and differences.
The type form of all is the sphere.

The SPHERE moves readilv. It is difficult to jj^et it
to rest. It is lively, full of life Tlie child deliohts
in objects that are full of motion or life. All ^^ames
that are played with a ball call forth activity of body
and mind. Nearly all fruits ai'e spherical and under
proper conditions exhibit signs of life. The sphere is
the ideal or type of all things that have unity,
niobility and life.

The child has seen blocks, bricks, boxes, houses
and books. He has played witli blocks and built
them into playhouses. The teacher places these or
similar objects alonj^ with the CUP>E. He may have
noticed their plane faces and straight edges, but until
now their relations have not been noticed. Tlie
relation in form is now clear, and, as before, he recalls
other similar objects for comparison. He learns
under the guidance of the teacher that the cube is the
type of sttthiliffi or rrst. He conti-asts the cube and
the sphere and the objects in each class, and he sei^s
that they are op/Khsitcs in action as well as
appearance.

384

METHODS TN TEACHING.

»r !l

The cliiM has observed barrels, pails, cups,
bottlt'S, stems of i)lants, and pillars. When the
teacher sliows him the type, the CYLINDER, he sees
the relation as before. He compares the cf/liiider
with the cnhc and tin; spjx'iu'^ and he sees that it has
sfahilifj/ like the cube and mobility like the sphere.
It partakes of the characteristics of both, and
consecjuently in a less degree than either.

The child when he sees that all objects may be
referred to certain well defined types, begins to
enquire irliy some objects are spherical, some cubical
and some cylindrical ; why some are more removed in
form from the type than others. He gets a grasp of
tiie great truth that the forms of both natural and
artificial objects are largely determined by the work
they are re(juired to perform.

This study of objects by referring them to types
gives clearer concepts than when studied in any
other way. It follows that their expression by a
drawing will be imjjroved. The expression of the
types by P; drawing is the best means of training
the child to see proportions, to judge of space-
relations, and also the best means of teaching him the
principles that underlie the representation of all
objects, on a plane surface. In other words all the
principles of drawing are exemplified when the types
are drawn singly and in groups. Surely then it is
not too much to expect that every person who
intends to be a teacher will master the rej^resentation
of the types.

There must be class teacliing in drawing. Every
member of the »lass should have the object under
consideration, and should place it so that the

DRAWING.

:^;]5

! I

lis, cups,
/hen the
, he sees
cyl'nider
lat it has

10 sphere.
)oth, and

s may be
)e^ins to
lie cubical
emoved in
a grasp oi*
itural and
the work

11 to types
in any

sion by a
on of the
f training
of space-
ig him the
on of all
ds all the
I the types
then it is
rson who
'csentation

Hg,

Every
ject under
that the

appearance will be approximately the same to
each. One large model should be used for class
instruction but not to draw from, as tlir ap))i'arance
to each pupil would then be ditrerent. Supervision in
such a case would exact too much of the teacher's
time that might be spent more profitably in general
instruction.

Materials — There is just now a diflri-ence of
opinion regarding the medium that should be used
for drawing in public schools. The pencil has been
the medium for many years, and its use has been
condemne«l by some because the results obtained
have not been all that they desire. In its place,
crayons, the brush, and pen and ink have been
recommende<l. A change of medium has in some
cases brouofht about better results than those
produced by the pencil. Such improvement has
been attributed to the medium when it should have
^""en credited to the increased interest taken in the
subject by the change, and the extra eltbrt put forth
by the teacher to make the work a success. The
quality of the d;'awing does not depend so much
upon the medium as upon the method of instruction.
For cheapness, simplicity and results, no other
medium in the lower classes is e(pial to the lead
pencil. In the higher classes the use of pen and ink
and the brush may be taught for the purpose of
o-iving all an insight into the method of usino; 'other
mediums. The best grade of pencil is an HB of any
reliable make. Pencils used for drawing shouM not

use(

I for

invthini:- else

le only sharpening

necessary in the lower classes is to cut aw
wood leaviiij

iiy

> If

ig about ^ of an inch of the lead exposed.

METHODS IN TEACHINC;.

■' i\

|l: '

This will insiiro a broacl lino. The lead .sliould
never be put in mouth as wetting' injuies it.

Paper — Any paper witli a mcdiuin i'uu<;h surface
will be suitable. First and second chisses should always
use a common scribbliny; book in which to make their
first drawinos. After the best form possible is obtained
the drawino- may })e recorded in a special (h'awing book.

Erasers — Pupils of the first and second classes
should not be allowed to use an eraser. Its use
may be taught in the bigher classes witb some
expectation that it will be used as directed. The
eraser is to be used to rub out the construction lines
and the light trial lines employed to get the perfect
outline. As the child learns to see and express
proportions, these trial lines will become fewer, and
if drawn lightly, may not be erased as they will form
part of the finished drawing. The eraser should be
soft and wear away itself without destroying the
surface of the paper. The secret of neat erasing is
the use of light lines.

Pen and Ink — After the proportions of an object
or group are obtained by the pencil, the drawing
may be accentuated with a pen and ink. Any pen
used for ordinary writing may be used. India ink
in the liquid form gives the best results.

Brushes — A brush about the size of a lead pencil
and tapering to a point so that a fine line may be drawn
with it is the best,when only one is used. Sepia or
India ink should be used for the first drawings.

For color work, water colors in soft cakes are the
best for beginners.

Position of Pupil, Book and Pencil- The l)ook
or surface on which the drawing is made should be

1(1 slioukl

(I'll surface
aid ill way H
make their
is obtained
vvingV)ook.
)ii(l ckisses
Its use
,vith some
eted. The
ictioii lines
the perfect
lid express
fewer, and
^ will form

should be
roying the

erasing is

|f an object
e ch-awing
Any pen
India ink

lead pencil
ly be drawn
Sepia or

igs.
:es are the

The V)ook
should be

DRAWING.

337

nciuly vertical with the topslighlly inelining away.
It sIkmiM lie placed so tluit tlir olijcct and its picture
ni!i\- l»e coiMparetl w itii as siinlit a clian«'e in tlie lin«'
of dir«'ction as possilde. If tliis position be
maintained t'lom tlie beii-inninii" the cliild will have a
much better understanding of what is meant by
picture plane than if the drawing surface is placed
upon the top of the desk and the explanation of its
true position given. This position aids free
movement of the hand and arm, so necessary in
fr('«'h(f n</ drawing. A small drawing board, or, in its
absence, a large slate, may be used on which to place
the book when drawing.

Pupil — The pupil should sit well back in the seat
so that the arm may have a free movement from the
shoulder. This is particularly necessary for young
pupils who have not yet acquired the control of
smaller movements of the fingers. Exercises on
common forms that have been drawn should be given
frequently to practise this free arm movement.
Drawing on the blackboard will aid in securing
freedom. The drawings of young children should be
much larger than those of older ones, because of their
having more control over larger movements of the
arm than over smaller ones.

Pencil — The pencil should be long and held
between the thumb and tirst two fingers about three
inches from the sharpened end. When the first light
sketch is made to the satisfaction of the child and
teacher, the pencil may be held nearer the point for
the purpose of finishing or accenting the drawling.

The Principles of Representation— Children

should be given every opportunity to express their
22

■^"-T

388

METHODS IN TEACHING.

Ih ••>'■

fiV

tliou^lits l)y a (Irawiii^. Sncli oxerciHes sliould be
used constantly, and tlie <lravvinj.'S supervised by the
teaclier, who sliould siioirt'st improvements and the
application of principles learned from the teacliing
of the types. This part of the teaching is often
nei^lected. Many teachers imagine that all that is
necessary is to learn to draw the type solids and a
few objects similar to them, singly, and in groups.
The drawing of the types and similar objects is
valuable as a means of teaching certain well-defined
principles but it falls far short of what the aim of the
teaching should be. The principles of teaching
drawing may be explained in a manual, but only a
general idea can be given of the application of
drawing to the other subjects. This application
depends upon the individuality of the teacher and
the opportunity given the pupils. There is no better
exercise for seat work than illustrating by drawings
some previous lesson in literature, geography, or
natui'e study. Th'm must be done if the pupils are to
maintain that naturalness of expression which is so
often lost by teaching the drawing of the types only.
The Sphere— Each pupil has a sphere resting on
a stand, the top of which is about as high as his chin

and at a distance of about
an arms length. A book
will answer the purpose and
may bo raised to a proper
height by some such device
as shown in Fig. I. The
sphere (a rubber ball will
answer the purpose) may
be kept in position hy a ring or three small sticks.

tl'l i

DRAWING.

339

onld be
(I by the

and the
teacliing

is often
1 that is
ids and a
1 groups.
)bjects is
ll-defined
ini of the

teaching
ut only a
pation of
ppli cation
icher and

no better

drawings
raphy, or

)ilH are to

lieh is so
ypes only,
resting on

IS his chin
of about
A book

I r pose and
a proper

uch device
1. The
ball will

)ose) may

1 sticks.

Each pupil looks at his sphere and draws its
appearance, about the size in«licated by the teacher.

The teacher passes around the class,

giving

suggestions and encouraging the pupils to make free
movements. He encourages them to compare the
picture with the object and to make corrections.

The teacher calls for volunteers to draw^ the
sphere on the blackboard from memory. Others are
asked to suggest improvements and to make them
until the final drawing is as well done as can lie
expected from the class. Each pupil feels that he is
interested in the picture and will try to correct his
own drawing. Each pupil is then asked to draw the
hctch edge of the book in its apparent position in
relation to the sphere. Many will not have it
properly placed as this is the first lesson in locating
lines in their apparent relation to each other. To
get them to see this relation the teacher (piestions
somewhat as follows: — Can the whole of the back
edge be seen at once ? What hides the part you
cannot see ? Do you show anything in a picture
you cannot see ?
How high on the
sphere does the back
edge appear ? Touch
the sphere jis high up
as the edge appears.
Corrections are then

made, and one pupil draws the edge upon the black-
board. The a[)parent position of the front edge is
located in a similar way (Fig. 2).

All corrections should be made by getting the
pupils to see the apparent positi(m of the object, not
by sf I owing him this position.

340

METHODS IN TEACHING.

To orot t]i(' pupil to ol)H(Tve correctly, the teacher
[)()iiils to .'I line ill the j)ieture, and the pupils point to
what it rrpicscnls in tin- ol>jeet, and nice, vei'sa.
Pupils sliould not only be able to point out what
each line in a picture represents, but to tell what
each line represents. They should be tau<jfht as
early as possible that a line, in outline; drawin<^,
represents an edge or their limit of vision on a
curved face. When the pupils are taught in this
way to draw what they see they will not make
dia<^rainniatic pictures.

Objects like the sphere may now be drawn, but
before drawino- any object its characteristics should
bo taujjjht, and then these characteristics will be
shown in the drawing. Common objects that may
be studied are a base ball, a foot ldll,a tennis ball, an
oran<^e, an apple, a plum, a peach, a pear, a pumpkin,
a melon, a tomato, an onion, etc.

When pupils can write, a description in words
should accompany the picture. Such an exercise is
valuable for seat-work.

To ^et pupils into the habit of observing every-
thing, they sliould be asked to look for examples of
the use of the sphere in ornament and in the
construction of objects.

Pictures of objects resembling the sphei'e may be
collected and pasted in the <l]'awing book, or kept for
refei'enee in some other way.

The drawing lesson may be varied by teaching
the use of terms such as up, down, right, left, front,
back, above, under, middle, vertical, horizontal,
obH(|Ue, parallel, etc.

The Cylinder- Each pupil places the cylinder in

^\l

^acher
)iiit to

what
what
r]it as
awin<;,
on a
n this
, make

vn, but
should
IV ill be
:it may
ball, an
mpkin,

words
jrcise is

every-

nples ot*

in the

may

A3achinpj
'(, front,
ri/ontal,

in<ler in

DRAWING.

341

Fio3

a vertical position, so that the top is s]i<^htly bolow
the eye-level. (In the absence of a wooden model a
tin can will answer every purpose). If the pupils
have observed correctl}^ the drawing
will resend)le Fig. .*! It is rarely that
pupils in the first class will make a
— drawing very accurate, nor must it
be expected. If the teacher insists on
correct drawings it tends to make the
drawings diagrammatic. If the pupils show by their
drawings that they are trying, improvement will be
the result.

In the first and second classes if three things are
observed it will be sufficient: (1) That the top
appears as an ellipse, (2) That the curve of the
bottom is greater than the curve of tin; nearest half
of the top, (3) That the lines that represent the limit
of vision of the curved face are vertical. 'I'he first
may l)e taught l)y moving the cylinder up to the eye
level and down; the second may be deduced from the
first, but more easily by tracing the shape of the
bottom on a piece of ])aper and moving the cylinder
to the right of the tracing, and comparing the
apparent vertical width of the tracing, and the top of

lind

When pupils reach the third class, guide lines may

)e us

ed t

o iret accur

ate d

raw nigs o

f tl

lind

ei;

The method of teachinii would then
be something like the following: — -
Draw .'I line to represent tlie nppnrent
length (►f tli(! cylinder-, as I -2, ( Kig. 4).
(The ap[)arent length fmni top to ^"s
bottom will differ but slightly from

;; '■

342

METHODS IN TEACHING.

the apparent length of the axis and so may he
taken to represent tlie lengtli of the axis). Tlirough
each end of this line draw a line to represent
the greatest apparent width of the cylinder, as 3-4,
and 5-6. These lines must bear the same proportion
to the first line diawn as the apparent width of the
cylinder bears to its apparent length. Find the
apparent vertical width of the top face. This may
be found by placing the pencil in a vertical position
against the curved face at its nearest part, and
moving it till the top of the pencil appears as high as
the farthest point of the top. Locate the nearest and
farthest point on the top as 7 and 8. Locate the
apparently lowest point as 9, by finding how much
lower tliis point appears than 5 and 6, the farthest
points visible on the bottom edge. Complete the
figure by drawing the vertical lines 3-5, and 4-6.

A valuable exercise in reasoning is getting the
pupils to locate the farthest point on the bottom of
the cylinder. This point is invisible but it may be
located, since the actual shape of the base is known.
Such i^xercises are valuable as they lead the pupil to
imagine the appearance of any object in a posititm in
which it has not been observed, provided its appear-
ance has been perceived in two or three other
positions.

The drawing may now be finished by erasing the
guide lines and any other lines not require<l, and then
accenting the outline as shown in the finished
drawing (Fig. 3).

The vei'ticnl <*ylind('i- m.iy now be drawn in other
positions, and objects similar to it in sliape.

il mi

DRAWING.

343

may be
Through
represent
r, as 3-4,
roportion
i\\ ot* the
Find tlic
Tliis may
I position
)art, and
IS high as
jarest and
jocate the
low much
le farthest
iplete the
d4-6.
etting the
bottom of
it may be
is known,
le pupil to
position in
ts appear-
iree other

irasin2j the
and then
e finished

,11 \u o

tlu'r

The cylinder may be placed in a horizontal

position, with its axis at right
angles, parallel, and at any
other angle to the line of
direction. The method of
locating the apparent position
of the principal points is similar to the last position
and does not re(iuire lengthy explanation. See Fig. 5.
Pupils may collect pictures showing the cylinder,
and may describv: places where it is found in
ornament and in architecture.

Man}^ useful conversational lessons may be taken
up with the drawing lessons on terms such as surface,
face, curved face, plane face, circle, circumference,
diameter, radius, edge, curved edge and axis.

The Cube— Each pupil places the
cube on a book so that one vertical
face is visible. Pupils draw the
appearance of this face which is a
square. When drawing a scpiare the
lines should be drawn in the order
shown in Fig. 6.

Lower the surface on which the cube rests so that

the toT) f}ic(; of the cube is

^ ' ^ slightly below tin? eye level.

Each pupil diaws the appcfir-
ance of the front face. The far

edge of the top face is located

and a line drawn to show its
position, Fig. 7. Its ap])arent
length MS compared with the front e<lg<', is found.
To do this hold two jx'ncils vcrlicjilly ngaiiist the fiont
face and move them, still keeping them vertical, till

344

til

METHODS IN TEACHING.

ids of tlie back erlj

to toucli til

icil.

tappoar

Notice whore tlie pencils touch the front ed^^e, and
mark these points. The back corners appear vertically
above these points. When the corners are located
the receding edges may be drawn and the drawing
finished as in the case of the cylinder. Re(jnire the
pupils to locate the position of the invisible edges.
A good exercise is to let several pupils draw the
cube on the blackboard, each drawing a line to
represent an edge when pointed out on the cube by
the teacher.

Many exercises may be given on objects like the
cube. For first and second classes two faces oidy
should be shown. Obj«.'Cts diawn similnrl}' to the
cube are — a box, a book, a table, a brick, a chair, etc.

The Cube in other Positions— Pupils in the

third class may be asked to draw the cube and other
objects in more difficult positions. Place two cubes
below the eye-level, one slightly to the right and the
other slightly to the left, so that the front and top
faces, and also the iiniei' faces of each are visible.

(Fig. 8). The ap})eM ranee of the two may l)e shown
similarlv as when onl\' two i'ncvs were visible.

Teach (he (ei'm lioiizon ;nul how it is i'e])iTsented
in a pietui'e. A hoii/oiilnl line ;if I he i'y{' IcncI is n
picture of the hori/on. lle(|uire [)Upils to obsei-ve the
appearance of long receding parallel edges as fences

DRAWING,

845

' pencil.
Ige, and
}rtically
located
drawing
|uire tlie
e ed<,^es.
raw the
line to
cube by

like the
ices only
y to the
L'hair, etc.
s in the
md other
wo cubes
t and the

and top
K' visible.

)(> shown

)n'ScMb'd
cvfl is t\
iservt' the
as fences

by tlie roadside, railway tracks, etc. Teacii that
horizontal receding parallel cdcrcs appear to meet on
the horizon and therefore in the pictui'e will meet at
the eye level. To prove the co

)ctn

observati(

ittl

less
le eye level may be

^'vation, a Jine to represen
drawn and the rece«lintj^ lines ol* the cube produced.
If the lines representing- parallel receding e(lges be
produced in the picture, and it* they meet at the line
that represents the eye level, the drawing is
accurately made. It is not expected that a freehand
drawing from observation will stand this mechanical
test, but it is well to know how to pnwe the
correctness (^f a drawing which should always be
approximately correct.

The Cube Turned— Place a cube below the eye
level with the two visible vi^rtical faces ('([ually

ranee and

pup

ipp

select some "edge as the unit of measurement. The
nearest vertical edge is the be.Nu in this case. Draw

a line to represent this edge; as 1-2
(Fig. 11.) Compare the distance of
the othei' two vertical edws from
the neaiest edue. If the cube is

pi-opm-ly placed these edges will
appear to be at the same distance from the nearest
edge. l)i-aw lines in proper position to i-epresent

iti(

le nosition o

ies<* e,dir(>s, as

8-4.

an*

1 T) -(). ])

raw

the lines nnich longer than ni'cessary. Ijoeate
the cornel's at the base of the last lines d?'awn. To
aid in their local ion hold Ihe jteneil horizontally
a<>-ainst the m.'arest scrlieal (wlgc mid iiio\e it till
those corners are just visible below it. Notici; tin;
relative position of the lower part of the pencil on

•i

346

METHODS IN TEACHING.

tlu3 vortical mh^L'. Mark tliis point in tlie picture as
7. Draw a horizontal line to represent the apparently
lowest part of th(; pencil, and where this line cuts the
•other vertical ed<^es there will be the position of the
corners as 4 and 6. Locate the uppei* corners in a
similar manner. Find the apparent hei<,dit of the far
corner <S above the near corner 1 at the top. Locate
«S. When the corners are located it is (piite an easy
matter to draw the ed^es. Erase the <;uide lines and
accentuate the c^^awiuLT.

The cube ii. !^'iis ])Osition may be drawn by
observin<^ the ap[. 'eiit slant of the edi^es from the
line 1-2, and drawing Iijas at this slant. To aid in
judj^in<( this slant, a jointed ruler may be uscmI, one
leg being hehl vertically against the nearest edge,
and the other moved to just cover one of the
recedino- t'clcres.

Test the correctness of your drawing by producing
the converiL!fin<r lines.

Turn the cube at various angles and compare the
effects. The most pleasing effect is obtained when
there is a slight ineipiality in the ap})arent width of
the vertical faces. T(j draw the cube in this position
proceed as in the last position. As the pairs of
corners are apparently of une(|U.'il height, each will
have to be located separately.

Groupings — Pupils should begin to draw objects
in a group as soon as they have drawn them singly.
Two apples, then three, in a groiip will be a simple
be<'iinun<»\ Tlu^ selection of objects and their
arrangement in a group will depend upon (Iw^ idea
intended to be e\presse<l. To diaw a group, first
block in the whole, then locate the apparent

DRAWING.

347

picture as
Lpparently
ic cuts the
ion of the
•rners in a
of the far
p. Locate
ite an easy
13 linoH and

drawn by
^ from the
To aid in
[3 used, one
arest edjjjo,
ne of the

producinj^

>nipare the
uned wlien

t width of
his position

ic pairs of
it, eacli will

raw objectK
leni sinj^iy.
be a simple

and their
on the idea

jroup, first
le apparent

position of the top and bottom of eacli individual of
the <;roup. Never complete the drawing of a sini;le
mend)er of the group before another is connnenced,
carry the drawing of the whole along simultaneously.
The leading idea suggested by the group will then
not be subordinated to the individual object. When
grouping choose the principal object and place it
near the centre of the group. Place the other objects
about it so that if the bases of the individual objects
were joined, an irregular figure would result. The
objects should appear at rest and their apparent
heights should not be in a straight line. Some of the
objects sliould be partly hidden l)}^ the others.

Shade and Shadow— When a puj)il ch i -e a

shadow of an object and that one part of m ii.ject
appears darker than another part of it because the
light does not fall upon it dinjctly, he s \ould be
allowed to express the shade and shado Express
shades or shadows on plane faces by straight parallel
lines, and on curved faces by curved lines. On
vertical faces use vertical lines, and on horizontal
faces use horizontal lines. The position and kind of
the surface can thus V)e suggested at the same time
as shade and shadow.

Color — Color should be taught in every school.
Children should be taught to recognize the standard
colors, their tints and shades. The method of
teaching may be obtained from any manual on color.

It,

i 1

348

METHODS IN TEACHING.

ii I

,: f'

CHAPTER IX.

WRITING.

Aims — Tniiniii<r in writiiio- slioulrl have a three-
fold purpoHc, legibility, liygienic conditions and
speed. '^J'o attain the first, two chanj^es are
essential, the adoption of vertical script consisting of
the simplest possible letter-forms, because every
unnecessary stroke, however insignificant in itself,
tends to obscure the essential characters; and the
general use of broad pens giving uniform strength to
fclie strokes. It were as reasonable to speak in a
thin, weak voice as to write in fine hair lines. The
hygienic conditions depend upon the naturalness of
the position and movement used, and upon the size
and character of the writing produced. Speed is
conditioned by the position and movement, the
simplicity of the letter-forms and the kind of training

given.

■\

Position — Tlie approved position of body, arm
and hand is shown in Fig. I. The body is self-
supporting. The elbows are kept w^ell back near the
sides so that the weight of the forearm is mainly
supported from the shoulder. To carry the forearms
forwanl and spread them upon the desk disturbs the
pose of body, and inevitably results in a decidedly
sto()])ing posture with a hunching of one shoulder
and a lateral curving of the spine. The writing page
should be in front of the body, with the writing line

WRITING.

349

1 I

^e a three-
tions and
iDjjfes are
nsisting of
use every
in itself,
and the
strenj^tli to
;peak in a
lines. The
uralness of
on tlie size
Speed is
enient, the
of training

body, arm
idy is self-
ck near tlie
is mainly
lie forearms
disturbs the
a (l('cid(Mlly
JO slmnlder
-riting page
writing line

Fin. 1.— Correct Position for Writing.

parallel to, and from three to ten inches from the
edge of the desk.

The position of the body and arm determines the
position of the hand, and lience the method of pen-

FiG. 2.- Right Method of PenlioldinK.

holdinir. If the forearm be raised to the liori/ontal
position while the elbow is kept near tlie side the

850

METHODS IN TEACHING.

lijiml will naturally turn with the palm Tafniij^
Hii;,^litly inwanls. Sco V'\<r. 2. That this is the most
natural method of jxinholding is attested \)y the fact
that little children instinctively adopt it, and almost
every wi'iter uses it no matter how long and carefully
he may have been trained in the utterly wrong
position shown in Fig. 3.

The pen should be held so that the end of the
first finger will be at least 1^ inches from the point
of the pen. The penholder should cross as near as
possible the end of the second finger. If the pen be

Fio. 3.— Wrong Method of Penholding.

held too near the point, or if the end of the second
finger be allowed to drop below the handle the third
and fourth fingers are likely to press upon the desk
thus restricting the free action of the hand.

These directions for position and penholding are
general and must not be applied rigidly to the
individual pupil. Physical conditions and tempera-
ment to some extent determine the precise position
that will be most natural for each.

On desks nearly flat or too high for the child the

WRITINO.

351

\ I'aeing
the most
' tlui I'act
id almost
carefully
y wrong

nd of the
the point
H near as
le pen be

he second
i the third .
I the desk

elding {ire
ly to the
I tempera-
le position

e child the

paper may ho moved a litth; to (lie ri^ht, and tnrned
at a sliojit aiiL-lc.

Movement -It is ohvious that the position ol'
body, arm and hand determines the kind of move-
ment one can use most easily and effectively. With
the position above described it is found that a
forward-dv (1-1 tack movement of the hand and fore-
arm at right angles to the writing line, and an
uin-estrained movement of the fingers for shaping
the letters, are easy and natural. At tii-st, and for a
considerable time, the learner should be encouraged
to write without resting the hand or arm upon the
desk ; as he gains confidence, power and skill, the arm
should be allowed to touch the desk. Even at the
later period it would be well for the pupil to
practise for a few minutes at the boirinninu" of each
lesson with the hand and arm entirely free from the
desk, but in doing this he should not rai ; the elbow.

Kinds of Wpiting-— The direction and the general
character of writing depend upon the movement used
in producing it. Exp(;rience has demonstrated that
the movements described produce the fundamental

LLLLLLL

^vrrrrm

I Ma to I.

forms shown in Plate I. At the left of the writing
line the natural tendency will be to a backhand, and
at the right to a forward slant, but in the middle of

352

METHODS IN TEACHING.

tlie pJiL-c the vertical will l»e roninl to ))e tlie normal
direction for tin- i^ieat in.ijoi'ity ol" \vi-it<'iH. 1'lie
essriilitl cli.'ii'act«'r of the most nuhir.il ,s<yli' of

TT\jz^Luu/rru

Plate II.

writini,' will b<' more clearly seen in IMate II. when
coiitraHtiiii^ it with that shown in Plate III. The
upstrokes as well as the down are vertical, and the
turns are full, cori'espondin^^ with the ends of the
ellipse. In Plate III, which represents a compromise

Plate III.

between slant writinj.^ and vertical, the upstrokes
are slantinjjf, nc^ccssitatiuix a ziii-zai; movement wh'ch
in rapi<i work, cannot V)e conti'olled for lej^ihilit v, the
i(i,n, i.and u forms becoming wholly indistinguish-
able.

Materials— Because the smaller nei*v<'s and
nuiscles of the young chiM are not d«'veloi)e<l, the
first writing shoiild always be lai'ge. The materials
for the first yenr's writing arc desirable in the
following order: 1. Uhickboaivl and crayon; 2.
Manilla |)a])er and broad, soft [xMicils ; .S. (Jood
writing pa pel*, broad, smooth ])ens and good black
ink. A poor/piality of pajter and fine ])ens arr bad,
and slates caiuiot b(» too strongly condennu'd. 'I'he
general use of line pens in the schoolroom is ])i'()bably
a result of the inlhience of the conception of school

tlic noinial
iters. Tlie
1 1 slylc <tt'

ite II. when
3 III. The

c.'il, aiul tlie
Liiids of tlie
('()inj)r()iiii.se

\ips(rol\(*s
iient svliH'li
(lihilit y, the
I listint^iii sh-
ier ves and
elope* I, the
le materials
il)le in the
crayon : 2.
s ; li. ( Jood
iiood liiiiek
niH arr had,
nuu'd. The
is ])i'()l»al)ly
n ol' school

WRITING.

353

writin<( as a tine art, a mistake, even from the art
point of view, for the best artists rarely, if ever, use
fine pens.

Under the conditions that now exist in mest
schools it is probable that headline copy V)ooks, in
conjunction with practice paper and the blackboard,
give best results. The exclusive use of the black-
board and practice paper is objectionable from four
points of view :

1. Few teachers are well qualified to place before
their pupils from day to day the best models.

2. A copy upon the blackboanl presents distorted
letters to pupils not directly in front of it.

3. Much use of the blackboard by youn^ children
is very injurious to the eyes.

4. Pupils will not usually work with as mucli
care upon ephemeral practice paper as upon a V)ook
which is a permanent record of progress.

Desks having a slope of about fifteen degrees are
to be preferi'ed. They tend to preserve erect posture,
bring the paper into better position for vision, and
favor freedom and power in both writing and
drawing.

With What to Begin— The first lessons sliould
involve co[)ying only single words which thc^ children
have learned to read. The copy should be very
large because :

1. Only large work is consistent with the child's
condition of nervous and muscular development.

2. The forms and iclations of lett«;rs are more
accurat(;ly perceived.

3. Mistakes are more easily seen.

4. Large forms necessitate a freer movement.
23

354

METHODS IN TEACHING.

There should be iiu <;ui(le lines but the single
base line. It is true that durin<^ the first year or
two children write with more precision upon specially
ruled paper, and the product may appear Ijetter, but
it must be remembered that the object is tratviny
rather than writlny product, and <,mide lines deprive
the child of the opportunity of jud«^in^- the forms
and proportions of the letters, and at the same time
restrain freedom of movement. This is quite in
accord with the most advanced thought regarding
related studies, and carefully conducted experiments
have shown that children trained without the special
space-ruling soon gain more real power than those
who are at once supported and liampered by the
guide lines. In case a pupil's writing is very
irregular it is better to let him space-rule a few
lines after he has written them that he may see the
irregularity.

The letter forms should be as simple as possible
and as much like the print foiins as is consistent
with easy execution. This implies several radical
changes in the old script alphabet, or rather, a new
alphabet.

1. The adoption of the simple proportion of one
to two for all letters and parts of letters.

2. Tho omission of manv worse; than useless
initial and final strokes.

8. The substitution of simple curves or sti'aight
lines for the compound curves so dithcult to leai'ti
and useless in practice.

4. The omission of many inconvenitjut joining
lines.

The schools have perpetuated no more absurd

WRITING.

355

'tion of OHO

notion tlifin tliat the writer must not lift his pen
while w ritin;^ a wonl. No one obsei'VM's the hiw, not
even those tcaehei-s wjio ur<^e its neeessity. The
most rapid, ie«jjible writers it^iiore it most. The skip
from tlu' tinishinfj stroke of one letter to the
beirimiiiio- of another rclii'ves the nervons and
nniscnlar tension. All ioiniiiiifs detract from rather
than add to le^i^ihility. Inconvenient joiniiiijra,
nsually npstrokes, retard speed. Mneh as insistence
upon these joinings hinders tht^ trained writer, it
hampers the learner infinitely more both in s».'ein«^
the essential form and i>i repi'oduciiii;- it. This is
rank heresy to many teachers, but a litth' invcstij^^a-
tion will convince the most skeptical that it is a
simple obvious truth.

Special Writing^ Lessons— 'I'hes. should always

be })i'ief, in primary classes from ei;^ht to ten miinites,
to be <^radually increased to about twenty minutes in
tlu! si.xtli year. This time shouhl be devoted mainly
to careful practice, but it should also include :

1. Trainin;^ pupils in concentrated attention to
the forms of h'tters and words, i.e., in clear per-
ception.

2. Correctin«( vvroni^ tendencies in position, pen
]»oldin<^ and mov»;ment, and connnon errors in f(jrm.

'\. In advanced classes, practice in spe(;d writin;^.
Ordinary Class Writing—While nnuh depends

upon tht^ spc^cial lessons <lurint^ the first five or six
years vastly more d(;pends upon how tlie ordinary
written exercises are done. 'I'lie teaclu^r who does
hei* own work niMitly, and luiiforiidy insists upon
careful work from her pupils can scarcely fail to
have a class of ;food writerH.

856

METHODS IN TEACHING.

■ Individuality — For class work there must l>c
s(;uie slrindiini.^ of (lircctiori jiikI lorin, but i!» sc
shouM be rc^ardeil rathin* as models for the loirnfr
iiiiiri as inHexible laws of handwriting. As the
pupils approach the higher gradei they should be
allowed and encouraged to find the peculiar style of
writing that is easy and natural for each, and beyond
the si.Kth or seventh year writing from copies should
be unnece.ssary. To insist upon conformity to any
mechanical standard is to repress the development of
the child's true self, his best character.

Speed in Writing*— The possibility of developing
one's greatest speed in writing is conditioned i)y :

1. The naturalness, eas(; and fi'eedom of the whole
posture.

2. The harmony of tlie movement with the
position.

»S. The harmony of the letter-forms witl. the
movemen<^.

4. Th«^ simplicity of the forms.

ft. Freedom from the arbitraiy law that all letters
in a word must be joined.

(). The kind of training.

Having dealt with the liihc five points only
training in rapidity remains to be considered. This
must conform to tlie general law of training, i.e.,
practice under favorable conditions. Aft(;r pupils
have been writing carefully (hree or four years, begin
one minute speed testa on such simple words as, (in,
and, thf or (Utn. Insist that the writing shall be
neat and plain, })ut give two or three one njii»'ite
tests eacli day and have pupils note progress in speed.
Souietimes give suMi t(»sts upon a particular letter

WRITING.

r}67

lUSt l>c
it tVi' ?He
; Icirner

As the
liould be

style of
(I beyond
BS should
y to any
pnient of

eveloping

1 ]>y :

the whole

with the

\\\t\< the

:, Jill letters

)()ints only

ered. Tids

aining, u'-,

J'ter piipila
years, bej^in

ords as, «'»,
n«r Hhall be
one n»ii"ite
•I'ssin speed.
1,'ular letter

thM.t \fi diffindt of execution. In hiirhcr (nvides ^ivi; a
Vviiole sentence or even n wtanzii of poetiy to be
written as often a.s i>ossiI)le in one ov two ndr.nt 's.
Besides <(iving speed this practice will he found the
best training in movement, ano to prevent degeneracy
of the writing in tlie Idglier grades where rapidity
becomes necessary.

Sug-grestions—l. In early traiiung have pupils
concentrate attention upon the word form, sometimes
going througli the movement of writing it in the air,
liien cover the copy and have tiiem write it from
memory.

2. Have tlie copyl)(X)k eopy practised on i>lank
paper until a fair degree of accuiacy is attained, then
tlie ^"jok becomes more important as a register of
the pupil's best work.

8. In going through the copybook the tirst time
have only the first half of eacli pagt; written, then
the second written some weeks later, should show
decided progress.

4. If, in onntting joining lines, pupils separate
letters too far, point out that to make words, letters
must be grouped as in print, and that writing is more
legible if words are well sepai'ated.

5. There is no valid objection to a slight backhand
and in some cases no amount of training will
overcome it. With little childi'(Mi, howiiver, it is
often due to wrong position, to too liigli and flat
desks, and to lack of control niid freedom Removal
of the cause I'emoves tlie result.

! ! .'

' I;

■'. 1

NEW VOLUMES IN THE INTERNATIONAL EDUCATION SERIES

-nROEBELS EDUCATIONAL LAWS FOR ALL
JT TEACHERS. By James L. Hughes, Inspector of Schools,
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Thin book is a real contribution to the Froebclian literature. It is a clear and
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r'HE PSYCHOLOGY OF NUMBER, and its appli-
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rf/E SCHOOL SYSTEM OF ONTARIO, CANADA.
Its History and Distinctive Features. By H ON. GEORGE W.
Ross, LL.D., Minister of Education for the Province of On-
tario. i2mo. Cloth, $1.00.

This volume contains an outline of the history of the School System of Ontario,
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GEORGE N. MORANG & COMPANY, LIMITED.
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r BACHING THE LANGUAGE-ARTS. Speech^
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rHE EDUCATION OF THE GREEK PEOPLE,
and its influence on Civilization. By Thomas Davidson.
i2mo. Cloth, $1.50.

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teach.ft. throu(fhout the country who are trying to do their duty, but arc suffering;
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its purpose." — Authors Preface.

I >

i
- ,|i

Cr*HE SONGS AND MUSIC OF FROEBEVS

M ' MOTHER PLAY. Prepared and arranged by Susan E.

Blow. Fully illustrated. i2mo. Cloth, $1.50.

This islthe second and concludinif volume of Miss Blow's version of Froebel's noted
work which laid the foundation for that important branch of early education, the
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carded.

rHE MOTTOES AND COMMENTARIES OF
FRIEDRICH FROEBEVS MOTHER PLAY. "Mother
Cominuninjij^s av.^ Mottoes" rendered into English verse by
Hknriktta R. Eliot, and "Prose Commentaries" translated
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ottataioiny the uoai; k and games.

GEORGE N. MORANG & COMPANY, LIMITED.
90 Wellington Street West, Toronto.

\ii r

SERIES

Speech,
D., LL.D.,
University

>ssonst" but a
the language-
M will prove

PEOPLE,
Davidson.

large body, of
t arc suffering
lable clearly w
lime import. 1
,n of humanity,
^ated to moral
turn their chief
at comes fronj
8 accomplished

WEBEVS

►y Susan E.

fFrt>ebel's noted
y education, the
^' may be deiig-
BJc." the present
ve been enlarged
I arc made of the
ared in the lit«a-
nal has bcei> di»l

\RIES OF
Y, ••Mother
iflish verse by
ies" translated
itiona. lamo.

i for a clearer ex-
have made a new
^tter Wjuipped lor
ion." has attested,
c value to mothers,
ty another volumf.

MIXED,