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FRANKFORT SCHOOL 
 
 REFERENCE LIBRARY. 
 
 No Book sliall be taken from the room except 
 by special pen 
 
 jCOjjr.'VIJ.O.N DF'^ 
 

 Ho^vs^ to TeaoE* 
 
 
 A 
 
 Manual of Methods 
 
 FOR A 
 
 GRADED COURSE OF INSTRUCTION: 
 
 EMBRACING THE 
 
 SUBJECTS USUALLY PURSUED IN PRIMARY, INTERMEDIATE, GRAMMAR, 
 
 AND HIGH SCHOOLS ; ALSO, SUGGESTIONS RELATIVE 
 
 TO DISCIPLINE AND SCHOOL MANAGEMENT. 
 
 FOR THE 
 
 USE OF TEACHERS. 
 
 BY 
 
 HENRY KIDDLE, A.M., 
 
 City Superintendent of Public Instruction, 2\ew YorTc. 
 
 THOMAS F. HARRISON, 
 
 First Assistant Superintendent of Grammar Schools, New York dty ; and Pro- 
 fessor of Methods and Principles of Teaching in Saturday Normal School. 
 
 N. A. CALKINS, 
 
 First Assistant Superintendent of Primary Schools ayui Departments, New York 
 
 City ; and Piofessor of Methods and Principles of Teaching in 
 
 Saturday Normal School. 
 
 NEW YORK : 
 
 J. W. Schermerhorn & Co., 
 14 Bond Street. 
 
 1875- 
 

 Entered according to Act of Congress, in the year 1S7S, by 
 
 J. \V. SCHERMERHORN & CO., 
 
 In the Office of the Librarian of Congress, at Washington. 
 
 SDt»rA-nnM oePTi 
 
 Lanak, Littlk a Co., 
 
 PKlNTKnS, KLKCTROTVPKRS AND STKIlBOTYPJtKS, 
 
 lOS TO lU WoosTKu Stkkkt, N. Y. 
 
PEEFACE. 
 
 The system of graded instruction, which has become 
 so general in this country, requires for its successful 
 application, the constant use, on the part of the teacher, 
 of a guide, or chart, to which he may refer in order 
 that his present work may harmonize with that which 
 preceded, and that which is to follow it. The ground . 
 to be covered in a complete course of school education, 
 however elementary, is quite extensive, and hence needs 
 to be divided and subdivided according to certain estab- 
 lished principles, so that the mind of the instructor may 
 not be diverted from that which should engage his im- 
 mediate attention, by the necessity of considering and 
 choosing the best means of supplementing it. Such a 
 graded system of teaching can best be prepared by those 
 who have had not only a long experience in the practi- 
 cal business of teaching, but whose field of observation 
 has been sufiiciently comprehensive to enable them to 
 give to the scheme an adaptability to a great variety of 
 circumstances. 
 
 The system laid down in the work here offered to 
 practical educators, whether teachers, superintendents, 
 or school oflBcers, is designed to afford such a guide as 
 
 f)4 4!1^4 
 
4 PREFACE. 
 
 is above indicated. It is essentially the system which 
 has been in use in the city of New York for some years, 
 only differing from it in the number of grades into 
 which the course is divided. This difference is, how- 
 ever, rather nominal than real, since the number of 
 grades into which a course of study is divided is en- 
 tirely arbitrary, except so far as it may be dictated by 
 special circumstances. WJiere schools are very large, 
 and the attendance of pupils is fluctuating, as must be 
 the case in so populous a city as New York, the neces- 
 sity of constantly reorganizing classes, renders frequent 
 promotions, or transfers from class to class, indispensa- 
 ble, and, hence, a large number of grades becomes a 
 convenience. In schools having a smaller and steadier 
 attendance, the number of grades need not exceed what 
 is requisite for a proper classification and division of 
 subjects for simultaneous study. The order of studies 
 — the main point in every course of instruction — cor- 
 responds, as here arranged, precisely with the New York 
 plan ; the time requisite for its completion is also about 
 the same. 
 
 This course, with its division into grades, constitutes, 
 however, only the frame-work for the series of practical 
 suggestions designed to assist teachers in the perform- 
 ance of their professional duties — that is, in some de- 
 gree, to show them what to teach, as well as hoio to teach. 
 All the precepts and directions here given have been 
 dictated by an earnest desire to aid in the effort now 
 universally put forth by the ablest and most intelligent 
 
PREFACE. 5 
 
 school officers to abolish the pernicious rote method of 
 teaching, by book and formula, formerly so prevalent, 
 and to make universal the system which appeals, from 
 first to last, to the intelligence of the pupil, and adapts 
 itself to its progressive stages of development. In the 
 lower grades, the objective, or perceptive, system is, of 
 course, made prominent, to be succeeded by those sub- 
 jects and methods which, as they dispense to a consid- 
 erable extent with the actual objects themselves, and 
 appeal to the acquired ideas of the pupils, may be prop- 
 erly denominated conceptive. 
 
 The natural and physical sciences, it will be observed, 
 are largely drawn upon for the materials necessary to 
 accomplish this object, the sciences of observation and 
 classification, such as zoology, botany, and mineralogy, 
 properly taking precedence of those which require a 
 more special application of the reflective aud reasoning 
 faculties, such as physiology, natural philosophy, and 
 astronomy. By this kind of teaching, it* is designed 
 that the pupil shall acquire the ability to gain an ex- 
 perience of his own, instead of depending exclusively 
 upon that of others, and at the same time, shall acquire 
 a taste for the observation and study of nature. 
 
 Certainly such a system for the common schools of 
 our country is far preferable to that which, although 
 insuring proficiency in the " three Ks " left the pujiil's 
 mind in a condition of matured stolidity, and while, 
 perhaps, a most ready talking, writing, and j)arsing ma- 
 chine, sent him fortli to go through this beautiful world, 
 
g PREFACE. 
 
 blind to its manifold wonders and glories, and fit only 
 to become the easy prey of the demagogue and the 
 bigot. 
 
 It is an CTidence of the increasing earnestness of 
 teachers, that the demand for practical suggestions 
 and exact information in regard to their work is now so 
 great. More especially is this so in the case of those 
 engaged in primary school instruction. This depart- 
 ment of teaching requires very much special knowledge 
 as well as peculiar tact to produce successful results. 
 A complete exposition of the yarious methods which 
 are applicable to each stage of this work would require 
 a much larger space than could be devoted to it in the 
 book here published. Hence, references to more full 
 and complete works on the subject have been given m 
 connection with several of the grades, in order to aid 
 teachers in finding the additional information which 
 they may need in this direction. 
 
 The demand for copies of the " Manual of Instruc- 
 tion and Discipline," recently prepared by the authors 
 of this work, for the use of the primary and grammar 
 schools of the city of ISTcav York, has induced them to 
 endeavor to put the work into a shape in which it might 
 be generally useful ; and they trust that, as it is now 
 presented to those engaged in practical education, it 
 will prove an acceptable addition to the literature of 
 ximericau pedagog}^ now so scanty and insufiicient. 
 
COJ^TENTS. 
 
 PAQB 
 
 INTRODUCTION 11 
 
 GRADED COURSE.— TENTH GRADE (Outline) 21 
 
 How TO Teach subjects op the Tenth Gkade. . . 23 
 
 Reading (23) ; Phonetics (27) ; Spelling (27) ; Aritli- 
 metic (29); Object Lessons (34); Drawing and 
 Writing (35) ; Management (36). 
 
 NINTH GRADE (Outline) 37 
 
 How TO Teach subjects of the Ninth Grade ... 39 
 Reading (39) ; Plionetics (40) ; Definitions (40) ; Spell- 
 ing (41); Arithmetic (41); Object Lessons (44); 
 Drawing and Writing (45) ; Management (45). 
 
 EIGHTH GRADE (Outline) 47 
 
 How TO Teach subjects of the Eighth Grade. . 49 
 Reading (49) ; Punctuation (50) ; Plionetics (50) ; Def- 
 initions (51) ; Spelling (51) ; Arithmetic (52) ; Object 
 Lessons (59) ; Drawing and Writing (61) ; Manage- 
 ment (62). 
 
8 CONTENTS. 
 
 PAGE 
 
 SEVENTH GKADE (Outline) 63 
 
 How TO Teach subjects of the Seventh Gkade. 65 
 
 Reading (65) ; Phonetics (66) ; Definitions (66) ; Aiitli- 
 metic (67) ; Tables (73) ; Object Lessons (74) ; Ge- 
 ograpliy— Preparatory Steps (80); Drawing and 
 Writing (81). . 
 
 SIXTH GRADE (Outline) 83 
 
 How to Teach subjects of the Sixth Gkade ... 86 
 Jleading (86) ; Phonetics (87) ; Definitions (87) ; Spell- 
 ing (88) ; Arithmetic (88) ; Tables (92) ; Object Les- 
 sons (94) ; Geography (98) ; Drawing and Writing 
 (102) ; General Suggestions (102). 
 
 FIFTH GRADE (Outline) 105 
 
 How to Teach subjects of the Fifth Grade . . . 107 
 Reading (107) ; Spelling (110) ; Definitions (111) ; 
 Arithmetic (113); Forms of Arithmetical Analysis 
 (118) ; Tables (120) ; Geography— General Sugges- 
 tions (121) ; Geography for the Fifth Grade (122) ; 
 Syllabus of Topics for Geography (123) ; Correction 
 of Language (125) ; Elementary Science— General 
 Suggestions (120) ; Outlines of Zoology (129). 
 
 FOURTH GRADE (Outline) 137 
 
 How TO Teach subjects of the Fourth Grade.. 139 
 Reading (139) ; Spelling (139) ; Definitions (140); Eng- 
 lish Grammar (140) ; Arithmetic (144) ; Syllabus 
 of Topics for Common Fractions (147); Syllabus 
 
CONTENTS. 9 
 
 PAGE 
 
 for Decimal Fractions (158) ; Geography (163) ; Ele- 
 mentary Science — Botany (1G4) ; Mineralogy (1G8) ; 
 Writing (172). 
 
 THIRD GRADE (Outline) 175 
 
 How TO Teach sttbjects of the Third Gkade... 177 
 Reading (177); Spelling (178); Englisli Grammar 
 (179) ; Composition (179) ; Arithmetic (180) ; Sylla- 
 bus for Arithmetic (182) ; Geogrnphy (186) ; History 
 of the United States— General Suggestions (189) ; 
 Outline Sketch of the History of the United 
 States (189) ; Syllabus of Topics (193) ; Physiology 
 and Hygiene (191) ; Syllabus for Physiology (196). 
 
 SECOND GRADE (Outline) 199 
 
 How TO Teach subjects of the Second Grade. . 201 
 Reading (201) ; Definitions and Word Analysis (202) ; 
 English Grammar (204) ; Composition (206) ; Arith- 
 metic (206) ; Syllabus for Arithmetic (209) ; Geog- 
 raphy (210) ; History (211) ; Elementary Science- 
 Natural Philosophy (216) ; Syllabus of Topics (220) ; 
 Astronomy (221). 
 
 FIRST GRADE (Outline) 223 
 
 How to Teach sttbjects of the First Grade — 225 
 English Grammar (225) ; Composition (226) ; Arith- 
 metic (226) ; Algebra (229) ; Geometry (232) ; Out- 
 lines of Physical Geography (236) ; History, Ancient 
 and Modern (238); Natural Philosophy (241); 
 Astronomy (243) ; Chemistry (245) ; Book-keeping 
 (250) ; Constitution of the United States (251). 
 
10 CONTENTS. 
 
 PAGE 
 
 GENERAL SUGGESTIONS RELATIVE TO CLASSI- 
 
 FICATIONAND INSTRUCTION 253 
 
 Reviews (253); Progress of Classes (252); Progress 
 of Pupils (252); Recitations (253); Lessons for 
 Home Study (254) ; Physical Training (255) ; Man- 
 ners and Morals (356). 
 
 GOVERNMENT AND DISCIPLINE 257 
 
 SCHOOL LIBRARY 203 
 
1 ?, J 5 > > 
 
 > 1 
 
 
 n^TEODUOTIO]^. 
 
 No task cau be more responsible, or require the exer- 
 cise of greater care than tbat whicli bas for its object 
 tbe proper education of tbe young. To perform it effi- 
 ciently, special preparation and study are indispen- 
 sably necessary, not only in. regard to tbe brancbes of 
 knowledge wbich may bave been selected as a basis for 
 the instruction, but also in respect to tbe proper metbods 
 and appliances to be employed, in order to render tbe 
 instruction truly effective. Tbese metbods must be 
 determined by a consideration of tbe faculties to be 
 trained and educated, as well as tbe nature of tbe 
 subject taugbt ; bence, tbe teacber sbould be familiar 
 with at least the outlines of mental science, — the office 
 of each of tbe faculties of tbe mind, tbe order in which 
 they are naturally developed, and the proper means of 
 aiding in this development, so that the training and in- 
 struction given may result in tbat most valuable of all 
 characteristics, a well-balanced mind. It is the remark 
 of Professor Henry, that " the laws (which govern the 
 growth and operations of the human mindjare as defi- 
 nite, and as general in their application, as tbose( which 
 apply to the material universe]; and it is evident that a 
 true system of education must be based .upon a knowl- 
 edge and application of those laws." How important 
 then that the teacher should make himself familiar with 
 these laws ! Certainly no true success can be obtained 
 
12 INTRODUCTIOX. 
 
 "witbont thisknowledo-e ; for destitute of it, the teacher 
 is only an empiric, applying rules the reason of which 
 he does not know, and mechanically following methods, 
 the rationale of which he does not understand. 
 
 "^ If the teacher have sufficiently mastered these elemen- 
 tary principles of his profession, it will not be difficult 
 for him at all times rightly to understand his pupils' 
 mental condition and grade of advancement — a matter 
 of the greatest importance, especially at the first stage 
 of school instruction. Failing in this respect, many 
 teachers are often found most laboriously occupied in 
 the useless task of attempting to do that for the child 
 which nature, without any assistance, has already ac- 
 complished. They do not seem to be aAvare of the ex- 
 tent to which the pupil's mental faculties, more especi- 
 ally these concerned in observation, have been developed 
 in this way. The acquisitions made by a child of four 
 or five years of age, before being placed under any regu- 
 lar tuition at all, or subjected to any of the manipula- 
 tions of the school teacher, are indeed wonderful. The 
 senses, actively awake, have brought the young mind 
 into communication with the multifarious objects of 
 external nature; the faculty of conception, peculiarly 
 active in childhood, has given it a number of ideas cor- 
 responding to its perceptions, and the faculty of speech 
 has enabled it to connect with thousands of these ideas, 
 words and combinations of words, so as to designate and 
 express them. 
 
 •• Thus is the foundation of the intellectual character 
 unerringly laid by the unaided operation of nature her- 
 self. Here is no senseless cramming of words, for 
 words are only learned after the ideas which they repre- 
 sent have been acquired. Under the guidance of a 
 teacher properly conversant with the laws of the mind 
 
INTRODUCTION. 13 
 
 and its growth, this natural process would be continued, 
 and would be directed to its proper objects ; but, instead 
 of this, a mental treadmill is often used, the effect of 
 which is to counteract the work of nature, and clieck 
 the mental activity of the young pupil. To learn 
 A, B, C is, of course, necessary as one of the rudimen- 
 tal steps of primary instruction ; but this, like every- 
 thing else, should be so done, that the intelligence of 
 the pupil may be fostered, not deadened, in the acquisi- 
 tion. In every stage of intellectual training, let the 
 teacher always remember, that his pupil's mind is not 
 to be treated as a "passive recipient " of the thoughts 
 and experience of others, but as an active agent, to be 
 enabled to acquire an experience of its own, and apply it 
 to useful purposes. Let him constan tly apply the princi- 
 ple, so tersely expressed by Sir William Hamilton : " The 
 primary j)rinci2Jle of education is the determination of the 
 impil to self -activity— the doing nothing for him which he 
 is alle to do for himself^ This principle is equally ap- 
 plicable to every stage of the mind's development, as 
 well as to the diflereut processes of instruction adapted 
 to these stages ; but it will be impossible accurately 
 and efiectively to apply it, without a complete knowl- 
 edge Ipf the order of mental development, and of the re- 
 lation of that development to the study of each of the 
 branches prescribed for the instruction and the cultiva- 
 tion of the mind. 
 ^ Knowledge is to be considered as the food of the 
 mind; since by the proper reception, digestion, and 
 assimilation of it, the mind is to attain a maturity of 
 strength and efficiency; and upon its quality and quan- 
 tity it must depend wliether that mind is to be liealthy 
 and vigorous, or puny, sickly, and imbecile. It is, 
 therefore, of the greatest importance to ascertain the 
 
14 INTRODUCTION. 
 
 eflFect iH'oduced upon the mind of the pupil by the 
 study of each separate branch of knowledge — what 
 faculties it exercises and develops, and what it keeps in 
 a state of abeyance or passiveness. The future wants of 
 the pupils as to information, must, indeed, be a promi- 
 nent consideration in selecting the subjects to be taught ; 
 but the teacher should, in the classihcation, as well as 
 the instruction, of his pupils constantly keep in view the 
 present status of their minds — what they especially need 
 in order to acquire vigor, promptitude, and efi&ciency of 
 action. In the first, stages of education, the latter 
 should be the almost exclusive consideration ; but as 
 education advances, the practical usefulness of the 
 knowledge imparted should have paramount weight and 
 importance. 
 
 The adaptation of the processes of teacliing to the 
 various subjects taught, as well as to the faculties which 
 they call into exercise, should be a prominent object in 
 tbe teacher's mind. Young, untrained, inexperienced 
 teachers commit the error of bringing into play, with 
 regard to all subjects, association or memory. This, 
 with imitation, enables the pupil to. present a show of 
 knowledge, very gratifying to the unintelligent obser- 
 ver, but exceedingly pernicious as a substitute for real 
 acquisitions. When a teacher conceives that the sole 
 end of his efforts is to enable the pupil to recite verba- 
 tim the contents of a particular text-book, or to repeat 
 with verbal accui-acy and fluency certain rules, defini- 
 tions, and formula), whether their true meaning is 
 grasped or not, it is natural that he should resort to the 
 shortest and most direct means of accomplishing it, that 
 is, constant rote drill — an appeal to the law of arbi- 
 trary association. The injur}^ however, done to the 
 mind by this continued process, is incalculable ; since, 
 
'INTRODUCTION. 15 
 
 finally, ideas and facts suggest each other according to 
 no intrinsic or philosophical relation, but only from 
 their accidental connections, or such as this constant 
 repetition may have established ; and thus all logical 
 flow of thought is necessarily precluded. 
 
 A determination of (what are the best methods of pre- 
 senting the subjects to be taughtjmust de^Dend upon the 
 relations here referred to. Eules and methods may, in- 
 deed, be arbitrarily learned and mechanically applied to 
 practice, without any investigation of principles, but no 
 such hap-hazard process can, in any case, be sure of 
 success ; while in very many it must result in failure. 
 This important part of the theory of teaching should 
 be carefully studied, not only as preliminary to entering 
 upon the duties of an instructor, but through every 
 stage of their performance. It involves not only a 
 knowledge of the laws of mind, but a thorough famil- 
 iarity with the subjects taught. "A teacher," says Ed- 
 ward Everett, "ought to know of everything much 
 more than the learner can be expected to acquire. The 
 teacher must know things in a masterly way, curiously, 
 nicely, and in their reasons. He must see the truth 
 under all its asjiects, with its antecedents and conse- 
 quents, or he cannot present it in just that shape in 
 which the young mind can apprehend it. He must, 
 as he holds the diamond up to the sun, turn its facets 
 round and round, till the pupil catches its luster." 
 
 A very important inquiry in connection with the right 
 manner of presenting the subjects to the pupils' minds, 
 is in what manner the subjects should be divided into 
 topics, and how these topics should be arranged, and in 
 what order they should be taken up. The following 
 work, embodying, as it does, a graded course of instruc- 
 tion, is designed to deal with this inquiry quite exhaust- 
 
16 - ■ INTRODUCTION. 
 
 ively, and it is in furnishing a guide to the teacher in 
 this important part of liis duties that its usefulness will 
 be found to consist. 
 
 The teacher should study, too, the phenomena of 
 morbid as well as of healthy growth ; for teaching, in 
 the complete discharge of its functions, has much to do 
 in reforming, as well as forming, the mind. While very 
 much, in this regard, can be learned only by experience, 
 there are many facts and principles already established, 
 which the teacher should, as an essential part of his 
 professional preparation, acquire. In this connection, 
 the automatic tendencies of the mind are to be studied — 
 the tendencies, that is, to fall into habits, these when 
 depraved constituting what may be called the morbid 
 growth of the mind. No part of the teacher's duty is 
 more important than the exercise of a constant vigi- 
 lance, in order to arrest the formation of deleterious 
 habits, or to aid in forming such as are calculated to 
 confirm the healthy progress and development of the 
 pupil's mind. It is on this account that teachers are 
 constantly to be reminded that habits are always more 
 valuable than facts — that it is not the qucintity of 
 knowledge acquired that constitutes a criterion of men- 
 tal advau cement, but the mode of employing the men- 
 tal faculties — the habits of thought into which the mind 
 has settled in making its acquisitions or in applying 
 them. In such useful arts as require a mixed exercise 
 of the muscular system and the mental faculties, such 
 as penmanship, drawing, elocution, etc., this automatic 
 tendency has a most important application. Elegant 
 hand-writing, distinctness of articulation, correctness 
 of intonation, ease and grace of deportment, may all be 
 made to rest so firmly on thoroughly fixed habits as to 
 become a kind of " second nature." 
 
intuoduction: 17 
 
 Hoiu to use text-hooTcs, as well as when and for what 
 j-iurposes to employ them, is at the present time particu- 
 larly, a most important subject of study to the teacher. 
 Though in some branches, and for the attainment of 
 certain objects of mental discipline, it is best to dispense 
 with them altogether and bring the mind of the teacher 
 in direct contact with that of the pupil, yet good text- 
 hooks must always be among the most important instru- 
 mentalities of school instruction, both as regards the 
 effect which their judicious use has upon the mind of 
 the pupil, and the economy of time and labor of which 
 it is the source to the teacher. The latter must have 
 learned how to use them aright in order to be successful 
 in his work, and the pupil must learn how to make ef- 
 fective use of books to be truly educated. 
 
 Most children enter school for the first time with 
 minds athirst for knowledge. They have received this 
 craving at the hands of Nature, and their whole existence 
 has been passed in the effort to satisfy it. By their own 
 unaided intelligence they are able to proceed to a certain 
 limited extent ; observation is on the alert, and reflection 
 begins to be active ; but without the guidance of a ma- 
 ture and trained intellect, there can be no method in 
 their acquisitions, and the limit of their researches is 
 soon reached. The teacher and the book are the instru- 
 ments for affording this necessary aid and direction ; but 
 in doing this, the tendency should always be to stimu- 
 late, not repress, intellectual activity — to bring into 
 play the higher faculties of the mind, not to render its 
 energies dormant by offering only the dry forms, the 
 mouldy skeletons of knowledge, instead of the vital 
 germs of intelligence and thought. If, after the various 
 grades of school study have been passed, the jiupil is 
 left with a torpid, vacant mind, the loss Avhrch he has 
 
18 INTRODUCTION. 
 
 sustained is too great to be compensated by even the 
 ability to read, write, and ciplier. On the other hand, 
 a pupil that has not only mastered the elementary prin- 
 ciples of science, but has learned how to use books so 
 as to supplement the result of his own observations by 
 the experience of others, has been more effectually edu- 
 cated than he could possibly be by an exclusive depend- 
 ence upon oral instruction. 
 
 One of the most serious abuses to which the employ- 
 ment of elementary text-books is liable, is the practice 
 of requiring the pupil to commit to memory, verhatim, 
 all the definitions of a subject before teaching the subject 
 itself, so as to enable the pupils to understand the nature 
 of the things defined. It is, of course, most logical in 
 the scientific treatment of a subject to place the defini- 
 tions first, and the reasoning based upon them afterward, 
 but this is not the order of investigation. The defini- 
 tions are the results of an induction based upon the 
 facts obtained by observation ; they are generalizations 
 of those facts, and arc unintelligible to those entirely 
 unacquainted with the facts themselves. Thus the order 
 of investigation is inductive; the treatment is deductive, 
 and in elementary teaching the method should conform 
 rather to the former than the latter. Give the pupil 
 accurate and vivid conceptions of the facts, encourage 
 hira to observe the phenomena— to collect an experience 
 of his own; tell Inm, or let him learn from the book 
 what has been discovered by the experience of others ; 
 and when the facts thus obtained form a sufiicient 
 ground-work, lead his mind to the proper induction, 
 after which the definition, principle, or rule, based upon 
 it, comes naturally, and will be thoroughly under- 
 stood. Tlie definitions thus taught should be brief and 
 accurate in language, and, as a general thing, should be 
 
INTROD UCTIOK 1 9 
 
 committed to memory verbatim ; for great skill is re- 
 quired to construct a good definition, and it is of the 
 greatest value to the scholar and thinker to have his 
 mind well stored with these landmarks and guide-posts 
 of knowledge. 
 
 There is a numerous class of subjects in which text- 
 books, in the hands of the pupil, are apt to be a bane 
 rather than a benefit. The general recognition of this 
 fact is quite an interesting feature in the educational 
 history of our times. Object Teacliing and Oral In- 
 struction have assumed a prominent place in every ra- 
 tional course of study. Both these terms necessarily 
 exclude the use of text-books. Teaching from objects 
 is merely training the young child to acquire knowledge, 
 in a systematic way, from his own experience; that is, 
 by the regular exercise of his observing faculties. It 
 presupposes the presentation of the actual object during 
 the early stages of the work, so that perceptions may 
 pass from it to the mind, and thus ideas be obtained. 
 In teaching natural science, at an advanced stage of the 
 course, the same method is needed; for it is of very 
 little use to attempt to teach facts in relation to the 
 phenomena of nature when those phenomena have never 
 been observed. It is of no use to talk of the laws of 
 light, heat, and electricity — of the movements and ap- 
 pearances of the heavenly bodies — or of the chemical 
 composition of ordinary substances, as if they were mere 
 abstractions. The teacher should never forget that the 
 study of the book is the instrument, not the end of in- 
 struction; its lifeless representatives of ideas cannot 
 dispense with those vivid expressions of thought which 
 come fresh from tlie lips of the teaclior. Besides, there 
 is a language other than words — a language to which 
 ■ the eye, the tones of the voice, the movements of the 
 
20 INTRODUCTION. 
 
 body, all give force and expressiveness, and added to 
 these there is the influence of sympathy, which, though 
 a kind of " unconscious tuition," is perhaps the greatest 
 element of the teacher's power; and this not alone, or 
 chiefly, in intellectual training, but in that which is far 
 more important — moral education. The government 
 of his pupils — the training of their sensibilities, their 
 emotional nature, and their impulses — the instilling of 
 right principles of conduct — all these constitute a 
 greater part of what may be called a good education, 
 than the teaching of the rudiments of knowledge. 
 " Give me the child," says Everett, " whose heart has 
 embraced without violence the gentle lore of obedience, 
 in whom the sprightliness of youth has not encroached 
 on deference for authority, and I would ratheu have him 
 for my son, though at the age of twelve he should have 
 his alphabet to learn, than be compelled to struggle 
 with the caprice of a self-willed, obstinate youth, whose 
 bosom has become a viper's nest of unamiable passions, 
 although in early attainments he may be the Avonder of 
 the day." 
 
Graded Course of Instruction. 
 
 TENTH GRADE, 
 
 (lowest primary.) 
 Time allowed, about five montlis. 
 
 LANGUAGE. 
 
 Heading, — Words, and what they represent ; their sounds, 
 and letters ; also short sentences composed of familiar words. 
 The alphabet, by review. 
 
 P/tOMe</cs.— Simple sounds of letters for traming the organs 
 of hearing and of speech. 
 
 ,S(/^e?;/n</.— Words of regular formation— to be taught from 
 the blackboard, charts, etc. 
 
 ARIXmiETIC. 
 
 Counting and ^rZrftwj/.— Objects— as balls on the Nu- 
 meral Frame, pebbles, etc. 
 
 Figures.— From. to 100, as symbols of the numbers, taught 
 by counting objects. 
 
 OBJECT LESSONS. 
 
 J'orwi.— Common shapes, as square, oblong, ball, cylinder, 
 cube ; different kinds of corners, and of lines. 
 
22 GRADED COURSE OF INSTRUCTION. 
 
 Celo7\— Common colors, as red, yellow, blue, green, orange, 
 purple, to be distinguished. 
 
 Objects. — Names of common objects, their uses, and principal 
 parts. 
 
 Human Body. — Principal parts of the body. 
 
 DRAWING AND WRITING. 
 
 On Slates, — Making dots and small crosses in rows ; draw- 
 ing short lines, corners, etc. Printing or writing simple letters. 
 
 ]VIANAGE]\IENT. 
 Length of Exercises. — Fifteen minutes at one time. 
 
 DiscijMne. — Constant, but varied employment the best 
 means. 
 
LANGUAGE. 23 
 
 How TO Teach 
 
 SUBJECTS OF THE TENTH (OR LOWEST PRIMARY) GRADE. 
 
 LANGUAGE. 
 
 Headiuff. — Children learn words as audible signs 
 or names of objects, actions, and qnalities, when they 
 begin to talk. These words are learned as wholes, at 
 once, by hearing them spoken; not by first learning 
 their elementary sounds. In this manner young chil- 
 dren gradually become familiar Avith new words until 
 they possess a vocabulary which enables them to make 
 known their wants, and to express their thoughts. The 
 words which the children thus learn make but little 
 impression upon their minds, as words, but they are so 
 intimately associated with the objects, actions, and 
 qualities which they represent that they convey to the 
 mind the same ideas as the objects or the actions them- 
 selves convey. 
 
 When a child first goes to school it has already learned 
 many words, by hearing, as symbols of objects, etc. The 
 first duty of the teacher is, to ascertain what words the 
 child thus knows, then to teach the young pupil to 
 recognize them by their forms. The spoken Avords are 
 first learned as wholes; the printed words should be 
 learned first as Avholes and associated with both the 
 spoken words and the objects which they represent. 
 
 Therefore, teach first sliort words, which the children 
 have learned by hearing; beginning with the names of 
 familiar objects which can be shown to the pupils, or 
 the pictures of which may be presented. Also, during 
 
24 MOW TO TEACH 
 
 the first lesson in reading, print the words on tlie black- 
 board several times, and point tlieni out on charts, etc. 
 Let the pupils point out the Avords on the blaclcboard, 
 and on charts ; also let them print tlie words on their 
 slates. 
 
 Special pains should be taken to lead the children to 
 associate the printed words with the objects which they 
 represent, either by the use of the objects themselves, 
 or by pictures. 
 
 In teaching words that are not names, care should be 
 taken to illustrate their meaning by simple phrases, 
 conversations, etc. During the earlier lessons, omit 
 words of irregular formation, having several silent let- 
 ters, such as tongue, hiife, know, tliougli, thought, etc. 
 This class of words may be j^i'esented when the pupils 
 have learned the alphabet, and its regular combinations, 
 and the sounds represented by the letters have been 
 taught. 
 
 Let each word be taught first al siglit, as a whole, 
 and the sounds and names of the letters which com- 
 pose the word be taught afterward. After the chil- 
 dren have learned a few words at sight, they may be 
 taught the sounds, and the letters which form those 
 words. For the purpose of teaching the sound-elements 
 of words, select those in which the sounds and letters 
 are similar, as cat, rat, hat, mat, ox, fox, box, etc. The 
 teacher should sound the elements or letters of the 
 words first, then require the pupils to imitate the 
 sounds thus made. But before this can be done suc- 
 cessfully the pupils must be trained to distinguish, and 
 to produce these sounds, as directed under tlie head of 
 Fhonetics for this grade, which see. As additional 
 words are learned, the children may be required to 
 name such of the letters as they know, in the new 
 
LANGUAGE. 35 
 
 Avoi'ds, and then taught the remaining onos in those 
 words. In this way let the twenty-six letters of the 
 alphabet be taught, progressively. Subsequently these 
 should be reviewed, and their usual order learned by 
 repetition. The small letters are, of course, to be 
 taught first. 
 
 After the j^upils have learned several single words, 
 simple sentences may be j)resented, as " The dog can 
 bark." "The horse can draw a cart." The other 
 words that make up these sentences can then be 
 learned easily, as parts of the sentence. 
 
 The rapidity with which a child may be taught to 
 read by learning to recognize the simple forms of 
 words, at first, is surprising. And no less astonishing 
 is the readiness Avith which spelling is afterward 
 learned. 
 
 Let the order of teaching reading he, first, the idea; 
 then, its sound- sijmhol, or spoken word ; next, theform- 
 symhol, or printed word ; and subsequently, its represen- 
 tation hy writing ; and the order of learning to read 
 the language will correspond with the order of using it. 
 Words, then, will become as mirrors, reflecting ob- 
 jects and ideas to the minds of the pupils. Sense, and 
 %ound, and form., and use will become so intimately 
 blended together that pupils may easily be led to use 
 conversational tones in reading, and a natural style of 
 expression will follow as the necessary result. 
 
 But it may be asked. How can the pupils acquire 
 the means of learning the new words which they will 
 find in reading ? By observing their resemblances to 
 words already learned. The child, while learning to 
 J-ead, is constantly comparing the forms of new words 
 with the forms and sounds of those previously mas- 
 tered. The teacher may and should aid the young pupils 
 2 
 
;iO HOW TO TEACH 
 
 in acquiring the ability to learn new words by arranging 
 in groups, on tlie blackboard, those already learned, 
 and showing them how to compare the forms and 
 sounds of these words with others. 
 
 For the purpose of leading the children to observe 
 readily the analogy of words, in their sounds and in 
 the arrangement of their letters, after they have 
 learned, objectively and singly, to recognize several 
 words at sight, place on the blackboard, in columns, 
 such of these words as are similar in spelling and in 
 sound, as in the following groups : 
 
 cat, 
 
 pin. 
 
 pen. 
 
 ox. 
 
 cup, 
 
 rat, 
 
 tin, 
 
 hen. 
 
 fox. 
 
 (jun. 
 
 hat. 
 
 fin. 
 
 ten. 
 
 lox. 
 
 Q'un, 
 
 mat. 
 
 in. 
 
 men. 
 
 top. 
 
 fmi. 
 
 When the children have learned to pronounce the 
 words in a column, at sight, let them learn to give the 
 sounds of each, as — k d t , cat ; rat , rat ; hat ,. hat ; 
 etc., not as a spelling exercise, but to impress upon their 
 minds the relation of sounds, and of letters as their 
 representatives. 
 
 As other words are learned, let new groups be arranged, 
 and comparisons made with words of similar form, as : 
 
 old, rake, me, line, mule, 
 
 cold, make, we, fine, rule, 
 
 told, cake, see, nine, cube, 
 
 scold. bake. bee. pine. ■ tube. 
 
 • 
 
 If further descriptions of methods for teaching chil- 
 dren to read during their first term in school be desired, 
 gee Suggestions for the Teacher, pages 329-332 of lietv 
 Primai'y Object Lessons. 
 
LANGUAGE. 27 
 
 Jefers's Panormnic Reading Cliart will be found ex- 
 ceedingly useful during the early lessons in reading, for 
 presenting the words objectively. 
 
 Phonetics, — The object of teaching this subject 
 should he, first — to train the organs of hearing^ so that 
 the children may readily distinguish the sounds heard 
 in speaking our language ; second — to train the organs 
 of speech, so that the pupils may learn to produce those 
 sounds correctly in using the language. In presenting 
 this subject — and this should be done as soon as the 
 children begin to learn Avords by sight — the teacher 
 should herself make the sounds, and then require the 
 pupils to imitate them, as : a, « ; d,d', 0,0; 0,0; e, e ; 
 ^, e; I, I; i,i; u,u; ^ii; a,d', a, a; afterward, thus: 
 a,d,d,q', e, e; ~i,i; o, 6, g ; ic, ic, u. 
 
 When their organs of hearing and of speech have thus 
 been trained, both to clistinguish and to imitate sounds, 
 proceed to teach what sounds are represented by the 
 letters of simple words, as — me, mat, cat, man, 
 no, not , pin, cup , met , caTce, make, late, 
 slate. 
 
 Should more definite directions relative to methods 
 for ginng the first lessons in Phonetics be desired for 
 this and the following grades, see pages 397-308 iu 
 Neio Primary Object Lessons. 
 
 Spell inff. — After the words have been learned by 
 sight and sound, let them be learned by spelling, and 
 the children requested to observe tliat similar spelling 
 and similar sounds usually accompany each other. Of 
 course many words must be taught simply as signs of 
 things, or actions, or qualities, etc., but the plan of 
 grouping words by similarity of sounds, as indicated 
 
28 HOW TO TEACH 
 
 on a preceding page, under the head of Beading, will 
 greatly facilitate learning to read, and to spell, also. 
 
 Various modes may be used in teaching the reading 
 and the spelling of words singly — for instance: Let the 
 pupil point out given words on the blackboard, and on 
 the charts, as they are named by the teacher. A word 
 may be erased from the blackboard, and the pupils re- 
 quested to pronounce the word, and name the letters 
 composing it. Parts of words may also be erased, and 
 the pujnls required to name the missing letters. Let 
 the pupils, also, print the words on slates, copying them 
 from charts, or the blackboard. 
 
 The list of familiar words taught during the first 
 term in school should include those commonly used, as, 
 names of articles of dress, food, furniture, and utensils 
 used in the house, different things used in the school- 
 room, common animals, plants, names of familiar quali- 
 ties, actions, etc. 
 
 It is not the small number of letters of which a word 
 is formed that renders it easy to be learned objectively, 
 but its familiarity by use in conversation. Do not, there- 
 fore, confine the pupils to words which are composed of 
 only three or four letters. Long, difficult, or anomalous 
 words should, however, be omitted in this grade. 
 
 N". B. — In all these exercises of reading and spelling, 
 the teacher should — 
 
 Trai7i the pupils to pronounce tvords readily at siglit. 
 
 Never allow them to use unnatural tones in speaking 
 or reading. 
 
 Correct their faults in the use of language as they 
 occur. 
 
ARITHMETIC. 
 
 29 
 
 ARITHMETIC. 
 
 Counting anil Addinff, — The child's knowl- 
 edge of QUimher commences with counting objects. He 
 cannot learn the value oi figures from 1 to 10 until he 
 can count ten objects. Therefore counting should be 
 attended to first. The Numeral Frame is the most 
 convenient apparatus to aid in teaching counting, and 
 in giving children first ideas of simple numbers. The 
 -following illustration is intended to represent one mode 
 of using the Numeral Frame for teaching counting. 
 This mode of using it consists simply in holding the 
 Frame before the pu- 
 pils, and moving the 
 balls on the first wire, 
 one at a time, while 
 the children count 
 "one, two, three, four, 
 five, six, seven, eight, 
 nine, ten." The same 
 counting may be re- 
 peated on the second, 
 third, and on each 
 succeeding wire. At 
 first the counting 
 should not extend be- 
 yond ten. "When all the 
 
 balls on each wire have been counted in this manner, 
 proceed to move one hall on each wire, and let the chil- 
 dren count to ten, as before. Let this exercise be con- 
 tinued, from day to day, until each child can count 
 from one to ten, alone. Afterward, the counting may be 
 extended to twenty, by moving the balls on two wires ; 
 then to tliirty, by moving the balls on three wires, and 
 
 COUNTINO. 
 
30 HOW TO TEACn 
 
 60 on to one hundred. When the pupils are allowed to 
 count in concert, care should be taken to have them 
 use the falling inflection at each number, to prevent 
 them from acquiring a sing-song tone. 
 
 Addluf/. — When the pupils can count to one hun- 
 dred by ones, the teacher may move two balls at a time,, 
 and thus train them to add by twos. As the teacher 
 moves two balls on one wire, and two more on the next, 
 and so on, the pupils say, " two, four, six, eight, ten, ^ 
 twelve, fourteen," etc. 
 
 After the pupils can count, or add thus by fivos, as 
 far as fifty, and have also learned to read and write fig- 
 ures as far as 20, the teacher may write a column of 2's 
 on the blackboard, and train the pupils to add the Jig- 
 ures in the same manner as the balls were added. 
 
 Next, the pupils may copy the column of 2's from 
 the blackboard, on their slates, and each one add it as 
 it was added on the blackboard, and write the sum 
 under the column. 
 
 When the pupils have had sufficient practice on a 
 column of 2's, both on the blackboard and on their 
 slates, to be able to add it readily, the teacher may again 
 take the Numeral Frame, move one ball on the first 
 wire, and two balls on each succeeding wire, while the 
 pupils say, "one, three, five, seven, nine, eleven," etc., 
 to fifty-one. When the pupils have learned to add the 
 halls, thus, the teacher may write a column of 2's Avith 
 a 1 under it, on the blackboard, so as to make the 
 combinations produce the odd numbers. After suffi- 
 cient training upon these combinations, both with the 
 Numeral Frame, and the blackboard, require the pupils 
 to Avrite similar columns of 2's with a 1 underneath, 
 and add as before, writing the sum below the column. 
 
ABITUMETIC. 31 
 
 Let the same process be pursued in teaching the ad- 
 dition of threes ; first, by balls on the Numeral Frame, 
 as three, six, nine, twelve, etc., then by figure 3's on 
 "the blackboard, and lastly by each pupil's writing the 
 figures in columns on the slate, adding them, and 
 writing the sum below. Then the threes should be 
 combined with one, next with tivo, so as to produce dif- 
 ferent combinations of numbers, as with the tivos. 
 
 During a still later stage, the pupils may be taught 
 to add by alternating twos and ones; then threes OMii 
 ones ; then threes and ttuos ; then threes, tivosj and 
 ones. Each of these steps should be taken first with' 
 objects, then -^'ith figures on the blackboard, and finally 
 by the pupils' writing the columns on their slates and 
 adding them. The same method may be pursued for 
 teaching the addition of four's, fives, and sixes, and 
 their combinations with 07ies, twos, threes, etc., in the 
 next or Ninth Grade. The order of the steps is indi- 
 cated by the objects employed in teaching, viz. : Num- 
 eral Frame, Blackboard, Slates. 
 
 Of course, these exercises with columns of figures 
 should not be introduced before the pupils have been 
 taught to know figures as symbols, and to make them 
 on their slates. 
 
 Value of Nunibers.—li is exceedingly impor- 
 tant that the first ideas of the value of numbers, and of 
 figures, be associated with numbers of objects counted. 
 Both the value of numbers and the value of figures 
 should be taught in connection Avith counting objects. 
 Here, ao-ain. the Numeral Frame is the most useful ap- 
 paratus. When the pupils can readily count ten, the 
 teacher may hold the Numeral Frame before the class, 
 move one ball on the second wire from the top, and 
 
32 
 
 HOW TO TEACH 
 
 request the pupils to say "owe ball." Then the teacher 
 may move huo balls, one at a time, on the third wire, 
 the piqiils counting them as moved, thus : " one, two ; 
 two balls." Then move three balls, one at a time, on 
 the fourth wire, the pupils counting thus : " one, two, 
 three ; three balls." Then mo\e four balls in the same 
 manner ; then Jive balls, and so on. The ^Josition of 
 the balls on the wire while the pupils are counting, 
 may be seen on the sixth wire in the accompanying 
 
 illustration of the 
 Value of Numbers. 
 While the pupils 
 are counting "one, 
 tAvo, three, four, 
 five," the teacher 
 does not move the 
 balls to the side 
 of the frame, but 
 leaves a space be- 
 tween each two 
 balls, as may be seen 
 in the illustration 
 on this page. 
 
 The illustration 
 on the next page 
 — Simple Value of 
 Figures— re'presents 
 the teacher in the act of moving the/i-e balls to the side 
 of the frame; and, as he does this, the pupils tell the 
 number of balls, thus, " five balls." Let the same mode 
 be pursued with each number, from one to nine. First, 
 the children count the separated balls, as each is moved 
 part way ; and as all are moved to the side of the 
 frame, the pupils tell the whole number of balls moved. 
 
 Value op Numbers. 
 
ARITHMETIC. 
 
 3y 
 
 Next let the pupils tell the niiraber of balls, on each 
 wire, thus: one ball, two balls, three balls, four balls, 
 five balls, six balls, etc., to nine balls ; nine balls, eight 
 balls, seven balls, etc., to one ball, no ball. By these 
 means the Value of Numiers will be learned thoroughly. 
 
 Figures, — Figures should be introduced as sym- 
 bols of the number of objects counted, and presented 
 first consecutively, in groups, or steps, as follows: from 
 to 9; from 10 to 19 ; from 20 to 29; from 30 to 39, 
 etc. No succeed- 
 ing group should 
 be presented until 
 the preceding one 
 has been thorough- 
 ly learned, so that 
 the pupils can read 
 them at sight, in 
 order, and out of 
 order. "While teach- 
 ing the Simple 
 Value of Figures, 
 the Numeral Frame 
 will be found a 
 most valuable aid. 
 
 During this stage simple value op Figures. 
 
 of instruction the 
 
 teacher should make frequent use of the blackboard, 
 
 and the pupils of slates. 
 
 Additional suggestions relative to methods for teach- 
 ing the First Ideas of Numbers and of Figures, may be 
 found on pages 194-209 of Neio Primarij Object Lessons. 
 
 2* 
 
34 HOW TO TEACH 
 
 OBJECT LESSONS. 
 
 X. B. — Each exercise in object lessojis sliould le con- 
 ducted 2oith a vieio to forming habits of attention and 
 careful observation through the use of the senses. 
 
 ^orni. — In Nature's school, cliildren first learn to 
 know things as wholes ; they learn to know their parts 
 afterward. The teacher who would be successful must 
 follow Nature's plan of instruction. Present, therefore, 
 common objects, as wholes, and lead the pupils to notice 
 resemblances in shape, first ; afterward direct their at- 
 tention to prominent differences. 
 
 A Box of Forms and Solids, containing forty-eight 
 plane Forms and fifteen Solids, has been prepared for 
 the special purpose of Object Teaching. This is the 
 most important aid in illustrating the various forms 
 and solids. 
 
 Select the Form to be taught from the Box of Forms, 
 and lead the pupils to observe it, then tell them its 
 name; next require them to mention other objects 
 having the same shape. Proceed in this manner with 
 each Form and Solid mentioned for this grade, and 
 continue these exercises until the pupils can recognize 
 and name each. 
 
 Color,— T\\Q pupils should be led to distinguish re- 
 semblances and difierences in color from "colored 
 cubes," or cards, and to group together objects of like 
 colors. They should also learu the names of the six 
 principal colors. 
 
DRAWING AND WRITING. 35 
 
 Object s. — The lessons on Common Objects in this 
 grade should be simple and conversational, treating 
 only of their most obvious parts and uses. Such com- 
 mon objects as a bell, chair, slate, pencil, hat, cup, knife, 
 etc., are appropriate for this purpose. The pupils should 
 be led to notice and point out the principal parts, and 
 encouraged to tell what they see and what they know 
 of each object shown them. 
 
 IIuTitan JBody, — In this Grade the lessons on the 
 Human Body should lead the pupils to notice and name 
 the parts, as head, neck, trunk, arms, hands, legs, feet; 
 also parts of the head, as crown, face, forehead, clieeks, 
 chin, mouth, nose, eyes, ears, etc. 
 
 N. B. — If more explicit information be desired rela- 
 tive to methods for giving lessons on shapes of lines, 
 corners, square, oUong, hall, cylinder, c%ibe, and common 
 ohjects ; also on colors, and on the Imman body, it may 
 be found in Kew Primary Object Lessons. 
 
 DEAWING AND WRITING. 
 
 Drawing on Slates^ etc.— The exercises of 
 Draioing and rrinting on slates should be introduced 
 in siich a manner as to give an interesting variety to 
 the class-work ; also, so as to aid in the discipline of 
 the class, by giving the children something to do that 
 will interest them after they have become tired with 
 their other lessons. The children might be allowed to 
 use slates for drawing, as a reward for good order and 
 attention. Short daily exercises may be made very 
 useful. 
 
36 HOW TO TEACH 
 
 MANAGEMENT. 
 
 Lenfftli of lExercises* — The exercises of this 
 Grade should not be continued upon the same subject 
 longer than fifteen minutes at one time, without mate- 
 rially changing the manner of the exercise. 
 
 Discipline, — Young children cannot attend to 
 the same thing for a long time without change in the 
 form of attention. Their natural activity demands fre- 
 quent changes in the position of the body; also con- 
 stant but varied employment. If the teacher does not 
 furnish the needed employment and changes of position 
 by variety in her methods of instruction, the children 
 will seek to gratify their needs by play. Therefore chil- 
 dren should never ~be compelled to sit without employ- 
 ment, either for the onind, the hands, or the lodii. 
 
 Children should be led to do right by encouragement 
 rather than driven by fear. Judicious praise is more 
 efficient than scolding. Teach them to be cleanly, 
 mannerly, truthful, and obedient. Let good examples 
 of these traits be commended frequently. 
 
]Sri]^TH GEADE. 
 
 (primary.) 
 7H,me allowed, about five months. 
 
 LANGUAGE. 
 
 Reading. — In the First Reader. 
 
 Phonetics. — Pupils to be taught to recognize and to make 
 the sounds of the letters in words of one syllable. 
 
 Dejinitions. — Pupils to be practiced in illustrating the mean- 
 ing of words by their use in short sentences ; also in telling what 
 the words mean. 
 
 Spelling. — Words fi-om the reading lessons; also familiar 
 words in common use. 
 
 ARITHMETIC. 
 
 Adding. — With objects, and with figures; twos, threes, fours, 
 and fives. 
 
 Figures. — Numbers of two and of three figures to be read at 
 sight, without numeration ; also, to be written on slates from 
 dictation. 
 
 Monian Numbers. — I, V, X, L, with their combinations 
 to sixti/, inclusive ; also their use on the face of the clock. 
 
 OBJECT LESSONS. 
 
 Form. — Common shapes, continued ; adding those of rhomb, 
 rhomboid, circle, semicircle, crescent, sphere, hemisphere, cone ; 
 also position of lines. 
 
38 GRADED COURSE OF INSTRUCTION. 
 
 Coior.— Shades of common colors, as light and dark red, 
 light and dark blue, etc. 
 
 Human Body.— Names and uses of the limbs, and of their 
 parts ; also the names and shapes of the prmcipal bones. 
 
 Objects.— The principal parts and chief uses of common 
 objects. 
 
 DRAWING AND WRITINQ. 
 
 On Slates.— Connect dots by lines ; draw squares, oblongs, 
 rhombs ; divide lines into equal parts. Write simple words with 
 small letters. 
 
 MANAGEMENT. 
 
 Doing.— Train children to see, to do, and to tell. 
 
 Manners and 3Iorals.—Vse the appropriate daily inci- 
 dents of school as occasions for giving instruction in Manners 
 and Morals. 
 
LANGUAGE. 39 
 
 How TO Teach 
 
 SUBJECTS OF THE NINTH GKADE. 
 
 LANGUAGE. 
 
 Headiiiff. — The manner of teacliing Reading dur- 
 ing the first term in which hooks are used hy the pupils, 
 has a very important influence on the future progress 
 of those pupils. In the processes of instruction, only 
 one difficulty should be presented to the pupils at a 
 time. Among the difficulties which children have to 
 encounter during their first lessons in reading from 
 books, are, learning to know the words at sight, so as to 
 pronounce them readily ; learning to Jcnoio lohat the 
 words and sentences mean ; learning to read in such a 
 manner as to imitate good conversatio7i. 
 
 First Step.— With, each new reading lesson the first 
 step should be to make the pupils familiar with the 
 words of the lesson, by printing them on the blackboard 
 in columns, and teaching the children to pronounce 
 them at sight ; next teach them to pronounce at sight 
 the same words in the book, but out of their order in 
 the sentences of the lesson, lest they learn them by rote, 
 instead of by sight. 
 
 Second Step.— Tram the pupils to find out what each 
 sentence means, and to tell the meaning in their oiun 
 language. 
 
 Third ^/ep.— Train the pupils to read each sentence 
 so that the reading may resemble good conversation. 
 
40 HOW TO TEACH 
 
 Finally, when the lesson has been read in a proper man- 
 ner, the teacher should talk with the children about it, 
 and encourage them to tell, in their oAvn language, what 
 they have read. 
 
 N. B. — Let the standard for (jood reading he its near 
 resemUance i?i manner to good conversation. 
 
 Further suggestions relative to first lessons in read- 
 ing from books may be found on pages 333-337, of Neio 
 Frimary Object Lessons. 
 
 ^** The work of teaching children to read may be facilitated 
 by using, for the First and Second Reading Books, those printed 
 with the modified types invented by Dr. Edwin Leigh. 
 
 Phonetics, — The object of exercises in Phonetics 
 should be the same in this grade as in the preceding — 
 to secure a ready recognition of the several sounds of 
 our language, and the ability to utter them distinctly in 
 conversation and reading. Time should not be wasted 
 in the endeavor to teach children definitions or descrip- 
 tions of the various sounds of letters. 
 
 Let the chief aims of the teacher be, to train the 
 organs of hearing to acuteness in the perception of 
 sounds, and the oi'gans of speech to flexibility and accu- 
 racy in producing sounds. 
 
 Definitions. — During the lessons of this grade, it 
 is appropriate to teach the children to use the principal 
 words of the lesson in brief sentences, to enable them 
 to show readily that they understand what the words 
 mean, as : "A horse can draw a cart" — " I must be 
 good." — "I can Jiotd a book." — "Snow is white." — "I 
 will try to learn to read." — *'I must obey my mother," 
 
ARITHMETIC. 41 
 
 etc., etc. Such exercises will be found to be much 
 more useful to young children thun teaching them 
 formal definitions to be recited. The meaning of diffi- 
 cult or unusual words must, of course, be exjjlained and 
 illustrated by the teacher. 
 
 Spelling, — In oral spelling, the words should be 
 distinctly pronounced by the pupil before they are 
 spelled, then each letter clearly uttered, a ])ause made 
 heiiveen the syllables, and the word again pronounced 
 after all the letters have been given. The familiar 
 words taught, in addition to those in the reading les- 
 sons, should include such appropriate words as the 
 children most commonly hear and use. These should 
 be printed or written on the blackboard by the teacher, 
 and copied by the pupils, on their slates. The same 
 words may also be spelled orally. 
 
 The chief use of spelling consists in Avriting words ; 
 therefore, as early as possible, it should be taught by 
 writing. As the first step in this direction, let pupils 
 commence in this grade to study sjjelliny lessons dy 
 co2)ying the coords on slates. 
 
 ARITHMETIC. 
 
 Addinf/, — It would be well for the teacher, before 
 commencing the lessons of this Grade, in Arithmetic, 
 to read the directions for teaching " Adding " in the 
 preceding Grade. 
 
 During the exercises of counting and adding witli 
 the Numeral Frame, do not allow the children to count 
 and add by rote. See that due attention is given to 
 the objects counted. "When the pupils can add readily 
 
42 now TO TEA en 
 
 single columns, eacli composed of like numbers, as all 
 2's, all 3's, 4's, 5's, etc., teach them to add single columns 
 composed of different small numbers, as 2's and 3's; 
 2's, 3's, and 4's ; also 2's, 3's, 4's, and 5's. 
 These combinations should be illustrated 
 on the Numeral Frame at first, then 
 taught with figures on the blackboard ; 
 and subsequently copied by the pupils on 
 their slates, and added by them silently. 
 In adding, let the pupils be trained from 
 the first to name only the sums, thus : 
 3, 5, 8, 10, 13, 15, 18, 20, 23, 25 ;— 4, 6, 
 9, 13, 15, 18, 22, 24, 27, 31 ;— 4, 9, 11, 
 14, 18, 23, 25, 28, 32, 37. 
 — — — To make the pupils familiar with the 
 25 31 37 sums produced by adding the separate 
 numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, to 
 each number below 20, arrange the figures on the black- 
 board thus : 
 
 12 3 4 5 6 7 8 9 10 11 12 13 14 15 etc. 
 111111111 1 1 1 1 1 1 1 
 
 2 
 
 4 
 
 5 
 
 3 
 
 3 
 
 4 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 2 
 
 2 
 
 3 
 
 5 
 
 3 
 
 2 
 
 4 
 
 2 
 
 4 
 
 3 
 
 3 
 
 3 
 
 2 
 
 2 
 
 2 
 
 5 
 
 3 
 
 4 
 
 4 
 
 1 2 
 
 3 4 
 
 5 6 
 
 7 
 
 8 
 
 9 10 11 12 13 14 15 16 
 
 1 
 2 2 
 
 2 3 
 
 2 2 
 
 4 5 
 
 2 2 
 
 G 
 
 2 
 
 7 
 2 
 
 8 9 10 11 12 13 14 15 
 22222222 
 
 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 
 
 Continue this arrangement until the pupils can add, 
 both on the blackboard and on slates, each number 
 from 1 to 9 to each number below 20, both in the order 
 given, and out of this order. 
 
ARITHMETIC. 43 
 
 Readinff and Writing Fir/tires, — Both the 
 reading and writing of numbers in figures can be 
 taught most thoroughly in steps, or grouj)s. The 
 figures should be presented first in their order, in con- 
 nection with counting ; then out of their order. In 
 this Grade the figures should be taught luithout nume- 
 ration. The following groups will indicate appropriate 
 steps : 
 
 First Step. 
 
 Second Step. 
 
 TJiird Step. 
 
 Fourth Step. 
 
 Fift?t Step. 
 
 10 
 
 100 
 
 100 
 
 200 
 
 300 
 
 11 
 
 200 
 
 101 
 
 .201 
 
 301 
 
 12 
 
 300 
 
 103 
 
 202 
 
 302 
 
 13 
 
 400 
 
 103 
 
 203 
 
 303 
 
 14 
 
 500 
 
 104 
 
 204 
 
 304 
 
 15 
 
 GOO 
 
 105 
 
 205 . 
 
 305 
 
 16 
 
 700 
 
 106 
 
 206 
 
 306 
 
 17 
 
 800 
 
 107 
 
 207 
 
 307 
 
 18 
 
 900. 
 
 108 
 
 208 
 
 308 
 
 19 
 
 
 109 
 
 209 
 
 309 
 
 20 
 
 
 110 
 
 210 
 
 310 
 
 21 
 
 
 111 
 
 211 
 
 311 
 
 etc.. 
 
 
 etc.. 
 
 etc.. 
 
 etc.. 
 
 to 
 
 
 to 
 
 to 
 
 to 
 
 99. 
 
 
 199. 
 
 299. 
 
 399. 
 
 These steps maybe continued in this manner through 
 999. As much time will be required to teach the fir.si 
 and thii'd steps as for any foiir other steps. Let the 
 children be trained to read and 2vrite the numbers con- 
 tained in each step, readily, before taking up the next 
 one in order. 
 
 If properly conducted, these lessons will train the 
 pupils to read and write numbers through 199 in one 
 month, and any number expressed by three figures in 
 two months. 
 
44 HOW TO TEACH 
 
 llonian JVutnbo's. — Besides teaching what num- 
 bers are represented by I, V, X, and L, and their com- 
 binations to sizfy, the pupils should be trained to tell 
 the time of day as indicated on the face of a clock. 
 
 OBJECT LESSONS. 
 
 Form. — When the pupils have learned to recognize 
 a given shaj^e by means of its representative form in 
 the set of " Object Teaching Forms and Solids," they 
 should be led to .discover the same shape in several 
 other objects. See remarks on page 34, relative to 
 Form and Methods for teaching it. 
 
 During the first lessons on lines, the attention of the 
 pupils Avas properly directed to their shajjcs only, as 
 straight, crooked, curved, waved, spiral. When they 
 are taught to recognize and name t\\Q positions of lines, 
 as vertical, slanting or oblique, and horizontal, they 
 should be trained to apply these names of positions to 
 objects as well as to lines. 
 
 Color, — In lessons on color, the name should first 
 be associated with the color which it represents, by 
 showing that color and requiring the pui)ils to point 
 it out on the chart, and among colored objects. To 
 recite names and descriptions of colors, without also 
 knowing the color when seen, is of no use. The teacher 
 should use "Color-Cubes," "Colored-Cards," "Color- 
 Cluirts," and other colored objects for illustrating these 
 lessons, and require the pu2:)ils to sliow, by placing in 
 groups colors that nearly resemble each other, with 
 what degree of accuracy they distinguinh colors; and 
 at the same time they should be taught to know com- 
 mon shades and tints by their names. 
 
DRAWING AND WHITING. 45 
 
 Human Sody, — In giving the lessons on the 
 Ininian body, let the pupils point out and give the 
 names and uses of parts, as parts and uses of the arm, 
 hand, leg, foot, etc. 
 
 Objects, — Let the pupils point out parts of objects, 
 and the teacher give their names and uses; then let the 
 children give the names and uses of the parts as the 
 teacher points to them. 
 
 N. B. — Should the teacher desire more explicit in- 
 formation relative to methods for giving lessons on 
 2)lane forms, solids, jjositiooi of lines, shades of colors, 
 the human body, and on common objects, for this and 
 the succeeding Grades, than the space will allow in this 
 book, it may be found in the treatment of these topics 
 in New Primary Object Lessons. 
 
 DRAWING AND WRITING. 
 
 On Slates,— In this Grade, the instruction should 
 be continued in a manner similar to that for the Tenth 
 Grade, which see. The teacher should give full illus- 
 trations on the blackboard, relative to each point and 
 step of the lessons. 
 
 MANAGEMENT. 
 
 Doinff,— Children learn much faster by doing than 
 by merely repeating what they have been told. There- 
 fore, whenever possible, arrange the exercises of each 
 subject so that the pupils may be called upon to do 
 something which relates to that subject, with their 
 hands; also so as to require them to tell what they see 
 and do. 
 
46 HOW TO TEACH. 
 
 Itegiilar Occujyation for all the JPiijnls. — 
 
 A teacher who furnishes that regular and constant oc- 
 cupation which commands the attention of all the pu- 
 pils during the several exercises of the day, thereby 
 gives the best assurance of ability to manage a school 
 successfully. Indeed, the secret of maintaining good 
 discipline chiefly lies in this. Hence the manner of 
 teaching becomes an important element of good man- 
 agement as well as of good instruction, for it is this 
 which chiefly determines the order of the class. Fur- 
 thermore, habits of learning are acquired from the pre- 
 vailing methods of teaching. 
 
 To learn how to manage a class or school, so that all 
 the pupils may have constant occupation, and may give an 
 interested attention to all the exercises, should be the 
 aim of every teacher. Proper changes in the manner 
 of presenting the diflerent lessons upon the same subject, 
 and even changes in the manner of conducting the ex- 
 ercise of a single lesson will be useful to the teacher 
 toward the attainment of this aim. 
 
 In a class composed of young children, frequent alter- 
 nations from answers by individual pupils to responses 
 by the entire class will aid in maintaining the attention 
 of all the pupils. Great care, however, will be necessary, 
 on the part of the teacher, to prevent the pupils, while 
 speaking in concert, from using sing-song tones. This 
 may be prevented by requiring them always to use the 
 falling inflection in answers by the entire class, and by 
 never allowing them to repeat the answer, or statement, 
 without a request from the teacher, made after each re- 
 sponse by the class. 
 
EIGHTH GEADE. 
 
 (PRIilAKY.) 
 
 Time alloiced, — about five vionths. 
 
 LANGUAGE. 
 
 JReading. — First Reader completed, and an easy Second 
 Header commenced ; pupils to be able to read fluently in good 
 conversational tones, with proper attention to the pauses. 
 
 Phonetics. — Sounds occurring in words of one syllable, and 
 silent letters to be distinguished. 
 
 Definitions. — Meaning of the words read to be shown by 
 using them in short sentences. 
 
 Spellitig, — From reading lessons ; and lists of other familiar 
 words. 
 
 ARITH^AIETIC. 
 
 Adding. — Single columns of ten figures ; adding by decades, 
 through 9s', 
 
 Nutneration and Notation, — Reading and writing figures 
 through nine places (987, 654, 321). 
 
 Mental. — Simple, practical questions which require the add- 
 ing of numbers from 5 to 9 to numbers below 30 ; also, subtract- 
 ing similar numbers. 
 
 3Iidfi plication table commenced. 
 
 JRonian Numbers. — Their combinations through two hun- 
 dreds. The Key to Roman Numbers to be taught. 
 
48 GRADED COURSE OB^ INSTRUCTION. 
 
 OBJECT LESSONS. 
 
 Form. — Parallel and perpendicular lines, angles, prisms, 
 pyramids, surfaces, circumference, diameter, etc. 
 
 Color. — Primaiy and secondary colors. 
 
 Suniaii Body. — Principal bones and their uses. 
 
 Animals. — Names and uses of familiar animals ; also where 
 they live. 
 
 Plants.— Names of trees, plants, flowers, fruits, etc. ; also 
 where they grow. 
 
 Objects, — Principal qualities, parts, and uses. 
 
 DRAWING AND WRITING. 
 
 On Slates. — Drawing plane figures ; writing simple words ; 
 formation of capitals taught. 
 
 manage:^ient. 
 
 Physical Training. — Daily physical exercise and pure 
 air are indispensable to the health of children. Provide them 
 with both during the hours of school duties. 
 
LA^'GUAGK 49 
 
 How TO Teach 
 
 SUBJECTS OF THE EIGHTH GRADE. 
 
 LANGUAGE. 
 
 Jteadhlff , — The exercises for teaching Reading in 
 the Eighth Grade may be divided into three stejjs, as in 
 the Niutli Grade. 
 
 First StejJ. — Training the pupils to know the words 
 at sight ; also what the words mean. 
 
 Second Step. — Attention to the thoughts expressed. 
 
 Third Stej). — Beading in easy, conversational tones. 
 
 1. The pnpils may be trained to know the words at 
 sight by writing them in columns on the blackboard — 
 by pronouncing them from their books, commencing 
 with the last word of the paragraph and proceeding in 
 an order the reverse of that pursued in reading. 
 
 2. As soon as the words are known readily at sight, 
 chief attention should he given to the thoughts exjjressed. 
 The pupils may be led to attend to the thonghts ex- 
 pressed by requiring them to find out what the senten- 
 ces tell, without reading them aloud. The teacher may 
 aid them in this matter by proceeding in a manner 
 similar to the following: Reqnest the class to look at 
 the first sentence, and each member to raise a hand when 
 able to tell what the sentence is about. When several 
 hands are held up, call upon different pupils to state, in 
 their own language, what the sentence tells. Proceed in 
 a similar manner Avith other sentences of the lesson, and 
 
 3 
 
50 JIOW TO TEACH 
 
 require the pupils to tell what those sentences say. The 
 teacher may ask : What does the first line tell us ? 
 What do the words in the next sentence say ? Who can 
 tell what the next paragraph is about ? 
 
 3, When the pupils have accomplished the first two 
 steps in a given reading lesson, they will be prepared to 
 take the third step, and will readily learn to read with 
 easy, couYersational tones. Special care should be taken 
 in this grade to train the pupils in habits of clearness 
 and distinctness of enunciation, also to read in an easy^ 
 speaking voice. 
 
 Faults in reading are most readily overcome when the 
 eflforts to correct them are chiefly directed to one kind 
 at a time, and the training continued until the pupils 
 clearly perceive the fault and take the proper means to 
 correct it. 
 
 J^imcfuafion, — The time commonly spent in teach- 
 ing children to recite definitions of punctuation-marks 
 is wasted. Instead of this, lead the pupils to observe 
 that a sJiort pause is viade at a comma, a Utile longer 
 pause at a semicolon, and still longer pauses at the 
 question-marh and 2Jeriod. Lead the pupils to see that 
 the question-mark points out a question, and a period 
 the end of a sentence. The uses of all the marks of 
 pauses, as well as the hyphen, apostrophe, and quota- 
 tion-marks, should first be explained from the black- 
 board, then examjiles of their use should be pointed 
 out by the pupils in their reading books. 
 
 Plionetics* — In this grade the pupils should be 
 taught to distinguish the sounds of given letters in 
 words of one syllable, and to make these sounds, as, the 
 sound of a in slate, a in Mil, a in not, o in do, u in full, 
 
LANGUAGE. 51 
 
 fin far, f iw of, h in kite, on in man, c in coio, etc. 
 When the pupils can distinguish and make the sounds 
 in words of one syllable, they may be required to tell 
 which letters have no sound in given words ; also, to 
 name the vowel sound by its number; as in the word 
 make, m-a-Jc, make, a has its first sound, the e is silent ; 
 loiiglif, h-a-t, bought; oil represents the fourth sound of 
 a, g and h are silent. 
 
 As a method for training pupils to distinguish the 
 silent letters, let them first sound a word, giving each 
 sound as heard when the word is properly pronounced 
 — then spell it, naming each letter in order — next tell 
 which letters have no sound. 
 
 Care needs to be taken, in each grade, to prevent the 
 pupils from making the short sounds of a, e, i, o, and u, 
 too long, when sounded alone. Let each of these 
 sounds be made very short, as heard in at^ net, it, not, 
 nut. 
 
 De/inifions, — In giving the meaning of separate 
 words, in some instances a description of the object, or 
 of its use, if the word be a name, or a simple statement 
 about that which is meant by it, will illustrate the 
 pupil's understanding of it better than the use of the 
 word in a sentence. Let this exercise be so conducted 
 as to avoid mechanical forms of definition, and with a 
 sufficient variety and simplicity to secure a clear knowl- 
 edge of the meaning of the ivords. The practice of 
 using the given words in sentences, so as to illustrate 
 their meaning, should be continued in this grade. 
 
 Sj^elliuf/,— Care should be taken in oral spelling to 
 have each pupil pronounce the word before spelling it, 
 to name each letter distinctly, to make a pause between 
 
62 HOW TO TEACH 
 
 the syllahhs, and to pronounce the word again when all 
 the letters have been named. 
 
 As soon as the pupils can write words on their slates 
 they should have much practice in spelling by writing 
 words from dictation. 
 
 In selecting familiar words it would be well to re- 
 quest the pupils to name words for the teacher to write 
 on the blackboard, and all the class, afterward, to copy 
 these on their slates. But teachers should not depend 
 entirely upon the pupils for such words ; they should add 
 to the list other appropriate common words. 
 
 ARITH]\IETIC. 
 
 
 Add 
 
 itig 
 
 . — Continue the 
 
 exercise of adding single 
 
 column t 
 
 ), iu 
 
 the 
 
 same manner as 
 
 in the Ninth Grade, 
 
 
 
 
 
 
 
 
 
 making them more 
 
 6 
 
 6 
 
 7 
 
 7 
 
 8 
 
 8 
 
 9 
 
 9 
 
 difficult, gradually. 
 
 6 
 
 5 
 
 7 
 
 6 
 
 8 
 
 7 
 
 9 
 
 8 
 
 until the pupils can 
 
 6 
 
 4 
 
 7 
 
 5 
 
 8 
 
 G 
 
 9 
 
 7 
 
 add readily, without 
 
 6 
 
 3 
 
 7 
 
 4 
 
 8 
 
 5 
 
 9 
 
 G 
 
 counting, columns 
 
 6 
 
 6 
 
 7 
 
 3 
 
 8 
 
 4 
 
 9 
 
 9 
 
 of ten or twelve 
 
 6 
 
 5 
 
 7 
 
 7 
 
 8 
 
 8 
 
 9 
 
 8 
 
 figures each, which 
 
 6 
 
 4 
 
 7 
 
 G 
 
 8 
 
 7 
 
 9 
 
 7 
 
 are composed of 
 
 6 
 
 3 
 
 7 
 
 5 
 
 8 
 
 G 
 
 9 
 
 G 
 
 7s, 8s, and 9s. 
 
 G 
 
 G 
 
 7 
 
 4 
 
 8 
 
 5 
 
 9 
 
 9 
 
 The progressive ar- 
 
 6 
 
 5 
 
 7 
 
 3 
 
 8 
 
 4 
 
 9 
 
 8 
 
 rangement of these 
 
 6 
 
 4 
 
 7 
 
 7 
 
 8 
 
 8 
 
 9 
 
 7 
 
 columns is illus- 
 
 6 
 
 3 
 
 7 
 
 6 
 
 8 
 
 7 
 
 9 
 
 G 
 
 trated here. When 
 
 • til ft -nnnils hnvft 
 
 learned to add a 
 column oil the blackboard, they should copy it on their 
 slates, and then each add it singly, writing the sum 
 underneath it. 
 
ABITUMETIG. 53 
 
 Adding ly Decades will greatly facilitate learning to 
 add accurately and rapidly. 
 
 Appropriate steps toward teaching pu2)ils to add hy 
 decades may be taken by Avriting various combinations 
 of numbers on the blackboard, in the following form 
 and order, and requiring the pupils to add the numbers 
 orally, and afterward to copy them on their slates and 
 
 add tli£m 
 
 again : 
 
 
 
 
 
 
 
 
 5 
 
 15 
 
 25 
 
 35 
 
 45 
 
 55 
 
 65 
 
 75 
 
 85 
 
 95 
 
 4. 
 
 4 
 
 4 
 
 4 
 
 4 
 
 4 
 
 4 
 
 4 
 
 4 
 
 4 
 
 9 
 
 19 
 
 29 
 
 39 
 
 49 
 
 59 
 
 etc. 
 
 
 
 
 7 
 
 17 
 
 27 
 
 37 
 
 47 
 
 57 
 
 07 
 
 77 
 
 87 
 
 97 
 
 7 
 
 7 
 
 7 
 
 w 
 
 ( 
 
 7 
 
 
 7 
 
 7 
 
 7 
 
 7 
 
 14 
 
 24 
 
 34 
 
 44 
 
 54 
 
 G4 
 
 etc. 
 
 
 
 
 9 
 
 19 
 
 29 
 
 39 
 
 49 
 
 59 
 
 G9 
 
 79 
 
 89 
 
 99 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 IG 2G 3G 4G etc. 
 
 When the various combinations with each of the nine 
 digits have been made thus in tlie form of decades, the 
 pupils may be required to review them by writing on 
 their slates, in groups, combinations of two numl)ers 
 each, that, when added, will produce in the unit figures 
 the following: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 
 
 By means of these and similar exercises, children 
 can be led to observe that the same numbers always 
 produce. a like figure Avhen added, as that 9 and 7 
 always give the unit G, whether the numbers be 19 
 and 7, or 29 and 7, or 37 and 9, or 87 and 9 ; and thus, 
 by attending to this fact, while adding single columns, 
 they can readily acquire the habit of adding icithont 
 cou7iting. One of the most effectual means toAvard se- 
 curing this habit, in addition to the adding by decades, 
 
54 HOW TO TEACH 
 
 is to teach the pupils to give special attention to the 
 figure representing the units as each successive number 
 is added, i. e., attention to adding the units. 
 
 To explain this process, the teacher may write a col- 
 umn of figures on the blackboard, as represented here 
 
 a. h. by the one marked a. Then the pupils may be 
 
 7 — led to notice the unit figure in each case by 
 
 8 — 3 the teacher's pointing to the successive num- 
 
 9 — 5 bers to be added, and saying: "8 and 9 
 
 6 — will give 7 for the unit figure ; 7 and 5 will 
 
 8 — give 2 ; 2 and 9 will give 1 ; 1 and 9 a ; 5 
 
 7 — 2 and 7 Avill give 2 ; 2 and 8 a ; 6 and 9 a 5 ; 
 5 — 5 and 8 a 3 ; 3 and 7 a 0." 
 
 9 — During this explanatory process, the 
 9 — 1 teacher may write the unit figure opposite 
 5 — 2 the number added which produces it, as rep- 
 9 — 7 resented in the column marked h. So soon 
 
 8 — as the pupils understand this process of 
 — adding and naming the unit figures only, the 
 90 teacher should erase the column, b, repre- 
 senting these units, and require the pupils to add by 
 naming the imits, as follows: 8, 7, 2, 1, 0, 5, 2, 0, 6, 5, 
 3, 0. AY hen they can do this readily from the black- 
 board, the pupils may copy the same column on their 
 slates, and add by naming the iinits in the same manner. 
 
 Then columns made up of other figures may be given 
 for similar practice. Afterward the pupils may be 
 trained to add by naming the snm, as each number is 
 added, as follows :"'8, 17, 22^ 31, 40, 45, 52, 60, 66,75, 83, 
 90. This last form should be followed in the usual 
 practice of addition. The preceding ones are intended 
 to be used in teaching pupils hoio to add, that they may 
 acquire correct habits. . 
 
 Teachers may observelthat the number of figures in 
 the column marked b, corresponds with the number of 
 
ARITHMETIC. 55 
 
 {e7is in the sum of column a — nineji—and that 9 te7is, 
 with the last unii figure, 0, gives tne sum of column a. 
 But this fact is not of sufficient practical importance to 
 rentier it desirable that much prominence should be 
 given to it. 
 
 After pupils have been thoroughly trained in adding 
 single columns, and understand Numeration and Nota- 
 tion, they can be taught the process of "carrying" in 
 examples of two or more columns, by a few lessons. 
 For teaching the pupils "to carry," at first the examples 
 should be very short, consisting of two columns, only. 
 Afterward the examples may be made longer, gradually, 
 more difficult ones being given by extending botb the 
 length of the lines and of the columns. Give many 
 more examples Avith a few long columns than with long^ 
 lines. Care should be taken not to embarrass children by , 
 giving them long and large examples in addition before 
 they can readily add short ones. Let the training be 
 thorough in each step, and the progress gradual. The 
 work of each succeeding week ought to embrace larger 
 examples than were given during the previous one, and 
 to furnish sufficient practice to enable the pupils to 
 master all the difficulties. 
 
 Wuineration. — On commencing Numeration, the 
 three places in the unit's period should be taught by 
 the order of their places, and by tlioir names ; as, iinifs 
 place, i\\Q first place on the right-hand side; toi's place, 
 t\\& second place from the right-hand side; liundred^s 
 place, the third place from the right-hand side. AYlien 
 the pupils can name each place at sight, both in order 
 and out of order, from the blackboard, and can write 
 any number in this period from dictation, proceed to 
 teach the thousand's period in a simihir manner. Tlie 
 places in this period should be taught first as the 
 
66 now TO TEACH 
 
 fourth, fifth, and sixth places ; then the pupils should 
 be led to observe the similarity of names between the 
 first, second, and third places of the unit's period, and the 
 first, second, and third places of the tJiousand's period ; 
 as units, tens, hundreds oi units ; units, tens, hundreds 
 of thousands. When the pupils can both read and 
 write any number readily, from units to hundreds of 
 thousands, proceed in the same manner to teach the 
 million's period. Train the pupils so that they can 
 name any place at sight, in order and out of order, and 
 give the order of any place when its name is men- 
 tioned ; also write readily any number through hun- 
 dreds of millions, from dictation. Care should be taken 
 to teach the pupils to write the figures neatly, and in 
 straight columns. Two or three weeks may be spent on 
 the unit's period, before proceeding to the thousand's 
 period. 
 
 Mental Arithmetic, — In the Eighth Grade the 
 answers to the questions in Mental Arithmetic should 
 be simple and concise. The language used should be 
 sufficient to render the solution of the example, and the 
 answer to it, clearly intelligible to a listener, yet so brief 
 as not to retard, unnecessarily, the process of mental 
 calculation. Appropriate forms for answering questions 
 in ]\Iental Arithmetic, in the Eighth Grade, may be seen 
 in the following examples: 
 
 How many are six apples and three ajiples ? 
 Ans. — Six apples and tliree apples are nine apples. 
 
 If a coat cost $15, and a hat $5, how much will both 
 cost? Ans. — Both will cost the sum of 815 and 85, 
 which is 820. 
 
 Henry had 8 marbles and bought 4 more ; how many 
 marbles had he then ? Ayis. — Henry then had the sum 
 of 8 marbles and 4 marbles, Avhich is 12 marbles. 
 
ARITHMETIC. 57 
 
 A boy had 9 apples and gave away 5 of them ; how 
 many apples had he left ? A)is.—ile had 4 apples left ; 
 because, when 5 apples are taken from 9 apples, 4 apples 
 will remain. 
 
 3lHltipUcation Table,— In presenting the Mul- 
 tiplication Table, it is very desirable that each step be 
 thorouglily mastered before taking the succeeding one. 
 This table may be illustrated first by means of balls on 
 the numeral frame, by arranging the balls in groups of 
 twos, tlien of threes. When the groups of tioos have 
 been illustrated by the balls, the teacher may write the 
 table of twos on the blackboard, thus : 
 
 First Form. Second Form. First Form. 
 
 2 times 2 are 4 3x2= 6 2x3= 6 
 
 3 « 2 " 6 6x2 = 12 3x3= 9 
 
 4 " 2 " 8 9x2 = 18 4x3 = 12- 
 
 5 " 2 "10 4x2= 8 5x3 = 15 
 
 6 « 2 "12 7x2 = 14 6x3 = 18 
 
 7 « 2 " 14, etc. 5 x 2 = 10, etc. 7 x 3=21, etc. 
 
 On placing the Second Form before the class for the 
 first time, the teacher should explain the use of the 
 signs x and =. The pupils may be told to read the 
 sign of multiplication the same as the word " times," 
 and the sign of equality the same as " are." 
 
 Let the pupils copy and learn the First Form, so as 
 to repeat it, both forward and backward. AfterAvard 
 place the Second Form on the blackboard, and let the 
 pupils give each answer orally ; also copy the table and 
 write the answers. When the table of twos has been 
 learned in both forms, teach the table of threes in the 
 First Form, then in the Second Form, and afterward 
 revieiu both of them, in combination, in a Tliird Form, 
 somewhat as follows : 
 
58 HOW TO TEACH 
 
 Third Form. 
 
 4x2= 8x3= 9x3= 4x3= 
 
 5x3= 5x2= 8x2= 6x3 = 
 
 9x2= 7x3= 2x6= 7x2= 
 
 2x3= 6x2= 3x4= 3x9 = 
 
 All the tables may be taught on the same plan — first 
 in order, then out of order, then by combination with 
 the tables previously learned. New tables should not 
 be presented before the pupils have learned thoroughly 
 each preceding one through the three forms. 
 
 Moinan Niunhet'S, — In the Eighth Grade, the 
 Key to Eoman Numbers should be explained to the 
 pupils, and numerous applications of it made to a vari- 
 ety of combinations, viz.: When letters representing 
 equal values stand side by side, and when a letter rep- 
 resenting a smaller number stands on the right-haxid 
 side of one rejDresenting a larger number, the values of 
 each are to be added, as II tioo, XX twenty, VI six, XV 
 fifteen, LX sixty, XXX thirty. When the letter repre- 
 senting a smaller number stands on the /f/V-hand side 
 of one representing a larger number, the value of the 
 Ze/^-hand letter is to be taken from the value of the 
 right-h^wd letter, as, the value of I is to be taken from 
 the value of V in the combination IV, which gives 
 four, the number represented by IV ; the value of X 
 taken from the value of L in XL gives forty as the 
 number represented by XL, etc. Training the pupils 
 in numerous applications of this Key Avill save much of 
 the time usually spent in memorizing the Roman Num- 
 bers. It will be well to give unusual combinations, 
 occasionally, as— VL ; VC; VX; VV; XXXX ; LC; 
 XLLV ; etc., and request the pupils to apply the Key 
 and tell what number each stands for. 
 
OBJECT LESSONS. 59 
 
 OBJECT LESSONS. 
 
 Fovni, — Special care should be taken, in teaching 
 various Forms and Solids, to cause the pupils to dis- 
 cover the given shape in other objects than those shown 
 by the teacher from the set of " Oliject-Teaching Forms." 
 For the accomplishment of this purpose frequent re- 
 views should be had, without presenting the forms which 
 represent the shapes that have ah'cady been learned, 
 when the pupils may be requested to mention several 
 objects of the given shapes. 
 
 Lead the pupils to observe that all prisms have oblong 
 sides, and all py)-amids triangular sides; that prisms 
 differ in the number of tlieir sides, and in the shape of 
 their ends ; that pyramids differ in the number of their 
 sides, and in the shape of their bases. 
 
 Lines and Angles. — In teaching pupils what consti- 
 tutes parallel lines, lead them to notice the fact that the 
 lines are side-bi/-side ; that they are the same distance 
 apart at all opjjosite points ; afterward, in a subsequent 
 grade, they can easily be led to observe that both lines 
 extend in the same direction ; also that they can never 
 meet. 
 
 In previous grades, the pupils have become familiar 
 witli the terms sharp, square, and blunt, as applied to 
 cornel's ; use this knowledge to illustrate the different 
 kinds of angles, and give the terms acute, right, obtuse, 
 to be applied to angles, instead of sharp, square, and 
 blunt. In explaining the terms relative to lines, angles, 
 diameters, etc., each of them should be illustrated on 
 the blackboard, and the pupils also required to repre- 
 sent them on their slates. 
 
60 EOW TO TEACH 
 
 Color, — All tlie lessons on Color should be illus- 
 trated with « Color-Charts," " Color-Cubes," " Colored 
 Cards," pieces of ribbon, silk, worsted, or other colored 
 objects ; also with good water-colors. Care should be 
 taken to make the pupils understand that by mixing 
 two Primary colors, a Secondary color will be jiroduced ; 
 also that no Primary color can be formed by mixing two 
 Secondary colors. They should also be taught Avliich 
 Primary colors will produce each of the Secondary 
 colors ; and what two Primary colors each Secondary 
 color contains. 
 
 If desired, more definite directions relative to this 
 matter may be found in New Primary Object Lessons. 
 
 Suniau JSody, — It is important that the pupils 
 should learn to point out the location of those bones 
 and other parts of the body for which they are taught 
 names and uses. 
 
 Animals* — The lessons on animals should at first 
 be conversational, and of such a character as to lead 
 the children to notice, when away from school, the 
 various kinds of movements of different animals, as, 
 walking, running, jumping, hojiping, flying, swimming, 
 etc. ; so that they may be able to tell Avhat animals 
 move in a given manner. 
 
 After the teacher has led the children to observe the 
 different classes of animals, as beasts, birds, fishes, etc., 
 by showing them pictures of each, let them be requested 
 to give the names of some animals of each class which 
 they have seen. The names thus given miglit be writ- 
 ten on the blackboard in groups corresponding to their 
 several classes. 
 
 During these lessons on animals, let the names of 
 those used for food, and of their flesh, be written on the 
 
OBJECT LESSONS. 61 
 
 blackboard as the children mention them, and the 
 spelling of each be taught. 
 
 Plants, — After talking with the children about 
 different kinds of flowers, plants, grains, fruits, trees, 
 etc., which they have seen, and after they are able to 
 name several of those most common, their attention 
 may be directed to different parts of trees, as, roots, 
 trunk, branches, limbs, leaves, etc. The teacher will find 
 efiicient aid in presenting this subject, by the use of 
 " Prang's Natural Jlidory Series, for Plants." 
 
 Objects, — Pupils should be led to point out and 
 name the parts of common objects, to tell the shape of 
 the parts, and the uses, color, etc., of the objects. This 
 exercise should be so conducted as to give the children 
 the ability to describe readily objects which they see. 
 
 Objects having special qualities in a prominent 
 degree should be shown, and the pupils led to observe a 
 given quality in several objects, as a means of teaching 
 them to recognize the same quality whenever it may 
 come within their observation. The spelling of the 
 words representing the objects, their parts, uses, color, 
 and qualities, may be taught. 
 
 DRAWING iiND WRITING. 
 
 Oil Slates, — AH. necessary explanations and illus- 
 trations as to the manner of drawing figures, the foima- 
 tion of small letters and capitals, should be made by the 
 teacher from the blackboard, first to the whole chiss ; 
 afterward, attention may be directed more to the work 
 of individuals of the class, for the purpose of giving 
 special instruction. 
 
G2 DRAWING AND WRITING. 
 
 Let the teacher of the class select, each day, six slates 
 from those pupils who have made the most comraeud- 
 able improvement in drawing and writing, and place 
 them on her desk for inspection by the class. If prop- 
 erly managed, this plan will prove a good incentive to 
 improvement in neatness in the drawing and writing. 
 
 Use of Pencils. — The pupils should not be allowed 
 to write with short pencils. Particular care must be 
 taken as to methods of holding both pencil and pen, 
 also to the position of the body while writing and draw- 
 ing, to avoid permanent curvature of the spine from 
 bending sideways ; and serious injury to the eyesight 
 from inclining the head too far forward, and holding it 
 too near the desk. 
 
 MANAGEMENT. 
 
 JPJiysical Traininr/, — The pupils in all the 
 grades should be exercised daily in such a manner as 
 to expand the lungs, develop the muscles, and impart 
 an easy and graceful carriage to the body. Calisthenic 
 exercises may be employed for the attainment of these 
 objects. 
 
 Five minutes spent once an hour, or even more fre- 
 quently, in simple changes of the position of the body, 
 by requiring the school or class to stand and to sit to- 
 gether three or four times in succession, also to exercise 
 the arms briskly, will do much for the physical comfort 
 of pupils, and even increase the progress in their studies. 
 
 The necessity of pure air in a school-room is a matter 
 too serious to be neglected by any teacher for a 
 single hour. Yet quite too commonly, even where 
 the means for securing it have been provided, teachers 
 carelessly neglect ventilation. 
 
SEYEISTTH GEADE. 
 
 (PRllrlARY.) 
 
 Time allowed, about jive months. 
 
 LANGUAGE. 
 
 Reading. — In a Second Reader ; with conversational tones — 
 the use of Italic letters to be explained. 
 
 PJionetics. — Sounds of short words in common use to Tjc 
 given by the pupils — exercises to be had for correcting indistinct 
 enunciation. 
 
 Definitions. — The meaning of words to be given, chiefly by 
 their use in sliort sentences. 
 
 Spelling. — Oral and written — words from the reading les- 
 sons ; also, other common words. 
 
 ARITHMETIC. 
 Addition. — With practical examples. 
 
 Subtraction. — The processes taught and practical examples 
 given. 
 
 Multiplication. — Multipliers from 1 to 12 inclusive. 
 
 Mental Arithmetic. — Practical questions \n Addition, Sub- 
 traction, and Multiplication. Also Oral Drills for rapid combina- 
 tions of numbers. 
 
 Multiplication Tafr^e.— Continued through 12 times 12. 
 
 Moman Numbers. — Reviewed. 
 
 Tables of Measure. — United States money ; time ; liquid 
 and dry measures. 
 
64 GRADED COURSE OF INSTRUCTION. 
 
 OBJECT LESSONS. 
 
 Form. — The polygons, arc, radius, and other forms. 
 
 Size. — Comparative, and measured. 
 
 Color. — Harmony of colors. 
 
 Human Body. — Organs of the senses. 
 
 Animals. — Comparison and simple classification by groups, 
 families, etc. 
 
 J'/ajjfs.— Shapes of roots, leaves, flowers, etc. Plants used 
 for food, etc. 
 
 Objects and Qualities.— Qon\hm.Q(\.. 
 
 OccujMitions. — Trades, tools, productions, commodities, etc. 
 
 GEOGRAPHY-PREPARATORY STEPS. 
 
 Place and Direction.— First. Position of objects on a 
 table. Seco7id. Position of objects in the class-room. Third. 
 Location and direction of streets and other objects near the 
 school. 
 
 DRAWING AND WRITING. 
 
 On Slates.— Words and short sentences to be written from 
 dictation ; Capitals to be used. Drawing simple figures. 
 
 On jPf/i>er.— Simple words of small letters. The pupils to 
 be taught to write their names, with theii' ages, and the date. 
 
LAIiGUAGE. 05 
 
 How TO Teach 
 
 UBJECTS OF THE SEVENTH GRADE. 
 
 LANGUAGE. 
 
 Reading, — The methods given for teaching Read- 
 ing in the Eighth Grade should be continued in the 
 Seventh Grade. It is exceedingly important that chil- 
 dren be early trained to give attention to the subject- 
 matter of what they read. 
 
 Should the teacher find her class using monotonous 
 or unnatural tones, several selections should be made 
 of reading lessons that are composed chiefly of conversa- 
 tions. These may be used for training the pupils to 
 read in easy, speaking tones. Afterwards, other selec- 
 tions may follow, and special care be taken to teach the 
 pupils to read in a pleasant, colloquial style. Call upon 
 different pupils to imitate the style of the best readers 
 in the class. 
 
 Two extremes, as to the amount of reading which the 
 class is taken over, should be avoided — that of keeping 
 the pupils too long on the same lesson, and that of 
 reading over many lessons without sufficient attention 
 to the matter and 'ina7iner of reading. The first extreme 
 destroys the pupils' interest in this exercise, and pre- 
 vents them from acquiring the habit of reading to gain 
 information ; the second leads to carelessness in manner, 
 and the habit of reading without sufficient attention to 
 the subject of the lesson, and to what is related con- 
 cerning it. 
 
CG HOW TO TEACH 
 
 The use oi Italics should be ilhistrated from the black- . 
 board first, and afterward the pupils should be required 
 to find examples in reading lessons, and to tell why the 
 given Italic words are used. 
 
 Phonetics. — Care should be taken, in conducting 
 the exercises in sounds, to train the pupils in habits of 
 distinctness of enunciation, and in the use of smooth 
 tones of voice ; — uttering the separated sounds of words 
 will aid in accomplishing the first ; and making the 
 sounds with varying pitches and different volumes of 
 voice will aid in producing the second. Silent letters 
 should be pointed out by the pupils. They should 
 also be required to tell what sound each letter has in 
 given words, and to make the sound. These sounds 
 may be described somewhat as follows: — Call, c has 
 the sound of h, a has its fourth sound, the first I 
 has its own sound, the second / is silent. Bought, 
 1) has its own sound, ou represent the fourtli sound 
 of a, gh are silent, t has its own sound. Think, th 
 are sounded together, i has its second sound, n has 
 the sound of ng, h has its own sound. 
 
 Definitions. — All modes of teaching that will 
 allow pupils to give mere memorized definitions, with- 
 out the ability to illustrate the meaning of the given 
 Avords by their use in complete sentences should be 
 avoided. During the exercises in definitions, the 
 pupils' faults of language should be corrected. 
 
 Spellinf/. — The exercises for teaching spelling in 
 the Seventh Grade may be continued as in the Eighth 
 Grade. 
 
ARITUMETIO. G7 
 
 ARITHMETIC. 
 
 Addition, — The exercises in this grade should be 
 extended to examples with from four to six columns of 
 twelve or fifteen figures each ; and with occasional 
 examples of six or eight lines, embracing millions. 
 Practical examples, relating to matters of daily occur- 
 rence in business, should be given. 
 
 Exercises for training the pupils to add without 
 counting should be continued in this grade in a man- 
 ner similar to those described for the Eighth Grade, on 
 pages 52, 53 and 5-i. 
 
 Suhtvciction. — The processes of Sultraction may- 
 be arranged in three steps, and taught in their order, 
 as follows, viz. : 
 
 First Step. — With short examples in which each figure 
 in the subtrahend represents a number that is smaller 
 than the one above in the minuend. 
 
 Second Step. — With examples in which it is neces- 
 sary to take or " to borrow " from the column of a 
 hi2:her denomination. 
 
 Third Step. — With examples having naughts in the 
 minuend, making it necessary to take from the third 
 or fourth column on the left. 
 
 The Second and Third StejJS may be illustrated first 
 by the use of bundles of sticks ; also by tlie use of cents, 
 dimes, and dollars, somewhat as follows : From 5 dollars, 
 4 dimes, and 2 cents take 2 dollars 8 dimes and 5 cents. 
 Since 1 have only 2 cents, I must take one of the dimes 
 
68 HOW TO TEACH 
 
 and get it changed into cents. This will leave 3 dimes, 
 and give me 12 cents in all. From the 12 cents I can take 
 5 cents, and 7 cents Avill remain. I wish to take 
 away 8 dimes, but find that I have only 3 dimes remain- 
 ing ; therefore I must take one of the dollars and get 
 it changed into dimes, which will leave 4 dollars, and 
 give me 13 dimes in all. Now I can take away 8 dimes 
 and have 5 dimes left. Then I can take 2 dollars from 
 4 dollars, and have 2 dollars left. This explanation 
 may be followed by another in which the same figures 
 (542 — 285), are used as uniis, tens, and Mmdreds. 
 
 The process of representing these illustrations may 
 be shown on the blackboard, thus : 
 
 40 10 
 
 4 3 10 4 3 10 
 
 $^ 4d 2c 0h. ^t. 2 units 
 
 2 8d 5c 2 8 5 
 
 $2 5d 7c 2 5 7 
 
 Afterward the process of the Second and Tliird Stejjs 
 may be further represented on the blackboard, with 
 common examples in subtraction, by cancelling the 
 figures from which one has heeji taken, and Avriting the 
 remainder above it thus : 
 
 
 
 9 9 10 
 
 3 10 5 10 
 
 5 10 1 10 
 
 3 i0 J:0 4 10 
 
 ^203 
 
 10 3^0 
 
 2 4 0^0 
 
 14 4 5 
 
 15 4 15 
 
 13 5 4 5 3 
 
 2818 905 104597 
 
 After this process, commonly called " borrowing " 
 
 (but which is really a change in a part of the higher 
 
 denomination without altering the value of the entire 
 
 number), has been illustrated on the blackboard by the 
 
ARITHMETIC. G9 
 
 teacher, the pupils should be required to copy on their 
 slates the same examples, also the process of takiiig 
 from a figure representing a number of a higher denom- 
 ination, by cancelling ; then similar examples should 
 be o^iven them to write out in full, that they may become 
 familiar with the process of taking from, by cancelling. 
 Fonns of illustration for explaining a subject should 
 be continued no longer than maybe necessary to enable 
 the pupils* to understand the subject. The process of 
 cancelling in illusti^ting subtraction should be used for 
 a few days only. When it is first dropped, another plan 
 may be adopted to represent the changes in the figures. 
 A dot may be placed over the figure in the minuend to 
 indicate that it must be considered one less in the sub- 
 traction, thus : 
 
 4263 16320 240050 
 
 1445 15415 135453 
 
 2818 905 104597 
 
 In subtracting these examples, the pupil might say : 
 3 from 10 leave 7 ; 5 from 14 leave 9 ; 4 from 9 leave 5 ; 
 5 from 9 leave 4 ; 3 from 3 leave ; 1 from 2 leaves 1 — 
 remainder 104,597. 
 
 This process is shorter and less liable to mistakes in 
 practice than the common way of " borrowing one " 
 from a figure in the minuend, and " carrying one " to 
 the next figure in the subtrahend ; besides, it prepares 
 the way for readily understanding the operations in 
 " Compound Numbers." 
 
 3Iiiltij)Ueation, — Instruction in regard to the 
 processes of mtdtiplication may be presented in four 
 steps, as follows: 
 
■^0 now TO TEACH 
 
 First Step. — Give examples in which no single prod< 
 net will exceed nine, as 
 
 243 3,142 3,231 231,232 
 
 2 2 3 - 3 
 
 486 0,284 9,693 693,096 
 
 Second Step. — Give examples in which it will be neces- 
 sary " to carry " to the next column, including multi- 
 pliers of a single figure only, from 2 to 5, as : 
 
 345 4,583 2,435 32,563 
 
 2 3 4 5 
 
 090 13,749 9,740 102,815 
 
 Tliird Step. — Give examples, including naughts in the 
 multiplicand, and use as multipliers 6, 7, 8 and 9. 
 
 2,034 3,102 14,020 10,050 
 
 6 7 8 9 
 
 12,204 21,714 112,100 90,450 
 
 Fourth Step. — Give examples Avith multiplicands, as 
 in the third step, and use for multipliers 10, 11 and 12. 
 Teach the pupils where to write thejlrst figure in each 
 partial product. 
 
 24,065 3,108 40,207 
 
 10 11 12 
 
 240,650 3108 80414 
 
 3108 40207 
 
 34,188 482,484 
 
 First, illustrate the step on the blackboard, then give 
 the pupils similar examples for practice on their slates. 
 When they have become familiar with one step, proceed 
 with the next in order. 
 
ARITUMETIG. 71 
 
 Mental AritJimetic. — The forms of the answers, 
 in this gnide, may very properly employ more language 
 than in the preceding grade. The following examples 
 and solutions of them will represent suitable forms : 
 
 Examples : — A man paid $12 for a barrel of flour, 88 
 for a ton of coal, and $5 for a load of wood ; how much 
 did he pay for all ? Ans. He paid for all the sum'of 
 $12, $8, and 15, which is $25. 
 
 A farmer paid $40 for a cow, and sold her for $36 ; 
 how much did he lose ? A71S. He lost the difference 
 between 836 and 840, which is $4. 
 
 What will 5 oranges cost, at 4 cents each ? Ans. If 
 one orange costs 4 cents, 5 oranges will cost 5 times 4 
 cents, or 20 cents. 
 
 Oi'cil Drills. — Exercises for the rapid combination of 
 numbers should be introduced during this grade, in 
 addition to a continuation of drills by the " decades." 
 
 The class may be trained to add several numbers, and 
 each pupil to write the result on a slate, or give it 
 orally. The teacher may give 7 + 3 + 4 + 5 + 6-1-4 + 2 + 4 
 + 5, are how many ? In giving these examples for ad- 
 dition, the teacher may say, at first, 7 and 3 and 4 and 
 5, etc. Subsequently the pupils should be taught the 
 meaning of the word phis^ and then these examples 
 may be given thus : 7 plus 3 plus 4 plus 5, etc. 
 
 Each pupil, having added these numbers mentally, 
 should write the sum obtained on the slate, and the 
 teacher should then ascertain which pupils have per- 
 formed the addition correctly. 
 
 3Iii7fipUcation Tables.— Vlhen all of these 
 tables, through 12 times 12 have been taught by the 
 
73 HOW TO TEACH 
 
 three forms as described in the Eighth Grade, they may 
 be reviewed from the blackboard in the following form, 
 the pupils reading thus: 5 times 6 are 30 ; 6 times 5 
 are 30 ; 9 times 5 are 45 ; 5 times 9 are 45, etc. 
 
 5 X 6 are 30 ; 6 x 5 are 30 
 9x5 " 45; 5 x 9 " 45 
 
 7x6 " 42; G x 7 " 42 
 
 4 X 8 are 32 ; 8 x 4 are 82. 
 6x8 " 8x6 " 
 
 5x8 " 8x5 " 
 
 4x9" 9x4" 7x9" 9x7" 
 
 In writing these tables on the blackboard for this 
 review, the several products may be omitted, and the 
 pupils required to give them from memory. At this 
 stage the teacher should explain the use of the sign ( x ) 
 of multiplication. 
 
 Monian Wumhers. — Eeview and give further 
 applications of the key, as indicated in the directions 
 relative to this subject for the Eighth Grade. 
 
 Tables of 3Ieasure, — The tables of weights and 
 measures should be introduced first, by talking with 
 the pupils al)Out their experience in the use of them, 
 and by familiar illustrations given by this means. 
 Tlius the table of United States money may be illus- 
 trated by cents, dimes, and dollars ; that of liquid 
 measure, by what the children know about buying milk, 
 molasses, kerosene, etc., by the pint and quart ; that of 
 dry measure, by purchases at the grocery, by quarts, 
 small measures, pecks, etc. ; that of time, by observing 
 the hours marked on the clock, aud by attention to the 
 days, weeks, months, etc. 
 
 After talking with the pupils about the uses of a 
 given table, write it on the blackboard, and let them 
 repeat it ; then they may coi)y the items on slates, both 
 
ARITHMETIC. 
 
 73 
 
 in the order of the table and in a different order. Con- 
 tinue the repetition and copying until the table is 
 thoroughly learned. Each of tlie tables may be present- 
 ed and learned in a similar manner. 
 
 TABLES FOR THE SEVENTH GRADE. 
 
 United States Money. 
 
 10 mills make 1 cent. 
 10 cents " 1 dime. 
 10 dimes " 1 dollar. 
 10 dollars " 1 eagle. 
 
 IjIQuid Measure. 
 
 4 frills make 1 pint. 
 2 pints " 1 quart. 
 4 quarts " 1 gallon. 
 3l| galls. " 1 barrel. 
 
 100 cents make one dollar. 
 50 " " one-half dollar. 
 25 " " one quarter of 
 
 a dollar. 
 75 cents make three quarters 
 
 of a dollar. 
 
 Dry Measure. 
 
 2 pints make 1 quart. 
 
 2 quarts " 1 small measure. 
 
 8 quarts " 1 peck. 
 
 4 pecks " 1 bushel. 
 
 60 seconds make 
 60 minutes " 
 24 hours " 
 
 7 days " 
 
 :^0 or 31 days " 
 12 months " 
 52 weeks " 
 
 365 days 
 
 100 years 
 
 Time 
 
 1 minute. 
 1 hour. 
 1 day. 
 1 week. 
 1 month. 
 1 year. 
 1 year 
 1 year. 
 1 century 
 
 Measure. 
 
 Seasons of the Tear. 
 
 Spring, 
 
 Summer, 
 
 Autumn, or Fall, 
 
 Winter. 
 March, J 
 
 April, V Are the Spring mos. 
 May, 
 
 Days of the Week. 
 
 Sunday, 
 
 Monday, 
 
 Tuesday, 
 
 Wednesday/ 
 
 Thursday, 
 
 Friday, 
 
 Saturday. 
 
 June, 
 July, 
 August, ) 
 
 September, 
 
 October, 
 
 November, 
 
 December, 
 
 January, 
 
 February, 
 
 Are the Summer 
 months. 
 
 Are the Autumn, 
 or Fall months. 
 
 Are the Winter 
 mouths. 
 
74 now TO TEACH 
 
 Revieiv. — In reviewing these tables, the teacher may 
 question the pupils somewhat as follows : Hoav many 
 hours make a clay? How many days make a year? 
 How many days make a week ? How many weeks 
 make a year? How many minutes make an hour? 
 How many months make a year? What is the shortest 
 measure of time ? What does it take to make the long- 
 est measure of time ? How many quarts make a gal- 
 lon ? How many quarts in three gallons ? How mSny 
 quarts make a peck ? How many pints in tAVO quarts ? 
 How many quarts in two pecks ? Which is more, one 
 bushel or three pecks ? 
 
 A variety of similar questions may be asked after the 
 tables have been learned in their order. 
 
 OBJECT LESSONS. 
 
 It is not intended that each topic under this heading 
 shall be made the subject of a lesson each day ; but it 
 is expected that a lesson will be given each day upon 
 some one of these topics, and that these shall be varied 
 so as to embrace all the topics of the grade during each 
 month. Much more time and a greater number of les- 
 sons will be required for some of these topics than for 
 others. 
 
 Form. — It is very desirable to have the manner of 
 presenting the lessons on this subject varied in eacli 
 succeeding grade, so as to avoid the possibility of mem- 
 orizing and reciting any formula. To secure this end, 
 let the reviews of the matter taught in preceding grades 
 be so conducted as to compel attention to the shape of 
 the various objects. 
 
OBJECT LESSONS. 75 
 
 By requiring the pupils to describe the shape of ob- 
 jects phicecl before the class, the teacher will be enabled 
 to test their knowledge of form. 
 
 Si^e. — This subject may be illustrated by various ob- 
 jects, as strings of different sizes and lengths, slips of 
 paper of different lengths and widths, and small pieces 
 of wood. The pupils Avill obtain clear perceptions of 
 size and of length, by being required to judge of the 
 size and length of objects before them, and of lines on 
 the blackboard, then to measure these and ascertain 
 the approximate correctness of their estimates. Draw- 
 ing lines of given lengths on the slate, followed by a 
 careful measurement of them, is a valuable means for 
 training pupils to accuracy in determining size and 
 length by the eye. 
 
 Color,~The lessons on color, for this grade, should 
 lead the pupils to perceive that some colors appear well 
 when placed side by side, while others do not. For 
 this purpose lead them to compare red and greeti with 
 blue and green j blue and orange with yelloiu and orange; 
 yelloiu and purple Avith blue and puriole, or red and 
 pur fie. 
 
 All lessons on color should be illustrated with colored 
 objects. Pieces of ribbon, silk, worsted, colored paper, 
 water colors, etc., may be used for this purpose. 
 
 Suinan Body. — In teaching children the names 
 and uses of the organs of sense, and their parts, special 
 effort should be made to lead them to understand the 
 subject by means of observations made with their own 
 organs of sense. The actual seeing, hearing, feeling, 
 tasting, and smelling of objects teach children facts 
 
76 now TO TEACH 
 
 which it is impossible to convey to their minds by 
 means of the memorizing of language, however 
 thorough and precise. 
 
 Animals, — The lessons on this subject should lead 
 the children to notice the most distinguishing points in 
 the structure of animals, and to see how their structure 
 is adapted to their habits of life ; for instance, how the 
 webbed feet of some birds fit them for swimming, and 
 how the long legs of others fit them for wading ; how 
 the strong claws and strong beaks of some birds enable 
 them to feed on flesh ; how the cusliion-like feet of the 
 cat enable it to walk noiselessly about in search of its 
 prey ; liow the teeth of the cat and dog are fitted for 
 tearing flesh, while those of the rat and squirrel are 
 formed for -cracking nuts and gnawing hard sub- 
 stances. 
 
 The chief aim of these lessons being to train the pu- 
 pils in habits of observing nature, so that they may be 
 enabled to gain therefrom the most useful knowledge, 
 the exercises should be conducted in such a manner as 
 to lead them to notice accurately the structure and 
 habits of the various animals that come within their 
 own observation. Tlie facts thus learned should be, by 
 the aid of the teaclier, properly classified, as a founda- 
 tion for subsequent study of the same subject. 
 
 JP ran ff^s Natural History Series, with the "Man- 
 ual " which accompanies it, will be found a valuable aid 
 in giving instruction on Animals and Plants. 
 
 JPlaiits. — The lessons on plants, in this grade, may 
 appropriately lead the pupils to learn the most common 
 sJuqjes of roots, as turnip-shaped, branching, fibrous, 
 
OBJECT LESSONS. 77 
 
 conical, tnberons, etc.; also the shapes of leaves, as 
 needle-shaped, arrow-sliaj)ed, egg-shaped, heart-shaped, 
 hand-shaped, etc.; also the common shapes of flowers, 
 as funnel-shaped, bell-shaped, pink-shaped, butterfly- 
 shaped, helmet, shaped, cross-shaped, etc. By suitable 
 exercises the teacher should also direct the attention of 
 the pupils to plants which are used for food, xind lead 
 them to observe their mode of growth, form, uses, etc. 
 
 Objects and Qualities, — Two distinct classes of 
 exercises may be given under "this heading. One con- 
 sists in training the pupils to distinguish given quali- 
 ties, by using several objects having the same quality, 
 for illustration ; the other, which is more appropriate 
 for review exercises, requires the pupils to ascertain 
 what qualities a given object possesses. Instruction on 
 this subject cannot be considered complete without the 
 use of both of thesa classes of exercises, in their proper 
 order. 
 
 Observation and Comparison, — Habits of 
 observing various objects, and noticing their several 
 shapes, colors, qualities and materials of Avhich they are 
 made, are exceedingly useful as a means of gaining 
 knowledge ; yet habits of comparing two or more ob- 
 jects, and observing what qualities, shapes, colors and 
 materials they possess in common, constitutes an ad- 
 vanced stage of development which not only adds addi- 
 tional power of gaining knowledge, but gives to the 
 possessor practical ability in whatever sphere of life that 
 person may be placed. 
 
 In the preceding grades the pupils have been taught 
 to distinguish, and to name the common forms, colors. 
 
78 now TO TEACH 
 
 and most obvious qiudities. It is therefore appropriate 
 that they now should be trained to discover which 
 of these forms, colors, and qualities may be found in 
 given objects to which their special attention may be 
 directed. 
 
 This kind of training should be so conducted as to 
 develop the individual powers of the pupils. To ac- 
 complish this, the teacher must avoid asking such 
 questions as might suggest to the pupil what to say, 
 rather than leave him to discover the shape, color, qual- 
 ity, or material without aid. The teacher should aim 
 to train the pupils to discover the principal character- 
 istics of an object, instead of telling them what those 
 characteristics are, and then asking them questions to 
 see if they remember them. 
 
 Steps somewhat like the following are appropriate to 
 be taken by the teacher : — 
 
 First. Write on the blackboard the words. Materi- 
 als, Shapes, Colors, Qualities, leaving room to Avrite 
 other words under each. Then place some object be- 
 fore the pupils, as a common slate, and i-equest them to 
 tell what materials, shapes, colors, and qualities they 
 observe in it. As these are mentioned by the pupils, 
 singly, the teacher may write the word on the black- 
 board under its appropriate heading. When the lesson 
 is finished, the blackboard will contain something like 
 
 the following : 
 
 
 
 Materials. 
 
 Shapes. Colors. 
 
 Qualities. 
 
 slate, 
 
 oblong, black. 
 
 opaque. 
 
 wood, 
 
 right angles. 
 
 brittle. 
 
 iron. 
 
 
 combustible. 
 
OBJECT LESSONS. 
 
 79 
 
 Occupations. — The exercises on this topic should 
 cause the children to ascertain the names of tools used 
 in different occupations, and Avhat is done with these 
 tools ; also what articles are made or produced. For 
 instance, the teacher might write on the blackboard 
 the word carpenter, shoemaker, or painter, and request 
 the pupils to ascertain what tools are used by those who 
 pursue the given trade, and report on the next day after 
 the subject is thus assigned — the teacher writing the 
 names of tools mentioned by the pupils on the black- 
 board, and the pupils copying them subsequently on 
 their slates. These exercises will furnish an excellent 
 opportunity for practice in observation, and in describ- 
 ing what has been seen. They may be made useful, 
 also, for first lessons in composition. 
 
 The form in which these lessons may be placed on 
 the blackboard is represented by the following : — 
 
 Name of Occupation. Tools used. 
 
 Carnenter \ ^*^' '^^^'^^' t'liisel, Auger, Awl, 
 ^ ■ I Hammer, Mallet, Rule, Square. 
 
 Shoemaker. 5 ^?^*'^°i;«'^^'' 
 ( Pincers, Hammer. 
 
 PAintpr 5 Pots, Brushes, 
 i-ainter. | Knife, Ladder. 
 
 CABINET-MAKER. 
 
 Tools Used. 
 
 Materials. 
 
 Articles Made. 
 
 Saws, 
 
 Black-walnut, 
 
 Tables, 
 
 Planes, 
 
 Mahogany, 
 
 Stands, 
 
 Chisels, 
 
 White Oak, 
 
 Bureaus, 
 
 Bits, 
 
 Cherry, 
 
 Sofas, 
 
 Hand-screws, 
 
 Pine, 
 
 Bedsteads, 
 
 Squares, 
 
 Glue, 
 
 Desks, 
 
 Scrapers, 
 
 Varnish, etc. 
 
 Book-cases, 
 
 Mallet. . 
 
 
 Sideboards. 
 
80 HOW TO TEACH 
 
 GEOGRAPHY- PREPARATORY STEPS. 
 
 Place and Direction, — The exercises in this 
 subject must be objective in their character ; and they 
 should be conducted with a view to prepare the 
 pupils for understanding the elementary steps of Geog- 
 raphy. The manner of giving the lessons in steps will 
 prove most useful to the pupils. 
 
 First Step. — Train the pupils to observe and de- 
 scribe the position of objects on the table in front 
 of them, using the terms right, left, front, back, front 
 left-hand corner, back right-hand corner, etc. Then 
 let the teacher represent the positions of these objects 
 on the blackboard. Afterwards request the pupils to 
 copy the representation from the blackboard, on their 
 slates. 
 
 Second Step. — Train the pupils to notice and describe 
 the positions of the parts of the class-room, and of the 
 principal articles in it, as: door, windows, blackboard, 
 seats, table, chair, closet, etc. 
 
 The teacher should draw the outlines of the class- 
 room, and represent the positions of the articles in it, on 
 the blackboard, at the same time requiring the pupils 
 to tell where to place the representation of each object, 
 before draAving it. Subsequently the pupils should 
 copy the same on their slates. 
 
 Thi7'(l Step. — Teach the pupils the location of the 
 streets near the school, and require them to observe and 
 tell in what streets they go while on their way to and 
 from school. Tlie terms of direction, as east, west, 
 north, south, may be introduced in this step, and the 
 
DRAWING AND WRITING. ■ 81 
 
 Points of Compass taught. Represent the locations of 
 streets, buildings near the school, etc., on the black- 
 board, and let the pupils coj^y them, as before. 
 
 DRAWING AND WRITING. 
 
 On Slates. — The lessons in Drawing and Writing 
 for this grade, must necessarily be simple, yet they 
 should be progressive, and so arranged as to lead to a 
 proper training of the eye and hand ; indeed this train- 
 ing should be made a prominent object. The black- 
 board should be used much in illustrating the exercises 
 of both drawing and writing. Enlarged copies of good 
 drawing cards, also simple drawings from objects may 
 be made on the blackboard, and the pupils required to 
 copy them on their slates. 
 
 Care should be taken to teach the pupils proper posi- 
 tions for sitting, for holding their slates, also for the 
 hand and fingers in holding the pen or pencil. 
 
 On Paper, — When writing is commenced with 
 ink, do not confine the pupils too long to making the 
 simple elements of letters ; let them learn to write 
 simple words as soon as practicable. It is not necessary 
 that the pupils should write all the lines under each 
 copy of a common writing-book. Whenever the pupils 
 have made sufficient progress to be able to proceed with 
 the next copy in order, let them go on with it. But 
 there should be system in the progress ; all the pupils 
 in the grade should receive instruction relative to the 
 same points, and write the same words simultaneously ; 
 thus all will attend to the same thing, at the same time, 
 and proceed to a new lesson together. Faults in writ- 
 
82, HOW TO TEACH. 
 
 ing should be pointed out and illustrated on the black- 
 board, and such directions given as will enable the 
 pupils to correct those faults. 
 
 Before leaving this grade, the joupils ought to be able 
 to write simple words neatly with the pen; and to 
 write their own names, and their age ; also the day of 
 the month, and the year, in a proper form for dating a 
 letter. Tliey should also be able to write familiar 
 words, and short sentences from dictation, readily and 
 plainly. 
 
SIXTH GEADE. 
 
 (highest primary.) 
 Time allowed, about five months. 
 
 LANGUAGE. 
 
 Reading. — Second Reader completed, or an easy Third 
 Reader coiumeuced. 
 
 Phonetics. — Words to be analyzed by sounds ; names of 
 the sounds to be stated; faults of enunciation to be cor- 
 rected. 
 
 Definitions, — The meaning of words to be given orally, 
 and in writing. 
 
 SjycUing. — Words from the reading lessons, also familiar 
 words, and short sentences from dictation, both orally, and by 
 writing on slates. 
 
 ARITmiETIC. 
 
 Addition and Subtraction reviewed. 
 
 3Iulti2)lication continued through multipliers of five figures. 
 
 Division. — Both the long and the short forms. Simple 
 practical examples to be given in each of these rules. 
 
 Mental Arithinetic. — Practical examples in each of the 
 four simple rules. 
 
 Division Table. — Taught in connection with a review of 
 the Multiplication Table, 
 
84 now TO TEACH 
 
 Tables of Weight and Pleasure.— The tables of Com- 
 mon or Avoirdupois Weight, of Long, Cloth, and Surface meas- 
 ure, also a miscellaneous table to be taught, and those of the 
 Seventh Grade to be reviewed. 
 
 OBJECT LESSONS. 
 
 Form. — The shapes of objects to be compared and described, 
 and their resemblances and differences stated. 
 
 Hnmafi Bodij.— Lessons to be continued as in previous 
 grades, and extended. 
 
 Animals. — Comparison and classification continued; also 
 size, and where found. 
 
 Plants. — Parts of leaves; shapes of margins; shapes of 
 flowers ; and comparison of members of the same, and of difier- 
 ent families of flowers. 
 
 Oftjecfs.— Various objects to be examined and their shape, 
 color, most obvious qualities, and properties to be stated. The 
 distinctions between miuer^ vegetable, and animal substances 
 to be taught. 
 
 Occupations.— Exercises to give the pupils habits of observ- 
 ing and describing common productions, commodities, etc. ; also 
 to give them ideas of the exchange and sale of these. 
 
 GEOGRAPHY. 
 
 First Step.— The location and direction from the school of the 
 most prominent objects near the school, and of the places in its 
 vicinity. 
 
 Second *S^dp.— Definitions relating to the forms of land and 
 ■ water, from cards, blackboard, and outline maps. 
 
DRAWING AND WRITING. 85 
 
 Third Step. — Teach the name of the city or town, the county, 
 and state in which the pupils live, and also of the places in the 
 vicinity, showing then- location on an outline map. 
 
 Fourth Step. — Teach the shape of the Earth by means of a 
 globe and hemisphere maps. 
 
 lYftJi Step. — Teach the location of the principal countries by 
 associations with their most familiar animals, inhabitants, and 
 productions ; also the location of the warm and the cold coun- 
 tries. 
 
 DRAWING AND WRITING. 
 
 On Slates. — Writing to be continued as in the Seventh 
 Grade. 
 
 On JPajicr. — "Writing in books, from copies, with necessary 
 instructions in regard to the position of the body, hand, and 
 paper. 
 
86 HOW TO TEACH 
 
 How TO Teach 
 
 SUBJECTS OF THE SIXTH GRADE. 
 
 LANGUAGE. . 
 
 Headiuff, — Before a new lesson is read, the unfa- 
 miliar and difficult words in it should be selected, written 
 on the blackboard, carefully pronounced by the teacher, 
 and repeated by the pupils ; also both the meaning and 
 the spelling of these words should be taught; — afterwards 
 the teacher should request the pupils to find the same 
 words in their reading lessons, and to pronounce them 
 again. 
 
 Occasionally call upon a pupil to read while the other 
 members of the class close their books and listen ; then, 
 at the close of the reading request those who listened 
 to state the substance of what was read. This exer- 
 cise will train pupils to habits of attentive listening, 
 and to a proper regard to the subject-matter. 
 
 In eflForts to correct the faults of a class in reading, 
 select first the most common fault, and direct almost 
 exclusive attention to that until it is understood and 
 easily overcome by the pupils. Then select another 
 common fault and proceed in the same manner, giving 
 attention to the first one also. AfterAvard select another 
 fault, and proceed in a similar manner, giving attention 
 to the three. By this means a class may be trained to 
 perceive and overcome faults in reading, much more 
 effectively than by trying to point out half a dozen 
 different kinds of faults at once. 
 
LANGUAGE. 87 
 
 JPJionetics, — The phonic analysis of words should 
 train the pupils readily to distinguish and make all the 
 sounds in given words, also to determine wliich letters 
 are silent. It should also lead the pupils to sueii habits 
 of distinctness in articulation as will remove the faults 
 of neglecting to sound the final consonants, as d in and, 
 &(ind', r in far, car; iiig in singing, e&iing, etc.; also 
 the errors of sounding improperly both consonants and 
 vowels in the pronunciation of common words. 
 
 Xo other means is so efficient for training the orjians 
 of speech in clearness and correctness of articulation 
 as that of elementary sounds. By suitable exercises 
 with these, the ear and the vocal organs may be suc- 
 cessfully cultivated, and the means furnished to the 
 pupils for determining what are tlie correct sounds 
 of the language, how to produce them, and the ability 
 to cultivate their own organs of speech and tones of 
 Yoice. 
 
 Definitions. — Exercises in which the definitions 
 are to be written on slates, in short sentences, should be 
 introduced in alternation with oral exercises of a simi- 
 lar character. It is desirable that an oral exercise of 
 this kind, given as a lesson on one day, should be fol- 
 lowed on the next day with the same words to be defined 
 in a Avritten exercise, thus training the joupils to write 
 as Avell as to talk. 
 
 In the oral definitions, let the pupils be required to 
 tell what given words mean, in their own language, as 
 well as to use them in short sentences. One jnipil 
 may be requested to give a brief definition of a word, 
 another pupil to use it in a sentence, and another one 
 to illustrate its meaning by describing its use. Habits 
 
88 EOW TO TEACH 
 
 of reciting formal, memorized definitions would be 
 avoided by using thus several modes of giving the mean- 
 ing of the same word, and the pupils would learn to 
 define, and use words intelligently. 
 
 Spelling, — More attention should be given to writ- 
 ten than to oral spelling, in this grade. Words may 
 be dictated for the pupils to write on their slates ; short 
 sentences may be given for the same purpose ; the pu- 
 pils may be req^uested to write the names of classes of 
 objects, as names of kinds of food, articles of clothing, 
 of furniture, kinds of tools, names of occupations, of 
 animals, of trees, of fruits, of articles tbat may be pur- 
 chased at a grocery etc., etc. These exercises will enable 
 pupils to learn the spelling of a large class of words 
 in common use. 
 
 ARITHMETIC. 
 
 Addition and Suhtraction,—lt is intended that 
 the jyrocesses of adding and subtracting shall have been 
 taught so thoroughly, before the pupils are placed in 
 the Sixth Grade, that each one will be able to add and 
 subtract with facility, and with a good degree of accu- 
 racy. Now, special pains should be taken to teach the 
 uses of Addition and Subtraction by means of prac- 
 tical examples. A brief review of these rules should 
 be had at least once each week, during the entire term 
 of the Sixth Grade. 
 
 3fidti2ylicrf t ion.— Inshuciion may be arranged 
 and presented in three steps, as follows : 
 
ARITHMETIC. 89 
 
 First Step. — Crive examples with multipliers of two 
 figures only — 12 to 99. 
 
 Second Step. — Give examples with multlj)liers of three 
 figures — 100 to 999 — including some Avith naughts in 
 the multiplicand. 
 
 TJiii'd Step. — Give examples with multipliers of four 
 or five figures, containing one or more naughts. Both 
 the multiplicand and multiplier should be so varied as 
 to include all the difiiculties arising from the different 
 positions of naughts. 
 
 Pupils should be carefully trained to write the first 
 figure of each partial product in its proper place — under 
 the figure used as a multiplier. 
 
 Revieiu each step with practical examples, embracing 
 transactions that come within the observation of the 
 pupils. 
 
 Division. — This rule can be taught most thor- 
 oughly by commencing the instruction with the " Long 
 Division " form, and using a small number for a divisor. 
 Four Steps will indicate the methods and order for 
 teaching Division. 
 
 First Step. — Give examples in which each figure of 
 the dividend will contain the divisor without a remain- 
 der, thus : 
 
 3)486(243 3)963(331 
 
 4_ 9_ 
 
 08 06 
 
 8_ 6_ 
 
 06 03 
 
 6 J 
 
 
 
90 now TO TEACU 
 
 Second Step. — Give examples with the divisor less 
 than ten, in which remainders will occur during the 
 partial divisions, thus: 
 
 4)976(244 
 
 8)9856(1233 
 
 8 
 
 8 
 
 17 
 
 18 
 
 16 
 
 16 
 
 16 
 
 25 
 
 16 
 
 24 
 
 
 
 16 
 
 
 16 
 
 
 
 
 Third Step. — Give examples with divisors from 10 to 
 15, then teach the " Sliort Division " form ; and subse- 
 quently require the pupils to use the Short form for 
 all examples where the divisor does not exceed 12. 
 
 10)2540(254 
 
 11) 35G4 (324 
 
 15)345(23 
 
 20 
 
 33 
 
 30 
 
 54 
 
 26 
 
 45 
 
 50 
 
 22 
 
 45 
 
 40 
 
 44 
 
 
 
 40 
 
 44 
 
 
 
 
 
 
 
 In illustrating the Short Division form, give the same 
 examples, each with only one figure in the divisor, to be 
 worked by both the Long and the Short forms, taking 
 care to arrange the two modes so that the difference 
 in their lengtbs shall readily illustrate why one form 
 is called " Long Division," and the other one " Short 
 Division." 
 
 Fourth Step. — Give examples with divisors embracing 
 numbers from 15 to 50. Arrange these examples so 
 
AIUTHMETIG. 91 
 
 that different quotients shall contain naughts in various 
 positions. Each ste]^ should be amply illustrated on 
 the blackboard, by the teacher, then a sufficient num- 
 ber of examples given to furnish the practice necessary 
 to enable tlie pupils to understand it, before proceeding 
 to the succeeding step. 
 
 Teachers should aim first to cause their pupils to un- 
 derstand the processes of the several rules, then to iise 
 them in an intelligent manner. The object of the drills, 
 by means of numerous examples, should be accuracy, 
 first; rapidity, second; never rapidity by neglecting 
 accuracy. Practical examples should be given, in each 
 of the rules, to insure an understanding of their uses. 
 
 Mental Arithmetic. — The forms for answering 
 questions in addition, subtraction, and multiplication 
 in this grade, may be the same as for the Seventh Grade, 
 which see. Questions may also be introduced which 
 Avill require both addition and subtraction for their 
 solution, as : 
 
 Henry had 18 cents ; he gave two cents for pencils, 
 and 6 cents for a sponge ; how many cents had he left ? 
 Answer. — Henry spent the sum of 2 cents and 6 cents, 
 which is 8 cents. He then had left the difference be- 
 tween 8 cents and 18 cents, which is 10 cents. 
 
 Division. — Hoav many tops at 3 cents each can be 
 bought for 12 cents ? Ans. — As many tops as 3 cents, 
 the price of one top, is contained times in 12 cents, 
 which is four times ; therefore foiir tops can be 
 bought. 
 
 If 2 apples cost 4 cents, what Avill one apple cost ? 
 Ans. — If 2 apples cost 4 cents, one apple will cost one- 
 half of four cents, which is two cents. 
 
92 
 
 now TO TEACH 
 
 Division Tables, — The Multiplication Table may 
 be so reviewed as to enable the pupil to learn the Di- 
 vision Table easily. The following form will illustrate 
 methods for accomplishing this : 
 
 4x7 are 28 ; 4 in 28 seven times. 
 
 7x4 " 28 ; 7 in 28 four " 
 
 6x7 " 42 ; 6 in 42 seven " 
 
 7x6 " 42 ; 7 in 42 six " etc. 
 
 This review, combining Multiplication and Division, 
 should be continued through each of the tables; and 
 subsequently the teacher may review the Division Tables 
 by questions similar to the following: 
 
 How many eights in 32 ? How many sevens in 5G ? 
 How many oiines in 45 ? How many twelves in 108 ? 
 How many eights in 96 ? How many jives in GO ? 
 How many sixes in 54 ? etc. 
 
 Tables of Weif/ht and Pleasure, — The tables 
 may be taught as in the Seventh Grade, first, objectively, 
 then memorized in order ; and all the tables of both 
 the Seventh and Sixth Grades should be reviewed thor- 
 ouglily during this grade. 
 
 TABLES FOR THE SIXTH GRADE. 
 
 Common, or Avoirdupois Weight. 
 
 Long Meaburk. 
 
 16 ounces make 1 pound. 
 
 12 inches make 1 foot. 
 
 8 " "1 half ponnd. 
 
 3 feet 
 
 " 1 yard. 
 
 4 " " 1 quartcrof apound 
 
 16J feet 
 
 " 1 rod. 
 
 100 pounds " 1 hundred weight. 
 
 5i yards 
 
 " 1 rod. 
 
 20 hundred wci<;ht make 1 ton. 
 
 40 rods 
 
 " 1 furlong. 
 
 2000 pounds make 1 ton. 
 
 8 furlongs 
 
 " 1 mile. 
 
 
 320 rods 
 
 " 1 mile. 
 
 
 3 miles 
 
 " 1 league. 
 
ARITHMETIC. 
 
 93 
 
 Cloth Measure. 
 
 3 feet make 1 yard. 
 3G inches " i " 
 18 " '• i " 
 
 9 " '< J a 
 
 i\ " " \ " 
 
 A quarters " 1 " 
 
 Surface Measure. 
 
 144 square inches make 1 square foot. 
 9 " feet " 1 " yard. 
 
 30J " yards " 1 " rod. 
 160 " rods " I acre. 
 040 acres " 1 square mile. 
 
 Miscellaneous Table. 
 
 12 things make 1 dozen. 
 
 144 " 
 12 dozen 
 12 gross 
 JO things 
 24 sheets 
 20 quires 
 
 1 gi-oss. 
 
 1 " 
 
 1 great gross. 
 
 1 score. 
 
 1 quire of paper. 
 
 1 ream. 
 
 32 pouuds " 1 bushel of oats. 
 
 4S pounds make 1 bushel of barley, 
 [or buckwheat. 
 ' " 1 bushel of corn. 
 " 1 '• " wheat. 
 " 1 barrel of tlour. 
 " 1 " " pork, 
 [beef, or fish. 
 " 1 " of salt. 
 
 58 
 
 60 
 
 196 
 
 200 
 
 2S0 
 
 Review. — After these tables have been thoroughly 
 learned in order, the teacher may conduct brief reviews 
 of those of both the Seventh and Sixth Grades, by 
 questions somewhat like the following : 
 
 How many inches in three-quarters of a yard ? How 
 many yards in one rod ? Hcnv many rods in a mile ? 
 How many square inches in a square foot ? How many 
 buttons in a gross ? How many sheets of paper in a 
 quire? How many in half of a quire? How many 
 pounds in a barrel of flour ? Which is heavier, a bushel 
 of wheat or a bushel of corn ? How many pounds in 
 half of a ton? How many pecks in two bushels? 
 How many quarts in two gallons ? How many days 
 in a year ? How many months in half of a year ? How 
 many square feet in a square yard? Which is longer, 
 six feet or two yards ? 
 
94 HOW TO TEACH 
 
 OBJECT LESSONS. 
 
 The various topics embraced in Object Lessons furnish 
 far more effective means for thoroughly developing the 
 minds of children than any exercises that pertain ex- 
 clusively to reading, spelling, arithmetic, etc. Children 
 whose powers of mind have been developed by proper 
 training, so that they observe, compare, classify, and 
 describe intelligently whatever comes within the range 
 of their observation, Avill learn every subject more easily 
 than they could have done without such training. For 
 these reasons suitable attention should be given in each 
 grade, to all the topics embraced under the head of 
 Object Lessons. And teachers should keep promi- 
 nently in view the importance of these lessons as a 
 means for proper mental discipline, and not regard the 
 knowledge gained by the exercises as comprising their 
 chief value. 
 
 Due attention to these considerations will lead teach- 
 ers to regard, as of much importance, the manner of 
 giving the lesson. 
 
 Form.— The character of the instruction in this 
 subject, especially so far as it pertains to learning to 
 recognize and describe the various /or???s and solids, need 
 not differ materially in the Seventh and Sixth Grades. 
 However, when the several shapes required have been 
 learned by means of the regular forms and solids pro- 
 vided for this purpose, the time given to this topic should 
 be chieily devoted to comparing and describing other 
 objects by their shape, stating wherein those compai-ed 
 resemble each other, and wherein they differ. 
 
OBJECT LESSONS. 95 
 
 Human Sody, — The lessons in tliis grade slioultl 
 be conducted so as to review the facts learned in pre- 
 vious grades, and also so as to extend tlie pu})ils' knowl- 
 edge of the laws of health, especially so far as these 
 pertain to the condition of the skin, habits of cleanli- 
 ness, and the manner of eating. 
 
 Animals, — The manner of conducting the lessons 
 on tliis topic for the Sixth Grade classes may be nearly 
 the same as that for the Seventh Grade ; but the pu})ils 
 in this grade should be led to consider a greater num- 
 ber of animals than those in the previous one, and to ob- 
 serve more carefully the peculiarities of structure, etc., 
 with a view to extending their knowledge of classifi- 
 cation. 
 
 To aid the pupils in making groups of animals, by 
 simple classification, let the teacher write on the black- 
 board the following and similar names for groups : 
 
 Swimming Birds, Cud-cheioimj Quadrupeds, 
 
 Wadiufj Birds, Flesh-eating Quadrupeds, 
 
 Climbing Birds, Gnaioing Quadriqieds, 
 
 Scratching Birds, Insects, 
 
 Flesh-eating Birds, Reptiles, 
 
 Perching Birds. Fish. 
 
 Then request the pupils to give the names of animals 
 to be written under each heading. 
 
 These lessons relative to animals should lead the 
 children to make comparisons as to form, structure, 
 habits, size, etc., .and to learn in Avhat countries and 
 localities the .various birds and quadrupeds may be 
 found. 
 
 Praxg's Xatural History Series Avill be found 
 adapted to giving this instruction. 
 
96 , HOW TO TEACH 
 
 Plants. — The lessons on this subject in the Sixth 
 Grade may lead the pupils to consider the parts and 
 uses of leaves, their margins, parts and uses of flowers, 
 as petals, stamens, pistil, etc. ; the comparison of pinks, 
 lilies, fruit-blossoms, etc., with a view to noticing re- 
 semblances in those of the same family, and differences 
 in others; also kinds of fruits which the pupils have 
 seen — the names to be written on the blackboard, anil 
 copied by the pupils on their slates, as a spelling exer- 
 cise. The names of fruits and grasses used for food, 
 etc., may be written in groups. Like the lessons on 
 animals, these exercises should be so conducted as to 
 lead tlie pupils to form habits of carefully studying na- 
 ture, as a means of pleasure and as a source of knowl- 
 edge; therefore, the time selected for giving the lessons 
 on plants, etc., should be during the seasons when the 
 pupils can personally examine these objects. 
 
 The teacher would do well to consult two excellent 
 works by Prof. Ghay — How Plants Groto ; and IIoio 
 Plants Behave. 
 
 Objects. — In the Sixth Grade the lessons on objects 
 should include their descriptions as to form, color, and 
 most obvious qualities. In this connection, it is desir- 
 able that the pupils be led to consider what qualities 
 are necessary in the substances used for various tools, 
 utensils, articles of dress, etc. For instance, Avliat qual- 
 ity is necessary for wagon and other springs? What 
 qualities make sponge useful ? What qualities render 
 salt and sugar valuable ? What qualities give value to 
 India rubber? Wliat qualities give value to glass? 
 What to steel ? to iron ? Why will not lead make 
 good springs, or knives ? 
 
OBJECT LESSONS. 97 
 
 The lessons under this topic should cause the pupils 
 to consider wherein animals, vegetables, and minerals 
 differ from each other. Pupils will understand this 
 subject more thoroughly by presenting the instruction 
 in three steps. 
 
 First Ste]). — Request the pupils to observe slate-pen- 
 cils, pieces of stone, iron, lead, chalk, and various pieces 
 of wood, small plants, etc., and then to tell what can be 
 done with the wood and plants, that cannot be done 
 with stone, iron, etc. Also lead them to consider whether 
 both of these classes of substances are obtained from 
 the same source, and whether the iron and stone grow 
 as the wood and small plants do. When the most ob- 
 vious differences between these two classes of substan- 
 ces have been perceived by the pupils, give the term 
 Mineral as the name for one class, and Vegetable as the 
 name for the other. 
 
 Second Step. — The teacher may next call attention to 
 the three great classes of substances — mineral, vegeta- 
 ble, and animal — and lead the pupils to observe, and to 
 tell what animals and vegetables can do (as take food, 
 breathe, grow, die), which minerals cannot do. 
 
 TJiird Step. — Let the pupils be led to notice what 
 animals generally can do which vegetables generally can- 
 not do (as move from place to place by their own pow- 
 er) ; also to observe the differences between the food of 
 plants and that of animals; as that plants feed on min- 
 erals, or simple substances from the earth and air, Avhile 
 animals feed on vegetables and other animals. 
 
 The pupils might also be taught that substances 
 which once formed a part of an animal, as wool, hair, 
 bone, skin, are called animal substances; that wood, 
 
 5 
 
98 JiOW TO TEACH 
 
 bark, gum, sugar, that once formed a part of a vegeta- 
 ble, are called vegetable substances. 
 
 Occupations, — The exercises on this topic should 
 not only lead the pupils to observe and describe com- 
 mon productions, and manufactured articles, but should 
 also lead them to consider the necessity for buying and 
 selling productions and articles of manufacture ; also 
 how these are taken from those who raise or make them 
 to those who want to use them. 
 
 GEOGRAPHY. 
 
 First Step. — Review the Points of Compass, in train- 
 ing the pupils, until they are able to name any direc- 
 tion, as the teacher points, and to point in any direction 
 named. 
 
 In connection with and following the instruction 
 relative to the points of compass, lead the pupils to 
 learn the location, and the direction from the school of 
 other streets near the school ; also of prominent build- 
 ings, as churches, post-office, hotel, railroad depot, 
 etc^; or of villages, lakes, farms, groves, forest, streams, 
 etc., within the range of the children's observation. 
 The teacher should represent on the blackboard the 
 situation of the school-house, and the location and direc- 
 tion from it of the places mentioned, and allow the 
 pupils to copy the same on their slates. 
 
 Second Step. — While teaching the definitions relative 
 to i\\Q forms of land and water, present first the picture, 
 or a drawing upon the blackboard, of the object under 
 consideration, as of an island, peninsula, cape, strait. 
 
GEOGRAPUT. 99 
 
 lake, bay, river, etc. ; then sliow how the same or a 
 similar object is represented on a map. Follow this 
 with a definition to be learned by the pupils. As the 
 characteristics of each form of land or water — as that 
 an island is land entirely sw'roimded hy water — is 
 learned, require the pupils to point out on a map several 
 representations of islands, omitting the names of the 
 particular islands in this stage. Proceed in a similar 
 way to teach all the definitions. 
 
 Colton's Geographical Cards will be found of great 
 assistance as pictorial and map representations to illus- 
 trate these definitions. 
 
 During this step the instruction has for its chief 
 object training children to recognize the various forms 
 of land and watei", by means of their characteristic 
 features, and to describe each by suitable definitions; 
 hence the attention of pupils need not be directed to 
 the names and location of particular islands, isthmuses, 
 straits, bays, etc., at this time. 
 
 Third Stej). — Commence the instruction relative to 
 the names and location of particular 2:>laces with the 
 town, village, or city in which the school is situated, 
 and extend it to other places in its vicinity. No fixed 
 limit to the extent of this exercise can be given, since 
 the length to which it can be profitably carried will 
 depend, in some degree, upon the personal knowledge 
 of the members of the class relative to these places. 
 The teacher should aim, however, so to use the knoAvl- 
 edge of those pupils whose personal visitations have 
 made them acquainted with the locations of the great- 
 est number of places, as to extend the knowledge of 
 the other pupils. 
 
100 sow TO TEACH 
 
 Such attention should be given to the location upon 
 a map of the town, village, or city in which the school 
 is situated, and to the relative location and direction 
 from it of the chief places in its vicinity, that the 
 pupils will be able to point them out on an outline 
 map. The name of the town, village, or city, of the 
 county, and of the State in which the pupils live, should 
 be tauglit, and their location shown on a map. 
 
 Fourth Step. — In teaching the shape of the earth by 
 means of a globe, lead the pupils to compare a marble 
 with an orange, and both the marble and orange with 
 a globe, and thus to notice that each one resembles the 
 other in shajje only ; also that each differs from the 
 other in size. By this means prepare them for under- 
 standing that the globe represents the earth only in 
 shape. Follow this with some simple illustrations as to 
 the comparative size of the earth. 
 
 Next lead the pupils to compare the outline forms of 
 the grand divisions of land, water, and of islands, etc., 
 represented on the globe, with their corresponding repre- 
 sentations upon hemisphere maps. 
 
 Fifth Step.—TsW with the pupils about people of 
 different races and nations, and point out on the globe, 
 also on outline maps, the location of the countries where 
 each may be found : as Africa, the home of the colored 
 men ; China, the home of the Chinamen ; Germany, the 
 home of Germans, etc. Proceed in a similar manner 
 with the most familiar animals, and the most common 
 productions of different countries. Give the name of 
 the country, and show its location on a globe, also on 
 an outline map. Point out Greenland as the home of 
 the white bear; Africa as the home of the lion, zebra, 
 
GEOGRAPHY. ; ■' ,.,;;• 101 
 
 ostrich and camel; Australia as the home of thokan-r, 
 garoo; Spain as the country Avhere cork afl(l'ra>sinS'uH'' 
 produced ; South America as the country from which 
 brazil-nuts and cocoa-nuts are obtained ; West Indies 
 as the place from whence we obtain oranges and bana- 
 nas, etc. 
 
 By means similar to that herein described the pupils 
 may be made to realize that Geography teaches them 
 about the homes of the different people, animals, and 
 productions which they have seen, and of which they 
 have heard. 
 
 The aim of the teacher should be to give the pupils a 
 good, general idea of the shape of the Earth, of the 
 different portions of it as the homes of races of men, 
 also as the places where particular fruits grow ; and of 
 some parts as having continuous cold weather, and 
 others continuous warm weather. This object must be 
 accomplished chiefly by oral instruction. However, the 
 work may be facilitated by placing in the hands of the 
 pupils suitable text-books on Geography, to be exam- 
 ined by the children after the lesson has been given 
 orally by the teacher; but in no case should the pupils 
 in this grade he required to study a lesson in the hook 
 hefore the subject of it has heen presented orally by the 
 teacher, as above indicated. 
 
 Each lesson may be gone over a second time by the 
 teacher, after the pupils have studied the subject in 
 their books. The order of the lessons, the topics pre- 
 sented, and the general character of the facts tauglit 
 should conform to the directions given here, without 
 regard to the order of presentation in the text-books in 
 common use. 
 
 After completing the course of objective instruction 
 in Geography, as indicated in the preceding steps, the 
 
102 HOW TO TEACH. 
 
 pupiJs will- be prepared to commence the study of this 
 su'bjeci: '• in' -an intelligent manner from good text- 
 books. 
 
 DRAWING AND WRITING. 
 
 The exercises in Drawing and Writing for the Sixth 
 Grade may be continued in a manner similar to those 
 of the Seventh Grade. Pupils should not be simply 
 alloived to write, they should be taught and trained how 
 to write by the teacher. Children need somethiug 
 besides copy-books, to become good writers. 
 
 GENERAL SUGGESTIONS. 
 
 Meviews, — Such a review of the previous lesson, as 
 an introduction to, and in connection with, each new les- 
 son of the same subject, should be had as will cause the 
 pupils properly to associate together the important facts 
 previously learned with those of the new lesson. 
 
 General reviews of subjects should be had at least 
 once during each month. On tliese occasions the lead- 
 ing facts learned in previous grades, upon that subject, 
 should be included. These remarks are intended espe- 
 cially for tho fii'st five grades of this course of instruc- 
 tion. 
 
 I*vo(/7'css of Classes, — Whenever it is found that 
 a class has advanced further in one or tAvo subjects of its 
 grade than it has in otliers, the teacher should devote 
 less time to the subject in which the class has thus 
 advanced, and give more time to the subjects in which 
 the class has made the least progress. By this means 
 the grade of the class may be equalized in all its studies. 
 
GENERAL SUGGESTIONS. 103 
 
 No study of a succeeding grade should be introduced 
 into a class of a lower grade before that class has com- 
 pleted the requirements of the grade in all its studies. 
 
 Time Given to Each Subject, — The pupils 
 belonging to the first five grades of this course should 
 not spend more than forty minutes, at one time, upon 
 the same subject. And in the first two grades tliey 
 should not spend more than twenty minutes upon the 
 same subject at one time. 
 
 The mind, as well as the body, needs rest Both a 
 change of subject, and a change in the manner of con- 
 ducting class exercises, are necessary to furnish the 
 opportunities for needed rest during school hours, be- 
 sides the usual recesses of school. 
 
 Vocal 3Iiisic, — Instruction in vocal music ought to 
 be given to the pupils of all the grades in every school. 
 
 PHnciples of Education Aj^plied, — Teach- 
 ers who learn to apply principles of Education in the 
 order of presenting knowledge, and in their metliods of 
 teaching, will rarely fail of becoming successful in their 
 work. They will early accpiire the ability to determine 
 for themselves how to commence the instruction of any 
 class under any conditions, and to proceed surely step 
 by step toward the end in view. The following hints 
 are given as suggestions to young teachers who desire 
 to attain this ability. 
 
 Princi2ile.—QommQ\iCQ instruction in each subject 
 with that which the pupils already know concerning it, 
 or with something known which is nearly related to it, 
 and proceed to the kindi'ed unknown which forms the 
 subject of the lesson. 
 
104 HOW TO TEACH. 
 
 To ascertain the known, or the related unknown, the 
 teacher must consider what previous opportunities the 
 children have had for obtaining knowledge of the sub- 
 ject, and then by questions determine the true attain- 
 ments of the pupils relative to the matter for the pro- 
 posed lesson. The next point for the teacher to decide 
 is, how can that which the pupils already know, con- 
 cerning the subject of the lesson, be used in the best 
 manner to aid them in learning that Avhich they do not 
 yet know of it. For illustration, let this principle be ap- 
 plied to teaching Beading to a class of young children 
 that have just commenced going to school. 
 
 What is the known to these children, which relates 
 
 to reading ? [See page 23.] 
 
 What is the unknown to be first taught as reading ? 
 [See page 23.] 
 
 How can the known be used to aid in teaching the 
 unknown, which should form the lesson for this stage 
 of the instruction ? [See pages 23, 24, 25.] 
 
 Suppose a class has made snfiicient progress in learning 
 to read to be ready to commence using the first reading 
 book. What then would constitute the unknown which 
 should be taught first? [See page 39.] 
 
 How, subsequently, may the known be used for teach- 
 ing that unknown which forms the main object of the 
 lesson ? [See pages 30, 40. ] 
 
 After this manner the subjects of instruction should 
 be examined by the teacher, in each of the grades; 
 and, as a most important part of the process of teach- 
 ing, the main points of each preceding lesson should 
 be reviewed, before proceeding with the new matter, as 
 a means of connecting the instruction of successive 
 lessons so as to make the knowledge acquired a complete 
 whole, so far as it extends. 
 
FIFTH GEADE, 
 
 (lowest grammar school.) 
 
 Time allowed, about five months. 
 
 OUTLlifE COURSE. 
 
 LANGUAGE. 
 
 Heading,— Of the grade of a Third Reader (first half), with 
 a review of punctuation, Roman numbers, and elementary 
 sounds ; and with exercises on the subject-matter of the les- 
 sons. 
 
 Spelling. — From the reading lessons, with miscellaneous 
 words, and words derived therefrom ; also exercises in writing 
 words and short sentences from dictation. Particular attention 
 to be given to the use of capitals. 
 
 Definitions. — From the reading lessons, to teach the mean- 
 ing of the words, with illustrations by forming sentences ; in no 
 case to be committed to memory and mechanically recited. 
 
 Ora»>wwar,— Correction of Language. 
 
 ARITHMETIC. 
 
 Mental Arithmetic. — As far as in written arithmetic, to 
 include exercises in the analysis of operations and examples, 
 and in rapid calculation without analysis. 
 
 Written AritJitnetic. — Through the simple rules and Fede- 
 ral money, with practical examples. 
 
 Tables of weights, measures, etc., completed and reviewed, 
 with practical illusti'ations and simple applications. 
 
 5* 
 
106 now TO TEACH 
 
 GEOGRAPHY. 
 
 First /S^e.— Simplest elementary and systematic general out- 
 line of the geograpliy of the world as a whole, with definitions 
 and illustrations by means of the globe, of the form, magnitude, 
 motions of the earth, zones, latitude, longitude, etc. 
 
 Second /5fa^e.— Outlines of North America and the West In- 
 dies, including local and descriptive geography. 
 
 ELEMENTARY SCIENCE. 
 
 Food, Clothing, and Building Materials— Zoology. 
 
 —By oral instruction, to develop the powers of observation and 
 reflection, and to cultivate facility in oral description. 
 
 DRAWING AND WRITING. 
 
 On Slates, — Continued. 
 
 On Paper. — Writing in books, with particular attention to 
 position, holding pen, etc., etc., as in Sixth Grade. 
 
 1. Words corrtaining easy combinations ; as man, name, 
 noon, soon, etc. 
 
 2. Words containing long and short letters ; as hearty long, 
 youth, etc. 
 
 3. Words with easy capitals ; as Ape, Cold, Ink, Lamb, Time, 
 Zfsefid, Vanquish, etc. 
 
LANOUAOE. 107 
 
 How TO Teach 
 
 SUBJECTS OP THE FIFTH GRADE. 
 
 LANGUAGE. 
 
 Heading. — In teaching reading in this grade and 
 in the two or three others immediately succeeding, tlie 
 chief difficulties to be overcome may be classed under 
 the following heads : 
 
 First. — Hesitation over, or tlie miscalling of familiar 
 words. 
 
 This arises from want of practice, and where strongly 
 marked should claim the chief attention. 
 
 Second, — Mispronunciation of recogiiized words, as 
 stun for stone, winder for window, theater for theater, 
 etc. 
 
 Tliird. — NeiD words of which the meaning and pro- 
 nunciation are not yet known to the pupil. 
 
 New and difficult words should be carefully pro- 
 nounced, and, if necessary, explained, before the piece 
 or paragraph is read by the pupils. 
 
 Fourth. — Faulty enunciation. This is in great part 
 a physical difficulty arising from deficient training of 
 the vocal organs and of the ear, though sometimes the 
 result of slight malformation. • ' 
 
 Distinctness of articulation and the avoidance of all 
 improper clipping of terminations, and of the omission 
 
108 BOW TO TEACH 
 
 or slurring of syllables, should receive careful and con- 
 stant attention. 
 
 Lists of common words liable to be mispronounced, 
 such as length and strength, should be made by the 
 teacher, and the class exercised upon them. The ele- 
 mentary sounds and their more diJBficult combinations 
 in words and phrases requiring great mobility of the 
 Yocal organs, and QS,^Qcm\\j final consonants, should re- 
 ceive frequent attention. It should not be forgotten that 
 the difficulty here is chiefly physical, and can be readily 
 overcome by suitable exercises. To show a class the im- 
 portance of mobility of the muscles of the lips, let the 
 teacher read a paragraph with the lips almost motion- 
 less, and then read it again, giving as much play as pos- 
 sible to these muscles. The great contrast in distinct- 
 ness of articulation will be at once manifest. Amons: 
 the best exercises for the purpose of improving the 
 enunciation are the well-known "Three gray geese and 
 three gray ganders," " She sells sea-shells." " Saw six 
 slim saplings," "Peter Piper," "Theophilus Thistle," 
 "Amidst the mists," etc., etc. A daily exercise of five 
 minutes would probably be sufficient in most cases. It 
 should be very spirited, the shorter sentences twice or 
 thrice repeated, and with the greatest rapidity consist- 
 ent with perfect distinctness. 
 
 Particular attention should be given to pupils of for- 
 eign birth or 'parentage, so as to insure their mastery 
 of the principal difficulties of English pronunciation. 
 Phonetic drills are very useful for this purj^ose. 
 
 Fifth. — Harsh or unnatural tones. The voice and 
 manner of the pupil should accord with the character 
 and sentiment of the selection. All drawling, sing-song 
 tones should be prevented. This is easily done when 
 
LANGUAGE. 109 
 
 the pupils are led to understand and enter into the spirit 
 of the piece. 
 
 In the employment of concert exercises in reading, 
 especial care should be taken to prevent any injury to 
 the voice by harsh or unnatural tones. 
 
 Sixth. — Vague or erroneous conception of the subject- 
 matter of the lesson as a whole, or of the meaning of 
 particular phrases, sentences, or paragraphs. 
 
 When the character of the paragraph or of the les- 
 son will permit it, the pupils should be accustomed to 
 state, in their own language, the important facts, prin- 
 ciples, and moral lessons therein taught. Words, phrases, 
 or allusions should be briefly explained, whenever neces- 
 sary for the proper understanding of the piece read. 
 
 Seventh. — Want of rhetorical training. Should a 
 large number of consecutive lessons in the Eeader be 
 of the same general character, a part should be omitted, 
 so as to give variety of style and subject. No selec- 
 tion, other than the best English poetry, should be so 
 long dwelt upon and so frequently repeated as to ren- 
 der the exercise a mere recitation. 
 
 As a test of the general condition of the reading, 
 classes should occasionally be called upon to read un- 
 familiar pieces of the same grade. 
 
 Where the primari/ object of the exercise is to teach 
 elocution, it is advisable, quite often, to require all the 
 pupils, except the one reading, to close their books, the 
 teacher also, only using the book for occasional refer- 
 ence. In this way, both the teacher and the class will 
 be better able to criticise, and the criticism will be more 
 just and valuable. Besides, the pupils will all be kept 
 on the alert to listen, and the one reading will unavoid- 
 
110 HOW TO TEACH 
 
 ably endeavor to pronounce correctly, enunciate dis- 
 tinctly, and emphasize naturally. Additional effect 
 will be given to the exercise by requiring the pupils to 
 reproduce, in their own language, the substance of what 
 is read to them. 
 
 Where a simple system of diacritical marks is used 
 in the Heading Book, the pupils should be taught to 
 understand and apply them. An occasional brief re- 
 view of the Konian numbers, and of the names and 
 signification of the marks used in punctuation, should 
 be required. 
 
 The successful application of these suggestions in- 
 volves the necessity of carefully grading the exercises 
 and selections, so that the pupils be not required to 
 read pieces which are above their comprehension. This 
 is a point of the greatest importance. 
 
 SPELLING. 
 
 The exercises in spelling should be both oral and 
 written, but principally written. 
 
 The selections of words from the reading lessons 
 should be so made that the class will not be prevented 
 from advancing from one reading lesson to another 
 with proper rapidity. "When a Spelling Book is used, it 
 should be made an auxiliary to the Reader, and not a 
 substitute for it. If the lists of the Speller contain 
 unusual words, these should be deferred until higher 
 grades are reached. No time should be spent in spell- 
 ing words which the pupil does not understand. 
 
 For purposes of review, teachers should keep lists of 
 those words of the lessons in which a large number of 
 mistakes are made by the pupils. 
 
SPELLING. Ill 
 
 In oral spelling, care should be taken to name each 
 letter distinctly, except in the case of the "doubles," 
 ■which are to be distinctly pronounced as such, and not 
 as " iVhlee " for " double-e," " d'bloiv " for " double-o," etc. 
 
 "Miscellaneous words" should include the ordinary 
 proper names of persons (not the surnames), words 
 naturally suggested by those of the reading lessons, and 
 common words of the daily life of the household, the 
 shop, and the street.. The derivatives required should 
 be those and those only which are in the commonest 
 conversational use. They may be readily obtained by 
 calling upon the class to suggest them. The modifica- 
 tions of the primitives required in order to form them 
 should be taught. 
 
 The written exercises should be as neat as possible, 
 care being taken to train pupils to habits of orderly 
 arrangement of their work. When sentences are given, 
 particular attention should be paid to the ordinary 
 troublesome monosyllables, to the proper use of cap- 
 itals, the sign of the possessive case, the period, the in- 
 terrogation mark, and the use of the hyphen, in a word 
 divided at the end of a line. 
 
 DEFINITIONS. 
 
 In selecting words for definition, two leading pur- 
 poses should be specially kept in view : 1. To impress 
 or illustrate the particular meaning of the word as used 
 in the lesson ; 2. To enlarge and correct the pupil's 
 oAvn vocabularv. 
 
 Very simple words, such a?, father, water, Jcnifc, knee, 
 hook, cltUd, etc., the meaning of which every child already 
 understands, should not, in the lower grades at least, 
 
112 now TO TEACH 
 
 be assigned for definition. Properly to define such 
 words requires a nice discrimination in the use of lan- 
 guage and a minuteness of analysis beyond the power 
 of a young ch'ild. Teachers are apt to go astray in this 
 direction. It is principally on this account that the 
 limitation, " to teach the meaning of the words," has 
 been introduced in prescribing this part of the grade. 
 The written exercises will necessarily contain many 
 such words, and tlius the child Avill learn to spell them. 
 
 Wliere a word has, in common use, two or more 
 meanings quite diverse, a separate oral illustration 
 should be required for each ; and where several words 
 differently spelled have the same or a similar pronuncia- 
 tion, a separate construction should be required for 
 each in the written exercises. 
 
 Defining one part of speech by giving another part 
 of speech as a synonym, is a common error. It may be 
 corrected or avoided by giving small groups of words, 
 each consisting of a primitive and some of its most 
 commonly used derivatives, and requiring, as an oral 
 exercise, a phrase or a sentence to illustrate the use of 
 each word in the group. 
 
 Teachers should be particularly careful to comply 
 with the direction, "in no case to be committed to 
 memory and mechanically recited." The mere com- 
 mitting of dictionary definitions to memory, or the sub- 
 stitution for the word to be defined of another word, 
 perhaps more difficult and unusual, is a perversion of 
 the exercise. It is not only useless but pernicious, for 
 it neither aids in mental development nor adds to the 
 pupil's information, nor does it benefit him in his use 
 of language. For this reason, the lists of words given 
 in a spelling book for the purpose of teaching spelling 
 are not well adapted for teaching the meanings of 
 
ARITHMETIC. 113 
 
 wordg, these being most clearly comprehended when 
 the words are put into sentences or phrases. 
 
 At this stage of tlie pupil's advancement, a fnll exer- 
 cise on a given word should comprise the following: 
 1. Pronounce it; 2. Use it in the construction of a 
 phrase or a sentence; 3. Define it ; 4. Write a sentence 
 containing it. [For the whole class.] 
 
 In the performance of the written exercises required 
 for definitions in this grade, the pupils may not only be 
 taught .the meaning of the words, but, by a skillful 
 application on the part of the teacher, be prepared for 
 the exercises in composiiion subsequently prescribed. 
 This point should be kept in view. Correctness in the 
 use of words, propriety in the thought, the accurate use 
 of capitals, punctuation marks, etc., should be invari- 
 ably insisted upon. 
 
 ARITHMETIC. 
 
 Ifental Arithfnetic, — The mental arithmetic 
 should both precede and accompany the written arith- 
 metic, step by step. The principal distinction between 
 these two divisions of the subject is, that when the 
 numbers involved are too great or too many to be readily 
 retained in the memory, the slate should be employed 
 as an assistant. 
 
 "Exercises in rapid calculation without analysis" 
 should, as far as possible, be of the most practical 
 character. Examples given should be silently wrought 
 by the whole class simultaneously as in Avritten arith- 
 metic, and the results obtained be written upon the 
 slates, promptly, and at a given signal. Tlie analysis 
 can then be separately required of as many pupils as 
 may seem expedient. 
 
ni ■ now TO TEACH 
 
 Ilhistration. — One method of conducting such an 
 exercise is subjoined. Teachers fertile in expedients 
 will devise others equally good, and involving the follow- 
 ing important elements: 1. The exercise to he simul- 
 taneous ; 2. Silent ; 3. Spirited throughout ; 4. All 
 copying, or wrongly claiming the answer prevented. 
 The detail may be greatly varied : 
 
 1. Pupils sit silent and erect; slates lying on desk, or 
 held vertically, resting on the knees, the hands being at 
 the upper corners; pencils in right hands. 
 
 2. Teacher gives question with distinctness. 
 
 3. Pupils work silently, remaining in position until 
 the answer is found, when each silently raises the right 
 hand, or stands. 
 
 4. When sufficient time has been given, teacher says 
 
 "Ready Write," with a pause between the words. 
 
 At the last word the answer is instantlij written in large 
 figures, but only by those standing, or whose hands are 
 up, and the slates instantly turned with the answer 
 toward the teacher. No further working or correction 
 allowed. These movements are better executed, after a 
 little practice, by using four light tajis of the pencil, 
 meaning, "Ready," " Write," " As you were," " Show." 
 
 5. Teacher calls upon some one to read the answer, 
 usually upon one whose results are frequently wrong. 
 Those claiming the same stand if sitting, or raise the 
 hand or the slate if already standing, the answer being 
 still turned toward the teacher. 
 
 G. If thought desirable, an oral analysis may now be 
 demanded of any pupil, whether he obtained the answer 
 or not. 
 
 The explanatory or analytic statements made by the 
 pupil should be of the simplest and most direct charac- 
 ter consistent with clearness, and all unnecessary repe- 
 
AEITHMETIC. 115 
 
 titions of formuh^ be ciirefully avoided. Where this is 
 not done, the principal effort of the pupil is to recall in 
 due order the set form of words, rather than to form the 
 arithmetical combinations necessary to the solution. 
 
 Besides simple examples in the four fundamental 
 rules and Federal money, A'ery simple operations in- 
 volving practical applications of the selected tables of 
 money, Aveiglit, and measure, should constitute a por- 
 tion of the exercises in mental arithmetic. 
 
 In the explanation or analysis of examples in mental 
 as well as written arithmetic, the pupils should gener- 
 ally be called upon, before solving, to state the question. 
 
 Mental exercises in arithmetic should be conducted 
 in a spirited manner. They should always have the 
 character of extemporized exercises, and in no case 
 form a part of the home-work of the pupil. 
 
 Written AritJinietic. — The slates should be kept 
 in tlie best condition as to cleanness; the figures should 
 be distinctly and neatly made, and written in lines par- 
 allel to the upper edge of the slate. A reasonable allow- 
 ance should be made for imperfections in the forms of 
 figures in those exercises Avhere haste is required; yet 
 every effort should be made to fix in the pupils habits 
 of care, neatness, and system in all that j^ertains to the 
 written exercises. 
 
 Exercises in adding columns of figures should be given 
 with such frequency as may be found necessary to pro- 
 duce and retain accuracy and rapidity. They should be 
 in both forms — the silent and the oral. 
 
 Every form of counting, whether by fingers, dots, 
 marks, or other devices, should be strictly proliibited, 
 and the class should be frequently tested for this special 
 purpose. 
 
116 HOW TO TEACH 
 
 The pupil should be allowed to name only the succes- 
 sive results arising from the addition of the sevei'al 
 successive figures, avoiding all that oral or mental repe- 
 tition of the tables which is known as the " spelling 
 process," and all other unnecessary formulae. 
 
 Illustration. 
 ' 789 
 
 457 
 
 632 
 
 178 
 
 Correct Metliod.—^, 10, 17, 26 ; 9, 12, 17, 25, etc., etc. 
 
 Incorrect Metliod. — 8 and 2 are 10, 10 and 7 are 17, 
 17 and 9 are 26, set down the 6 and carry the 2, etc., etc. 
 When this method is once fixed, it is difficult to change 
 it. It acts as a clog to the mental activity of the pupil, 
 who finds himself unable to think out the result in any 
 otlier way. It is as if he should spell aloud every word 
 as he reads. 
 
 The above remark, in regard to the oral or mental re- 
 petition of the tables, applies to all the fundamental 
 rules and their applications. The processes should be 
 reduced to the most concise form practicable. 
 
 When pupils show an ability to add in two or more 
 figures at a time, they should be encouraged to do so in 
 exercises that are wrought out silently. 
 
 When tlie divisor is less than 13, the long-division 
 process is not to be- employed or allowed. 
 
 Short practical examples, involving two or more of 
 the rules, should frequently be given, and in such a 
 Avay as to cultivate the intelligence of the pupil. 
 
 Examples requiring a very large number of figures 
 
ARITHMETIC. 117 
 
 for their solution should be avoided, except as far as 
 they may be necessary in order to give practical expert- 
 ness. 
 
 Examples should be given to test the pupils' accuracy 
 in writing numbers requiring O's, and their knowledge 
 of the proper methods where the multiplier or divisor 
 contains O's. 
 
 Exercises should be given to insure focility in read- 
 ing and writing Federal money, and in reducing, by iu- 
 spedion and without analysis, dollars, or dollars and 
 cents, to cents or to mills, etc., etc., and conversely. 
 This reduction becomes important in certain cases in 
 division of Federal money. (See Analysis B.) 
 
 Analogous exercises in Federal money should be sub- 
 stituted for those in the simple rules referred to in the 
 preceding sections, as soon as may be found expedient. 
 
 In all practical examples, instead of telling pupils to 
 add, subtract, multiply, or divide, give the question in 
 such a manner as to oblige them to exercise their own 
 judgment as to the method and principle to be em- 
 ployed. 
 
 Xo detailed analysis is necessary in addition or sub- 
 traction. 
 
 Give short examples of bills of purchase or sale in- 
 volving several items, and similar to those required in 
 daily life. Let them be put into proper form on the 
 slate, with names and date, and occasionally receipted, 
 and the receipt explained. 
 
 The following examples involve the points upon which pupils 
 are most apt to fail in the arithmetic of this grade. They are so 
 highly important that a drill upon a series of similar examples 
 is recommended. No pupil should be allowed to proceed fur- 
 ther till he has thoroughly mastered them. 
 
 Write 30,003,050— 7U0,50U,009i 
 
118 now TO TEACH 
 
 Multiply 30850 by 307 ; by 4070 ; by 2009. 
 
 Divide 732427 by 200 ; by 40000, etc.— Should of course only 
 be done by short division. 
 
 Divide 732427 by 100; by 10000, etc.— Should only be done 
 by pointing olf. 
 
 Write 3 dollars and 5 cents ; 10 dollars and 7 cents, etc. 
 
 Bought for $2095.07, sold for $2500. How much did I gain or 
 lose? 
 
 Sold 320 bushels for $176. How much a bushel ? Analyze. 
 
 Spent $42 for tea at 87^ cents a lb. How many lbs. did I 
 buy ? Analyze. 
 
 Spent $8 for coffee at 40 cts. a lb. How many lbs. did I buy ? 
 Analyze. 
 
 If 24 yards cost $20.40, what will 17 yards cost ? Analyze. 
 
 If 24 yards cost $20.40, how many yards can be bought for 
 $14.45 ? Analyze. 
 
 Note.— If fractions arise in the first stage of examples eimilar to the last 
 two, they may be rejected in the second stage in this grade. 
 
 The following are all the forms of arithmetical analysis neces- 
 sary to the fifth grade : 
 
 FORMS OF ARITmiETICAL ANALYSIS 
 
 FOK BOTH MENTAL AND WRITTEN ARITHMETIC. 
 
 A. ( Fundamental) — Multiplication. 
 
 Question. — If one yard cost $3, what will 4 yards cost ? 
 Analysis. — If one yard cost $3, 4 yards will cost 4 times $3, 
 which are $12. 
 
 Note.— Avoid the too concise form, " will cost 4 times 3, which are 12." 
 
 B. [Derived) — Division. (1.) 
 
 Question.— li one yard cost $3, how many yards may be bought 
 for $12 ? ■ ' 
 
 Analysis.— If one yard cost $3, $12 will buj^ as many yards as 
 $3 are contained times in $12, which are 4 yards. 
 
 Note.— Avoid the too concise form "as many as 3 are contained in 12." 
 Question.— ^\ni\\\: $43 for tea, at 87^c. a pound. How many 
 pounds did 1 buy ? 
 
ARITHMETIC. 119 
 
 Analysis.— $42 are 42000 mills, and 87* cents are 875 mills. I 
 can buy as many pounds as 875 mills are contained, etc. 
 
 See preceding '• Suggestions " for remark about reducing Federal money 
 without analysis. 
 
 C. {Derived) — Division. (2.) 
 
 Question.— If 4 yards cost $12, what will one yard cost ? 
 Analysis.— IC 4 yards cost |13, one yard will cost i of $13, 
 which is $3. 
 
 Note.— Avoid the very faulty forms " as much as 4 is contained in $13," 
 or " times in $12," or "4 is contained in 12." 
 
 Quesiion.—If: 5 lbs. cost $3, what will X lb. cost ? 
 Analysis.— If 5 \hs. cost |3 or 300 cents, 1 lb. will cost i of 300 
 cents, which is 60 cents. 
 
 Combinations op A, B, and C. 
 
 Cand A. Division and Multiplication. 
 
 Question.— If 4 yards cost |13, what will 9 j'ards cost ? 
 Analysis. — First by C for price of 1 yard, then by A for price 
 of 9 yards. 
 
 C and B. Division. (2) and (1). 
 
 Question. — If 4 yards cost $13, how many yards may be bought 
 for $37 ? 
 
 Analysis. — First by C for price of 1 yard, then by B for num- 
 ber of yards. 
 
 Note 1.— Avoid set forms of giving questions. Vary the order of statement 
 as far as is consistent with perfect clearness. For instance, the last question 
 might have been put thus: Spent $27 for cloth. How many yards did I buy, 
 if $12 bought 3 yards; or, How many yards for $27, if 4 yards cost $12? 
 etc., etc. 
 
 Note 2.— In this grade avoid examples in which fractions form a part of the 
 qnotient. 
 
 Note 3.— It is frequently an assistance to some pupils to have them divide 
 each question into crmditions and demand— v^s in C and A. " The condition is, 
 that 4 yards cost $12. The demand is, what is the price of 9 yards." Such 
 devices should he sparinirly nsed. 
 
 Note 4.— Analysis A and B apply to questions in the tables, snhstituting 
 the word since for t/. Examples: How many quarts in five pecks? Since one 
 peck contains eight quarts, five pecks contain, etc., etc. How many feet in 
 84 inches? Since \i inches make 1 foot, 84 inches contain as many feet, etc., 
 etc. 
 
120 HOW TO TEACH 
 
 TABLES. 
 
 In this grade, the tables of the preceding grade should be 
 thoroughly reviewed, with the following additions : 
 
 Titne, — Teach about leap-year. 
 
 Avoirdujwis Weiglil.— 1000 grains = 1 pound ; 2240 
 pounds — 1 old ton ; 62^ i)ounds, or 1000 ounces = 1 cubic foot 
 of water. 
 
 Troij Weight.— 'Explain its use, the great difference be- 
 tween its pound and ounce, and those of Avoirdupois Weight, the 
 grain being the only identical element. 24 grains = 1 penny- 
 weight ; 20 pennyweights = 1 ounce ; 12 ounces, or 5760 
 grains = 1 pound. 
 
 Aiiothecaries'' 7rctgr7t«.— Explain its use. Show that it 
 differs from Troy Weight in nothing but the method of subdivid- 
 ing the ounce. Teach that the fluid ounce is a measure, and not 
 a weight. 20 grains = 1 scruple ; 3 scruples = 1 dram ; 8 drams 
 = 1 ounce ; 12 ounces = 1 pound. 
 
 Long Measure.— Add the following : Explain the use of 
 each term. 4 inches = 1 hand ; 3 feet = 1 pace ; 6 feet = 1 
 fathom ; 1^ miles = 1 knot. 
 
 Surveyors' Long Measure.— A rods, or 66 feet, or 100 
 links r= 1 chain ; 80 chains = 1 mile. 
 
 Surveyors' Square 3Ieasiire.—Exp\ain the local use of 
 section and township. 16 square rods = 1 square chain ; 10 
 square chains = 1 acre ; 640 acres = 1 square mile or section; 36 
 square miles = 1 township. 
 
 Solid or Cubic Measure.— Explain its use, and the 
 difference in kind between the linear, superficial, and solid units of 
 the same name. 1728 cubic inches = 1 cubic foot ; 9 cubic feet = 1 
 cubic yard ; 128 cubic feet = 1 cord of wood ; 2150 cubic inclies 
 = 1 busliel ; 231 cubic inches = 1 gallon. 
 
 Angtdar Pleasure.— Teach the following terms : Circle, 
 
GEOGRAPHT. 121 
 
 circumference, quadrant, radius^ diameter. Teach the notation. 
 Give examples in reading, as 1G° 17' 45". 60" = 1 minute ; 
 GO' = 1 degree ; 90" = 1 quadrant ; 3G0° = 1 circle ; 360° = 
 circumf. of the Eartli ; 69|^ miles = 1 degree of latitude ; cir- 
 cumference of a circle = 3| times the diameter. 
 
 English 3Ioney, etc. — The usual table. Teach the value 
 of a pound sterling — $4.866|. Teach the value of a franc — 18 
 cents 6 mills. 
 
 If any foreign dollar is taught, let it be the thaler of Germany 
 = 69 cents. 
 
 GEOGRAPHY. 
 
 General Suggestions for all Grades* — It 
 
 is of the first importance that geography should be 
 so taught and reviewed, as not to leave in the mind of 
 the pupil a mere collection of facts, without mutual re- 
 lation or dependence. On the contrary, he should, 
 from the first, be led to consider the earth as man's 
 dwelling-place — its motions as bringing him the neces- 
 sary vicissitudes of day and night, and the changes 
 of the seasons — its land-surface as the chief theater of 
 animal and vegetable life — the ocean as the world's broad 
 highway, and the exhaustless source of clouds and rains, 
 so necessary to every form of life on the laud-surface — 
 the great permanent air-currents as carrying to the 
 land this moisture from the sea — the mountains as its 
 condensers, as well as the chief source of mineral wealth 
 — the sjjrings andn'wers, with their branches, as carry- 
 ing back again, and over the land, the. ever-circulating 
 water of the ocean — and of cities and toiuns, not as black 
 dots on a map, in colored patches, which he has learned 
 to call countries, perhaps near some crooked black 
 streaks Avhich he has learned to call rivers, but as the 
 
 6 
 
133 SOW TO TEACH 
 
 centers of social life and development, the seats of 
 government, and the crowded, busy hives of human in- 
 dustry and intelligence. 
 
 When geography is thus taught, it is one of the most 
 interesting, important, and practical of studies; but if 
 it is taught chiefly as a description, by unvarying for- 
 mula?, oflong lists of rivers, capes, peninsulas, boundaries, 
 etc., supplemented, perhaps, by a precise, verbatim repe- 
 tition of the descriptive geography, as contained in 
 even the very best text-book, it is one of the dullest and 
 most unprofitable of studies. 
 
 The text-book is a most important, and even indis- 
 pensable auxiliary, but there is no more common and 
 pernicious error, than that of suhstituting it in place of 
 the teacher, who thus is degraded into a mere stupid, 
 profitless, and mechanical hearer of lessojis. The requi- 
 sites for successful teaching are a globe, a blackboard, 
 an outline map and pointer, and a good text-book. The 
 pupil's first impressions should be formed from the 
 globe, rather than from the flat and distorted repre- 
 sentation of the map. When the text-book is to be used, 
 and important and comprehensive lessons given, such 
 as the presentation of the general outline of the world 
 as a whole, or of a continent or grand division, or of the 
 United States as a whole, the subject should first be gone 
 over orally, in outline, l)y the teacher. If this be done 
 in a spirited manner, and the results carefully tested, the 
 detailed study of the text-book will be greatly assisted 
 and unified by the comprehensive view thus imparted, 
 and the important details more surely remembered. 
 
 Geoffraphtf of the Fifth Grade.— In the 
 
 preceding grade, the pupil has been taught the leading 
 elementary ideas upon which geography is founded ; in 
 
OEOGRAPUT. 123 
 
 the present grade, these are to be reviewed, expUiined, 
 and systematized, beginning with a general view uf the 
 world. The following is a syllabus of the points which 
 should claim attention : 
 
 Syllabus for the Fifth Grade. Part 1st.— The form of 
 tlie earth, its vuignitude, the continents and grand divisions, their 
 relative positions, their connecting isthmuses, and a lew of their 
 most important projections — l\ie oceans, their positions, and prin- 
 cipal arms and islands — live or six of the great mountain systems 
 of America, and from eight to ten in the rest of the world ; three or 
 four well-known volcanoes — about a doijen each of the chief rivers 
 and straits, and about half as many great lakes — from ten to a 
 dozen of the most important cities of the world, and, iu a very 
 general way, the location of the most important countries, such 
 as the United States, Great Britain, Germany, Japan, China, etc. 
 With each of these cities and countries some interesting or im- 
 portant /ac^ should be at once associated. 
 
 Part 2d. (To be taught as facts, in the simplest outline, and 
 without attempting to explain according to any of the hypothe- 
 ses of scientific physical geography, using the map and globe, 
 whenever necessary, to impress any particular statement on the 
 pupils' minds.) A brief notice of the ocean currents, their direc- 
 tion, temperature, and use, pointing out only the equatorial cur- 
 rent, one Arctic current, one Antarctic current, and the Gulf 
 stream — the trade winds (very briefly), their location, direction, 
 use in commerce, and their influence (in assisting to produce the 
 great South American rivers, the Nile, etc.) — a general notion of 
 clirnfite,' as affected by distance from the equator, and by eleva- 
 tion — the motions of the earth, and the inclination of its axis — the 
 zones, their limits, and a very few of their well-known and char- 
 acteristic plants and animals, and, in a very general way, the 
 location of the chief races of mankind. 
 
 ^'Outlines of Noi^h America."— First : Treat the con- 
 tinent as a whole, pointing out its separate countries, most im- 
 portant capes, peninsulas, islands, and arms of the sea ; its 
 divisi(ms into mountains, plateaux, and lowland plains, naming 
 only a few of the most important of each. 
 
124 EOW TO TEACH 
 
 Iceland, Greenland, Alaska, and all other Arctic Geography to 
 be treated very briefly, and chiefly with reference to climate, re- 
 sources, and people. — Newfoundland; the Dotninion of Canada, its 
 surface, its provinces and territories, with their climate, resources, 
 and people, and our trade with them ; the form of government ; the 
 capital of the Dominion and those of the provinces, and the other 
 most important towns; the commercial and international im- 
 portance of the St. Lawrence River and the Great Lakes, and the 
 small importance of the other rivers, of which three or four will 
 be enough. 
 
 United States. — A simple outline will embrace the follow- 
 ing: 
 
 Local Geography. — The boundaries of the country -as a 
 whole ; its dimensions in round numbers ; the location of the great 
 mountain systems ; the western plateaux Ta section of the country 
 roughly drawn in chalk upon the blackboard will be found effi- 
 cient] ; the high western plain; the low central plain; the eastern 
 slope, and the California basin ; about a dozen of the chief rivers, 
 with the great branches ; about five or six each of the great 
 lakes, bays, and capes ; about twenty of the principal cities. 
 
 Dcscrliitive Geography will include a very brief descrip- 
 tion of the highlands, lowlands, and drainage system already 
 pointed out ; the climate and its gradual modifications by lati- 
 tude, elevation, and distance from the sea ; and a general state- 
 ment of the leading agricultural staples in the order of their 
 latitude— rice, sugar, cotton, tobacco, corn, and wheat. 
 
 3Iexico.—l\9, surface, climate, resources, and people ; their 
 language, government, and social condition ; about five or six of 
 the principal cities. 
 
 Central America very briefly; the names of its states and 
 their capitals, and their general similarity to Mexico. 
 
 West Indies, the principal groups, about ten or a dozen of 
 the most important islands ; five or six principal ports ; the 
 climate, resources, and people ; their colonial relations, and their 
 commerce with the United States, if important. 
 
LANGUAGE. 125 
 
 LANGUAGE. 
 
 Correction of Language. — In all the grades 
 the pupils should be trained in the correction of lan- 
 guage, and taught to avoid common errors of speech. 
 Tliis is best accomplished in connection with the dicta- 
 tion exercises required in the several grades; also by oral 
 exercises specially adapted to this purpose, and by inci- 
 dental instruction during the recitations and lessons in 
 other subjects, as in the definition exercises, the lessons 
 in elementary science, etc. Indeed, every exercise in 
 which the pupils are required to use their own language, 
 either orally or in writing, should be made a vehicle for 
 this instruction, the object being to impart the liahit of 
 using correct language. It is of the greatest importance 
 that this habit should be acquired at an early age, for 
 without it, the technical study of grammar will scarcely 
 prove adequate to impart fluency in the correct use of 
 language. The old habits, in spite of the knowledge of 
 principles and rules, will be always apt to show them- 
 selves. 
 
 On this account, teachers cannot be too careful them- 
 selves in the use of language. Their words as well as 
 their acts should present a model for the imitation of 
 their pupils ; and example in this, as in other things, 
 will prove far more potent than precept. For special 
 exercises in this department of the instruction, the fol- 
 lowing suggestions are made : 
 
 AVrite on the blackljoard such faults in expression as 
 are liable to be committed, including — 1. Ungrammati- 
 cal expressions : as I haven'' t no hook ; I luivenH got my 
 jjeiicil J I seen him do it, etc. 2. Slang: This is an aivful 
 easy lesson, etc. The faulty ex^iressions written in this 
 
126 HOW TO TEACH 
 
 way should, however, consist of such as may have been 
 committed by 'some of the pupils of the class, lest those 
 who have acquired good habits of speech be contami- 
 nated by having their attention called to such errors. 
 
 Award premium marks, or some other kind of reward, 
 to those who succeed in pointing out improper expres- 
 sions on the part of their classmates; but let this be 
 done in the right spirit, and not for the purpose of 
 subjecting any of the pupils to jeers or ridicule. The 
 ftict that their language may be made the subject of 
 criticism by their fellow-pupils, will put all on the alert 
 to use the best modes of expression in their power, and 
 then correctio2i will have a permanent effect in improv- 
 ing them in the use of language. 
 
 Sometimes one or more pupils may be selected by 
 the class to act as censors for a definite period (say a 
 week), and to call attention to errors made by any of 
 the pupils of the class. The object of this and the pre- 
 vious suggestion is to make the pupils critics on them- 
 selves and others, most of the inaccuracies committed 
 resulting rather from carelessness and inattention than 
 from a want of knowledge. The teacher will, of course, 
 often find it necessary to give direct instruction in rela- 
 tion to certain expressions. 
 
 Of course, no instruction in technical grammar, or in 
 any grammatical rules, is required until the next grade. 
 
 ELE]kIEXTARY SCIENCE. 
 
 (By Oral Instruction.) 
 
 General Suggestions for all Grades. 
 
 The leadinfi ohjcct in this branch of instruction is to 
 cultivate habits of ohservaiion and reflection, and to give 
 
ELEMENTARY SCIENCE. 127 
 
 facilUy in oral description. Avoid everything tend- 
 ing to convert these lessons into recitations of set forms 
 of words, however these forms may have been obtained, 
 however well they may be understood by the pupils, and 
 however important the facts thus stated. 
 
 *' Familiar objects," and familiar animals, plants, and 
 minerals take jirecedence of all others in the selection 
 of topics. 
 
 It is neither possible nor desirable to attempt to teach 
 all, or even the greater part of the topics that might be 
 classified with the requirements of any grade. JS'o topic 
 should be treated exhaustively, nor should the topics 
 selected be so few, or so frequently reviewed, as to nar- 
 row down or suspend the discipline of the observing 
 faculty. The selection and limitation must be left to 
 the good sense of the teacher. 
 
 The objective method of teaching presents two dis- 
 tinct, though intimately related departments. Percep- 
 tive teaching, in which the object, as an acorn or an Qgg, 
 is directly presented to the pupils' senses ; and conceptive 
 teaching, in which impressions previously received are 
 recalled, arranged, and utilized, the objects themselves 
 not being presented to the senses during the lesson. 
 An oak, an elephant, or a thunder-storm, would fall 
 under the latter department. 
 
 TJie use of pictures, models, ov other sensible repre- 
 sentations of objects, constitutes an important combina- 
 tion and modification of the two principal methods, 
 and should be often employed. 
 
 Definitions should be very sparingly introduced, and 
 never in the first stage of a subject. If given at all, 
 they shotald sum up knowledge already attained. The 
 terms organic, inorganic, vegetable, animal, and mi?ieral, 
 are promineiit among the very few terms requiring defi- 
 
128 EOW TO TEACH 
 
 nitiou. Such definitions should be prepared for by a 
 process at once inductive and objective. 
 
 No fact which the teacher can readily lead the pupil 
 to discover for himself, should be imparted by the 
 teacher. Important facts not readily derived from the 
 pupil's own observation, must, of course, be supplied by 
 the teacher. Avoid overloading a tojDic by details. No 
 topic should be selected in which the number oi facts 
 to he told bears a large proportion to those which the 
 pupil may be led to discover for himself. 
 
 The language used hy the inipil should he entirely his 
 oivn, excepting, of course, the few indispensable defini- 
 tions. 
 
 The jjrocess employed will present two distinct stages: 
 First, the analytical or preparatory, in which the teacher 
 leads the pupil by questions to discover or to remember 
 the properties or peculiarities of an object, or to state 
 any other important facts associated with it. The re- 
 sponses by the pupil will be, of course, in his own words ; 
 and the additional statements which the teacher him- 
 self may find necessary fo make, will be given in the 
 form of conversations. This stage gives the principal 
 discipline of the powers of observation and reflection. 
 
 The points thus considered, and the facts thus stated 
 should be Avritten upon the blackboard in the briefest 
 possible synoptical form, but each only after it has been 
 considered. While some such synopsis is indispensahle 
 to the teacher as the first step of preparation for giving 
 the lesson, it should never be presented to the p^qril ex- 
 cept by the gradual process above indicated. 
 
 The second or revieiv stage of the process is based upon 
 the results of the first, and furnishes the principal dis- 
 cipline of the powers of description or oral staternent. 
 The facts already considered should be re-arranged, if 
 
ELEMENTARY SCIENCE. 129 
 
 necessaiy,^into an orderly synopsis upon the black- 
 board, the pupils being called upon to assist in this 
 arrangement. They should then be required, in turn, 
 to state what they can recall of each item of the synop- 
 sis, then of each group of items, and, lastly, of the whole 
 subject. Then the synopsis may be wholly or in part 
 removed or hidden, and the oral process of review re- ' 
 peated. As a final stage, and before dismissing the sub- 
 ject, an extempore comjmsUion, with or without the aid 
 of the synopsis upon the board, should be written by 
 each pupil uj^on his slate. 
 
 Outlines of Zoology. 
 
 In relation to this part of the fifth grade, the fol- 
 lowing suggestions are made : 
 
 Zoology being a science of classification, it is indis- 
 pensably requisite to teach the distinctions upon which 
 the classification depends. 
 
 Only the simplest outline need be taught, with such 
 facts and details as seem most naturally appropriate to 
 illustrate the subject. 
 
 The process of classification being naturally ohjective, 
 that is, animals being classified by their obvious pecu- 
 liarities, tlie pupil should be led, by an exercise of the 
 observing faculties, to discover the leading peculiarities 
 himself. 
 
 For instance, suppose the teacher wishes to lead to 
 the perception of the basis of the classification into 
 tlie four great types or sub-kingdoms. Write upon tlie 
 blackboard the names of a sufficient number of fa- 
 miliarly known animals without classification. If he 
 have their pictures in books, or on charts, let each be 
 shown before asking and writing its name. Let the 
 
 6 
 
 * 
 
130 • HOW TO TEACH 
 
 pupils spell each name before the teacher writ.es it. Sup- 
 pose them to be lobster, ox, oyster, dog, beetle, starfish, 
 snail, and coral. Lead the pupils to see and decide for 
 themselves which two or three most resemble each 
 other. Adroit questioning, and a little patience, will 
 soon make them group together the lobster and the beetle 
 on account of their hard, jointed rings, and tiieir many 
 equally hard limbs ; the ox and the dog, from their 
 four legs, and their similarity as to eyes, ears, and other 
 organs ; and the oyster and the snail, from their hard 
 shells and soft bodies. The remaining starfish and coral 
 will present difficulties, because not so familiarly known ; 
 but these may readily be overcome by- the use of pic- 
 tures or even rough sketches on the board. 
 
 Having thus grouped the names upon the blackboard, 
 a few questions will lead to the perception that the ani- 
 mals of one group have a backbone, composed of many 
 pieces, and an internal bony skeleton ; those of another 
 are made up of distinct rings and joints ; and so on of the 
 other groups, each of which nniy now be readily ex- 
 panded, by asking the pupils for the names of other ani- 
 mals, and the reasons for assigning them to a particular 
 group. 
 
 Then, and not till then, the teacher should give 
 and explain the terms vertebrate, articulate, etc., care- 
 fully reviewing and questioning the class, to see that all 
 is understood. 
 
 In the same manner, the classes of the vertebrates, and 
 the principal orders of the mammalia, etc., may easily be 
 drawn from the pupil's own observations of resem- 
 blances and differences. 
 
 The terms mineral, vegetable, animal, organic, and in- 
 organic, should be previously taught or reviewed in a 
 similar manner, through the perceptions of the pupil, 
 guided by the questions of the teacher. 
 
ELEMENTARY SCIENCE. 131 
 
 Rememher that the skillful use of ititerrogation is 
 the teacher's chief means of aivahening thoiight, ayiil pro- 
 ducing lasting iinprcssions. 
 
 Well-knowu typical animals should be taken as the 
 ohjective basis of the classification ; sucli as 'niau, 
 monkey, hat, cat, rat, horse, deer, coiu, and tohale ; — 
 eagle, parrot, canary, rooster, ostrich, snipe, and duck ; — 
 turtle, alligator, rattlesnake, a.nd frog; — jjerch, cod, shark, 
 etc.; — ice, butterfly, beetle, etc; — spider, cray-fish, and 
 crab; — squid, snail, and oyster ; — starfish, jellyfish, and 
 corals. 
 
 The simplest names should be used, where possible, in 
 preference to the more scientific, or, at least, as pre- 
 paratory thereto ; thus, it is better to use the term four- 
 handed than quadrumana ; gnaivers than rodentia; 
 scratchers than rasorcs ; two-icinged than diptera, etc. 
 A few scientific terms, such as mollusc and bivalve, are 
 in such common use that they may be readily explained 
 and applied. 
 
 Associated facts not strictly scientific — such as the 
 uses of animals, anecdotes concerning them, their pecu- 
 liarities and habits — which the pu})ils themselves may 
 have observed, will form a valuable part of these exercises, 
 and a means of increasing the interest of the lessons. 
 
 The pupils should be encouraged to acquire as many 
 facts as possible by their own observation and research 
 out of school. 
 
 The exercises should be conversational, the reviews 
 frequent ; the instruction should also embrace exercises 
 in classifying well-known animals from a miscellaneous 
 list, giving the reasons in each case. Too much ground 
 sliould not be attempted at first. 
 
 Some system o{ diagrams, roughly sketched in chalk, 
 will be found of great service in assisting the pupils to 
 
132 now TO TEACn 
 
 remember the classification. The best and simplest is, 
 probably, thatnsed in the ordinary "genealogical tree." 
 The diagram should be gradually developed as the 
 lessons proceed, and not the whole of it given in the 
 preliminary stages. 
 
 No teacher can give such a classified " outline" with- 
 out having first, by careful study, acquired it. This 
 can be readily accomplished by means of any good school 
 manual on the rudiments of Natural History. 
 
 Excepting in important instances, it is not expected 
 that the classification should extend to species and 
 variety, sometimes not even to genera. It is desirable 
 that the pupils should have some definite ideas as to the 
 relations of the following terms used in zoology: king- 
 dom, branch or type, class, order, family, gemis, species, 
 variety, individual. These can be best exhibited by a 
 diagram, but they should in no case be presented by 
 formal definition. All but the last four should be 
 mentioned in describing any given animal. 
 
 The exercises should include a portion, at least, of 
 the topics suggested in the following synopsis, Avhich is 
 here presented for the guidance of the teacher. This 
 synopsis comprehends three successive outlines, each 
 complete in itself, or taken with that preceding it : 
 
 FmsT General Outline. 
 
 Distinction of organic and inorganic objects tanglit objectively. 
 Differences between animals and plants. What is an organ ? An 
 animal? Four great types of animals (Cuvier's, and omitting the 
 protozoa). Exercises in classifying, by types only, such animals as 
 the dog^ lobster, clam, coral, shad, icasp, goose, starfish, garter-snake, 
 shrimp, toad, tortoise, oyster, etc. The reasons for the classification 
 should be given in each case. Each type to be then briefly de- 
 fined. Why vertebrates are placed first. 
 
ELEMENTARY SCIENCE. 133 
 
 Second General Outline. 
 
 Classes of Vertebrates, — (Tenney's arrangement is here 
 selected as being brief and simple, but any other may be taken.) 
 Illustrate, as by types, by mentioning animals belonging to the 
 several classes, mammals (^those which feed their young witli 
 milli), birds, reptiles, batrachians (frog kind), fishes ; brief de- 
 scription of each class to be given. Name common vertebrates 
 to be classified, occasionally mentioning an animal not a verte- 
 brate, in order to test the attention and accuracy of the pupils ; 
 for example : alligator, robin, mouse, 'worm, lierring, toad, lion, 
 jelly-fiah, rattlesnake, elephant, flea, hawk, turtle, etc., etc. 
 
 Classes of Articulates to be treated very briefly, but in 
 the same manner as the vertebrates. Simplest division, as in- 
 sects, Crustacea, and worms, to be employed. 
 
 Classes of Molluscs.— Treat also briefly, by referring only 
 to their general characteristics. Teach the meaning of the terms 
 univalve and bivalve. Sp'ecimens of shells vrill be useful for illus- 
 tration ; but it must be remembered that the structure of the ani- 
 mal itself is far more interesting and important than that of the 
 shell which incloses it. A- living oyster or clam, opened and 
 carefully examined, a living snail, and a tumbler of water con- 
 taining a few of the small molluscs found in every pond, will 
 give clear ideas. A small aquarium will be found veiy useful. 
 
 Classes of Hadiates, probably treated with sufficient full- 
 ness in connection with types. Review if necessary. 
 
 Here it would be well to mention the grouping of animals as 
 herbivorous, carnivorous, and omnivorous ; also the general rela- 
 tions of the teeth of animals to other peculiarities, such sts feet, 
 forms, food, dif/estive apparatus, and habits ; also, as for as may 
 be possible, illustrations of the importance of their several func- 
 tions in nature. 
 
 " TnrRD General Outline. 
 
 In this outline some orders should be omitted, or but briefly 
 considered, because not readily treated objectively. If all tlie 
 prescribed classes cannot readily be taught, owing to the limited 
 
134 //Oir TO TEACH 
 
 available time, selections sufficiently complete in themselves 
 may easily be made, as of the class mammals, or birds, or of the 
 type articulates. 
 
 Mammals. 
 
 Two-handed {Bimana). — To be treated briefly. The five races 
 of men, with their characteristic peculiarities. The geographi- 
 cal distribution of each to be also briefly referred to. 
 
 Four-handed {Quadrumana.) — A few examples, according to 
 the experience of the pupils. Refer to the geographical distri- 
 bution. 
 
 Hand-winged (^Cheiroptera).— V&e, a drawing, or a dried, or a 
 living specimen, if one can be procured. Any interesting facts 
 about bats, and their nocturnal habits. 
 
 Insect-eaters {Inseciivora). — Treat very briefly. The mole, its 
 habits — refer to its small, hidden eyes, etc. 
 
 Flesh-eaters (Carnivora).— To be treated more fully. Refer to 
 general structure of teeth, feet, and stomach. Refer to cat family, 
 using common cat as type ; dog family, using dog as type; weasel 
 family, their form, habits, etc., naming sable, marten, ermine, and 
 mink, and referring to the value of their furs ; bear family ; also 
 briefly to seal family. 
 
 Pouched Animals {Marsupials).— Hefer to the geographical dis- 
 tribution. The exception of the opossum. 
 
 Gnawers (Rodents).— Vse the rat or squirrel as a type. Refer 
 to peculiarity of teeth, and the provision for their continued 
 growth. Teach about the rat, mouse, squirrel, beaver, rabbit. Re- 
 fer to the woodchuck, porcupine, and guinea-pig. 
 
 Thick-skinned (Pachyderms).— Treat briefly of the elephant, the 
 rhinoceros, and swine families ; more fully of the horse flimily, in- 
 cluding Aorse, ass, and zebra. Geographical origin of the horse, 
 its dispersion, and its influence in human affairs. 
 
 Cud-chewers (Ruminants).— Tlelntions of food to teeth, stomach, 
 feet, etc., etc. Teach three families • 1. Deer family, horns solid, 
 deciduous ; 2. Hollow-Jwrned family (horns permanent) ; 3. Camel 
 family (hornless). Refer to lUnna and mcu7ia. 
 
 Whale-like (Cfetoea).— Refer to the fish-like character of the 
 
ELEMENTARY SCIENCE. 135 
 
 whale ; how it differs from a fisli ; its uses. The porpoise and the 
 dolplLiii. 
 
 Note.— Two of the preceding orders (8th and 9th), are sometimes classified 
 uiidw the Ibllowiiiij arrangement, which may be readily substituted for the 
 above if thought desirable. 
 
 Hoofed (Ungulates) into two sub-orders : A, cud-chewers (Ruminants), and 
 B, (Non-Ruminants). These are again divided into the following groups of 
 families: — 
 
 A. illollow-horned) ox, sheep, and antelope families. 
 (Solid-horned) deer, giraffe families. 
 (Hornless) camel family. 
 
 B. (Solid-hoofed) horsf family. 
 
 (Thick-skinned or Pachyderms) elephant, swine, hippopotamus, rhinoceros, 
 and tapir families. 
 
 Birds. 
 
 Birds of Prey (Raptores). — Vulture, falcon, owl, condor, hawk, 
 eagle. 
 
 Climbers {Scansores). — Parrot, woodpecker, etc. 
 
 Perchers (Disessores). — Humming bird, swallow, kingbird, 
 thrush, sparrowj canary, etc. 
 
 Scratchers {Rasores). — Gallinaceous birds and dove family. 
 
 Runners (Gursores). — Ostricli ; its habits. 
 
 Waders {GralUitores). — Crane, stork, snipe, etc. 
 
 Swimmers {Natatores). — Duck family : Swan, petrel, penguin, 
 albatross, etc. Refer to ?iests of birds, also their migrations, in- 
 stinct, etc. 
 
 "Reptiles and Frog Family. 
 
 Treat very briefly, tenching something of turtles, crocodiles, 
 and alligators; serpents and their fangs; the frog and its trans- 
 formations. 
 
 Fishes. 
 
 Treat the classification very briefly ; show distinction between 
 the two groups, bony and cartilaginous fishes, with the orders 
 spine-finned and soft-finned ; also the shark and the sturgeon. 
 
 Articulates. 
 
 These present many advantages for the school-room. They are 
 small, and easily procm-ed for perceptive teaching. A simple 
 
136 BOW TO TEACE 
 
 microscope is of great assistance in awakening an interest. Of 
 insects, collections of type specimens can easily be made. Only 
 the simplest and most interesting facts, however, need be taught. 
 The general characteristics of this class of animals should be ex- 
 plained — their structure and the functions of their chief organs. 
 Their wonderful transformations should be explained and exem- 
 plified ; also the difference between insects proper, spiders, and 
 many-footed articulates {myriapods). 
 
 The following orders should be taught and exemplified : 
 
 1. Membrane-winged {Hymenoptera). — Including the bee family, 
 the ant family, the wasp family, the ichneumon family, their 
 peculiarities, habits, and instinct. 
 
 2. Scale-winged (Lepidoptera). — ]\Ioths and butterflies, how dis- 
 tinguished; caterpillars, etc., clothes-moth, geometer. 
 
 3. 2'hjoo-winged {Diptera). — Mosquito fvmil}^, wheat-fly, house- 
 fly, etc. 
 
 4. Case-winged (Coleoptera). — Beetle, fire-fly, weevil, etc. 
 
 5. Ilalf-winged ( Hemiptera) ; or bugs, cicadas or harvest-flies, 
 tree-hopper, cochineal, boat-fly, etc. 
 
 6. StraigJit-winged{Orthoptera). — Cricket, katydid, locust, grass- 
 hopper. 
 
 7. Net-winged [Neuroptera). — Dragon-fly, May-fly. Refer to the 
 white ants. 
 
 Spiders {Arachnida). 
 
 Many-footed Insects {Myriapods). — Centipedes. 
 
 Crustacea. — Crab, lobster. 
 
 Worms. — Earth-worm. 
 Note.— It is important to distinguish carefully the three terms, insect (i. e., 
 eix-footed [hesapod]. or true insects), arachnids, or eight-footed spiders and 
 Bcorpions, and myriajwds, or many-footed millipeds and centipedes. In using 
 a representative of one of these groups as an object, it should be the primary 
 aim to establish the obvious characteristics by which they are distinguished 
 firmly in the pupils' minds. Thus, in the insect proper, the body is divided 
 into three divisions — the head, the body (or thorax), and the liind-l)ody (or 
 abdomen). The head is furnished with feelers, {antenna) ; the body supports 
 three pairs of legs, and generally one or two pairs of wings ; the abdomen 
 shows more or less clearly a number (seven) of rings or joints. In the arach- 
 nids, the head and body are consolidated into one division, which has no 
 antennte, supports four pairs of legs, but no wings. In the myriapods, the 
 entire body consi.sts of a series of verj' similar joints, not grouped into divi- 
 sions separated (insected) from one another, but of which the first serves as a 
 head, whilst each of the others, however numerous, supports either one of 
 two pairs of more or less imperfect legs. 
 
rOUETH GEADE. 
 
 OUTLIISTE COUESE. 
 Time allowed, about five months. 
 
 LANGUAGE. 
 
 Reading.— Oi the grade of a Third Reader Gatter half), with 
 exercises as in the preceding grade. 
 
 Spelling and Definitions. — From the reading lessons, 
 with exercises in miscellaneous words and sentences, as in the 
 preceding grade. Also easy exercises on the prefixes and 
 suffixes, and their applications. 
 
 English Gratnviar. — To include the analysis, parsing, and 
 construction of simple sentences, and with such definitions o?ily 
 as pertain to the parts of the subject studied. 
 
 ARITHMETIC. 
 
 Mental Arithmetic. — As far as in written arithmetic, with 
 exercises as in the Fifth Grade, including practice in the simple 
 applications of the tables of weight, measure, money, etc. 
 
 Written AritJiinetic. — Common and Decimal Fractions, 
 with their simple practical applications, and their conversion one 
 into the other. Also, practice in the simple rules and Federal 
 Money, for the purpose of securing rapidity and accuracy. 
 
 GEOGRAPHY. 
 
 Geography.— O^ the United States in detail. Local and 
 descriptive geography treated as in the Fifth Grade. 
 
138 now TO TEACU 
 
 ELEMENTARY SCIENCE fob okal instruction. 
 
 Sotany, — An outline knowledge of Botany, including the 
 general structure and common uses of such plants as most 
 pupils may readily observe. 
 
 This should, if possible, be taught during the spring and 
 summer months, 'in order to make it in the highest degree ob- 
 jective by the use of specimens. 
 
 Mineralogy/. — A simple outline knowledge of Mineralogy, 
 illustrated by specimens. 
 
 This may constitute the foil and winter course, the specimens 
 being previously collected. When the time permits the teaching 
 of only one of these branches, the season of the year should 
 determine the choice between them. 
 
 WRITING. 
 
 On Slates. — Continued with practice, to give expertness and 
 fluency. 
 
 Oil Paper. — Review of the elementary forms ; their com- 
 bination in words containing long and short letters, without 
 capitals ; next, in words containing both capitals and small 
 letters ; an explanation of the elements involved in each. 
 
 Instruction as to proper position, holding the pen, etc., as in 
 the preceding grade. 
 
 DRAWING. 
 
 Oil Slate or I*aj)€r. — Review of the Fifth Grade as far as 
 may be necessary, and drawing curve lines, and figures formed 
 from them, as the circle, ellipse,. etc. 
 
SPELLING. 139 
 
 How TO Teaoh. 
 
 SUBJECTS OP TUE FOURTH GRADE. 
 
 LANGUAGE. 
 
 Readhiff. — See directions and suggestions given 
 for tlie Fifth Grade. 
 
 Tlie latter half of a Third Header usually comprises 
 selections appropriate to this grade. Particular atten- 
 tion should be given to clearness of articulation, to 
 naturalness of intonation, and to general style. 
 
 Spellhiff. — The exercises in spelling, both oral and 
 written, should be the same as in the previous grade, 
 with the following additional suggestions. The names 
 of important cities, states, and countries, which occur 
 in the geographical lessons of the class, and especially 
 such as are in frequent use in post-office addresses, or 
 are liable to be mis-spelled, should form a part of the 
 miscellaneous luords taught in this grade; also, familiar 
 personal names. An excellent occasional modification 
 of this exercise is, to have the pupils draw the out- 
 line of a letter-envelope upon the slate, or use a neatly- 
 trimmed piece of writing paper of the same shape, and 
 dii-ect it to some person whose address is given by the 
 teacher. The ingenuity of the teacher will suggest 
 many other similar modifications of the exercise. 
 
140 now TO TEACH 
 
 JDefinitioiis. — These should be as in the previous 
 grade, with the following additional exercises designed 
 to lead to the study of etymology. 
 
 " The easy exercises on. the prefixes and suffixes " 
 shoukl be with English primitives at first, without re- 
 gard to the etymology of tliose primitives. The affixes 
 of Anglo-Saxon origin will therefore be taught first; 
 afterward the meaning of such as ah, con,2yre, pro, sub, 
 ion, ent, etc., may be taught as illustrative of the diver- 
 sity of meaning of such Avords as abstract, subtract, con- 
 cede, accede, precede, etc. Also as showing that, for 
 example, all words having the prefix sub convey the 
 signification of under, and all having the suffix ion 
 mean the act of. 
 
 2. Each group, with its common radical or primitive, 
 after being written on the slate or blackboard, should be 
 made the subject of an oral exercise in definitions, in 
 order to impress upon the pupils' minds the modifica- 
 tions of meaning produced by the affixes. The exem- 
 plification of the words in sentences should be also care- 
 fully attended to. 
 
 JEnfflish Grainmar. — The instruction in this 
 subject required for the Fourth Grade includes analysis, 
 jKirsing, and construction, and in the order mentioned. 
 Grammar is the science of the sentence ; and, therefore, 
 the fundamental idea to be imparted is, what consti- 
 tutes a sentence. Oral lessons should precede the study 
 of the text-book, as a preparation for it. The ideas in- 
 volved in the dpfinitinns should first be developed, before 
 the pupils are required to commit these definitions to 
 memory. The contrary practice, once so common, is 
 
LANQ UAOE. 141 
 
 very discouraging and injurious to the pupil, since it 
 compels him to learn by rote a mass of verbiage which 
 is perfectly unintelligible to him. 
 
 Let a short sentence be written on the slate or black- 
 board ; and then, by analysis, let the pupils be made 
 familiar with the relations of the words used as subject, 
 verb or predicate, and adjuncts, or modijiers. The dis- 
 tinctions comprehended in the parts of siJeech can all 
 be successively taught in this way, and the pupil en- 
 abled readily to point them out, before he is required to 
 say what a noun, or pronoun, or verb, etc., is. The 
 learning of the definitions will be easily accomplished as 
 he proceeds. 
 
 The object of the analysis is to find out in what rela- 
 tion the words used in the sentence stand to one another 
 (general grammar) ; the object of the jMrsing (only an- 
 other kind of analysis) is to apply the principles and 
 rules proper to these relations (particular grammar) ; the 
 object of the construction is to impart practical skill in 
 applying these rules and principles, as well as to give 
 thereby clearer ideas of their nature and use. Thus, 
 when the teacher presents the sentence, " Industrious 
 pupils learn very rapidly," the pupil is made to discover, 
 first, the principal parts — subject and verb, or simple 
 predicate ; next, that indnstrious is added to pu2)ils, 
 raindly to learn, and very to rapidly. The jiupil then 
 knows that industrions, being an adjunct of a noun, is 
 an adjective ; that rapidly, being an adjunct of a verb, is 
 an adverb ; and that very, being an adjunct of an adverb, 
 is also an adverb. This instruction can be supplemented 
 by requiring the pupils to construct sentences of a 
 similar kind ; as, sentences containing a simple subject 
 and predicate, — sentences containing a subject and ad- 
 juncts with a simple predicate, — sentences containing a 
 
U2 SOW TO TEACH 
 
 subject and predicate, with adjuncts of both. Some of 
 these sentences may be required to be declarative, some 
 interrogative, etc. In this way the ingenuity or inven- 
 tion of the pupil is brought into play in connection with 
 his knowledge of grammar ; and the exercises glide pro- 
 gressively into extended composition. 
 
 The sentences presented should at first be carefully 
 classified, so that no difficulties may be presented which 
 are beyond the pupils' ability or actual attainments to 
 solve. In grammar, especially, should the instruction 
 be systematic and logical. 
 
 Etymological exercises should be interspersed, espe- 
 cially in the use of the apostrojjhe as the sign of the 
 possessive case — in the proper plural termination of 
 nouns — the proper forms of the pronouns, etc. This is 
 a point of considerable importance. 
 
 The sentences required to be studied in this grade in- 
 clude : 
 
 1. Sentences with a simple subject and a simple pred- 
 icate ; 2. Those with simple word adjuncts of either sub- 
 ject or predicate, or both ; 3. Those with simple phrase 
 adjuncts (so as to teach the preposifio)i); 4, Those 
 with compound subjects or compound predicates, or 
 both, but of an easy character ; as, " John, William, and 
 Samuel are diligent boys," — "The animals turned, look- 
 ed, and ran away." This class of sentences will serve 
 to introduce the conjunction. 
 
 It is especially requisite in all the lessons given on 
 this subject, that the instruction sliould not be allowed 
 to degenerate into tlie repetition of formulae, and instead 
 of being made a means of developing the analytic and 
 reasoning faculties of the pupils, become a piece of 
 worse than useless mechanism. Grammatical instruc- 
 
LANGUAGE. 143 
 
 tion has a distinct office as an educational agent, — an 
 office that can be performed by no other subject. It is 
 addressed to faculties that probably cannot be trained 
 in any other way ; and, therefore, no educational cur- 
 riculum would be complete without it. It should, how- 
 ever, be carefully kept within proper limits, both as to 
 time and place, and should not be permitted to encroach 
 upon other branches of e([ual importance. Each depart- 
 ment of it should also have its due share of attention. 
 
 Of course the study of grammar as prescribed in this 
 grade does not supersede the " exercises for correction " 
 required in all the grades. These exercises, however, 
 by degrees lose their empirical character, and become 
 scientific. They should not be exclusively eitlier ety- 
 mological or syntactical, according to the technical dis- 
 crimination followed in most text-books on English 
 Grammar. Indeed, nothing has done more to bring 
 upon this study an unmerited depreciation, as being a 
 senseless waste of time, than the unwise separation of 
 these correlated departments of the subject. 
 
 For instance, instead of teaching the declension of 
 the pronouns /, tlioiL^ lie, and she, long before the appli- 
 cation of any syntactical rule, the diversities of inflec- 
 tion and their proper use may be observed and studied 
 by the pupil in connection with tlie ordinary analysis 
 of simple sentences, and consequently at a quite ele- 
 mentary stage of the study. Tlie transformation of 
 "John can see James'' into "/can see him," will teach 
 him the nature of a pronoun, how to distinguish it, and 
 then how to define it. An attempted change of places, 
 as in " Him can see I," when taken in connection with 
 the analysis, will show him the reason of the change of 
 form from he to him and from / to me. 
 
 Similar exercises upon the other pronouns, used in 
 
144 liOW TO TEACH 
 
 both numbers, will lead him to see that each of them 
 takes one form when used as the subject of a sentence, 
 and a different one when used as the olject. He will 
 then be ready to use intelligently the terms singidar, 
 plural, nominative, aud objective, as applied to varied 
 inflections, and to correct such errors As, " Who saw 
 him ? i/e." " Me and her saw him," etc., as well as to 
 give the reason for such corrections. Then, and not 
 till then, can he be profitably required to construct,je- 
 j)eat, and explain the declensions of the pronouns. A 
 similar plan should be followed in tlie comparison of 
 adjectives and the conjugation of verbs. 
 
 *A.few common errors are subjoined as a further illus- 
 tration of the kind of work proper to this grade. 
 
 Errors in Etymology.— 1. The Possessive Sign. A. goos'es 
 foot. Three geeses' heads. Two fox's tails. A mans hat. 
 
 2. Improper form of tenses. They done it. We seen him. 
 He would have went. If I had have seen it. 
 
 3. Improper use of verbs. He must set still. The book lays 
 on tlie desk. He laid still. 
 
 Errors in Syntax. — 1. Subject. Me and her can sew 
 2. Predicate. We was there. He don't know. She dare not 
 do it. 3. Object. He struck my brother and I. Who did you 
 gee ? Attribute. If I were him. She looks beautifully. 
 
 ARITHMETIC. 
 
 Mental AritJinietic— The character of the ex- 
 amples to be given in this grade is suggested by the 
 exercises in Written Arithmetic. The same processes 
 and forms of analysis should be employed in both. In 
 connection with the commonly-used tables of weight, 
 measure, etc., should be given such questions as, " In 
 I of a pound of sugar, how many ounces ? " " 18 
 quarts are what part of a bushel ? " etc., etc. 
 
AlUTUMETIC. 145 
 
 Written Ariflinietic. — Federal Sloney sliould 
 also form a part of the regular Avork of this grade at 
 least once a week, and should be frequently reviewed. 
 
 Particular care should be taken in the selection of 
 examples that no one of them be so intricate and prolix 
 as to consume a large amount of time, without afford- 
 ing sufficient exercise of thought in the application of 
 arithmetical principles. 
 
 Too much importance, nevertheless, can scarcely be 
 given to the requirement of "practice for rajjidity and 
 accuracy " in Federal money, as well as the simple rules 
 of Arithmetic. To this should invariablv be assigned a 
 brief portion, at least, of the time given to every lesson 
 in this subject. No part of the arithmetical discipline 
 has a higher utilitarian value, whether for the purposes 
 of practical life, or for progress in the more advanced 
 portions of the study ; for nothing is more discouraging 
 to the pupil than to find that, in any exercise involving 
 other than a few figures, his results are almost always 
 incorrect, from a want of habitual accuracy in perform- 
 ing the simple combinations involved in the elementary 
 rules. Teachers are, therefore, especially advised to 
 employ every variety of proper stimulus to make the 
 exercises for this purpose thorough and effective. 
 
 For general suggestions see the preceding grade. 
 
 Common Fractions. — No part of the study of 
 arithmetic is of more importance than the subject of 
 fractions. When properly tauglit, their value, as a 
 mental discipline, is of the highest order. WIkju 
 taught merely, or chiefly, by memorized formuhe, 
 called " rules," they are, for the greater part, a waste 
 of precious time. 
 
 Jio principle should he prcsenteii until the impil is 
 
146 IIOW TO TEACH 
 
 about to make tise of if, and no defiiiition slimild he given 
 or required before the ideas which it embodies have been 
 deduced, and clearly presented by preliminary illustra- 
 tion and questioning. 
 
 No rules should be' given until a sufficient number 
 of examples for practice liave made them a succinct 
 statement of principles previously understood, or the 
 results of the application of principles, rather than mere 
 mechanical formulse for working. 
 
 In teaching the fundamental principles of fractions 
 the objective process is indispensable. 
 
 The most effective method of treating the subject as 
 a whole, is to give first a very simple offline course of 
 exercises, covering all the essential principles, but by 
 means of examples requiring only small numbers for 
 their solution. Such examples, though readily solved 
 mentally, after some practice, should, in the first stages, 
 be wrought upon the slates, in order to secure correct- 
 ness in notation, and to allow the pupil more easily to 
 give the necessary analysis without the additional men- 
 tal tax required by the effort to retain the numbers. 
 
 In the written exercises pupils should use the signs 
 
 of operation, H x ^, and the sign of equality, to 
 
 indicate the work performed, and its result. 
 
 This outline should then be folloAved by a, full course, 
 in which the substance of the first constitutes the exer- 
 cises in mental arithmetic, while the written arithmetic 
 comprises the more difficult portions of the general sub- 
 ject, as well as a systematic statement of definitions 
 and rules, and practical examples, involving numbers 
 too large to be readily retained in the memory. Such a 
 plan, though apjiarently long, is in reality the most ex- 
 peditions. The })upil soon obtains a clear, comprehen- 
 sive, and connected view of the essential principles, and 
 
ARITHMETIC. 147 
 
 the expanded review which constitutes the second 
 course will then require but little time. 
 
 Syllabus of Topics for Outlines of Common" 
 
 Fractions. 
 
 (with suggestions and examples.) 
 
 I. — The idea of a fractiou developed objectively. 
 
 The equality of the parts to be very carefully illustrated. 
 
 The relative value of various fractional parts, as greater or less, 
 as i, i, -h, etc. 
 
 The definition of a fraction. One or more of the equal parts 
 of a unit. 
 
 The terms of a fraction defined and the 07'der o\^ statement. 
 
 The notation of ti'actions and location of terms, or order of 
 ■writing. 
 
 Exercises in writing and explaining fractions. 
 
 Fractional expressions less than a unit. 
 
 Proper fractions defined, and examples. A proper fraction is 
 one that is less than a unit. 
 
 Fractional expressions equal to or greater iJian a unit. 
 
 Improper fractions defined and illustrated. An improper frac- 
 tion is one that is equal to, or greater than a unit. 
 
 Exercises in writing proper and improper fractions. 
 
 n 
 II. — Fundamental Axiom 1= - 
 
 n 
 
 Reduction of units to improper fi'actions. — Analysis A. 
 (Page 152.) 
 
 Reduction of mixed numhersio improper fractions. — Analysis A. 
 Definition of mixed numbers. 
 
 Exercises in mixed numbers, limited to small denominators. 
 Reduction of improper fractions to mixed numbers. — Analysis B. 
 {Page 153.) 
 
148 liOW TO TEACH 
 
 III.— Reduction effractions togreater denomhiatoris — orbiglier 
 terms. [Wliat may lialvos, thirds, etc., be clianged iujo ? f's ? etc.] 
 To be illustrated objectivel}'. 
 
 Examples with greater denominators than can readily be solved 
 by inspection. 
 
 Analysis G. (Page 152). (Begin with fundamental axiom.) 
 
 Term Divisor or Factor, with exercises in finding, by inspectidn 
 onli/, a Common Divisor or Common Factor. Definition to be 
 given. 
 
 Note.— Too great importance can hardly be given to this exercise of in- 
 spection. The application of the principle is indispensable in many of the 
 arithmetical exercises in every succeedin<^ grade. With proper training, it 
 will become, witliin reasonable limits, a lixed mental habit, requiring no con- 
 scious effort. 
 
 Reduction, of Fractions to Lotcer Terms or Less Denominators— 
 Examples— ^4 /irt^^sis D. (Page 152). Definition of " Lowest 
 Terms." 
 
 Examples in finding what part one whole number is of another 
 — corresponding examples in tables. 
 
 IV. — Multiple — term illustrated and defined. 
 Common Multiple " " " 
 
 Exercises, to be solved by inspection. 
 
 Reduction to Comman Denominatm' — use two fractions only. 
 
 Application of common multiple in reducing to common 
 denominator. 
 
 Distinction between common multiple and common denomi- 
 nator. 
 
 Definition of common denominator. 
 
 " " least common denominator. 
 
 Examples in reduciug to least common denominators. — 
 Analysis C. 
 
 Examples involving previous reduction to lowest terms, by in- 
 spection. Reduce |^ and /« to their least common denomi- 
 natox'. 
 
 Use of common denominator as the simple but indispensable 
 basis for the working and explanation of Addition, Subtraction, 
 and Division of Fractions. 
 
ARITHMETIC. 149 
 
 v.— Impossibility of adding quantities with unlike names, 
 illustrated : Add 3 elms and 4 oaks; add 3 trees and 4 trees = 7 
 trees. 
 
 In teaching tlie elementary principles, the subject of fractions 
 should, as far as possible, be divested of technicalities, and be 
 made to coincide with the acquired experience and simple 
 notions of a child. 
 
 On this account it is much better at first, to say, find \ of |, 
 than to say, multiply | by %, or find % times |. 
 
 Adding things of like names. 
 
 Adding fractions of the same denominator — Examples. 
 
 Adding fractions of different denominators — Examples — 
 Analysis C. (Page 152). 
 
 Necessity of reducing to common denominator. 
 
 The numerators o«/^ added ; why? 
 
 Note.— In no example give more than two fractions. The common 
 denominator to contain not more than two digits. 
 
 Addition of small mixed numbers — Examples — AiialyslsC. 
 
 Note.— See that the sign of operation and the equality sign are not omitted. 
 Avoid reducing to improper fractions. , 
 
 Rule. — 1st. See that the fractions are in their lowest terms ; 2d. 
 Reduce to common denominator ; 3d. Add their numerators, etc. 
 
 Subtracting fractions of different denominators — Analysis C. 
 
 Rule. — 1st. See that the fractions are in their lowest terms ; 2d. 
 Reduce to common denominator ; 3d. Subtract the less nume- 
 rator from the greater, etc. 
 
 The same examples may be used as in addition. 
 
 Questions should be occasionally varied by asking: "Which is 
 
 the greater ? " or " What is the difference ? " 
 
 l 1st. Reducing to improper fractio.ns. 
 NOTB.-In mixed numbers avoid -j ^^^ r^,,,^ amc.n\t case, 7^-2^ (deferred 
 
 ' to review.) 
 
 VI. — " Multiplication of fractions " and " compound fractions" 
 identical. 
 
 Such expressions as | of 2|, 5 of |, etc., only involve the find- 
 ing of a //v/cijowa; ;)aW, and should be treated at first as such, 
 rather than as a special kind of fractions. 
 
 It must not be forgotten by the teacher that from the nature and 
 definition of a fraction, every example in fractious must involve 
 or relate to division in some way. 
 
150 HOW TO TEACH 
 
 There are two cases in the so-called multiplication of 
 fractions : 
 
 1st. Where a fraction or mixed nnmber is to be 
 actually multiplied. In this case the multiplier must 
 be a whole number — as 3 times f, or 3 times 4^. 
 
 2d. Where o^ fractional 23art is to be taken of either a 
 whole number, or of a fraction, or of both; as f of 17, 
 or I of f , or I of 7|-. 
 
 Note. — Mutliplication by a mixed number is a combination of the Ist and 
 2d cases. 
 
 Only in the first case should the expression "rt»nes" be used. 
 
 In the second case the expression " o/"' only should be used. 
 
 In the case of multiplyinn; by a mixed number, the expression " times'''' is 
 used for conciseness, though not logically correct. The proper expression is 
 too cumbersome in practice—" 4 (imes the nuinber and % of the number.''' 
 
 Only the two varieties of the first case, and the first two varieties of the 
 second case should be required until the subject is reviewed. 
 
 Examples : (7 times J Analysis as in simple 
 
 J X , tlieu B. (Page 152). 
 
 Multiplication of Fractions 1 7 times 41 Analysis as in 
 
 t simple X , then B. (Page 152). 
 
 i of 24; ^il of $24. No analysis, 
 except reducing to lowest terms. 
 
 I of 25 ; iJ of 125. Analysis E. 
 (Page 152). 
 
 I of f^ ; II of |. Analysis F. (Page 
 153). 
 
 Multiplication by Fractions 
 = taking part = division : 
 
 For rule and its origin, see Analysis F. 
 
 Examples to be given in the practical form at as early a stage 
 as can be made expedient. 
 
 Find how many cents, or cents and mills, in a given fraction 
 of a dollar. 
 
 Occasional examples involving preliminary reduction to lowest 
 terms. 
 
 Hule. — 1st. See thatthe fractions are in their lowest terms ; 2d. 
 Multiply the numerators for new numerator, and the denomina- 
 ters for a new denominator. 
 
 Solutions by direct cancellation should not be required until the 
 review. 
 
ABITHMETIG. 151 
 
 VII. There are, theoretically, two cases in the Divis- 
 ion of Fractions : 
 
 1st. Division of a fractlonal number by an inte- 
 gral number, as | -^ 7, and 4| -^ 7; evidently identical 
 with i- of |, and ^ of 4| in the so-called multiplication 
 of fractions. 
 
 2d. Division of any nnmberj integral or fractional, by 
 
 A FRACTIONAL NUMBER, aS 5 -^ ^, | -f- |, 8f -f- |, 8|- -^ 9|. 
 
 • 
 
 The form of piittiag the questions should be varied as much 
 as possible, so as to traiu pupils to select and apply the right 
 principle and method. Sometimes the divisor, sometimes the 
 dividend, should be first named. 
 
 "Sow many times are 4| contained in 9 ? " Use this form of 
 questioning at least as frequently as the more technical form, 
 Divide 9 by 4^. 
 
 The two varieties of the first case, and the first two varieties 
 only of the second case, should be required before the review. 
 
 Examples in Division qfandby Fractions — Analysis: 
 
 The method and analysis to be by common divisor. The first 
 case may also be analyzed by Analysis F (page 152), if desired. 
 
 The method hy invertitig the divisor is deferred to the 
 review. See Note 1 under Analysis G (page 153.) 
 
 Ride.— 1st. See that the fractions are in their lowest terms ; 
 2d. Reduce to a common denominator ; 3d. Divide the numerator 
 of the dividend by the numerator of the divisor. 
 
 Examples in finding what part one fractional number is of 
 another. Begin with integers : .5 are wliat part of 8? '3 what 
 part of 11 ? (Analyze from the unit, 1 is ^ of 8, 5 are f of 8, etc., 
 etc.) 
 
 t are what part of | ? f are what part of ^ ? etc., etc. 
 
152 HOW TO TEACU 
 
 Practical Examples ; j If 7 j-ards cost $J, what will a yard cost ? ) 
 1st Group. ( " 8 yards " $4f , " " " " [ 
 
 rif a yard cost $J, how much can be~ 
 
 2d Group. \.,^''''S^'^f'''^V^i 1 
 
 '^ it a yard cost $J, how much can bo 
 
 (, bouglit for $^ ? 
 3d Group. \ \^, I yf ^^ ^ost 1^ ^}:^^ ^:|" * yard cost ? j 
 
 FOKMS OP ANALYSIS FOK THE OUTLINES OF COMMON. FRACTIONS, 
 
 Analym^A.— Example.— Reduce 5^ to halves, or to an improper 
 fraction :— 1 =r f ; 5 = 5 times | =-1^,^ . in. ^ i^ii_ 
 
 Anali^sis B. — Example. — Reduce -"^A to units, or to a mixed 
 number : — 1 = f ; heuce, in -l/ there are as many units as | are 
 contained times in -2-, equal to 7k 
 
 Analysis C— Example. — Reduce | to 7iinths : — In a unit there 
 are % ; hence ^ = |, and f = 2 x f = f . 
 
 Note.— Avoid saying " a wtiole number," or " one whole number," when 
 speaking of a unit. 
 
 Analysis D. — Example. — Reduce iJ to its lowest terms :— By 
 inspection the greatest common divisor is 6, hence it may be re- 
 duced to tliirds ; -,% = \ ; hence there are as many thirds as -j^g are 
 contained times in \\, or <wo-thirds — %. 
 
 Analysis !£,.— Example.— FmHi | of 2-5. \ of 25 is3i ; I of 25 are 
 3 times 3i = 9| ; or (using as a basis the Axiom f of a unit = ^ of 
 3 units ; f == | of 3, first illustraling objectively by lines divided 
 into parts), f of 25 = i of 3 times 25 = ^ of 75 = 9i The former 
 process is, in many respects, preferable. 
 
 Analysis ¥.— Example.— F'md \ of f . (First, as a basis, show 
 OBJECTIVELY that i of ^ = i ; i of i = i; ^ of ^ = -,\-, etc., etc.) 
 i of I = 2^^- ; i of f = 5 times --h = -h ; i of ^ = 3 times -h = i|. 
 
 Note 1st. — Make the same question " practical," and apply the same 
 analysis. If a yard cost $y, how mucL will | of a yard cost ? It will cost J 
 of f- of a dollar, etc., etc., as before- 
 
 Note 'Hd.— After a few simple examples have been carefully analyzed, 
 point out the numerical relation of the numerator and the denominator of the 
 product to those of the factors, and then, not before, deduce or give the follow- 
 ing 
 
 Bule for tlie Multiplication pf Fractions : 
 
 1st. See that the fractions are in their lowest terms ; 2d. Mul- 
 
ARITHMETIC. 153 
 
 tiply the numerators for the numerator of the product; and 
 multiply the denominators for the denominator of the product. 
 
 Analysis G. — Example. — If a yard costs $J, how much can be 
 bought for %l ? 
 
 (See Aiialy.ns B, 5th Grade, to be combined with reduction to 
 Common Denominator.) 
 
 If a 3'ard cost $|, $^ will buy as many yards as %% are con- 
 tained times in ||, or, reducing to Common Denominator, f == 
 fi. 9 = fl. as many yards as tk are contained times in f |, or 2/7" 
 yards. 
 
 Note 1st.— To "invert the divisor and proceed as in multiplication," is 
 much more concise as a method, but it is not in any sense an analysis, but a 
 condensed and valuable rule, wliich is to be l)oth taught and analyzed in the 
 review. When this concise rule is taui^ht before the analysis by reducing to 
 a common denominator, the teacher will usually find three undesirable results: 
 first, the pupils are as likely to invert the wrong fraction as the right one, 
 unless the question is always put in one particular way, and even then, until 
 after much practice ; thus showing that they are not guided by any principle : 
 second, they cannot explain the process ; and third, it is then niiicli more 
 difficult to teach the analysis, because their minds are preoccupied by the 
 brief rule, which naturally seems to them so much more desirable, as it costs 
 little or no mental effort. 
 
 As the study of fractions is an important biental discipline, any course 
 which practically excludes the fundamental principle of division by a fraction 
 should be carefully avoided. 
 
 Note 2d.— It will be perceived that the analysis of the division of one frac- 
 tion by another by the process of reducing to a common denominator, is essen- 
 tially identical with the analysis of reducing an improper fraction to a whole 
 or mixed number. 
 
 Analysis H. — Example. — If f of a yard cost %l, what will a 
 yard cost ? 
 
 (See Analysis C, in 5th Grade, with which the following is es- 
 sentially identical.) 
 
 If f of a yard cost $ J, | of a yard will cost \ of $f (note that this 
 division by the numerator is the vital step in the process), which 
 is $:/u ; and a yard or } will cost 7 times $-2^;, or $|i, equal to $l-/o- 
 
 Note 1st.— This is one of the most important analyses in the entire range 
 of the arithmetic of the grammar-school grades. If neglected, or badly taught, 
 it seriously deranges the work of the teachers of more advanced grades, where 
 it must be so frequently applied. If the teacher will present it immediately 
 after, and then in connection ivilh, a review of Analysis C, in the Fifth Grade, 
 and dwell particularly upon the step noted in parenthesis, a great part of the 
 difficulty in fixing the entire process will disappear. 
 
154 HOW TO TEACH 
 
 Note 2.— It is, of course, understood that the examples given to the class 
 will not be confined to yards and dollars. Even the order of these should be 
 at times inverted ; as, in the problem last treated, we might have — 
 
 If $6 purchase ^ of a yard, how much will a dollar buy ? 
 
 * 
 
 Syllabus op Topics for Expanded Review op Common 
 
 . Fractions. 
 
 I. Systematic Review of Definitiom of terms used in fractions, 
 with illustrative examples. Omit complex fractions having fractions 
 in the denominator. Complex fractious having an integral de- 
 
 nominator, such as ^, read 3^ fifths, are to be " reduced to higher 
 o 
 
 terms." See AnalysisC, page 153. The multiplier to be used is 
 
 evidently the denominator of the fraction found in the numerator. 
 
 All other cases of " complex fractious," so called, should be 
 
 71 
 
 treated as indicated division. Such expressions as — * are not 
 
 Jj 
 
 to be explained as fractious. A unit cannot be divided into 9J 
 
 equal parts. 
 
 Examples in finding (he Greatest Common Factor of numbers by 
 inspection. — Mental. 
 
 Examples where the factor cannot be readily found by inspec- 
 tion, as 292 and 365 ; — 315 and 573. The special method re- 
 quired is too difficult for analysis in this grade. It is one of the 
 few points to be taught empirically. 
 
 The result always should be tested or proved in accordance 
 with the definition of Common Factor or Common Divisor. 
 
 II. Reduction of Fractions to their Lowest Terms. 
 
 Examples to be reduced by inspection ; jlSg-, ff §, Analysis D, 
 page 153. 
 
 Examples involving the special method of finding the Greatest 
 Common Factor ; as §g|, f f §, etc., etc. JJfot too long. — Analysis 
 D, page 153. 
 
 Reduction of Improper Fractions and Mixed Numbers. 
 
 1st. Examples solved mentally or by inspection. 
 2d. Examples with larger numbers. — Analyses A and B. 
 Examples in finding the Least Common Multiple of two or 
 more numbers — and definition. 
 
ARITHMETIC. 155 
 
 1st. By inspection, as 5, 3, 2 ; 10, 20, 30. 
 
 2d. When not readily solved by inspection, as 28 and 39 ; 72, 
 25, 88 ; 6, 12, 18, 24, 3fi, and 48. 
 
 Statement of Method or rule. 
 
 Relation of Least Conimon Multiple to Least Common De- 
 nominator. 
 
 Distinguish carefully between the two, and define each. 
 
 Examples in reducing to Least Common Denominators. — 
 Analysis C. 
 
 Give occasional examples involving preliminary reduction to 
 lowest terms by inspection. 
 
 III. Analysis C. Examples in Addition of Fractions and of 
 
 Mixed Numbers, 
 
 Say " Reduce to Least Common Denominatoi'" rather than, "Find 
 the Least Common Multiple of the Denominators. Of course the 
 latter forms a pai't of tlie process of the former. 
 
 Examples in Subtraction ; as -h—ti ; 87^ — 29ig. Do not allow 
 reduction to improper fractions. 
 
 Make both kinds of examples as practical as possible. 
 
 Practical Examples {not too long), each involving both addition 
 and subtraction. 
 
 Note.— Teachers should remember, that arithmetic is not only a science, 
 but also a practical art ; that this art involves imporUant devices, many, or 
 most, of which have been alrrady taught, and their principles explained. 
 These devices, such as reducing to lowest terms, cancellation, rejecting ter- 
 minal O's of a divisor, should not be at any time lost sight of. Examples 
 should be occasionally given of such a character as to require these devices. 
 The omission or neglect of these important matters would be a serious defect 
 in the character of the instruction given. 
 
 Principle of Cancellation. — Siiow its identity with dividing by 
 common factors, and •wiih.reduciriy to lowest terms. Show this by 
 examples in fractions. 
 
 Exainples of simple applications of cancellation to whole 
 numbers. 
 
 IV. Multiplication of Fraction* 
 
 Give examples where cancellation cannot be applied. — 
 Analysis F. 
 
 H X 3/5-; X ^f ; Ux 144; 161x12}; abstract and p?vzc^jOTi. 
 
 Give examples that should be done by cancellation.— ^«a/y«w. 
 Lowest terms. 
 
156 now TO TEACH 
 
 125 X -,^ ; It of $17,38 ;— if 39 barrels cost $84, what will 26 
 barrels cost ? 
 
 If a ton of hay cost $17^, what will H ton cost? 
 
 If 1 acre cost $237-, what will 19-|V acres cost ? 
 
 Pupils should be made familiar with the following principle 
 and its applications. It is frequently the most convenient 
 method of solution. See Analysis E, page 152. f of a number 
 are equal to i of 3 times the number, etc., etc. 
 
 f of40 = iof3times40. 
 
 V. Division of Fractions. 
 
 1st. Review and apply the method by common denominators. 
 
 2d. Review thoroughly its analysis. Analysis G, page 153. 
 
 od. Teach carefully the following analysis, giving a variety of 
 short examples to fix it thoroughly. See Analysis I, page 157. 
 
 4th. Teach the brief and useful device of inverting the divisor, 
 but in no case let the analysis of the rule be forgotten. Let it be 
 given by the pupils as often as may be found necessary to insure 
 its retention. The teacher is again reminded of the importance 
 of the proper application of the principle of repetition of mental 
 effort. 
 
 Examples in finding what part of one number is of another; 
 as 7i are what part of 9^ ? $4f , what part of $7| ? iJ what 
 part of 11 ? — See Analysis I, page 157. 
 
 Give examples where cancellation cannot be applied : 
 
 At $lf a yard, how many yards can be bought for $13^? 
 
 If 5j bushels cost $18f, what will 1 bushel cost? 
 
 Give examples where cancellation is to be applied : 
 23i-^13A ; 21f ^2^1, etc. 
 
 Give short examples involving simple combinations of the 
 multiplication and division of fractions ; also addition or sub- 
 traction, with multiplication or division, like the following : 
 
 Bought 7| yards and 3|- yards at $1| a yard ; what is cost of 
 the whole? 
 
 Bought 36 yards ; kept 9^ yards, sold the remainder at $j a 
 yard ; how much did I get for it ? 
 
 If I had sold it for $7^, how much a yard would that be ? 
 
 If I yard cost $?-, what will S' yard cost ? 
 
 If % yard cost $f, how much can be bought for $51- ? 
 
ARITHMETIC. 157 
 
 Forms op Aiiai,tsi3. 
 
 The following is the simplest form of the analysis of the im- 
 portant practical rule of " inverting the divisor," etc. The in- 
 troductoiy step of using a unit as the dividend, is only a case 
 of dividing one fraction by another. 
 
 Analysis I.— Example.— Ti'iw'vSe f by f. 
 
 {Begin with a unit for the dividend, and apply the principle of 
 common divisor.) 
 
 1st Step.— A unit divided by f^, or ^ -r- f = Hwhich quotient, it 
 will be observed, is the divisor inverted). 
 
 2d Step.— Therefore | of a unit divided hy\ = %oil = lh- 
 
 Condemed form.— {I -i- ^) = (} -i-^) = I ; therefore (t -- f ) = f 
 
 of^=H- 
 Example.— li^ of a yard cost $|, how much can be bought for 
 
 Analysis. — Combination of H and G. Page 153. 
 Example.— K^ of a yard cost $*, what will A of a yard cost? 
 Combination of H and F. 
 
 Note.— Give a thorough review of analyses F, G, and H, before attempt- 
 ing the above combinations. 
 
 Decimal Fractions. — The exact nature of decimal 
 fractions should be explained and illustrated ; also the 
 meaning of the word decimal. Show that decimal frac* 
 tions may be used like common fractions by writing 
 the denominator. Illustrate by the decimal notation, 
 showing that whole numbers greater than 9 are also ex- 
 pressed decimally. 
 
 Show also that decimal fractions are really only a 
 kind of common fractions, the two having the relations 
 of species and genus. The methods of writing, and the 
 various analyses are essentially identical, case for case, 
 as shown by the following syllabus. 
 
158 SOW TO TEACH 
 
 The illustrations may embrace the following : — 1. 
 How to write decimals, as 7-tenths, 7-hundretlths, 7- 
 thousandths, 7-ten-thousaudths, etc. 2. Show that the 
 mimerator is first written, as in common fractions. 
 
 3. Show that the *' decimal point" and the cii)hers, 
 when used, are only required to indicate the denominator. 
 
 4. In reading decimal fractions, the pupils should be 
 cautioned to avoid such expressions as " tens of thou- 
 sands " for ten-thonsandtlis, " hundreds of thousands " 
 for hundred-thousandths, etc., etc. In connection with 
 the reading of such fractions, pupils should be trained 
 to recognize readily the comparative value of different 
 fractions; as that .3 is greater than .0987 or .01 than 
 .009596, etc. They may also be made to perceive readily 
 the approximate value of decimals as compared with 
 simple common fractions ; as, that .7634 is a little more 
 than I ; that .8741 is somewhat less than f, etc. Pre- 
 vious to this, however, it is well to teach the exact value 
 of certain decimal expressions: as .75=1, .125 = ^, 
 .375 r=|, etc. These exercises will serve to render the 
 subsequent work of the pupil intelligible. 
 
 Syllabus of Topics. 
 
 I. Exercises in reading decimal fractions. 
 
 Exercises in telling how many places are necessary for a given 
 denominator, and vice versa. 
 
 Exercises in writing decimal fractions. 
 
 Reduction of decimal fractions : 
 
 1st. By Inspection, with analysis as in common fractions. 
 
 Examples, mental, oral, and written. 
 
 .3 to .OO's, to .OOO's, etc. ; .15 to .OOOOO's. To higher terms. 
 Analysis C, common fractions. Page 153. 
 
 3 to .O's, to .OO's, to .OOO's, etc. ; 11X\ to .O's, to .OOO's, etc. ; to im- 
 proper fractions. Analysis A, Page 153. 
 
 Reduce .700 to lowest decimal terins. Give Analysis D, Page 153. 
 
ARITHMETIC. 159 
 
 NoTK.— Avoid saying " the ciphers to the right are crossed off because 
 they are of 710 use." The statement that " they do not affect the value," is 
 not satisfactory unless the pupils show why they do not. 
 
 II. Reduce common fractions to decimal fractious. Give Analy- 
 sis E. 
 
 Use axiom — J of a unit =r ^^ of 3 units ; f = ^ of 3. 
 
 Make this definite by objective illustration, using lines divided 
 into parts. 
 
 Example. — \ to tenths ; to hundredths ; f of 1 = ^ of 3 = ^ of 30 
 tenths = 7i tenths = .7i = .75. 
 
 Note.— Pupils should be accustomed to read decimal fractions, especially 
 hundredths (in subsequent grades applied to per cent.), so as to include out- 
 standing fractional parts, where there are any. 
 
 It is generally better to state what denominator i.s required, instead of the 
 more indefinite requirement to " reduce to a decimal fraction." 
 
 .Ecawi^fe.— Reduce -,a,- to a decimal fraction of two places, or reduce -^^ 
 to hundredths. 
 Am. Two places will give hundredths for the denominator. 
 
 4 1 1 \4.00 
 
 — := — of I = — of four-hundred hundredths = 11/ 
 
 11 11 11 .36 4-11 
 
 240 240 24 3 \3.00 
 
 Reduce — to a decimal: — = — = - = K of 3 = 3^ of 300 hundredths =4^ 
 
 320 320 32 4 .75 
 
 RiiU 1. 1st. Reduce the numerator, considered as a whole 
 number, to an improper fraction with the required denominator. 
 2d, Divide by the given denominator. Or, 
 
 Rule 2. Divide the numerator by the denominator. 
 
 Note.— Give examples to show what common fractions in their lowest 
 terms can fjt. made entirely decimal, and which can not. In the general work 
 of the class, pupils should rarely be required to continue the division 
 beyond three or four places. 
 
 Beducing Decimal Fractions to 'Common Fractions in their 
 
 Lowest Terms. 
 
 i2ttfe.— Write the fraction as a common fraction and reduce to 
 lowest terms. Analysis D, common fractions. 
 
 Examples: .G25 .4125 .87500 14.125 
 
 .071 .'6k -661 5.1 H .87i 
 
 Note.— Pupils should be made thoroughly familiar by rapid mental exer- 
 cise, usually without analysis, with the decimal expressions for halves, .■Jds, 
 4ths. 5ths, 6ths, 7ths, Sths, 9ths,llths, l-2ths, and vice versa, using preliminary 
 reduction to lowest terms whenever possible, as in -^j, §, etc., etc. 
 
160 SOW TO TEACH 
 
 III. Addition -of Decimal Fractions. 
 
 Examples : Add .2, .05, .008, .7283. Add .0005, .97, .0101, etc. 
 " Give mixed numbers. 
 
 Analysis as in common fractions, by principle of reducing to 
 lowest terms. The necessary additional ciphers may be " under- 
 stood " in the solution, but not in the oral anal^'sis, which should 
 be as brief as possible. 
 
 IV. Subtraction of Decimal Fractions. 
 
 Examples : .1 - .075 ; 1.001 - .01009, etc. 
 
 Explain as in common fractions, with the same analysis. 
 
 V. Multiplication of Decimal Fractions. 
 
 Note. — Do not give large denominators. Use the bi-ief rule of common 
 fractions. Cases as in common fractions. . 
 
 Ist. When a fraction or a mixed number is to be multiplied, as : 
 4 times .7&, 17 times 8 047. 
 Value of 1.3 barrels at $8,375 a barrel. 
 
 2d. Wh.Gnsi fractional part is to be taken, as : 
 .4 of .83, .4 of 75, .4 of 8.75. 
 
 How much is .7 of $38.45 f .079 of $120 ? .90fef of $160.48 ? 
 Value .17lt of ton @ $93 a ton ? at $92.87>!i a ton ? 
 
 3d. Combinations of the 1st and 2d cases, as : 
 3.4 lbs. at 79 cts. a lb. ? $.79 x 3.4. 
 8 cwt. 75 lbs. ® $2.47 a cwt. $2.47 x 8.75. 
 
 Note. — As preliminary to 2d and 3d cases, give mental exercises in finding 
 the product of two decimal denominators, as " lOths by lOths, how many 
 places? " " lOOOths by lOOths, how many places ?" etc., etc. 
 
 Examples of cases involving reduction : 
 
 .024 X .15 = ? Product of numerators, 24 x 15 = 360, the new 
 
 numerator, lOOOths by lOOths = lOO.OOOths, or 5 decimal places 
 
 for denominator. Ans. .00360 = in lowest decimal terras .0036. 
 
 "Why cross off the last ? To divide both terms by 10. 
 
 Note.— Many questions are as well solved by the application of principle 
 (E) in common fractions. See Analysis E, page 152. 
 
 .079 of $14.8.3=. 001 of 79 times $14.83, etc., etc. 
 Use or not as may be judged expedient. 
 
 VI. Division of Decimal Fractions. 
 There are two cases, as in common fractions : 
 
ARITHMETIC. IGl 
 
 1st. When the divisor is an integer : 
 
 7 -^ 8, 8 ^ 7, 6-i-5, G -J- 130, 7.2 ^ 6, 3.6 -^ 120, etc. Put ques- 
 tion in several ways : 1st, Divide 7.2 by G; 2d, How much is 
 \ part of 7.2? 3d, How many times is 6 contained in 7.2? 
 
 . etc., etc. 
 
 This simple case does not require the principle of the common 
 denominator. 
 2d. Wlien the divisor is or contains a decimal fraction : 
 
 G -f-.03 ; .8 -r- .005 ; .004 h- .8 ; .003G h- .024 ; 7.2 ^ .009 ; 8 ^ 5.45 ; 
 
 3 -5- 7.203 ; .2 -^ 8.75 ; .3006 -i- 7.4 ; 8.5 -f--9.78 ; 8.G38 h- 9.5 ; 8.638 
 
 -T- 4.3, etc., etc. 
 
 Solution and analysis by the principle of common denominator. 
 
 There are two forms of applying this principle : 
 
 1st. Where the denominator of the divisor is the greater, 
 (.003)^,) INCREASE the denominator of the dividend to .OOO's. 
 
 2d. Where the denominator of the divisor is the less, (.12).1728G,) 
 DIMINISH the denominator of the dividend to .OO's (hundredths) 
 by cutting off the last three figures. 
 
 A General Rule. — 1st. Reduce the denominator of the dividend 
 to the denominator of the divisoi-; 2d, Divide the numerator of 
 the dividend by the numerator of the divisor. 
 
 The quotient will then be a whole number. Other decimal 
 places either added to the dividend or cut off from it, are to be 
 " brought down " in the further division, and will give the frac- 
 tional portion of the quotient. 
 
 Applications. — The applications of decimal fractions will be 
 prinoii)ally found in Federal Money. Simple combinations with 
 common fractions should occasionally be used ; also simple com- 
 binations of two or more of the rules of decimal fractions. 
 
 Use the \ifu\c\\)\Qs,o^ cancellation und reduction to common frac- 
 tions whenever they will simplify the operation. 
 
 E.xamples in finding what decimal fraction one decimal fraction 
 is of another ; especially how m-Arxy hundredt?is—\\sQ only small 
 amounts or very simple examples : 
 
 8 cents, how many hundredths of 64 cents? 
 $7.25, how many hundredths of $9.75 ? 
 
1C2 MOW TO TEACU 
 
 a 
 
 ei 
 
 CO 
 
 a 
 
 S s^-S o^^^a) . lo <=» t„ 
 
 ^ -«— ^3 oj ^ ^ «— ' -*-j rf ^ 
 
 n a '-S "C 'a 73 a .2 ■" ^" 
 
 " r- .-.s.ri > o t- ^^ 
 
 
 5y5 
 
 rt .ti . t: s- 
 
 
 « -^ § &; § Cod® r =5^i£2 =^ § « « 
 
 2 ^ a 2 ^ «'y?: se ^s-r-So a c CO ^• 
 
 .2 " "^ g 5^3 .^ t? > 2 ^ ^-^ a ---^ rn- « 
 
 w S'^ S ~ = « !=o^c>2«p So'"?? 
 
 g o a -a 11:^ § IZ-'^-^H ^ .2 g ^ 
 
 
 t^jrgapC e>.. >>a =^10 *" 
 
 •rl O -S ^ §,-,a^« O . fr' SSoJd 
 
 ga=3^E^o_^^^2 2S^ aSSg 
 
 '^fla^SS-"" -as «wll^ 
 
 •S .£ ^ a a S ^ I I E^ ^ ^ ^ - 
 
 « .3 -g fe fe a — • F^ 2 . -claJ Ha> S 
 
 ^ " -^ c o rt o1 .2 •" ^. S -2 .2 ^ 
 
 3 KW> o S^ ^ --o H» 5d 
 
 ' «^ CO a^ m- 
 
 i 
 
QEOGRAPUT. 163 
 
 GEOGRAPHY. 
 
 Geography of the United States in detail. — Iisr teach- 
 ing tlie geography of the United States, it is particularly 
 important that the time of the pupil be not exclusively 
 taken up with the study of mere local details — with 
 learning the several courses, etc., of long lists of rivers, 
 and the exact situation of still longer lists of towns. 
 A certain, but carefully limited, amount of local geo- 
 graphy is indispensable as a basis for the more im- 
 portant descriptive geography. 
 
 The necessary local geography embraces the names of 
 the several States and Territories, and their division into 
 several groups, as New England, Middle, States etc., etc.; 
 their boundaries or relative positions; their important 
 rivers, lakeSj bays, capes, islands, mountain ranges, and 
 peaks ; the capital of each State, and a few of its other 
 leading cities or towns, if of any importance. All these 
 should be carefully learned as a basis for the subsequent 
 jDortions of the study. 
 
 Tlie descriptive geography should include the simplest 
 physical outlines of the country as a Avhole ; the eleva- 
 tions, the great mountain ranges, plateaux, and plains; 
 the drainage by single rivers on the Atlantic slope, and 
 by extensive complex river systems in the remainder of 
 the country ; the climate, with its modifications in the 
 several sections, as cold or hot, Avet or dry ; the leading 
 industries and the staple agricultural, mineral, and 
 manufactured productions, with their dependence upon 
 the physical conditions. 
 
 Add to this a simple and very brief outline of the 
 general and State governments, the population, its four 
 races and their distribution ; the great commercial 
 
164 HOW TO TEACH 
 
 routes, natural or artificial, and the cities, as the centers 
 of manufacturing and commercial industry. 
 
 The descriptive geography of individual States or 
 Territories may then, in great part at least, be deduced 
 from a consideration of these general facts. All tire- 
 some sameness and repetitions Avill thus be avoided, and 
 the pupil will be made to appreciate the real importance 
 of the study. 
 
 ELEMENTARY SCIENCE. 
 
 (By Oral lustruction.) 
 BOTANY. 
 
 The general suggestions relating to the object of this 
 branch of instruction, given in connection with the 
 subject of zoology, in the preceding grade, and tbe re- 
 marks there made in regard to the extent of classifica- 
 tion, the terms employed, etc., are equally applicable to 
 the subject of botany. As a science of observation, this 
 subject has a decided advantage over zoology, especially 
 for educational purposes, inasmuch as the objects of 
 which it treats are examined, dissected, and analyzed 
 with more facility. They also possess more obvious 
 beauty, and are devoid of the repulsiveness which at- 
 taches to so many objects of the animal kingdom. An 
 insect, apparently disgusting at the first view, when 
 closely examined, often shows more beautiful properties 
 and more striking evidences of design than the most 
 elegant blossom ; but the natural aversion to handle it, 
 or come in contact with it, must first be overcome. 
 
 The classification of plants, being based upon dis- 
 tinctions often very minute, must, for the purposes de- 
 signed to be accomplished in these simple lessons, be 
 
ELEMENT All Y SCIENCE. 1 Go 
 
 carefully limited. Only common plants need to be 
 classified. The limitations of the classification to be 
 taught are indicated below. 
 
 The first feto lessons should show the structure of 
 plants and the general functions of each of their parts, 
 — the root, the stem, the leaf, the Jloivcr, the seed ; the 
 groivth of the plant from the seed, both as to root and 
 stem,, the food of plants, buds and branches, — how a 
 plant grows from them ; the distinction between herbs, 
 shrubs, and trees ; also between annuals, biennials, and 
 2)'erennials. Examples of each to be given. 
 
 Classification of leaves — a beautiful and very useful 
 department of the subject, especially as a means of 
 training the powers of observation — may then be 
 taught, the children being encouraged to gather speci- 
 • mens for careful scrutiny. The vocabulary employed 
 to indicate the peculiarities is very interesting, and will 
 serve to teach something of etymology — as ovate, cordate, 
 palmate, digitnte, serrate, etc., etc. Give the pupils /or- 
 mulce for methodical examination and description. 
 {See Miss Yoiunans^s ^^First Booh of BotanyT) 
 
 Classification of roots and stems, to be taught in a 
 similar manner, but much more briefly. Next, that of 
 blossoms. First, show the parts of a blossom, taking a 
 regular one to begin with — as of a lili/, a morning- 
 glory, or a butter-cui). Analyze so that the pupils can 
 see the parts, showing the cahjx and sejxils, the corolla 
 and petals, the stamens and tlie p)istil ivith its ovary. 
 Give a sufficient number of exercises to make this fami- 
 liar, and let the pupils analyze for themselves. The 
 2Jrincipal forms of flowers, as bell-shaped, wheel-shaped, 
 salver-sha^jed, cross-shaped, butteifiy-shaped, etc., etc., 
 may then be shown. The arrangement of the blossoms 
 on the stem (inflorescence), as far as it can be exempli- 
 
IGG IIOW TO TEACH 
 
 fied by actual specimens, as head, raceme, spiJce, umbel, 
 etc., may also be learned. 
 
 The following outline of classification may be 
 taught : — 
 
 A. (Series.) Flowering (pJicBnogamous) plants. 
 
 B. (Series.) Flowerless {cry2)togamous) plants. 
 
 At first use o\\\j i\ve familiar terms. The scientific 
 may often be dispensed with entirely. Give examples 
 of plants in each series ; as — 
 • Hose, Lily, Geranium ; Fern, Moss, Mushroom. 
 
 A, including a (class). Outside-growing {exogenous) 
 
 plants 
 h (class). Inside-growing [emlngenous) 
 plants. 
 
 Illustrate by stems, showing the rings or annual lay- 
 ers of growth in the former, with harh, wood, and pith, 
 and their absence in the latter. Teach the coincident 
 peculiarities of the leaves, as netted-veined and parallel- 
 veined, affording a ready method (approximate) of dis- 
 tinguishing these plants, and thus giving opportunity 
 for useful exercises ; also those of the seeds, as of two 
 seed leaves (cotyledons) or only one {dicotyledonous 
 and monocotyledonoUs). 
 
 Familiar examples to be found by the pupils ; such 
 as Rose, Buttercup, Geranium, Pea, Potato, Grape-vine, 
 etc., etc., and Lily, Indian Corn, Common Grass, etc. 
 
 {a), Including 1. Orders or families of plants, with 
 blossoms of many petals {polypctalous) ; and, 2. Orders, 
 or families, of those, with blossoms of one petal {uiono- 
 petalous). The pupils will readily find specimens of 
 each, the names of which they have already learned. 
 
 The orders of {h) should not be taught. Nor need 
 any instruction be given in relation to the classification 
 of cryptogamous plants, ferns, mosses, etc., this being 
 
ELEMENTARY SCIENCE. 167 
 
 too difficult, and depending upon distinctions not suffi- 
 ciently obvious for the purpose of these lessons. Atten- 
 tion, however, may, if occasion offers, be called to the 
 fructiJiGation of ferns. 
 
 Such of the orders or families, should be taught as 
 are very familiar, and depend upon quite obvious dis- 
 tinctions, familiar names being exclusively used. Thus 
 the Mustard Family, the Pulse Family, the Crowfoot 
 Family, the Rose Family, the Lily Family, etc., etc., 
 may be taught as far as the collection and presentation 
 of specimens render it desirable ; that is, not the mere 
 fact that there are such families, but in connection 
 with an actual object, and when the inquiry is, to what 
 family does it belong ? If the season permits, and there 
 is an opportunity for the pupils to seek for specimens, 
 this part of the instruction may be extended. Here the 
 judgment of the teacher (never to be superseded) must 
 be carefully exercised, it being constantly in view that 
 the object of these lessons is not to make the pupils 
 hotanists, but to create a basis for the study of natural 
 objects, and to develop the faculties of perception and 
 reflection. Species need not be taught, although the 
 pupils may, as occasion offers, be made to perceive the 
 diversity presented by different individuals of the same 
 family, so as to learn what is meant by species. 
 
 The common uses of plants may be taught to some 
 extent incidentally with some of the above instruction, 
 but more fully at this stage. This will embrace their 
 uses for food, clothing, medicine, etc. Take our own 
 plants first. Show that the roots of some plants are 
 useful; of others, the see^6' ; oi\\Q\'S,, i\\Q leaves ; others, 
 the fruit ; others, the iark, etc. Some few plants of 
 other climates and countries may then be referred to, 
 as cotton, rice, sugar, tea, coffee, etc., etc. The relation- 
 
1G8 HOW TO TEACH 
 
 ship of these plants to our own may then be shown; 
 that is, i\ie families to which they belong. 
 
 MINERALOGY. 
 
 Before commencing instruction in this branch, the 
 teacher should again read the general remarks on teach- 
 ing elementary science in the Fifth Grade. This sub- 
 ject presents some peculiar advantages for attaining the 
 special object of oral instruction — the discipline of the 
 observing faculties. In no other department of natural 
 science, is it so completely within the power of the 
 teacher to present the facts to be acquired to the im- 
 mediate perception of the pupils in the class-room, and 
 in no other is more delicacy of discrimination required 
 in the exercise of the senses upon which the perceptions 
 are based. But while the objective method is thus seen 
 to be peculiarly applicable to this branch of science, it 
 must, at the same time, be remembered that no other 
 subject perhaps requires so large a share of imparted 
 information. This, however, should be given not arbi- 
 trarily, but as something needed to supplement the 
 knowledge gained by the pupil in the exercise of his 
 own faculties, and, as far as possible, in answer to his 
 inquiries, the determination of the i\\\wi\.io self -activity 
 being the great desideratum in this kind of teaching; 
 hence, the important princijile should be kept steadily 
 in view that nothing should be done for the pupil which 
 he can be made to do for himself. 
 
 The teacher should also bear in mind that it is utterly 
 impossible to teach the subject without special prepara- 
 tion for it — without being practically familiar with at 
 least the outline facts of the science. Tliis preparation 
 may readily be made with the assistance of even a small 
 
ELEMENTARY SCIENCE. 1G9 
 
 cabinet of minerals, properly labeled {Dat/'s Grammar 
 School Cabinet, for example), and any of the smaller 
 raannals of Mineralogy (Dana's, for instance). 
 
 What has been said in the preceding grade, as to the 
 propriety or necessity of attempting only a part of the 
 gnbject, is eqnally applicable here. What is done should, 
 however, be systematic — not miscellaneous and unre- 
 lated. Do not attempt to treat any of the tojiics ex- 
 haustively. A large part would not be understood or 
 remembered, and valuable time would be misapplied. 
 
 The investigations made by the pupils in relation to 
 each mineral shon^ild be guided by the teacher by means 
 of a regular formula, considering in a fixed order its 
 form, structure, cleavage, fracture, hardness, weight, 
 color, luster, etc. , etc. These special characteristics and 
 their proper order will be readily remembered after a 
 little practice. Eacb term thus used should be care- 
 fully illustrated and explained as soon as its introduc- 
 tion becomes necessary. 
 
 Begin with Minerals — RocTcs to be afterwards con- 
 sidered as mineral aggregates. A clear conception of 
 the general jiroperties of minerals may readily be given 
 by commencing with ice — water — steam. 
 
 As a preparatory step, lead the pupil to form some 
 definite idea of the variety of forms of crystals, by briefly 
 comparing coarse salt, alum, borax, quartz, mica, rock- 
 candy, etc. Use only the term crystal, without giving 
 the names of substtincos. 
 
 In treating of ice, draw attention, not by telling, but 
 by proper questioning, to its transparency, color, luster, 
 weight, solidity, hardness, fracture, and to the needle- 
 like crystals which can be so readily shown in ice-films 
 when water begins to freeze, and in the frost-flowers on 
 
 the window-pane. Lead him now to see that a block of 
 
 8 
 
170 1^0 W TO TEACH 
 
 ice, or a snow bank, mnst be made up entirely of such 
 crystals, even though their individual forms are no 
 longer perceptible. Show next that many other fluid 
 substances, like water, upon losing their heat, crystallize 
 into definite solid forms, under favorable conditions, as 
 in melted sulphur, and in the beautiful zinc crystals 
 which cover the surface of so-called galvanized iron. 
 Dwell somewhat upon these phenomena of crystalliza- 
 tion, and draw attention to the mysterious and inde- 
 structible force which somehow rebuilds the atoms of 
 the water into the same forms, no matter how often the 
 ice may be melted. 
 
 The next step in this preliminary lesson will be to 
 show that crystals may also be formed from substances 
 in solution. Alum, salt, borax, etc., will furnish ready 
 means of illustration. Lead the pupil further to 
 notice, that, as in the case of the ice, so with the sulphur, 
 zinc, alum, etc., the crystals may become so massed as to 
 be no longer individually distinguishable. 
 
 The principal points to be fixed in such a lesson are 
 that there are many kinds of crystals, €ome formed from 
 liquids which have become solid by a loss of heat, and 
 others deposited from solution. These facts will be found 
 of great importance in further treating the subject. 
 
 The pupil is then prepared to compare ice with a 
 quartz crystal, which should be presented but iiot at 
 first named, and should be compared first as to the re- 
 semblances, then the differences. When the pupils can 
 be made to furnish no more ideas, the teacher should state 
 where it is found, its relative abundance, geological im- 
 portance, economic uses, etc., etc. Be particular not to 
 introduce an unexplained term — such as the 7iame of any 
 rock or mineral, as gneiss, or gypsum. The name means 
 nothing until explained as quartz has been. Other forms 
 
ELEMENTARY SCIENCE. 171 
 
 of quartz may then follow, each treated in the same way, 
 and each in its turn compared with those that have pre- 
 ceded it. This will constitute an excellent review, and will 
 thoroughly fix what has been already taught. Encour- 
 age the pupils to look for and bring in specimens which 
 they think to be of the same character as those studied. 
 Let them tell why they think they are the same. Let 
 others tell why they think they are not. 
 
 Having thus treated of quartz, next consider, in the 
 same way, /t'/f7s/?ar and mica. The pupils will noAV be 
 ready to consider a rock. 
 
 Let it be gneiss or granite. Let the pupils look for 
 the minerals in it [a cheap single lens as a magnifier 
 will often be of service]. Then consider the texture, 
 structure, where found, uses, etc. The mineral horn- 
 llende and its important varieties may then follow, and 
 after that the rock syenite. 
 
 All needful information may be obtained from any 
 of the manuals in use. 
 
 It will not be necessary here to follow out in detail all 
 the minerals and rocks of which it is desirable that pupils 
 should have some knowledge. A list of the more imi)or- 
 tant, mostly from Dana, is subjoined, from whicli the 
 teacher can make such selections as will conform essenti- 
 ally to the above plan. 
 
 Minerals. 
 
 Watel'; carbon, diamond, coal and coal-mining, an- 
 thracite, bituminous, jet, plumbago, amber, petroleum, 
 asphalt ; sulphur ; saltpeter, salt, borax ; lime, gypsum, 
 alabaster, selenite, calcite spar, chalk, stalagmites, lime- 
 stones (crystalline and compact), marbles, quicklime, 
 hydraulic lime, dolomite ; alum ; talc, soap-stone, 
 (French chalk), meerschaum, pyroxene and hornblendej 
 
173 1^0 W TO TEACH 
 
 corundum and emery, feldspar, albite, orthoclase, gar- 
 net, mica. 
 
 Metals. 
 
 Mineralized [ores] or native — Ores of tin, iron, 
 nickel, zinc, lead, mercury, copjier, gold, silver, plati- 
 num. Enter into no details of Metallurgy ; a few sim- 
 ple facts in regard to smelting, fluxes, etc., will not be 
 out of place. The economic uses of these. metals and 
 the poisonous properties of some of them should receive 
 very careful attention. 
 
 KOCKS. 
 
 As single minerals — example pure limestone. As 
 compounds — granite or conglomerate. Rocks as crys- 
 talline and uncrystalline, Gratified and unstratified, 
 aqueous, igneous and metamorphic. 
 
 The relative position of important rocks — granite, 
 syenite, gneiss, mica-slate, steatite, trap, basalt, lava, 
 pumice, slate, shale, schist, quartz-rock, burr-stone, sand- 
 stones, grits, conglomerates, limestones, marbles, sand, 
 clay. 
 
 Such of tliese rocks as are found in the vicinity of tlie school, 
 or are frequently seen by the pupils when used for paving, flag- 
 ging, building, etc., should receive particular attention. 
 
 WRITING. 
 
 Pen^nanship and Slate-Writinf/. — Pen- 
 manship should be carefully taught in each grade of the 
 Course, in addition to the constant i)ractice which is re- 
 quired in slate-ivriting. By means of the latter, if a due 
 attention is given to it, much may be accomplished in 
 aiding the pupil to acquire readiness and fluency in the 
 exercise of this art; but if he be allowed to fall into 
 
WRITING. 173 
 
 careless habits, his style of writing, both with pen and 
 pencil, Avill be almost incurably vitiated.. 
 
 The exercises in spelling from dictation, etc., should 
 be performed with punctilious accuracy, even if some 
 sacrifice of rapidity be at first required. Of course, there 
 should be a constant effort to imjirove both in rapidity 
 and accuracy — quantibj as well as quality being made 
 a criterion of merit and success. 
 
 The slate-writing should, as far as it is practicable, 
 exemplify the principles and methods formally taught in 
 the lessons in Penmanship. Pupils should not be per- 
 mitted to violate in the one class of exercises the rules 
 and precepts taught and practiced in the other. This 
 caution is especially applicable to the holding of the 
 pencil, which should be sufficiently long to be held as 
 a pen. 
 
 The lessons in penmansMp should be methodical and 
 -progressive, whatever system may be employed. In this, 
 as well as the preceding grade, the exercises should be 
 rudimentary, but the pupil should be advanced as fast 
 as jjossible. He should be permitted to tvrife as much 
 as is practicable, — making strokes and curves is not 
 writing, although it may be valuable as leading to it. 
 A few of such exercises will suffice. 
 
 Neither should the use of trial papers be carried to 
 the extreme of withholding the pupil for a considerable 
 time from the use of his copy-book, so that months are 
 required to finish the latter. The pupil should be 
 taught the necessity of doing everything as well as ho 
 can do it; but perfection -in details should not be ex- 
 pected in the rudimejital stages. It should, from the 
 first, be deemed essential (at least meritorious) to exe- 
 cute the work prescribed with dispatch, provided there 
 is no want of care or attention. Festina leiite, however. 
 
174 SOW TO TEACH 
 
 is a motto that applies to the acquisition of this art, as 
 well as others, ^n its first stages. 
 
 A proper distinction should be made between the 
 lessons given to show the pupils how to write and the 
 exercises designed to practice them on what they have 
 thus learned. In the former, the whole class should 
 invariably be occupied in the same work, the teacher 
 explaining and illustrating from the blackboard the 
 principles and methods which form the subject of the 
 lesson ; in the latter, practice being the object in view, 
 it is not so essential that all the pupils should be doing 
 the same thing at the same time, although even here 
 it is a convenience to the teacher, since it facilitates 
 supervision. 
 
 It should be carefully kept in view that the 7ia}id and 
 the eye as well as the mind of the pupil are to be 
 trained in this brancli of instruction, — the ha)id to exe- 
 cute, the eye to discern, the 7)1 ind to judge. These are 
 not to be educated separately and successively, but 
 simultaneously. The pupil must be taught to. know 
 what is the correct form of every letter, and his hand 
 must be so trained by correct practice, that it will exe- 
 cute the dictates of mind and eye. 
 
 Hence a correct method of holding the pen, a proper 
 position of the body while sitting at the writing-desk, 
 and a suitable placing of the book or paper, are all in- 
 dispensable pre-requisites to the acquisition of a good 
 hand-writing. The first of these demands especial at- 
 tention, and every lesson should, for some time, be 
 introduced by distinct directions as to the proper me- 
 thod of holding the pen, and these the pupils should 
 not be permitted to violate. With regard to the latter 
 — position of body and position of book — a few simple 
 directions will be all that are requisite. 
 
THIED QEADE. 
 
 OUTLllfE COURSE. 
 T^me allowed, from eight to ten monfla. 
 
 LANGUAGE. 
 
 Jteading. — Of the grade of a Fourth Reader, with attention 
 to the elocutionary principles, rules, and exercises required to 
 teach expression; also special exercises in vocal culture. 
 
 Spelling. — From the reading lessons, with additional exer- 
 cises, both oral and written ; careful attention to syllabication. 
 
 Definitions. — In connection with the reading lessons ; also 
 a review of the prefixes and suffixes taught in the preceding 
 grade, and exercises in their combination with various easy 
 roots. 
 
 English Graminar and Composition. — Continued, 
 with the analj'sis, parsing, and construction of easy complex and 
 compound sentences ; also the writing of short compositions 
 under the inspection of the teacher. 
 
 ARITHMETIC. 
 
 Mental Arithmetic— l!hroMg\\. denominate numbers and 
 fractions, with their practical applications ; also a review of the 
 preceding grades by exercises in both calculation and analysis ; 
 and a careful review of the tables. 
 
 Written ArifJimetic— As far as in mental arithmetic, with 
 similar processes and methods of analysis ; also with exercises 
 to give practical expertness in simple computation. 
 
176 SOW TO TEACH 
 
 GEOGEAPHY AND HISTORY. 
 
 Geograp7iij,—0f South America and Europe, both local and 
 descriptive ; the topics of the preceding grades to be occasion- 
 ally reviewed in outline. 
 
 History.— Oi the United States, including an account of the 
 early discoveries, and tlie outlines of the Colonial History to 
 17G3, only such dates to be taught as are essential to a clear un- 
 derstanding of the narrative. 
 
 ELEMENTARY SCIENCE 
 
 (for oral mSTRUCTION.) 
 
 A review, as far as possible, of the topics of the preceding 
 grades, and, in addition thereto, the simple outlines of Physio- 
 logy and Hygiene. 
 
 WRITING. 
 
 On Slates. — Continued as in the preceding grades. 
 
 On Paper. — Words containing difficult elementary forms ; 
 also phrases and sliort sentences. Instruction and practice in 
 the elementary forms, continued. 
 
 DRAWING. 
 
 Review of the work of preceding grades, to which add scrolls, 
 and simple geometrical solids in outline, sucli as the cube and 
 parallelopiped, in various positions; also the cylinder, cone, pyra- 
 mid, and prism. The drawings of simple objects, domestic 
 utensils, etc., may also, occasionally, be copied from cards. 
 
READING. 177 
 
 HOAV TO Teach. 
 
 SUBJECTS OP THE TIIIIID GRADB, 
 
 LiiNGUAGE. 
 
 JReadinf/, — In the preceding grades, due attention 
 i^ required to be given to emphasis and modulation ; 
 but in this grade the exercises should take tlie special 
 direction indicated by these departments of elocution, 
 so as to lead to the higher stages of this art, required in 
 the more advanced grades. It is not enough that the 
 pupils should be accustomed to read with clear articu- 
 lation and proper inflections of the voice; they should 
 be taught expression — to comprehend the character of 
 the piece read, to enter into its spirit, and, to some ex- 
 tent, at least, communicate it justly and forcibly. 
 
 Considerable attention should also be given to vocal 
 culture. For this purpose exercises should be emj)loyed 
 with the view to impart the pliysical as well as mental 
 capabilities required for this purjiose. Tlie pupils shoujd 
 be taught the pro|5t?r position of the body, and the right 
 mode of using the lungs and the vocal organs so as to 
 make their utterance efi'ective. This kind of discipline 
 has a most important bearing upon the general physical 
 development of the pupils, as well as on the invigoration 
 of the organs specially concerned in vocalization. 
 
 For the attainment of the special objects of this 
 
 grade, the elocutionary rules, principles, and exercises 
 
 contained in the Reader, should be made available : a 
 8* 
 
178 HOW TO TEACH 
 
 portion of each reading-lesson being devoted to this 
 kind of instruction and practice. 
 
 It is essential that tlie pupils should be required to 
 stand while engaged in these exercises — either the whole 
 class, or the particular pupil called upon to read. The 
 other pupils, in a proper manner and in the right spirit, 
 may be permitted to criticise the performance of the one 
 called upon to read, and to exemplify the criticism by 
 reading the same passage. 
 
 Lessons, especially such as involve a difficulty, should 
 not be hurried over; they should be read and re-read, 
 until an approximation, at least, to correctness has 
 been attaihed by one or more pupils. 
 
 Concert reading and declamation may be resorted to 
 occasionally, with very beneficial results. 
 
 Spelling, — Oral spelling, except for the purpose of 
 teaching syllabication, should be discontinued. The 
 proper division of words into syllables is an important 
 matter, and should receive due attention. In this con- 
 nection the correct use of the hyjjJien in comiwunds 
 should be taught, and the pupils exercised therein. 
 
 The written exercises should be correctly performed, 
 with care not only as to penmanship, but as to capitals, 
 punctuation, etc. These exercises should be carefully 
 inspected, and after the errors have been pointed out, 
 should be revised and corrected by the pupil himself The 
 sentences used for dictation should contain a sufficient 
 number of common icsi-words, including proper names, 
 both of persons and places, so as to impress the orthog- 
 raphy of such terms firmly on the pupils' minds. 
 
 JDefinitions. — For suggestions, see the preceding 
 grade. 
 
GRAMMAR. I79 
 
 English Grammar, — Analysis, parsing ^niJi con- 
 struction are to be continued in this grade, the class of 
 sentences employed being of a more difficult character, 
 but still carefully kept within the assigned limits of 
 " easy complex and compound sentences." 
 
 By these are meant such as involve: 1. Complex sen- 
 tences, containing simple adjunct clauses, or brief 
 clauses used as subjects, objects, or attributes,— those 
 containing long and involved or intricate phrases being 
 reserved for the next grade; 2. Compound sentences, 
 formed by the union of simple clauses, or of complex 
 clauses, such as those above described. The analysis 
 should be sufficiently minute, to keep before the pupil's 
 mind the relations upon which grammatical distinctions 
 are based. The simplest phraseology should be used. 
 
 The exercises in construction should be made to 
 correspond with the advanced character of the analysis ; 
 and the pupils, in the "short compositions" required to 
 be written, should, as far as possible, exemplify the in- 
 struction in the other portions of' the subject. They 
 should be required to analyze and parse the defective 
 sentences which occur in their own compositions, so as to 
 discover the inaccuracies and to apply the necessary 
 principles and rules for their correction. 
 
 The exercises for the special purpose of accustoming 
 the jiupils to care and criticism in the use of language 
 should be continued. 
 
 Com2)Ositiou.—T^he compositions should, as far as 
 possible, be imp7-omptu, and Avritten under the immediate 
 inspection of the teacher, so that the pupil may be made 
 to depend upon himself in performing what is required. 
 Much practice of this kind is needed before the formal 
 
180 EOW TO TEACH 
 
 writing of compositions is assigned as a liome tasTc. To 
 many jiupils this very essential part of school education 
 is made utterly repulsive by the impossible requirement 
 that they should, with scarcely any previous training, 
 write out at their homes, long compositions on difficult 
 themes assigned by the teacher. 
 
 ■ The compositions proper for this grade should be 
 irief, and on simple subjects, Avhicli should be either 
 selected by the pupils themselves, or, when prescribed 
 by the teacher, should be of such a character as to in- 
 terest the mind of a child. Those which require the 
 pupils to relate the incidents of their own experience — 
 what they have seen, heard, or enjoyed, are chiefly to 
 be preferred, since tliey are thus required to make use 
 of their own language, while their attention is given 
 rather to the thought than to the expression. And this 
 is an important consideration^ for exercises of this kind 
 should not be designed to teach the use of language sim- 
 ply, but language as the vehicle of thought. 
 
 ARITHMETIC. 
 
 JMental ArifJimetic. — For the purpose of review, 
 brief examples in fractions, both jcommon and decimal, 
 should be employed, both as a test, and more thoroughly 
 to fix in the pupil's mind a knowledge of the principles 
 and applications of fractions as taught in the preceding 
 grades. The improvement made by the pupils in ac- 
 curacy and rapidity, as well as in the ready application , 
 of arithmetical principles to particular cases, involving 
 an exercise of the judgment and reasoning powers, 
 should be progressive from grade to grade, and there- 
 fore should be carefully tested in the mental work. 
 
ARITUMEIIC. ■ 181 
 
 The special province of this grade being Denominate 
 Numlers, the exercises, both in mental and written 
 arithmetic, should deal largely with the applications of 
 fractions to that class of numbers, including Fed- 
 eral money, and should, of course, combine' practice in 
 all the essential tables of weight, measure, etc. 
 
 The teacher need not, perhaps should not, conform 
 himself to the order or kind of examples presented by 
 any particular text-book. If the questions given out to 
 the pupils to be solved insfanter are spontaneously con- 
 structed by the teacher, they will be more appropriate 
 to the special needs of the pupils, and the exercise will 
 have far more spirit, and be of much greater value. It is 
 among the dullest of all the occupations of the class- 
 room to read from a book questions in mental arithme- 
 tic, of little variety, hackneyed in form and character, 
 and which the pupils have previously been required to 
 con over. To expect an uninterested, drowsy class to 
 perform any intellectual "exercise, is absurd; but the 
 absurdity is greater, perhaps, in mental arithmetic tlian 
 in any other subject. For suggestions in rL-l;ition to 
 this point the teacher is referred to the statements made 
 under the fifth grade. 
 
 The review of the analysis previously taught should 
 be systematic and thorough, but should not consume a 
 large part of the time of the pupils. 
 
 Wriffeii Arithmetic, — The arithmetic specially 
 prescribed in this grade, both mental . and written, is 
 of a practical character, perhaps more generally so than 
 in* any other grade of the course. All that precedes 
 has been, to a considerable extent, a preparation for the 
 work of this grade, and will be found involved in it. 
 
 The whole subject of compound denominate numbers 
 
182 SOW TO TEACH 
 
 is strictly utilitarian. Practical utility should, there- 
 fore, be the controlling element in all the exercises em- 
 ployed. The daily necessities of the house, the shop, the 
 market, etc., indicate the general cbaracter of the selec- 
 tions to be made. These will furnish at least as good 
 mental discipline in calculation and analysis as those of 
 a less severely practical character. 
 
 It is usually the case, that pupils who have reached 
 this grade can spend but little more time in school. In 
 view of this fact it is important to attend first to the 
 more practical, and therefore more essential, parts of the 
 arithmetic of the grade. To this end, the tables, its in- 
 dispensable basis, should be thoroughly reviewed, and not 
 only memorized, but understood. Pupils should be 
 trained to work with reasonable rapidity, and all long 
 and complex examples, as well as those involving ob- 
 solete "^weights, measures, or money, should be care- 
 fully avoided. Reduction should not be so long dwelt 
 upon as to lead to the omission of important practical 
 points in other rules. It is desirable that a record of 
 the points covered by the class-work should be method- 
 ically kept to be used as a basis of the necessary re- 
 views. 
 
 Syllabus. 
 
 deduction Descending. — Show why it is so called. The 
 denominations should always be written with the exanii. 
 Pupils should not be allowed to " add in" by a separate line; 
 it greatly increases the work, absorbs the time unproiitably, and 
 indicates mental feebleness. The explanation or anal3-sis should 
 be given by processes which make the multiplier an abstract 
 number. The impossibility of multiplying by a comvete number 
 should be carefully shown. 
 
 As an illustration of the above, suppose the question to be, 
 
ARITHMETIC. 183 
 
 " How many pints in 75 gallons, 3 quarts ? " There are at least 
 two correct methods of analysis for this question. 
 
 Analysis 1.— Since 4 quarts make 1 gallon there are 4 times as 
 
 gals. qts. many quarts as there are gallons (75), which are 
 
 "^^^ ^ 300 quarts ; 300 quarts and 3 quarts are 303 
 
 — _ quarts ; and since 2 pints make 1 quart, there are 
 
 cy'^^' twice as many pints as there are quarts (303), 
 
 T^TTTT , "which are 600 pints. 
 
 606 pts. ^ 
 
 In this analysis the work done on the slates is directly ex- 
 plained, the multipliers 4 and 3 used in the slate-work and in the 
 analysis being identical. 
 
 Analysis 2. — Since in 1 gallon there are 4 quarts, in 75 gallons 
 there are 75 times 4 quarts, which are 300 quarts ; 300 quarts and 
 3 quarts are 303 quarts ; and since in 1 quart there are 2 pints, 
 in 303 quarts there are 303 times 2 pints, which are 606 pints. 
 
 In this analysis, wliich is concise, and perhaps more clear 
 than the other, the work done on the slate is indirectly ex- 
 plained, the multipliers 75 and 303 not being those actually 
 used. When this method is employed, an illustration of the 
 following principle should be occasionally required : " The prod- 
 uct of two or more abstract numbers is the same, whatever 
 maybe the order of the factors." Also the modification of this 
 principle, in the case where one of the numbers, as in the given 
 instance, is concrete. 
 
 The following errors are frequently heard and should be 
 avoided : " I multiply 75 gallons by 4 quarts, etc." Four quarts 
 times 75 gallons is, of course, absurd. 
 
 I multiply 75 gallons by 4, etc. Four times 75 gallons is of 
 course 300 gallons, not 300 quarts. 
 
 It will be seen that the above analyses and that required for 
 Reduction Ascending are identical with those already given in 
 the preceding grades. The " adding in " is the same as in the 
 reduction of mixed numbers. 
 
 JReduction Ascending.— T\\\s. is best taught and under- 
 stood in immediate connection with Reduction Descending, at 
 first by reviewing the same example. Long division by divisors 
 less than 13 should not be allowed, nor if cutting otF O's will 
 change to short division. 
 
184 • HOW TO TEACH 
 
 Explanation may be by any process "which will clearly ac- 
 count for the denominations of the successive quotients and re- 
 mainders. 
 
 Weights. — Teacli briefly by examples the relations of Avoirdu- 
 pois and Troy weights, and the essential identity of Troy and 
 Apothecaries' weights. Let most of the examples in Reduction 
 be in the first of the three. They should be few and very short, 
 in the last. 
 
 Remember that the quarter of a hundredweight is seldom 
 used now, excepting in text-books — the Avoirdupois dram no- 
 where else. 
 
 In addition and subtraction, give only Avoirdupois weiglit. 
 Remember that in things sold by the ton, the ounce is not taken 
 into account. Review the principle of carrying, if that plan 
 is used ; of its better substitute, if not. A short question in Troy 
 weight ma}^ be written upon the lioard or read from tlie text- 
 boolc if pupils have one. Then requiie them to state succinctly 
 what process will be required in working it, omitting detailed 
 analysis. 
 
 Note.— To avoid repetition, it may here be stated, that the plan just men- 
 tioned may be taken in multiplication and division as well as in reduction, 
 addition, and subtraction, with those portions of the weights, measures, 
 etc., practice in which is of less general utility. Many practical examples in 
 multiplication and division will arise under Avoirdupois weight, such as 
 finding values at so much a pound, hundredweight or ton, ox vice versa. Such 
 examples may involve preliminary addition or subtraction, or both 
 
 Linear Measure. — Reduction. — Employ the denominations 
 most in use — the inch, the foot, the yard, tlie rod, and the mile 
 — very rarelj--, if ever, all in the same example. Omit cloth 
 measure, or if briefly referred to, use only ^s, \s, iths and i^ths. 
 Give a very few examples to show the use of the chain and its 
 subdivisions. Measuring-tapes usually have feet on one side and 
 chains and links on the other. One may be employed to advan- 
 tage in the class-room. To convert feet or yards into miles, and 
 vice versa, use only 5,280 and 1,700; for instance, so many miles 
 of railroad track having so many lbs. of iron to the yard, at so 
 much a ton, etc., etc. Omit addition and subtraction, multipli- 
 cation and division. 
 
 Surface Measure. — {Of very great practical importance.) — Treat 
 briefly, in reduction. When 30^ is used as a divisor let it be in 
 very short examples. Give examples in addition and subtrac- 
 
ARITmiETIC. 185 
 
 tion. In multiplication and division give examples in finding 
 areas of rectangular figures, in feet, in yards, etc. Give the feet, 
 or the chains, on the sides of rectangles, to find acres and value ; 
 acres and hundredths the most usual form. Omit roods. Sim- 
 ple questions may be given occasionally, involving cost, in esti- 
 mating for plastering, briclcs, carpets, dress-linings, etc. ; also 
 yeiy simple questions in finding the area, circumference, or di- 
 ameter of a circle when- square root is not involved, usijig tf or 
 3.141G for ratio. 
 
 Solid Measure. — Employ only the inch, the foot, tlie yard, and 
 the cord ; use the last but little. See that pupils understand the 
 mutual relations of linear, surface, and solid measures, and that 
 they are not convertible, the units being of totally different na- 
 tures. Reduction — a few simple questions. Omit addition and 
 subtraction. Give examples in finding cubic inches, feet, or 
 yards, in boxes, bins, cellars, cylindrical cisterns, etc., etc. 
 Some knowledge oi board measure, giving very simple practical 
 examples involving cost. 
 
 Dry and Liquid Measures. — Use no obsolete denominations. 
 Omit beer measure. Remember that the barrel and the hogs- 
 head are not often measures in commerce. Simple examples in 
 reduction. Omit addition and subtraction. Give the simplest 
 possible examples, in connection with solid measure, in finding 
 bushels or gallons in bins, vats, cisterns, etc., using 281 and 
 2150 cubic inches, and omitting fractions. No other multiplica- 
 tion or division should be required. 
 
 Circular Measure. — Treat briefly ; explain the terms and their 
 use ; omit signs. Reduction — Short examples of two or three 
 terms. Addition and Subtraction— Questions in difference of 
 latitude and longitude. Geographical and statute miles on the 
 meridian, on the equator, on parallels of 60". 
 
 Time. — (In part veiy important.) Treat reductions very 
 briefly. Do not involve more than two or three denominations 
 in one example. Leap-year. Addition and subtraction. Dif- 
 ference of dates — by days, and by years, moutlis and days. Re- 
 lations of difference of longitudes to time. Explanations and 
 examples. Conversion of longitude into time and vice versa. 
 
 Miscellaneous. — Practical examples in vahies, involving dozen, 
 gross, quire, ream, quintal, barrels of flour, fish, etc., making 
 out simple bills, receipts, etc. 
 
186 HOW TO TEACH 
 
 Money. — Reduction and other simple exercises in Federal 
 money are always in order from the Fifth Grade. Give but 
 few examples in each rule in sterling money. Reduction of 
 sterling to Federal and vice versa, omitting, of course, all refer- 
 ence to the percentage of exchange. 
 
 Pupils should know something of the money of Canada — 
 identical with our own — the value of the franc, and the dollar 
 of the Zollverein. 
 
 Fractional Compotmd Numbers. — The consideration of this sub- 
 ject has been deferred to avoid complicating it with simpler and 
 more important matters. Reject all examples in addition, sub- 
 traction, multiplication, and division. In reduction there are 
 but two cases, and the second of these is simply the converse of 
 the first. Each divides into two varieties, in one of which the 
 fraction is common and in the other decimal, but the principle 
 applied in working is the same. 
 
 Be careful to select only those denominate numbers in which 
 such fractional quantities are likely to need consideration, chiefly 
 sterling money. 
 
 iA. ff of a bushel to pecks, quarts, etc. 
 B. .673 of a £, how many shillings, pence, 
 etc., or dollars and cents. 
 
 A. 7ft. 95 in., what common fraction of a 
 cubic j'ard ? 
 
 B. 15 cwt. 38 lbs. are what decimal frac- 
 tion of a ton ? 
 
 £8 14s. 9^d are how many dollars and 
 cents (at |4.866i) ? 
 
 Case 2d. 
 
 GEOGRAPHY. 
 
 SOUTH AMEEICA. 
 
 Ziocal Geography, — Begin with the continent of 
 South America, as a whole, its boundaries, the names 
 and rehxtive positions, or boundaries, of its political 
 divisions — a few of the chief capes and islands, the posi- 
 tion and direction of the great plateaux and mountain 
 ranges [use chalk sections roughly drawn on blackboard] 
 — five or six of. the most famous volcanoes. In the 
 
GEOGRAPHY. 187 
 
 drainage, only two or three lakes, the courses of the 
 Oriuoco, the Amazon, the San Francisco, and tJie Pa- 
 rana described, and their great branches named and 
 pointed out as systems, but not described. 
 
 The local geography of the several countries taken 
 separately should be very brief, and should include a 
 revieiu of the matter previously considered in the study 
 of the continent — that is, the relative positions or 
 boundaries, the positions of the mountains and pla- 
 teaux, the principal rivers, etc., etc., together with the 
 capitals of the several countries, and about twenty-five 
 of the other principal interior cities and seaports of the 
 continent. 
 
 Descriptive Geograjyhy, — It will also be found 
 most expeditious and effective to teach the descriptive 
 geography of the continent first as a whole. From 
 this, that of the several countries may be very easily 
 deduced and distinctly remembered. It should include 
 the surface of the country as mountain, plateau, or 
 plain ; the zones ; the climate as modified by latitude, 
 elevation, and the prevalent winds; the leading char- 
 acteristics of the great plains and plateaux ; a brief no- 
 tice of volcanoes and earthquakes ; a few of the princi- 
 pal />Zan/s and animals; the three rrtce?*-, their distribu- 
 tion, and their principal occupations, and the influence 
 of the physical geography thereon ; the European Icm- 
 gnages spoken; the chief j-j/'OfZwc^iows and eayorts, vege- 
 table, animal, and mineral, and the forms of govern- 
 ment. 
 
 EUROPE. 
 
 JjOcal Qeoffraphy. — The geography of Europe 
 should be so taught as to avoid the presentation of a 
 
188 JfOW TO TEACU 
 
 large amount of minute detail. In local geography the 
 boundaries of the continent, the names and relative po- 
 sitions or boundaries of its states; the position of its 
 principal peninsulas, capes, gulfs, bays, seas, and straits ; 
 its chief highlands and lowlands; from twelve to fifteen 
 principal mountain systems, the famous volcanoes, the 
 great islands and groups of islands, seven or eight im- 
 portant lakes, including two or three in Switzerland ; 
 from twenty to twenty -five of the important rivers, spe- 
 cifying those which are important as commercial water- 
 Avays ; the names and positions of the capitals of the 
 several countries, and from fifty to seventy of the other 
 important cities. 
 
 Descriptive Geo(jraphy, — The descriptive ge- 
 ography to be on the same plan as for North and South 
 America. It should include the general surface, climate, 
 and productions, the people and their industries, to- 
 gether with their relations of blood, language, com- 
 merce, etc., with the people of tlie United States. In 
 reviewing the chief cities, state any important or inter- 
 esting facts in relation to each. 
 
 Hevieiv. — The topics of the preceding grades should 
 now be reviewed in outline. 
 
 This important requirement may best be met by mak- 
 ing the exercise a comparative one. It should not be a 
 home-lesson, but a vigorous class-room exercise, dis- 
 carding for the time the text-book, and using the out- 
 line maps, the pointer, and the globe. For instance, a 
 rapid pointing out and naming of all the countries of 
 America and Europe, and their capitals, might consti- 
 tute one lesson; all the mountain systems, plateaux, 
 plains, and .volcanoes, another; the climate and produc- 
 tions, a third ; and so on. 
 
HISTORY. 189 
 
 HISTORY OF THE UNITED STxVTES. 
 
 General Sugfjestioiis.—Thn leading purpose oi 
 this study is that the pupil may understand the origin, 
 character, and condition of the nation of which he is a 
 part, and that he may be fitted for an intelligent exercise 
 of his duties and responsibilities as a citizen. 
 
 It is obviously impossible to treat so comprehensive a 
 subject exhaustively. The immaturity of the pupil's 
 mind and the pressure of other studies alike forbid. 
 Yet the leading facts and principles may be readily 
 comprehended and remembered, and the outline which 
 he is to retain be made from the first coherent and defi- 
 nite. To this end a simple preliminary outline sketch 
 should be carefully fixed in the minds of the pupils of 
 this grade, and frequently reverted to in the reviews of 
 all the grades in which the subject is taught. The ge- 
 ography already learned will greatly simplify the process. 
 This outline can be given most expeditiously and effi- 
 ciently by means of oral instruction and the use of the 
 map. It should be very brief, and, if it be thought ex- 
 pedient, should be reduced to writing by the pupil for 
 reference. All detail should be reserved for the study 
 of the text-book. 
 
 The following sketch is presented only as illustrative 
 of this suggestion. Its modification byre-arrangement 
 or otherwise, or the substitution of another in its place, 
 may be found desirable. 
 
 Outline Sketch. 
 
 1st. The people of the United States are of European descent, 
 excepting the negroes. 
 
 2d. Less than 400 years ago our ancestors knew nothing of 
 the existence of this continent. 
 
190 HOW TO TEACH 
 
 3d. Spain, guiclecl by Italian genius, letl the way to its discov- 
 ery, exploration, and colonization. 
 
 4th. The first permanent English settlement within onr limits 
 was not effected until more than a century after the voyage of 
 Columbus. In the interval, Spain and Portugal had possessed 
 themselves of the shores and islands of the Mexican Gulf and of 
 nearly all South America. 
 
 5th. For a century and a half the English colonies were con- 
 fined to a narrow strip east of the Alleghanies. 
 
 Gth. Spanish slavery exterminated the Indians of the West 
 Indies. This led directly to the opening of the African slave 
 trade, and indirectly to the introduction of slaves into our own 
 country. 
 
 7th. The colonies had wars with the Indians m whose coun- 
 try they had settled, and with the neighboring French colonies. 
 The French were subjugated and their territories occupied. 
 
 8th. Less than a century ago all European settlements were 
 still dependent colonies. 
 
 9th. The necessities of distant colonial settlements had de- 
 veloped in the English colonies a spirit of self-reliance and po- 
 litical freedom, and a system of local and elective self-govern- 
 ment. 
 
 10th. The expenses of the French wars left a heavy debt and 
 led to unusual taxation. A tyrannical system of taxation led to 
 the War of Independence, which fixed the national boundary 
 at the Mississippi. The colonics had become States. 
 
 11th. The present form of government (the Constitution) was 
 established soon after the close of the war, about eighty-three 
 years ago. 
 
 12th. The number of States has been greatly increased by im- 
 migration and emigi-ation. The population and wealth have 
 increased many fold. 
 
 13th. By purchase and otherwise the national territory has 
 been expanded to the Gulf of Mexico and to the Pacific and 
 Arctic oceans. 
 
 14th. Since the War of Independence there have been three 
 important wars : 1. A war with Englatid in defense of naturalized 
 citizens and in vindication of the rights of neutrals ; 2. A wai- 
 with Mexico, resulting from our aunexation of Texas; 3. A great 
 
UISTOBT. 191 
 
 civil war, arising in p.irt from questions originating in our colo- 
 nial history and in part from more recent causes. 
 
 • Lessons and Recitations. — Lessons i n ni>^ory should 
 be assigned by topics and not by pages. 
 
 All verbatim recitations of sentences ana paragraphs 
 Bhould be strictly forbidden, and the pupils should be 
 required to state the facts in their own language. 
 
 Only such dates should be committed to memory as 
 are indispensable as landmarks in history. The se- 
 quence of events, rather than the precise date of each, 
 is what is chiefly necessary. 
 
 Maps, especially those of the text-books, snould be 
 used whenever the subject may require it. 
 
 Historic episodes, however interesting, should not re- 
 ceive the careful study given to the essential narrative. 
 The stories of Juan Ponce de Leon, the Conquest of 
 Mexico, De Soto's Expedition, John Smith, Pocahontas, 
 the Salem Witchcraft, etc., should indeed be carefully 
 read, and, as far as may be necessary, explained; but, 
 unless great care be taken by the teaclier, the pupils will 
 be apt to conceive that these are the most important 
 portions of the history. 
 
 Important incidental allusions to European history, 
 such as the rise of the English Puritans, the expulsion 
 of the Stuarts, the French Revolution, etc., should be 
 carefully but briefly explained. Great caution should 
 be exercised throughout these lessons to state tlie facts 
 in such a manner as not to wound the religious or 
 political sensibilities of any. 
 
 Hevieivs. — Eeviews of the portion already taught, 
 with frequent references to the preliminary sketch, are 
 of the higliest importance. These re^'iews sliould lake 
 three distinct forms: the Chronolorjical, the metliod 
 
192 SOW TO TEACH 
 
 usually followed in the text-book; the Biographical, 
 requiring the pupil to state all that has been learned in 
 regard to particular individuals; and the Geographical, 
 requiring a statement of all important facts relating to 
 tlie history of a locality. Many of the topics treated 
 by the second and third of these methods necessarily be- 
 come cumulative. For instance, the facts relating 
 directly to George "Washington will be gathered from 
 at least three distinct and important periods in our his- 
 tory. A connected statement of the important events 
 that have taken place in Philadelphia, or in the valleys of 
 the Hudson and of Lake Champlain, or in the State of 
 Virginia, will necessarily cover a large part of th« gen- 
 eral subject in the higher grades. Such statements 
 must, of course, be brief, and will often be a mere chro- 
 nological table. 
 
 Many of these reviews and certain parts of the regu- 
 lar recitations may be made spirited general exercises 
 for the whole class by the use of the slate or of paper. 
 The writing of the few essential dates, the sequence of 
 important events, the names of imjiortant individuals, 
 etc., are instances. The narrative reviews will neces- 
 sarily be, for the most part, oral. 
 
 It will be observed that the system of reviews above 
 suggested must, if faithfully carried out, result in a 
 thorough unifying of the general subject in the mind 
 of the pupil. 
 
 Suggest ions for the Tliivd Grade. — The 
 
 essential points requiring careful study and frequent 
 review in the history assigned to the Third Grade are 
 given below. Other interesting facts usually stated in 
 text-books should be carefully read, but should receive 
 a less proportionate share of attention. In no other 
 grade is a frequent reference to the maps so important. 
 
niSTORT. 193 
 
 Syllabus of Topics. 
 
 The voyage of Columbus ; the naming of America ; the occu- 
 pation of the West India Islands and all the neigliboring por- 
 tions of the continent by the Spaniards ; their enslavement of 
 the Indians and its results (the last very briefly). 
 
 The discovery, exploration, and occupation of the St. Lawrence 
 and Nova Scotia by the French. 
 
 Virginia. — Th settlement of Jamestown and the events 
 directly leading to it. The cultivation of tobacco ; the intro- 
 duction of slavery ; the navigation acts and Bacon's rebellion. 
 
 Maryland. — The Calverts ; religious freedom ; Clayborne. 
 
 New England. — The Plymouth Company and the settlements 
 under their patent. The Puritans ; their previous history and 
 why called Pilgrims. The settlement of Plymouth ; of Boston ; 
 of Dover ; the Massachusetts Bay Colony. Tlie settlement of 
 Connecticut; of Rhode Island; provisions for religious freedom. 
 The Union ; Indian Wars {read only, and do not commit the 
 details to memory). Andros ; King William's War, its causes 
 and results. The Salem Witchcraft {read). Queen Anne's War, 
 its causes and results. King George's War, its causes and 
 results. 
 
 Neio Netherlands.— Henry Hudson ; the settlement on the Del- 
 aware ; at Fort Orange; at Manhattan Island; the Dutch Gov- 
 ernors ; Kieft's conduct : Stuyvesant. 
 
 New York. — Changes of name; reconquest by the Dutch and 
 final restoration to England. Andros; the extent of his rule. 
 Dongan; Leisler; the burning of Schenectady; the Negro plot. 
 
 New Jersey.— Its, name ; its division ; imioa with New York ; 
 final separation. 
 
 Delaware. — Its settlement by Swedes; its conquest by Stuy- 
 vesant. 
 
 Pennsylvania. — William Penn ; his grant ; his objects. The 
 settlement of Philadelphia; the relations of Pennsylvania to 
 Delaware. 
 
 North Carolina. — The grant of Charles II. ; its geographical 
 limits ; John Locke. 
 
 South Carolina. — Charleston settled ; Carolina divided into 
 two separate governments in 1729. 
 
 Georgia. — Savannah settled ; character and purposes of Ogle- 
 thorpe. 
 
 9 
 
194 HOW TO TEACH 
 
 The general condition of the English colonies in 1752. Their 
 population ; their national derivation ; their industries, social 
 condition, planters, patrons, and proprietors ; the causes which 
 were developing a love of liberty. 
 
 Review chronologically under heads of the following sovereigns 
 of England : Elizabeth ; James I. ; Charles I.; Cromwell ; Charles 
 II.; James II.; William and Mary; Anne ; George I.; George II.; 
 also, 5w5r?-a^7«'ca%, referring to Columbus, De Soto, Cortez, Car- 
 tier, Raleigh, etc., etc. 
 
 Tlie French and Indian TF«?-.— This should be taught in out- 
 line, the principal points being : — The gradual extension of the 
 Englisli and French settlements leading to conflicting claims ; 
 the explorations and posts of the French in the valleys of the 
 Mississippi, the St. Lawrence, and the Lakes ; Marquette and 
 La Salle ; the debatable land on the upper Ohio ; relatively 
 small population of Canada ; the building of Fort Du Quesne, 
 1754 ; Colonial Congress at Albany, 1754 ; Braddock's and 
 Johnson's Expeditions, and their results, 1755 ; Monckton's 
 Expedition in 1755 ; cruel expulsion of the Acadians ; capture of 
 Oswego, 1756 ; Fort William Henry, 1757 ; siege and capture of 
 Louisburg, 1758 ; repulse at Ticonderoga, 1758; concentration 
 of French forces at Quebec, by abandoning nearl}^ all otlier 
 posts ; battle of Quebec, 1759 ; results ; Treaty of Paris, 1763 ; its 
 conditions. 
 
 In teaching the French and Indian War let the ten dates 
 marked be studied by the years only. Eead, but do not memor- 
 ize, the details of military movements and events ; fix the se- 
 quence of events ; use the map. 
 
 In the biographical review, let the pupil tell ver}' briefly of 
 Washington, Braddock, Johnson, Monckton, Amherst, Aber- 
 crombie, Howe, Wolfe, Dieskau, and Montcalm. 
 
 ELE^klENTARY SCIENCE. 
 (For Oral Instruction.) 
 
 PHYSIOLOGY AND HYGIENE. 
 
 The chief purpose of this study as a branch of Com- 
 mon School instruction is, to give useful practical 
 knowledge of the laws of health. As the subject can 
 
ELEMENTARY SCIENCE. 195 
 
 receive, at most, but a small part of the time assigned to 
 a single grade, it is the more important that only those 
 parts of the study should be considered that are essen- 
 tial to the main purpose. Anatomy, which occupies so 
 much space in many text-books, should not take up the 
 time of the pupil, excepting so far as it may be absolutely 
 necessary in order to teach the physiology and hy- 
 giene. It is a matter of little consequence to the pupil 
 to know exactly the number of bones, or of pairs of mus- 
 cles in his body, or to repeat their scientific names. 
 Only those terms and facts should be introduced that 
 are actually necessary in order to deal intelligently 
 with the main subject. Oval description of structure 
 or function should take the place of defimiions. 
 
 The appliances necessary for teaching this branch are, 
 the blackboard and charts. The teacher should care- 
 fully consider, at every step, to what extent the subject 
 can be treated objectively. This can, in part, be done by 
 drawing the pupil's attention to his own body, as in 
 the case of the pulse, the veins, arteries, respiration, etc. 
 For several very important parts of the subject, there is 
 no better apparatus than that which can be procured 
 without expense at any butcher's stall, such as the lungs 
 and windpipe of a sheep ; the diaphragm, the heart and 
 part of the great tubes leading to and from it ; the brain 
 and the bony cavity which contains it ; the eye ; por- 
 tions of the spinal cord and nerves ; small glands ; and 
 portions of limbs, shoAving the relations of muscles, ten- 
 dons, ligaments, and joints. None of these need present 
 anything offensive or disgusting. Add to these a small 
 knife, and reasonable preparation on the part of the 
 teacher, and the instruction given will be both interest- 
 ing and profitable. AVhere it would not be expedient to 
 resort to this means of illustration, preparations (simi- 
 
196 now TO TEACH 
 
 lar to those manufactured by Auzout) could be used, if 
 procurable, and in their absence, diagrams and charts. 
 A syllabus of leading points is subjoined. It should 
 not be expected that all these can be taught in one 
 class, though all are important, nor that any point 
 should be treated exhaustively. 
 
 Syllabus of Topics. 
 
 ■ The pupil should be led to look upon the body as a complex 
 apparatus for the use of his muid. To know that it consists pri- 
 marily of — 
 
 First, a bony frame-work (the skeleton) ; second, a motor ap- 
 paratus attached to the frame (the muscular system) ; tMrd, a 
 directing apparatus by which the mind controls the body (the 
 brain, the nervous system, and the sensory organs) ; fourth, a 
 general envelope protecting all the preceding, as well as serving 
 other purposes (the skin). 
 
 He should then be led to see that every motion of the body or 
 of its minutest part, however slight, and whetber voluntary or in- 
 voluntary, requires the destruction of a minute part of the organ- 
 ism and the removal of the destroyed part from the system ; 
 that this constant destruction and removal make necessary a cor- 
 responding reconstruction and reneical, by means of new mate- 
 rial ; and that for these purposes there are provided, ^/^/i, a cir- 
 culatory apparatus (the blood-vessels), to carry away old material 
 and to distribute the new ; sixth, an aerating apparatus (the res- 
 piratory system), to purify, warm, and enliven the circulating 
 fluid ; seventh, a system of drainage (the skin and the kidneys), 
 to take from the blood a large part of the worn-out material ; 
 and eighth, an apparatus to prepare and supply the new ma- 
 terial (the digestive and assimilative organs). 
 
 Under each of these heads a few points are noted : 
 
 1. The bones, — their composition and various uses ; joints and 
 their lubrication ; important peculiarities of the spinal column ; 
 cautions as to injuring the large bones of an infant ; the repair 
 of broken bones, how effected. 
 
 2. The muscles and tendons, — their uses ; their arrangement in 
 
ELEMENTAR Y SCIENCE. 197 
 
 pairs, and why ; how attached; how able to contract; effects of 
 exercise ; use of calisthenics. 
 
 3. The nervous system, — the means of becoming conscious of tlio 
 external world; the spinal cord; its importance and protectum; 
 its ramificntlons; effects of severing or injuring the spinal cord; 
 care of infants iu tliis respect. The sympathetic system ; the 
 nerves as telegraph wires; the brain and its principal functions; 
 uses of sleep ; late hours, stimulants, etc. 
 
 The organs of the special senses, — touch, papilla) ; taste ; smell ; 
 the ear, its mechanism, hearing ; the eye, its mechanism, sight ; 
 abuse of the eyes ; myopy, its causes and prevention. 
 
 4. The skin, — its structure and uses ; tlie perspiratory glands 
 and tubes ; uses of perspiration ; importance ol bathing ; the 
 proper time for bathing ; proper clothing ; sympathy of the skin 
 •with the lungs, with the digestive organs ; caution against the 
 exposure of the limbs, arms, or chests of little children ; the skin 
 as an absorbent ; danger of cosmetics and hair-dyes ; treatment 
 of burns and scalds, etc. 
 
 5. The circxdatory system, — the general relations of the heart, 
 arteries, veins, and capillaries ; the valves ; the pulse ; its rate ; the 
 rapidity of circulation. Effects of fresh air and exercise on the cir- 
 culation ; limits of exercise ; dangers of excessive rope-jumping, 
 etc. Effects of sleep on the circulation ; effects of tight gar- 
 ments ; of insufficient or imjiroper food ; wounds ; how to know 
 when an artery is wounded, and what to do. 
 
 6. The respiratory system.— (Practically the most important part 
 of hygienic knowledge). The a"pparatus ; how protected ; ar- 
 rangement of the ribs for flexibility, and for the expansion of the 
 lungs ; the muscles of the chest and the diaphragm ; importance 
 of the diaphragm; (show its positions at the beginning and at 
 the end of an inspiration;) the trachea; the vocal chords; 
 structure of the lungs ; its air cells, and their membrane ; exos- 
 mosis and endosmosis as concerned in respiration ; intimate re- 
 lations of the capillaries and air vessels ; frequent full inspira- 
 tions a means of increasing the capacity of the lungs; perni- 
 cious effects of tight lacing on the capacity and action of the 
 lungs. The air,— Ms composition ; relations of oxygen to the 
 carbon and the hydrogen introduced with the food ; products of 
 respiration all invisible excepting watery vapor ; tlie poisonous 
 nature of carbonic acid ; danger from it iu wells, and in vats ; 
 
198 BOW TO TEACH. 
 
 the effects of smaller quantities ; the other substances thrown off 
 by the lungs and the skin ; the ventilation of class-rooms 
 and of sleeping-rooms ; effects of foul air from cellars, sewers, 
 sinks, water-pipes, garbage, gas-lights, stoves, etc. ; simple and 
 cheap disinfectants ; chloride of lime ; chlorine ; sulphate of 
 iron ; carbolic acid, etc. Respiration as affected by position, in 
 standing, or in sitting, and especially in sitting to write or to 
 draw. 
 
 7. T/ie digestive apparatus, — the teeth, their uses, structure, and 
 hygiene ; a brief notice of the salivary glands, their position and 
 uses ; of the gullet ; of the structure and function of the stomach ; 
 a brief notice of the duodenum, the intestines, and the lacteals ; 
 the importance and functions of the liver ; the thoracic duct as 
 the link between the digestive and the circulatory systems. Dys- 
 pepsia, its preventable causes and terrible consequences ; common 
 errors to be avoided in the preparation of food ; common poisons 
 and their antidotes. 
 
SEOOiq'D GEADE 
 
 OUTLINE COUESE. 
 Time allowed^ about ten montJis. 
 
 LANGUAGE. 
 
 Heading. — Of the grade of a Fifth Reader, with instruction 
 and exercises in elocutionary principles, and in vocal culture, as 
 in the preceding grade. 
 
 Spelling. — Continued as in the preceding grade. 
 
 Definitions. — As in the preceding grade, with word analysis, 
 or etymology. 
 
 English Grammar. — Analysis, parsing, and construction 
 continued ; also the correction of false syntax. 
 
 Composition. — Continued. 
 
 ARITHMETIC. 
 
 Menta^ and Wr iff en.— Commerciid rules, through per- 
 centage, including profit and loss, commission, insurance, stocks, 
 interest, discount, etc. ; with carefully graded exercises in analy- 
 sis and calculation. 
 
 The problems, to teach and illustrate the methods of compu- 
 tation employed in ordinary business transactions. 
 
 GEOGRAPHY AND HISTORY. 
 
 Geography.— O^ Asia, Africa, and Oceanica, both local and 
 descriptive ; an outline review of the topics of .he preceding 
 grades. 
 
200 HOW TO TEACH 
 
 History.— Oi the United States, from 1763 to the present 
 time, inchidiug the outlines of the Revolutionary "War, the forma- 
 tion of the Union, the chief events of the national history, includ- 
 ing also a brief outline of the great Civil War of 1861-5, and ita 
 results. 
 
 ELEMENTARY SCIENCE. 
 
 JJY ORAL INSTRUCTION OR WITH A SIMPLE TEXT-BOOK. 
 
 Natural Philosojihy, — The outlines of mechanics, hydro- 
 statics, and pneumatics. 
 
 Astronomy, — Elementary astronomy, to include an explana- 
 tion of the ordinary phenomena, and a brief account of the bodies 
 constituting the Solar System. 
 
 WRITING AND DRAWING, 
 
 Fenmanship, — Instruction and exercises of a similar char- 
 acter to those of the preceding grade, but more advanced. 
 
 Draiving.— Cor. tinned practice in the work prescribed for the 
 preceding grades, to which sliould be added the sphere, the ob- 
 late and oblong spheroids, the hemisphere, with first lessons iu 
 shading ; also the drawing of rectangular solids from blocks in 
 various positions, with a few simple directions as to perspective. 
 
BEADmG. 201 
 
 How TO Teach 
 
 SUBJECTS OP THE SECOND GRADK 
 
 LANGUAGE. 
 
 Meading. — In this grade, the simple principles of 
 elocution, taught in the preceding grades, should be 
 carefully reviewed, and exercises to cultivate the voice, 
 and confirm habits of distinct articulation should be 
 continued to some extent. The rationale of good read- 
 ing should, as occasion offers, be more fully exj^lained, 
 particularly as regai'ds emphasis and modulation. Emo- 
 tional reading should receive a fair share of attention. 
 In classes or schools for males, exercises in declamation 
 and recitation will be useful as an auxiliary. 
 
 The pieces read, being of a higher order of style and 
 subject, should receive a more careful analysis on the 
 part of the teacher, so as, by interrogation, to lead the 
 minds of the pupils to a proper understanding of their 
 subject-matter, and enable them to obtain all the infor- 
 mation and culture of mind which they may be made 
 the vehicle of imparting. Much time is apt to be mis- 
 spent in this grade by simply permitting the pupils 
 to read mechanically and listlessly pieces of difficult 
 prose and poetry, which by earnest teaching might be 
 made to fix in the minds, and often in the hearts, of the 
 pupils so much that is valuable. Few tests of the ear- 
 nestness and skill of a teacher are so thorough as the 
 teaching of reading in this grade and the next. The 
 
202 liOW TO TEACH 
 
 subject, the style, the diiSeult ornniisual words, the al- 
 lusions, the course of reasoning, mode of treatment, 
 etc., may all be made the basis of useful investigation 
 by the pupil or of comment by the teacher. 
 
 The pieces read should comprehend a sufficient vari- 
 ety, both as to style and subject, to afford scope for what 
 is above suggested. They should include didactic, narra- 
 tive, argumentative and oratorical selections; extracts 
 from distinguished writers in history, biography, popular 
 science, etc., as well as the various departments of poe- 
 try ; an important object of tlie instruction being to give 
 a taste for reading more fully the Avorks or compositions 
 from which the extracts are made. Some account of the 
 authors should be given in connection with the lessons. 
 
 Definitions and Word Analysis. — The pre- 
 fixes and suffixes learned in the preceding grades should 
 be reviewed by means of appropriate exercises involv- 
 ing the application of easy roots. For this purpose such 
 words as the following may be used: — Drunk^rc?, 
 Thralk/o;», Dep///, Ah&xxci, Verstow, Locrt/, — involving 
 English, or Anglo-Saxon, and Latin affixes only. 
 
 Next, the exercises should involve the nse of easy 
 Latin roots, such words as the followinsf beinff used: 
 Avert, Adivert, Convert, V^rvert, etc. — verse, version, 
 daverse, etc. The application of various affixes, so as to 
 form several words from the same root, will serve to im- 
 press the meaning of the root, in its various fo7'nis, on 
 the mind of tlie pupil, as well as to review the affixes. 
 Latin words need not be taught. 
 
 After a few exercises of this kind, words containing 
 miscellaneous roots maybe used; as, Pre^Z/cif, Submit, 
 'Reject, Invade, etc. ; then words containing prefixes and 
 suffixes, as, Sub;«is*ion, Obyec^ion, Con/?2<ent, Vvocedxxve, 
 
DEFINITIONS AND WORD ANALYSIS. 203 
 
 etc. ; care being taken at first to select such words as 
 are regularly formed, and the literal signification of 
 which exactly or nearly agrees with the actual meaning 
 as used. 
 
 The following form of analysis is suggested: Ahchict, 
 — formed from the root duct which means to lead, and 
 the prefix ah, Avhich means away. Hence, abduct 
 means to lead aiuay. Actual meaning, to take aivay iy 
 stealth ; as, " Tliey tried to abduct the child from his 
 parents." 
 
 In this form of analysis, the root and its meaning are 
 first stated; next, the suffix ; then, the jt>7r/a:, and then 
 the literal meaning of the word, to be followed in all 
 cases by the actual meaning, which is to be exemplified 
 in a sentence. 
 
 After the pupil is sufficiently initiated in the method 
 so as to analyze words with some degree of facility, the 
 principal Latin roots should be taken up and taught 
 exhaustively, alphabetically, or in the order of their 
 difficulty. These should be followed by a few of the 
 Greek roots, suffixes and prefixes, to be followed by the 
 French or other foreign roots. The Anglo-Saxon or 
 English roots should, if taught at all, follow these. 
 All beyond the Latin roots, and if necessary some of 
 these, may be reserved for the First Grade. 
 
 Exercises in i\\Q formation of loords from given roots 
 should form a prominent part of the exercises used to 
 familiarize the pupils with the meaning of the roots, as 
 well as the meaning of words derived from them. For 
 the purpose of this instruction the English form of the 
 root is all that needs to be taught. In this way the 
 subject will be freed from much complexity. Thus, 
 after analyzing the word dentist, the pupil gives, as far 
 as he can recall to mind, the words derived from the 
 
204 SOW TO TEACH 
 
 root dent ; as dentdl, dentate, dentoid, dentition, denti- 
 frice, dentiform, indent, etc. Words such as dentistry 
 are to be considered as of secondary formation, and to 
 be analyzed by considering dcnUst the primitive. In 
 this way the analysis of a very large class of words will 
 be greatly simplified. 
 
 The analysis of words is, of course, etymological ; but 
 it is rather introductory to the study of etymology 
 than, properly considered, a part of that study. The 
 science which treats more directly and specially of the 
 origin and relation of verbal forms, their primitive 
 meaning, their combinations, and the varied significa- 
 tions Avith which their derivatives have been used from 
 time to time, is scarcely appropriate at this stage of the 
 pupil's progress. The instruction derived from such 
 exercises as are above indicated is exceedingly valuable 
 for its practical usefulness ; but such facts as that licdf 
 is the Anglo-Saxon liealf, liome the Anglo-Saxon lidm, 
 and the German lieim, etc., etc., are interesting and 
 useful for a very different purpose, and should occupy 
 a more advanced place in an educational scheme. 
 
 E^ifjlish Grammar. — In this grade, the pupils 
 should be exercised in the analysis and ^mrsiJig of sen- 
 tences of a higher grade of difficulty ; but those of anom- 
 alous or peculiar construction should be avoided. The 
 analysis, except for review, should be only in outline, 
 so as to show the "general structure of the sentence," 
 and enable the pupil to see clearly the relation of the 
 clauses or members. This is essential to a correct and 
 definite understanding of the meaning of the sentence, 
 as well as for the application of rules having reference 
 to the construction of sentences. Some knowledge of 
 punctuation should be imparted in this connection. 
 
GRAMMAR. 205 
 
 The following sentence analyzed will illustrate the 
 requirements of this grade in this respect: 
 
 "Pay tJte debts which thou oivest ; for he who gave 
 thee credit relied vpon thy honor, and to luithhold from 
 Mm his due is both mean and utij\istJ" 
 
 Analysis. — This sentence consists of two members: 
 1. *' Pay the debts'' etc., to " oivest ;" 2. ''He who gave 
 thee,'' etc., to " unjust." These members are connected 
 by "/or." 
 
 The first member contains the clause "tvhich thou 
 oivest," used as an adjunct of " debts." 
 
 The second member consists of the two clauses: ''He 
 who gave thee," etc., to "honor," and "To ivithhold," 
 etc., to " unjust." 
 
 This should be followed by the jjarsing of the most 
 important words, which will show whether a more mi- 
 nute analysis of the sentence should be required of the 
 pupil or not. 
 
 As far as may be necessary, the structure of the sen- 
 tence, discovered by analysis, should be made the subject 
 of rhetorical criticism, with reference to its clearness in 
 expressing the meaning intended to be conveyed, its^jj'O- 
 priety, iinity, harmony, etc. The thought itself may be, 
 to some extent, analyzed, and subjected to critical remark. 
 
 The parsing, as an application of the rules and prin- 
 ciples peculiar to our own language, should also, as 
 far as possible, be so conducted as to have a critical end 
 in view. This will greatly improve the pupils in their 
 use of language, by rendering them more alert in dis- 
 covering inaccuracies, as Avell as by impressing more 
 deeply upon their minds a knowledge of the rules l)y 
 which they should be guided in expression. 
 
 Exercises in the correction of false syntax should be 
 abundantly used in this grade. 
 
206 SOW TO TEACH 
 
 Comjyosifion, — The construction of sentences 
 should assume the character of extended composition, 
 tlie themes being selected by the pupils themselves or 
 assigned by the teacher. Of course, care should be 
 taken that the themes are of a simple character — ap- 
 propriate to the mind of a child, and calculated to 
 awaken thought, not to repress it, as is too often the 
 case when difficult subjects, of an abstract or too 
 comprehensive character, are chosen for the exercise. 
 
 AEIXmiETIC. 
 
 The commercial arithmetic of this grade differs from 
 that taught in the preceding grades, chiefly in the in- 
 troduction of the various forms of percentage. The 
 divisions of percentage should be presented in the fol- 
 loAving order : First, simple 2^ercentage, in four cases — 
 one fundamental and three derived; second, the appli- 
 cations of simple percentage, technically known as Com- 
 mission, Brokerage, and Profit and Loss, following the 
 same order and with the same analysis as in the four 
 cases of simple percentage. 
 
 Those who prefer to do so may readily combine these 
 divisions under the general head of "percentage not in- 
 volving time." 
 
 The third division of the subject is interest, or *' per- 
 centage involving time." It has five cases — one funda- 
 mental and four derived. 
 
 In treating the percentage rules many skillful teach- 
 ers prefer to introduce algebraic formula, in which the 
 initial letters of the several terms employed in percen- 
 tage are the elements. To this course there is no ob- 
 jection, provided that the formula be not employed in 
 the mental arithmetic, and that they accomjoany the 
 
ARITHMETIC. 207 
 
 nsiml analysis and be not used as a siihstitute for it. 
 AVith this exception, tlie processes and explanations of 
 the mental arithmetic should not differ from those of 
 the written arithmetic, the chief distinction between 
 the two being, that in the latter the numbers are too 
 large to be carried in the mind. 
 
 The subject of arithmetic being necessarily to a 
 great extent cumulative, the teacher of this grade is 
 especially advised to read over the directions given in the 
 preceding grades, and in particular the table on page 
 162. For the sake of brevity^ the terms base, percent- 
 age, etc., are employed in the following syllabus of top- 
 ics in the usual technical sense of the text-books. 
 
 Syllabus op Topics. 
 
 The term percentage — exercises in reading per cent. 
 
 Examples — Read the following, exemplified and defined first 
 as decimal fractions, and then as per cent. : .75, .8, .G05, .003, 
 .08i, .001, etc. 
 
 Exercises in changing common fractions to per cent, and 
 vice versa : 
 
 Examples— I, "I, f§g, ff, 2^, li^i, j^, etc., how many hun- 
 dredths ? what per cent. ? 
 
 Examples — 25 per cent., 75 per cent, 33^ per cent, 14f per 
 cent., BSJ per cent., 325 per cent., 137^ per cent., etc., are equiv- 
 alent to what common fractions ? 
 
 Note.— The common business fractions, halves, thirds, etc., to twelfths, 
 inclusive, should be reduced to per cent., and the pupils made thoroughly 
 familiar with them. 
 
 SIMPLE PERCENTAGE. "- 
 
 1st Case {Fundamental).— To find the percentage, the base and 
 rate being given. 
 
 See table, page 163.— To find a given fractional part of a 
 given number. 
 
208 HOW TO TEACU 
 
 Examples— How much is 9 per cent, of 750 ? Had $750 in 
 
 the bank; drew out 9 per cent. How much was it? 
 
 Analysis as in the multiplication of decimal fractions. 
 
 Note.— When this form of the case has been taii;;ht, its modifications 
 should immediately follow. 
 
 Example— Had $750 : paid out 9 per cent. How much had 
 Heft? 
 
 Example— Had $750 ; earned 9 per cent. more. How much 
 had I then ? 
 
 2d Cask (Derived).— To find the rate when the percentage and 
 base are given. 
 
 See table, page 163.— Tofind what fraction one given number 
 is of another given number. 
 
 Examples — 140 is what per cent, of 400? 
 
 " Had 400 sheep ; sold 140. What per cent, did I 
 
 sell? 
 
 Analysis as in reducing a common fraction to a decimal fi-ac- 
 tion whose denominator is hundredths. 
 
 Modifications of Case 2d : 
 
 Example— I had 400 sheep ; I now have 540. "What is the 
 per cent, of increase ? 
 
 Example— I had 400 sheep ; I now have only 260. "What is 
 the per cent, of decrease ? or, what per cent, have I left ? 
 
 3d. Case (Derived). — To find the base when the percentage and 
 the rate are given. 
 
 See table, page 162. — To find the number of which another 
 number is a given fraction. 
 
 Example— 140 is 35 per cent, of what number? 
 
 " Sold 140 sheep, which was 35 per cent, of my flock. 
 
 How many had I at first ? 
 
 Analysis as in simple fractions— 140 is A-o of what number? 
 
 Modifications of Case 3d : 
 
 Example— Sold 140 sheep, which was 35 per cent, of my 
 flock. How many had I left ? 
 
 Example — Sold 140 sheep, and have 65 per cent, of my flock 
 remaining. How many had I at first ? 
 
 4th Case {Derived.) — To find the base when the amount (or 
 difference) and rate are given. 
 
 To find a number which diff"ers by a given fractional part of 
 itself from a given number. 
 
Analysis 
 of last Iwo^ 
 examples. 
 
 AlUTUMETIG. 209 
 
 Example — What number is by 8 per cent, of itself more than 
 351 ? or 351 is 8 per cent, more than what number ? 
 
 Example — My flock of sheep increased 8 per cent.; I then had 
 351. How many had I at iirst ? 
 
 Example — I lost 8 per cent, of my sheep, and had 299 remain- 
 ing. How many had I at first ? 
 
 Note.— Axiom.— The base is 100 per cent, of itself. Tliis is only a form of 
 
 the fundamental axiom of fractions, 1= — 
 
 n 
 
 'First, find the per cent, of the base, represented 
 
 by the given number ; 100 per cpnt. + 8 per cent. 
 
 =108 per cent, of the base ; 100 per cent. — 8 per 
 
 cent. =93 per cent, of the base. 
 
 Second, proceed as in 3d case — 351 is \%% of what 
 
 number ? — 399 is -^^ of what number ? 
 
 As a part of the general review, give an example in the fun- 
 damental case, and let the pupils derive the other three cases 
 from it, and then their modifications. 
 
 Commission and Brokerage and Pi'ofit and Loss are but appli- 
 cations of simple percentage. Each presents itself under all 
 the four cases,but requires no special additional teaching, except 
 in regard to the technical terms employed. 
 
 Interest. — Teach the definitions of the terms employed ; the 
 distinction of simple from compound interest ; the legal rate of 
 U. S. and of the State in which the school is situated. 
 
 Note. — In classes of an average character, one good method, in solving ex- 
 amples in interest, will be found to give better results than two or more. 
 Whatever method be employed, the pupils should, from the first, l)e carefully 
 guarded against considering and calling the multiplier a concrete number. 
 For instance, multiplying $15, the interest for 1 year, by 3 years, etc., is, of 
 course, an absurd statement. 
 
 If the six per cent, method be employed, it should be carefully 
 analyzed, and the pupils should not be allowed to sacrifice 
 sense to conciseness by such statements as " the half of 7 months 
 is 3 cents-and-a-half" — one-sixth of S-l days is 3 mills, etc., etc. 
 As a preliminary to applying this method, the class should have 
 a thorough training on such questions as the following : Find 
 .207 of $185.75 ; find .0085 of $36.35 ; (see preceding grade).— In 
 2 years, 3 months, and 20 days, at C per cent, per annum, what 
 decimal fraction of the -principal is equal to the interest ? at 7 per 
 cent ? at 5 ? at 8 ? at 7^ ? etc. 
 
210 now TO TEACH 
 
 Give examples involving the various forms of the difference 
 of dates— the application of the six per cent, method to a given 
 or ascertained number of days. Example : Interest of $340 from 
 Jan. 5th to July 2d, at 6 per cent. Examples involving the 
 method when the year is estimated to consist of 365 days, should 
 also be given. 
 
 Give examples in Bank Discount, and explain its similarity 
 to Compound Interest in being the interest on the amount. 
 
 Note— (On the derived ca^es of simple interest.)— In teaching the four 
 derived cases of simple interest, begin with an easy example in the funda- 
 mental case, and from that d< rive the others in their order, being particu- 
 larly careful to teach that, being derived, they all require division; that, to 
 find the rate, the given interest is to be divided by the interest of the given 
 principal at 1 per cent.; to find the time, by the interest of the given prin- 
 cipal for 1 year; to find the jnincipal, by the interest of a principal of $1 ; 
 and that, in the fifth case, the given amount is to be divided by the amount 
 o/$l. 
 
 Give examples in True Discount, distinguishing carefully its 
 difference in principle, and therefore of method, from Bank and 
 Commercial Discount 
 
 Partial Payments and Compound Interest should be very 
 briefly treated, and witli very simple examples. 
 
 The form and nature of a promissory note, and the meaning 
 of the several terms applicable to it, and the form of bills and 
 receipts are included in the work of this grade. 
 
 GEOGRAPHY AND HISTORY. 
 
 GcoffvajiJiy. — Complete the local and descriptive 
 geography of one continent or gi'aud division before 
 beginning that of another. The same general plan 
 should be pursued as in. the preceding grades. If the 
 prominent physical features of Asia, for instance, be 
 first taught as a whole, including the climate, the 
 pointer and the outline map being used to expedite the 
 process, the descriptive geograpliy of the individual 
 countries will - involve but little labor, and will be 
 easily remembered. 
 
niSTOBY. 211 
 
 The geography of Asia is by far the most important 
 and interesting; that of Africa and Oceanica is com- 
 paratively simple, and should be reduced, in teaching, 
 to the narrowest limits that will give a clear view of 
 the general physical conditions of surface and climate, 
 and of the social conditions of the various races, to- 
 gether with a knowledge of the leading productions and 
 exports, and the location of the principal cities. 
 
 ltevieiv,—l^\\Q review should be as in the preced- 
 ing grades. One of the most comprehensive and im- 
 portant elements of a general revieiu of the entire sub- 
 ject is, to show the relations of Europe to all the other 
 grand divisions of the globe, as to conquest, settlement, 
 colony, language, etc. This may be taught in a very 
 brief and general way, and is indispensable to a correct 
 outline knowledge of the present condition of the 
 human race, — one of the most important objects of the 
 study of geography. 
 
 History , — The teacher is particularly referred to 
 the General Suggestions in regard to U. S. History, in 
 the preceding grade. 
 
 Tlie Outlines of the Hevolutionary TFa**.— (Teach as 
 in the French and Indian War.) 
 
 Causes of the Revolution. — Navigation Acts — Restriction of Co- 
 lonial manufactures — effects of war on the national debt of Eng- 
 land — taxation without representation— the Stamp Act, 1705 ; its 
 nature — causes which led to its repeal — the Tea Tax — riot in 
 Boston, 1770— the Boston " Tea Party," its immediate causes, 
 and its consequences — nature of the Port Bill, 1774— first Con- 
 gress at Philadelphia — its measures— im^ii/to?)-, Aprill^, 1775-113 
 effects upon tlie country— Bunker ITill— siege of Boston— Wash- 
 ington appointed Commander-in-Chief— evacuation of Boston, 
 
212 HOW TO TEACH 
 
 and subsequent general drift of military events towards the west 
 and south — Declaration of Independence, July 4, 1776 — battle of 
 Long Island — its purposes and results — retreat to the Delaware 
 — capture of the Hessians at Trenton — Princeton — La Fayette — 
 British move on Philadelphia, 1777 — Chad's Ford — its conse- 
 quences — Burgoyne's invasion, its route and purpose, 1777 — 
 Schuyler — Burgoyne's disasters— Gates — the two battles of Still- 
 water — Chnton's movements — Burgoyne's surrender, October, 
 1777 — its far-reaching consequences — the French alliance and 
 assistance — British retreat from Philadelphia — Battle of IMon- 
 moulh, 1778 — New York tlie base of the British — destruction 
 along the coasts of Connecticut and Virginia — Wyoming — battle 
 of the Chemung, 1779 — it breaks foiever the power of the Iro- 
 quois — Paul Jones — Charleston captured, 1780 — large numbers of 
 Tories in the south — consequent years of guerrilla warfare — Sum- 
 ter — Marion — Gates at Camden — destruction of his army, and of 
 Sumter's force — Arnold's treason — the mutiny at Morristown, 
 1781 — its causes — condition of the army — Robert Morris — Ar- 
 nold's ravages — Greene's retreat — battles in Carolina and their 
 consequences — Cornwallis at Yorktown — combination of the 
 French and American forces — Surrender of Cornwallis, October, 
 1781 — its effects in America and in England — Treaty of Paris, 
 1783— its terms— condition of the country at the close of the 
 war. 
 
 Articles of Confederation, 1776-1777-1781— the government 
 before 1781— after 1781— Shays's rebellion, 1786— leads to a con- 
 vention to revise the Articles — anew ComtitutionA(iw\?,G*\ instead, 
 1787— adopted by the States— ^-^jes into operation, 1789. 
 
 In the biographical review include a brief notice of Henry, 
 Hancock, Franklin, Lee, Jay, Livingston. 
 
 1789-1797. — Washington's Administration — Domestic history ; 
 the cabinet — leading measures — States admitted — their former re- 
 lations. Foreign relations— Trouble with France, and its causes. 
 
 Note 1 .—Bead the Indian war. The teacher will give a brief statement con- 
 cerning Boone, Clark, the original extent of Virginia, and the Ordinance of 
 1787. 
 
 Note 2.— Give, orally, a very brief outline account of the French Revolution, 
 the resulting relations of France and England and of Europe generally ; the 
 continnance of these wars to 1815. Refer particularly to the fact that political 
 differences in the United States were, to a great extent, based upon our foreign 
 
HISTORY. 213 
 
 policy, and that wc were at last drawn into the vortex of the great European 
 wars ill 1812. 
 
 Ecfer also to Washington's Farewell Address, and give, briefly, a very few 
 of its leading point*. 
 
 1797-1801. — Adams' a Administration. — Foreign relations; — 
 coutinued troubles with France. — Domestic history ;— unpopular 
 measures — the death of Washington— removal of the Capital. 
 
 1801-1809. — Jefferson's Administration. — Domestic Iiistory ; — 
 admission of Ohio — its previous relations— the Louisiana pur- 
 chase — its immediate and subsequent importance — Hamilton 
 and Burr, 1804— a sketch of the history of each — Fulton's 
 first steamboat, 1807. — Foreign relations; — Tripolitan war, 1801- 
 1805, its causes and results.— (i2(;«(Z the detail.) The state of 
 Europe, and the importance of our carrying-trade — extraor- 
 dinary measures of France and England in relation to the 
 rights of neutrals — English claims of right of search and im- 
 pressment — bearing of the impressment claim upon our natural- 
 ized citizens, and our national honor — " Once a subject, always 
 a subject " — affair of the Leopard and Chesapeake, 1807 — Or- 
 ders in Council and the Milan Decree, 1807 — Embargo, 1807- 
 1809— Non-intercourse Act, 1809. 
 
 1809-1817. — Madison's Administration. — The entire interest 
 centers in the Foreign relations—they control the Domestic history, 
 Berlin Decree abolished, 1810. 
 
 Note.— Bead the affair of the Little Belt— Indian War. 
 
 War declared June 19, 1812 — its two chief causes. 
 
 'SoT'E.— Bead the detail ol the military and naval operations ; show briefly, in 
 outline, first, the several aggressive expeditions into Canada, from Detroit to 
 the St. Lawrence— tlieir general failure ; second, the smallness of the navy— its 
 brilliant success, but little direct influence on the fortunes of the war, except- 
 ing on the lakes— utter destruction of American commerce ; third, the aggres- 
 sive expeditions of the British, the Americans being chiefly on the defensive 
 after 1812— Indian war in the West and Southwest— invasions from Canada- 
 blockade of all important ports— naval and military expedition against 
 Washington and Baltimore— invasion by the way of Lake Champlain— expe- 
 dition against New Orleans, and its purposes— final repulse of all these at- 
 tempts, and similar fate of renewed aggressions of the Americans against 
 Canada — destruction of the Indian power. 
 
 Give the sequence of leaduig events, omitting the dates, except as to years. 
 
 The Hartford Convention — its alleged purposes — its effects — 
 treaty of peace, December, 181-4— a part of the general pacifi- 
 
2U now TO TEACn 
 
 cation of Europe upon the fall of Napoleon— the causes of tlie 
 war not even alluded to in the treaty — have tliese questions 
 ever been settled ? If so, when and how ? 
 
 l^ox-E.— Read the second B.'irbaiy war, 1812-1S15— its causes and results. 
 
 In the biographical review include a brief notice of Hamilton, 
 Burr, Randolph, Fultou, Whitney, De Witt Clinton. 
 
 1817-1825. — Monroe's Administration. — Domestic history ; — Mis- 
 souri Compromise, 1820— formation of new parties on questions 
 of commerce and fiuauce — Whigs and Democrats — the leading 
 questions until IMo.— Foreign relations ; — purchase of Florida — 
 the Monroe Doctrine, 1822, its origin and importance. 
 
 1825-1829. — John Quincy Adams's Administration. — Tariff of 
 1828— leads to the defeat of the Whigs and the election of Jack- 
 son. 
 
 1829-1837. — Jackson's Administration. — Domestic liistory ; — 
 United States Bank— nullification, 1832— Clay's Compromise. 
 Foreign relations ;— the French indemnity. 
 
 1837-1841. — Van Buren's Administration.— Fiimc of 1837— Sub- 
 Treasury Bill, 1840— political revolution. 
 
 1841-1845. — Harrison — Tyler's Administration. — Domestic his- 
 tory ;— the Bankrupt Law— Dorr's 'Rch&W'iow.— Foreign rela- 
 tions ; — the Maine boundary — annexation of Texas. 
 
 1845-1849. — Polk's Administration. — Domestic relations now 
 give direction to Foreign policy — Oregon boundary — chain of 
 causes leading to the ]\Ie.\-ican war — boundary claimed by 
 Texas— Mexican war. May, 1846, to Feb., 1848. 
 
 'Rote.— Eead the details ; give the leading military events in sequence, 
 omitting all dates, excepting years. Teach with the following grouping. 
 Iiorthe7-nopern'io>is— Taylor east of the Rio Grande— west of it— Wool— Kear- 
 ney— Doniphan— Fremont. Southern ojJej'atmis—ScotVs campaign. 
 
 Treaty of Guadalupe Hidalgo— its terms — discovery of Cali- 
 fornia gold in 1848— its important subsequent influence upon 
 the national development. 
 
 1850-1853. — Taylor and Filhnore's Administration. — The Slave- 
 ry question the leading element in the subsequent history — the 
 California question, 1850 — its alleged relation to the Missouri 
 Compromise — death of Taylor — Clay's Compromise Bill, 1850. 
 
 1853-1857.— P/e?'ce's Administration. — Effects of the Fugitive 
 Slave Bill— the Kansas-Nebraska Bill, 1854 — it annuls the 3Iis- 
 
HISTORY. 215 
 
 souri Compromise — rise of a new parly, " Free-soil " or Republi- 
 can — civil war in Kansas, its causes — flow of immigrants into 
 that tcrritoiy. 
 
 1857-1861. — Buchanan^s Administration. — Continuation of the 
 Kansas trouble — John Brown's affair — its effects — split of the 
 great Democratic party — four Presidential candidates — election 
 of Lincoln — extreme doctrine of State Rights — secession of 
 South Carolina, Dec, 1800— Fort Sumter— more States secede — 
 Confederate government formed, Feb., 18G1. 
 
 1861-1865. — LincohCs Administration. — Civil war — Fort Sum- 
 ter, April 12, 1861— effects upon the North— the President's 
 proclamation — more States secede, making eleven in all. 
 
 T^iofE.—Read the details of the war ; show the importance of the question 
 of foreign intervention, and the efl'orts on both Fides in regard to it. 
 
 In the Review show that the operations of the Confederates were mainly- 
 defensive, except in the great sorties of Lee at Antietam and Gettysburg, of 
 Hood at Nashville, and of Early at Chambersburg— all of which were repelled. 
 That the main objects of the aggressive movements of the Union troops were, 
 let, the destruction of Lee"s army; 2d, The opening of the lMissisi?ippi— that 
 after the opening of that river by the fall of Forts Henry and Douelson, and 
 the subsequent capture of New Orleans and Vicljsburg, the lines were con- 
 tracted by a movement from the northwest to the southeast, ending in Sher- 
 man's march from Atlanta to Savannah and Goldsboro'. The leading inci- 
 dents will then readily fall into place.— Show the importance of the blockade, 
 the chief function of the fleet— also, but very briefly, the enormous expendi- 
 ture of men and money on both Bides, and the measures Ijy which they were 
 obtained. 
 
 1865-1869. — Johnson's Administration. — Death of Lincoln— the 
 two subjects of leading importance — 1st. Providing for the pub- 
 lic debt — 2d. Reconstruction — the 13th Amendment — tlie 
 President and Congress quarrel — impeachment — the French 
 in Mexico, and the demand of tlie United States Government — 
 purchase of Alaska — laying of the first Atlantic telegraph 
 cable. 
 
 1869-1873.— (?ranrs Administration.— Vvicxfic Railway— 14tli 
 and 15th Amendments— the Alabama question— leading pro- 
 visions of the treaty of Washington — the Geneva Arbitration— 
 the settlement of the northwest boundary question. 
 
 Addenda — The rapid development of the country since 1815 
 — the leading elements in that development — emigration and 
 immigration — the Erie Canal and the Lakes as the great water- 
 
216 EOW TO TEACH 
 
 way — steam and steamboats — railways — telegrapns. In the 
 biographical review include a notice of prominent men, such 
 as Calhoun, Clay, "Webster, Seward, Greeley, Morse, etc., etc. 
 
 ELEMENTARY SCIENCE. 
 
 Natural Philosoj^hy, — The suggestion to use 
 "a simple text-book" should not be interpreted as a 
 recommendation to dispense with oral instruction in 
 this branch. On the contrary, the proper use of i\\Q 
 text-book is as an auxiliary, as a general guide to the 
 teacher in the selection of subjects, and as an important 
 help to the pupil in preparing at home for the recita- 
 tion of a lesson which has been previously explained 
 and illustrated in the class-room. 
 
 Any system of procedure which omits this prelimi- 
 nary oral instruction is certainly not worthy of the 
 name of teaching. The text-book should be indeed 
 brief and simple, and its illustrations must necessarily 
 be few. But the teacher should supply the further 
 illustration and experiment which will certainly be 
 found to be necessary; it is also of especial importance 
 that the pupils should themselves be in every way en- 
 couraged and led to report such instances of the appli- 
 cations of the principles they have been taught, as they 
 can themselves discover in the phenomena and inci- 
 dents of their daily life and experience, both in and out 
 of school, so that, as far as possible, they may form 
 habits of observation and reflection. 
 
 The teaclier will find a wide difference in the readi- 
 ness with which individual pupils will conceive and 
 apply scientific principles. "With a few, the bare state- 
 ment of a principle will often enable them to point out 
 
ELEMENTARY SCIENCE. 217 
 
 its simpler applications. The results of a certain order 
 of experiments, and the simpler deductions from them, 
 will be promptly anticipated by such minds. But it 
 will not be so with all ; and with some, only by careful 
 and repeated illustration will the principles which in- 
 terpret the facts presented, be clearly apprehended. In 
 all experiments the pupils themselves should be made 
 as far as possible particij)ants. In reviews they should 
 be called upon to repeat the experiments or statements 
 made by the teacher or given in the text, and to give 
 the proper explanation. They should also be encour- 
 aged to try further experiments for themselves at home, 
 and to furnish an account or a repetition of them in 
 the class-room, if possible. 
 
 The teacher should also particularly remember that 
 it is not necessary to follow slavishly the exact order or 
 selection of topics given in the text-book. The teach- 
 er, and not the book, should be the master. An intel- 
 ligent papil will not be long in finding out whether or 
 not the statements in the text are tire limit of his teach- 
 er's acquisitions. The great majority of young minds 
 are hungry for this sort of knowledge, and it will un- 
 questionbly be the teacher's fault if that appetite be 
 not at the same time both gratified and stimulated. 
 
 Care should be taken, when the scientific meaning 
 of a common term differs greatly from the popular one, 
 to point out clearly such difference, in order that the 
 pupil be not misled by thinking that he knows that of 
 which he is really ignorant. Among the many cases 
 in which this will be found necessary, the terms jjoros- 
 ity, porous, solid, and impejietrahility may be taken as 
 instances. It is by no means necessary that the pupil 
 should be able to give an exact and com])roheusive sci- 
 entific definition of such terms; a few analytical ques- 
 
 10 
 
218 SOW TO TEACH 
 
 tions by the teacher -will readily show if the subject is 
 understood. 
 
 When a lesson from the text-book is to be giyen for 
 home study, it should first be carefully illustrated and 
 explained. No teacher will be likely to do this as well 
 as he should, if he give the subject no thought until 
 about to assign the lesson. After receiving these expla- 
 nations the jjupil will be far less liable to misconceive 
 or, as sometimes happens, to fail utterly to comprehend 
 the statements of the text. As far as the subject will 
 allow, he should be led through the medium of experi- 
 ment to a knowledge of the facts. The facts once as- 
 certained, the p7'lnciples underlying them may be de- 
 duced. A limit will, sooner or later, be reached, where 
 the more recondite parts of the subject, so far as they 
 may be entered upon, imist be taught empiricaUn, in 
 consequence of the pupil's limited knowledge of other 
 departments of science. 
 
 For instance, suppose that the teacher has already 
 experimentally established in his pupil's mind a general 
 idea of the terms force and gravity, and that he now 
 wishes to lead him to know that " the weight of a body 
 is the measure of the force of gravity" acting upon it, 
 and after that to establish the law of its variation. 
 Let the teacher or one of the pupils borrow a common 
 spring-scale — the smaller and simpler the better — let a 
 pupil piull, and at the same time notice that he is ex- 
 erting a force, that the position of the index will vary 
 with the degree or amount of force, that the motion is in 
 the direction of the force, however the instrument may 
 be held ; now place a succession of heavy bodies in the 
 scale, and let him notice that tlie effects are identical 
 with those produced by his muscular force. He will 
 no longer vaguely conceive that the effect produced 
 
ELEMENTARY SCIENCE. 219 
 
 upon the scale is because the body is heavy (which was 
 to him a vague term), but because the earth actually 
 pulls it as he did, though no connecting bond is visible, 
 as when he pulled. A knitting-needle suspended and 
 balanced upon a thread and acted upon by a simple 
 magnet, will clearly convince him that o, force may bf 
 exerted by one body upon another without actual con-- 
 tact. You have clearly defined for him the idea that 
 " the weight of a body is the measure of the earth's at- 
 traction upon it." If now you Avish to teach the law 
 of the variation of the weight of a body of invariable 
 mass, as should indeed be done, the next step must be 
 emjyirical. The pupil's deficiency in mathematics for- 
 bids any other course of procedure. The "Law of 
 Gravitation" must be s^a^etZ /fo him, together with the 
 reason for so doing without proof. It will develop in 
 many a mind an earnest desire to supply that deficiency. 
 The law of the variation of weight may now be readily 
 deduced by first adding to the pupil's mathematical 
 knowledge the technical meaning of the term square, 
 and then giving a variety of simple arithmetical prob- 
 lems to illustrate it. 
 
 There is, perhaps, no graver or more common error 
 in relation to this subject, among earnest teachers who 
 are called upon to teach it, than the notion that this 
 requires expensive or complicated apparatus. The very 
 contrary is the case in the great majority of instances. 
 Expensive apparatus, with its show of brass and glass, 
 has a direct tendency to repress the most precious ele- 
 ment and evidence of a teacher's success — experiment- 
 ing at home by the pupils themselves. The principles 
 of the Jcvcr may he just as Avell developed by means of 
 a pen-handle, a pointer, or a window-pole, as by a pol- 
 ished brass or steel bar ; a large spool makes an excel- 
 
220 SOW TO TEACH 
 
 lent wheel and axle; a ribbon-block a good single pul- 
 ley, fixed or movable ; a slate, a book, or a shingle, an 
 inclined pla?ie ; a pocket-knife will soon furnish a good 
 wedge from a little piece of board, while the use of the 
 blade itself is an excellent illustration of the applica- 
 tion of the principle; and a large screw or a discarded 
 auger-bit, with a knitting-needle or a pen-holder for a 
 lever, makes an efficient single screvj. And so through 
 every department of the subject. Nothing marks more 
 fully the ability of a teacher than fertility in such re- 
 sources. Strings, tops, balls, and marbles; pop-guns, 
 potato-mills, bean-shooters, and putty-blowers, and the 
 thousand and one nameless articles to be found in pu- 
 pils' pockets, furnish an exhaustlcss mine of apparatus, 
 and good apparatus too, for the skillful teacher. The 
 immortal Dalton wrought out his atomic chemical the- 
 ory with apparatus which may be excelled in many a 
 junk or old bottle shop ; and the teacher determined to 
 succeed will find that " where there is a will there is a 
 way." 
 
 SYIiLABUS OF TOPICS. 
 
 {^To be illustrated as far as possible objectively) 
 
 Constitution, Forms, and Properties of Matter. — Illus- 
 trate the following terms — body or mass, molecule, atom ; solid, 
 fluid, liquid, gas; sensible or cellular pores, as in bread or 
 sponge ; physical or intermolecular pores, as in iron, water, air, 
 and every form of matter ; porosity. 
 
 Extension, impenetrability, rarity and density, compressibil- 
 ity and expansibility, inertia, mobility. 
 
 Force and its forms. — Attraction aiid repulsion : refer brief- 
 ly to the fact that atoms and atomic forces are treated of in chem- 
 istry. Indestructibility of matter to be briefly explained. 
 
 Molecular forces. — Cohesive force : the properties of matter 
 which are dependent upon cohesion ; tenacity, flexibility, brittle- 
 ness, hardness, ductility, malleability; the properties depend- 
 
ELEMENTARY SCIENCE. 221 
 
 ent upon cohesion and molecular repulsion ; elasticity. Illustrate 
 the elasticity of flexure ; of compression; of expansion; of tor- 
 sion. Relations of solids, liquids, and gases to molecular attrac- 
 tion and repulsion. 
 
 Adhesive force : properties dependent upon adhesion; capil- 
 lary attraction and its uses in organic and inorganic nature. 
 
 Divisibility of matter — into particles by mechanical force; into 
 molecules by heat, solution, etc. — What forces are overcome iu 
 each case, and by what other force. 
 
 jMechanical foece. — Gravity — why called universal gravita- 
 tion ; its simplest phenomena ; its law ; weight, a measui-e of 
 gravity. 
 
 Mechanics of solids.— Center of gravity ; line of direction, 
 plumb-line ; stable, unstable, and indilTereut equilibrium. 
 
 Simple. MacJUnes. — Lever, witli simple problems in mental 
 arithmetic ; pulley, wheel-and-axle, inclined plane, wedge, screw. 
 
 ^Mechanics op liquids {Hydrostatics). — Mobility of liquids, 
 and its cause; their small compressibility; pressure in every 
 direction ; gravity the primary cause ; equality of pressure at a 
 given point ; variation of pressure with depth ; meaning of the 
 term level; why still water has a level surface; why the hy- 
 drant water flows from the open tap ; at what heiglit it ceases to 
 flow, and why ; other illustrations of the same principle ; what 
 that principle is ; the hydrostatic paradox ; the hydraulic 
 press ; specific gi-avity ; the hydrometer ; why iron ships float. 
 
 Mechanics op oases {Pneumatics). — Air — its compressibility, 
 expansibility, and elasticity; chief mechanical ditlerence from 
 liquids ; its weight ; its pressure in all directions ; upward press- 
 ure and how shown ; tlie mercurial barometer, its construction, 
 principle, and uses; Torriceili's experiment; Pascal's experi- 
 ment ; tlie aneroid barometer ; height of the atmosphere, and 
 gradual diminution of its density. 
 
 Astronomy. — The teacher should, at first, en- 
 deavor to awaken an interest in the subject by referring 
 to some of tlie most impressive and beautiful phenom- 
 ena connected with the sun, the moon, the stars, planets, 
 
222 SOW TO TEACH. 
 
 comets, and rneteors. He should endeavor to induce 
 the pupils to observe more attentively these phenomena, 
 and to excite their curiosity to know about them. En- 
 courage them to ask questions in relation to what they 
 observe ; as, Why does the moon change its appearance ? 
 Why does the sun rise so. far from the east point, or set 
 so far from the west point at certain times in the year? 
 What bright star was in the west on a certain night, at 
 a particular time ? and other such questions, some of 
 which the pupils are, of -course, to be told cannot be 
 answered until they have further studied the subject. 
 Thus they will learn to study the science from nature 
 as well as from the book. 
 
 Let the general phenomena of the hearens be first 
 explained ; the movements of the sun, moon, stars, and 
 planets in relation to the horizon ; the circles of daily 
 motion ; the difference between planets and fixed stars; 
 how to distinguish some of the former, etc. 
 
 The following topics may then be taken up in their' 
 order: The Earth, its form, magnitude, motions, etc. ; 
 Circles, and angular distances on the Earth and in i\\Q 
 heavens; Day and Niglit ; the Seasotis, etc: these topics 
 should be illustrated by the use of a Tellurian, and 
 Problems for the Globe should be used for the purpose 
 of exercise and illustration. 
 
 Next, teach the general arrangement of the Solar 
 System. Inferior and suj^erior planets — their magni- 
 tudes, revolutions, position of orbits, periodic times, 
 and apparent motions. 
 
 The mathematical definitions necessary for the jirop- 
 er understanding of this portion of the subject should 
 be taught incidentally thereto. 
 
FIEST GEADE. 
 
 Tiine allowed, about twelve months. 
 OUTLINE COURSE. 
 
 LANGUAGE. 
 
 Heading, Spelling, Definitions, and Word Anal- 
 ysis, continued as in the preceding grade. 
 
 English Grammar,— Analysis, Parsing, and Syntactical 
 criticism and correction, «ipntinued; the anomalous and idio- 
 matic forms to be taught and explained. 
 
 Composition. — Exercises on selected themes; Practice m 
 Letter Writmg, commercial and social. 
 
 MATHEMATICS. 
 
 Mental and Written Arithmetic. — Continued and re- 
 viewed, including the rules pertaining to the mensuration of 
 regular plane surfaces and solid bodies ; with exercises in anal- 
 ysis and calculation, continued. 
 
 Algebra. — Through equations of the first degree. 
 
 Geometry. — The geometry of plane figures, with practical 
 applications. 
 
 GEOGRAPHY AND HISTORY. 
 
 Geograjilig. — The Outlines of Physical Geography. 
 Sistorg.— The Outlines of Ancient and Modern. 
 
224 SOW TO TEACH 
 
 ELEMENTARY SCIENCE. 
 
 BY OKAL INSTRUCTION, OR WITH A SIMPLE TEXT BOOK. 
 
 Natural Philosojihy. — Simple outlines completed, to in- 
 clude Acoustics, Pyronomics, Optics, Magnetism, and Electricity. 
 
 Astronotny. — Elementaiy, continued and completed. 
 CJiernistry. — Elementary principles and facts. 
 
 WRITING ANT) DRAWING. 
 
 PeilTnanship. — Instruction to be continued as in the preced- 
 ing grade, with practice in the writing of paragraphs, verses, 
 business forms, notes, superscriptions, etc. 
 
 Draiving. — Drawing objects of regular form in perspective, 
 block combinations, etc., with shading; copying pictures of fami- 
 liar objects, animals, etc. , with easy landscapes, as far as the 
 time may permit ; also (for males) simple architectural and me- 
 chanical drawing. 
 
 MSCELLANEOUS BRANCHES. 
 
 Book-keepinff. — Single and double entry; with careful in- 
 struction in the principles of the latter. 
 
 Constitution of the United States.— History of its adop- 
 tion ; its various provisions and amendments ; the reasons for 
 the same to be explained as far as may be necessary or appro- 
 priate. 
 
GRAMMAR. oo 
 
 •40 
 
 How TO Teach 
 
 SUBJECTS OP THE FIRST GRADE. 
 
 LANGUAGE. 
 
 Heaclinf/f Spelling f and Definitions, — See 
 
 the preceding grade. 
 
 EnfflisJi Grammar, — The exercises of this 
 grade comprise those of analysis, parsing, and com- 
 position. Sentences of an irregular or idiomatic con- 
 struction, should be presented to the pupil, with the 
 "view to show how far their analysis can he made to 
 harmonize with the usual syntactical rules, and to 
 teach the just limits of their use. Anything bordering 
 on slang should be discountenanced and condemned. 
 An improper construction — that is, one that contra- 
 venes well-established rules and principles — should not 
 be sanctioned by any ingenious analytical contrivance 
 or substitution. 
 
 The exercises in analysis should embrace the careful 
 and critical study of select passages from some of the 
 best English and American writers ; as Shakespeare, 
 Milton, Pope, Cowper, Young, Bryant, Longfellow, etc., 
 etc. Prose writers, such as Addison, Johnson, L'ving, 
 etc., should also be drawn upon for exercises, — always, 
 however, with a critical end in view, — to discover and 
 correct errors, as well as to find excellencies and beauties. 
 
 Such exercises, to however limited an extent it ia 
 10* 
 
23G now TO TEACH 
 
 possible to carry them, will always exert an important 
 influence upon the pupils' style of composition, if not of 
 daily speech. They will serve, moreover, to cultivate the 
 taste of the pupils, and to awaken an interest in their 
 minds in the study of English and American literature. 
 A good reading-book will be found an important auxili- 
 ary in carrying on the instruction here suggested. 
 
 Coinposition. — The exercises in composition in 
 this grade, as in those preceding it, should be, to some 
 extent, im2)rom2)fti, so as to develop that fluency and 
 readiness in the written expression of thought which is 
 of so much service in almost every sphere of life. The 
 writing of letters, etc., as suggested in the outline 
 course, should receive a very careful attention at this 
 stage of the pupils' progress. 
 
 MATHEMATICS. 
 
 AritJunetiCo — In this grade, the teaching of arith- 
 metic consists in large part of a review of what has 
 gone before, with exercises sufficient in number and dif- 
 ficulty to familiarize the pupils with the principles, and 
 render them expert and accurate in their application. 
 For suggestions in regard to this part of the work, the 
 teacher is referred to the preceding grades. 
 
 The advanced work should comprise the following: 
 Exchange, Equation of Payments, Proportion, Partner- 
 ship, Square Root, and Cube Root, with their simple 
 applications, and Mensuratio7i. The exercises em- 
 ployed to teach these departments of arithmetic, should 
 be of as practical a character as possible ; and all the 
 processes should be specially analyzed, the rules given 
 
ARITHMETIC. 237 
 
 being in all cases deduced from tlie analysis. A careful 
 explanation of the business tra7isactio7is involved in any 
 of the rules or their applications, should always be given 
 before the pupils are required to solve the jiroblems. 
 Failure more frequently arises from a want of this knowl- 
 edge than from a deficiency in arithmetical attainment. 
 
 The following syllabus contains a brief summary of 
 what is suggested to be taught in this grade. 
 
 Syllabus of Topics. 
 
 Exchange. Its nature ; bills of exchange ; par of exchange ; 
 acceptance; domestic exchange — to include two cases: — 1. To 
 find the cost of a draft when its face and the rate are given ; 2. 
 To find the face, the cost and rate being given ; foreign exchange 
 — including the consideration of bills on England and France 
 (cases as in domestic exchange) ; analysis as in percentage. 
 
 Note.— Remember that the old par value of the pound sterling is now 
 prohibited by law, and that the new le^al value is $4,860;^. 
 
 Equa-tion of Payments. Cases :— 1. To find the average time 
 of payment, when the items have the same date, but different 
 credits ; 2. When the items have different dates ; 3. To find the 
 average time for paying balance of account, having both debits 
 and credits. Analysis, on the principal of interest, reducing each 
 principal concerned to $1. 
 
 Pkoportion. Ratio ; proportion defined : relation of ante- 
 cedents and consequents ; ratio of 4 to 12, 4 : 12=-,% ; method of 
 finding the missing term; simple and compound proportion dis- 
 tinguished ; problems involving each : these problems should 
 be only such as are required to illustrate the principle, since 
 they are ordinarily to be solved by analysis previously given. 
 
 Partnership. Terms defined. Cases : — 1. To find each part- 
 ner's share when the profit or loss is divided accoj'ding to capital 
 only ; 2. To find it when time is considered. Analysis, fractional, 
 or by means of proportion. 
 
 Square Root. Involution and evolution defined : simple 
 examples of each; powers of roots; illustration of what is 
 meant by finding the square of a number ; what is meant by 
 
228 SOW TO TEACH 
 
 square root. Illustrate by simple powers, integral and fractional — 
 common fractions and decimals (tlie latter carefully). Problems 
 in wliicb the root contains denominations other than units. Illus- 
 trate by geometrical construction (square of the sum of two lines). 
 
 The following are specimens of " simple applications," which 
 should be taught in this grade : — Given the area, to find the side 
 of the square containing it. 
 
 Given the length and width of a rectangle, to find the side of 
 a square equivalent to it. 
 
 Note.— In teaching the pupils how to find the area of a rectangle, avoid 
 giving the erroneous impression that we absolutely multiply the length by 
 the width, as expressed by denominate numbers. Show that the number of 
 superficial units corresponding to the linear units of the length, is multiplied 
 by the number (abstract) of linear units in the width. Thus, if the length be 
 10 feet, and the width 5 feet, the area must be, not 5 feet times 10 feet, but 
 5 times 10 square feet, equal to 50 square feet. 
 
 Given any two sides of a right-angled triangle, to find the 
 other side. Teach and illustrate the geometrical theorem on 
 wliich this problem depends. Give various questions requhing 
 an application of this problem. 
 
 Cube Root. How to extract it, with an illustration of the 
 process. This is best given by means of the blocks constructed 
 for that purpose. If the pupil has studied Algebra sufficiently, 
 a demonstration by the Binomial Theorem may be given. The 
 formula representing the cube o-f the sum of two quantities, will 
 enable the pupil to remember clearly the details of the rule. 
 
 The applications of the Cube Eoot should include the com- 
 putation of the contents of similar solids. 
 
 Mensuration. This should at least include the following 
 cases:—!. To find the area of a parallelogram when the base 
 and altitude are given; 2. To find the area of other quadri- 
 laterals, with sufficient data ; 3. To find the area of triangles ; 
 4. To find the area of a circle ; 5. To find the diameter and 
 circumference of a circle when the area is given ; 6. To find the 
 solid contents, from sufficient data, of a cube, parallelopiped, 
 prism, pyramid, cylinder, cone, and sphere ; 7. To find the con- 
 tents of a cask, or other vessel, with the requisite data. 
 
 Every topic to be treated in the arithmetic of this 
 grade should be introduced by corresponding mental 
 exercises, the slate being used only when the numbers 
 
ALGEBRA. 229 
 
 involved are too large to be readily retained in the mind. 
 The pupils should be very frequently practiced in this 
 mental work. The text-hooh in mental arithmetic should 
 be sparingly used, and great care should be exercised in 
 assigning lessons for home-study in this branch. 
 
 Algebra,— "This, subject should be taught as a pe- 
 culiar mathematical language, by means of which the 
 relations of quantities and the results of their combina- 
 tions may be expressed, and thus the reasoning in re- 
 gard to them facilitated. The symbols, both of quanti- 
 ties and relations, or operations, should at first be care- 
 fully taught and illustrated. 
 
 The simple operations of addition, subtraction, mul- 
 tiplication, and division, should not be exhaustively 
 treated, as is usually done, before the pupil is made 
 acquainted with the nature and use of equations. The 
 equation is to algebra Avhat the proposition is to ordi- 
 nary language. It is the means of definitely expressing 
 a mathematical truth, either particular or general. In- 
 equations (technically so called) express truths, but not 
 exactly; as, when Ave say, a; + ?/7 5, we do not indicate 
 Tioiv much the sura of x and y exceeds 5 ; but if we say, 
 x-{-tj=Q, we express a precise fact. It is suggested, 
 therefore, that equations be presented very soon after 
 the preliminary explanation of the symbols employed. 
 The examples of equations first presented should be of 
 the simplest character ; and their use in the solution of 
 problems should be objectively shown. This may be 
 done by employing a few very easy questions, such as 
 are given in some of the text-books, for mental solution ; 
 as, What number is that, to the half of which if 5 be 
 added the sum will be 11 ? Even the dullest pupil can 
 be easily made to perceive the use of expressing tliat 
 
230 BOW TO TEACH 
 
 condition so that it can be clearly kept in view ; as (x 
 rein-esenting the unknown number) | + 5 = 11. 
 
 In solving such a problem, the successive steps or jt>ro- 
 cesses of reasoning should be kept in view. Thus, sub- 
 tracting 5 from each member, the result (expressed by a 
 second equation) is, f=6; and, multiplying by 2 the 
 result (expressed by a third equation) is a;=12, which 
 gives the solution. (Applied axiom to be referred to.) 
 
 Such an exercise, properly performed, will develop 
 more intelligence than whole months of mechanically 
 working out by blind rules long sums in addition, 
 subtraction, multiplication, and division, such as Multi- 
 ply x-—^x + b by x^—x' + 2; Divide a;^— ^ by x—y, etc., 
 etc. These exercises are proper in their place, but of 
 themselves they have but little, if any, educational or 
 practical value. 
 
 Syllabus op Topics. 
 
 1. Preliminary explanation of symbols, both letters, as repre- 
 sentatives of quantity, and the signs of relation or operation, as, 
 + — X ~ = etc. ; exercises to familiarize the pupil with their 
 significance and the mode of reading them. 
 
 Note.— It will be of great service to accustom the pupil to read algebraic 
 expressions iu such a way as at once to indicate their meaning ; as, a +6, the 
 the sum of a and 6; a—b, the diflerence between a and b\ ax 6, the product 
 of a and b, etc. Exercises in finding the numerical value of expressions, 
 when particular values are attributed to the representative letters, will greatly 
 aid in accomplishing this result. Thus, find the value of a^b—b3 when 0=3, 
 b—2, c=l, etc. c 
 
 2. Easy problems in arithmetic, the solutions of which may 
 be facilitated by tlie use of equations, the latter to be of the 
 simplest form, and involving only an application of the pupil's 
 acquired knowledge of symbols. This will at once show the 
 pupils the value of the algebraic notation, and interest them in 
 the study of the subject, as being of practical value. 
 
 3. Mental practice in solving such problems, by means of equa- 
 tions. Most of the text-books in use will aflord a sufficient variety. 
 
y 
 
 ALGEBRA. 231 
 
 4. Practice in solving equations of this cliaracter ; each equa- 
 
 X X 
 
 tion to be read previously in the form of a problem ; as = 
 
 3 8 
 10 ; which may be read : 
 
 What number is that one-third of which exceeds one-eighth 
 of it by 10? 
 
 The method of clearing equations of fractions and transposition 
 should be taught, not by applying mechanical rules, but as pro- 
 cesses of analytical reasoning. Thus in the equation above 
 given, the pupil will easily be made to perceive, that the multi- 
 plication of both members by 24 will produce an equation with- 
 out fractions. 
 
 24x 24x 
 
 (The intermediate step = 240 should be at first used.) 
 
 3 8 
 
 5. After the pupils have' acquired a clear idea of the nature 
 and use of equations, and some espertuess in operating with 
 those of a simple character, those of a more difficult or complex 
 form should be presented, giving occasion for the use of the 
 operations of addition, subtraction, multiplication, and division, 
 which can then be more exhaustively treated, with sufficient 
 practice on the part of the pupil. 
 
 6. The nature of literal equations or general expressions should 
 be then taught, and examples given, some of which may be 
 made to involve an application of all these processes. 
 
 Such as the following are suggested : 
 
 X + a X — a 
 
 (1.) = d 
 
 b c 
 
 X — a X — b 
 
 (2.) + = 2 
 
 b a 
 
 x — a? X — b2 
 (8.) = 
 
 (4.) ^1 
 
 a — b a + b 
 
 (a-fb)x (a — b)x ^ 
 
 (5.) - = \ 
 
 a — b a + b * 
 
232 1^0 W TO TEACH 
 
 Such equations as the above involve much useful practice, not 
 only in adding, subtracting, multiplying, and dividing, but also 
 in fractions and in factoring. The latter should receive careful 
 attention. 
 
 6. The method of solving equations containing more than one 
 unknown quantity — involving the various methods of eliini?iailon 
 — should follow this, and sufficient practice in the solution of prob- 
 lems should also be afforded. The latter, with the preparation 
 herein indicated, may be made a most important aid in training 
 the mind to careful and exact analysis, and logical reasoning — 
 perhaps the most important object, generally, of the study of 
 this subject. 
 
 Note. — This syllabus is not designed to be entirely exhaustive, but to afTord 
 hints as to the order and method of presenting the most important topics. 
 
 Geometry. — This subject, from its extremely ai- 
 stract character, is quite difficult for young students 
 fully to comprehend. It is essential that the abstract 
 ideas with which it is concerned shotild be developed 
 in the minds of the pupils at the preliminary stage of 
 the study. Unless this is done, they cannot be bene- 
 fited by the instruction, nor, indeed, take any interest 
 in it. They will, moreover, be wholly incapable of 
 carrying on the processes of reasoning involved in the 
 demonstrations, unless they clearly apprehend the na- 
 ture of the truths to be proved, as well as of those as- 
 sumed as premises, or arguments. 
 
 The first idea to be developed is that of a solid, as 
 conceived in geometry, involving three dimensions of 
 extension ; next, that of a surface, abstracted from the 
 solid, involving two dimensions ; next, that of a line, ab- 
 stracted from the surface, involving one dimension; 
 and, lastly, that of a point, as indicative of a position 
 in the line, or at either of its extremities, and involving 
 no dimeiisions. These terms, reversing the order, should 
 then be defined; namely, point, line, surface, solid. 
 
GEOMETRY. 233 
 
 Unless these fundamental conceptions are clearly and 
 thoroughly impressed upon the minds of the pupils, 
 no true progress can be made. 
 
 The classification of lines and surfaces may then be 
 taught, the fundamental idea used being that of direc- 
 tion ; as of a straight line, never clianginy its direction ; 
 a curve line, changing it at every 2)oint ; of a broken 
 line, changing it at certain points. The classification 
 of surfaces into pla7ie, curved, and broken may be made 
 in an analogous manner. 
 
 "With this, the idea of parallel U7ies may be made to 
 harmonize by conceiving them as lying side ly side 
 (literal meaning of parallel), and all in the same direc- 
 tion, i. €., tending to a point at an infinite distance, or 
 tending to points, at a finite distance, which, wherever 
 assumed, are at the same distance from each other (the 
 latter may be the easier to develop at first). 
 
 The idea of a plane angle should be made to harmo- 
 nize with these conceptions of a straight line and par- 
 allel lines, being conceived as expressing the difference 
 in direction of two straight lines that meet at a point. 
 
 Note— This, it will be seen, hannonizes with the idea of parallel lines, 
 which tend to a point at an infinite distance, and hence never meet, and can- 
 not form an angle; while the straight lines that form an angle tend to a point 
 at Si finite distance, and meeting at that point, form the angle. 
 
 The definitions of Geometry form the groundwork of 
 the subject, constituting the basis upon which all the 
 subsequent reasoning rests; hence, it is very important 
 that these definitions should be clearly understood and 
 carefully committed to memory. 
 
 It is desirable, before the pupils are required to study 
 demonstrations, that the different methods of reasoning 
 should be carefully explained, and that they should, to 
 some extent, be exercised in the same. This can easily 
 be done by bearing in mind that geometrical truths 
 
234 HOW TO TEACH 
 
 have reference to a comparison of magnitude, and lience 
 involve the idea of equality as a definite fact, and ine- 
 quality indefinitely. Thus, it is required to be proved 
 that the sum of the three angles of a triangle is equal 
 to two right angles ; also, that, of any two sides of a 
 triangle, that Avhich lies opposite to the greater angle 
 is greater (not how much greater). Hence, as a pre- 
 liminary exercise, the following might be given : — 
 Question — If A is equal to B, and B is equal to C, how 
 does A compare witli C ? Ansioe?- — They are equal. 
 Question — Why is A equal to C ? Answer — Because 
 they are both equal to B. Question — How does that 
 prove it? Answer — Because things that are equal to 
 the same thing are equal to each other. Question — 
 Can that be proved? Ansiuer — It cannot; it is self- 
 evident. Question — What are self-evident truths called ? 
 Answer — They are called axioms. 
 
 A variety of such exercises may be employed ; and, 
 in this way, the pupil, before beginning formal demon- 
 strations, may be made clearly to apprehend the nature 
 of geometrical reasoning — so different from that- which 
 he has generally employed during all his previous stud- 
 ies, or which he is accustomed to use in daily life. If 
 the foundation, as here suggested, is well laid, the pupil 
 will soon find it as easy a task to read his geometry, 
 and to learn it by reading (not roio study), as to read 
 any other book of science. 
 
 Of course, in hearing recitations in geometry, the 
 teacher should vary the method, so as to preclude en- 
 tirely the possibility of any rote study, or merely verbal 
 recitation. For this purpose, the figures employed 
 should be diflferent from those in the text book, the 
 letters used in connection with the figures should be 
 changed, or numerals used in tlieir stead. The demon- 
 
GEOMETRY. 235 
 
 strations should sometimes be given withoi^t using 
 either letters or numerals; and, in the case of such as 
 are very easy, the figures themselves may be dispensed 
 with. In most cases, the pupil should be required 
 briefly to recapitulate the arguments employed. 
 
 The amount of ground to be covered in this grade is 
 defined as the " Geometry of Plane Figures." The fol- 
 lowing Syllabus (intended to be only suggestive) em- 
 braces everything required. 
 
 Syll.u3t:s op Topics,. 
 
 I. Elementary definitions — axioms — symbols. 
 
 II. Theorems relating to straight lines, angles, and polygon^ ; 
 
 1. The sum of any two adjacent angles is equal to two right angles. 
 
 2. Vertical angles are equal to each other. 3. The various theo- 
 rems pertaining to the angles formed by the intersection of two 
 parallel lines and a third line. 4. Angles having their sides 
 parallel are equal. 5. Tjiangles are equal, («) when they have 
 two sides and the included angle in each respectively equal ; (S) 
 when they have two angles and the interj acent side in each re- 
 spectively equal ; (c) when they have three sides in each respec- 
 tively equal. 6. The sum of the three angles of a triangle is 
 equal to two right angles, 7. The sum of the interior angles of 
 a polygon is equal to twice as many right angles as the figure 
 has sides, less four right angles. 8. The sum of the exterior 
 angles of a polygon is equal to four right angles, 9. Theorems 
 relating to a comparison of the perpendicular and oblique line 
 drawn from the same point to the same straight line. 10. Only 
 one perpendicular can be drawn from a given point to a given 
 straight line. 11. The greater side of any triangle is opposite to 
 the greater angle ; and the converse, 12. The opposite sides and 
 angles of a parallelogram are equal ; and the converse. Vd. Any 
 problem, either after, or in connection with, these theorems, 
 which can readily be performed ; as, to construct an equilateral tri- 
 angle, to bisect a given straight line, or a given angle, etc. In 
 order to aid in the solution of these, it will be necessary to teach 
 the definition of a circle, its construction, and parts. 
 
 Compass and ruler exercises may also be profitably interspersed. 
 
236 now TO TEACE 
 
 III. Ratio and Proportion. 
 
 IV. The Circle : — 1. lielations of angles to cliords. 2. Relations 
 of angles to arcs. 
 
 V. Area: 1. Comparative areas of parallelograms and of trian- 
 gles. 2. Measure of areas, of a parallelogram, of a triangle, of a 
 trapezoid, etc. 3. Of sqxiares described on the sides of triangles. 
 
 VI. Similarity of figures: 1. Of triangles. 2. Of polygons. 
 
 VII. Problems, pertaining to the circle, the polygon, area, 
 and similar figures. 
 
 VIII. Practical applications in mensuration. (See arithmetic.) 
 
 Outlines of FJi y steal Geofjraphy, — Some 
 departments of physical geography, though perhaps not 
 known to the pupil by that name, have always been the 
 necessary introductory element to the most rudimentary 
 outline of political geography. — Describing the course 
 of a river, the position of a peninsula or a cape, the direc- 
 tion of a mountain chain, or the boundaries of a conti- 
 nent, is as truly a part of physical geography, as is the 
 explanation of the oscillation of the tropical rain-belt, 
 of the formation and transport of icebergs, or of the 
 theories of the trade-winds and ocean-currents. 
 
 The physical geography specially described in this 
 grade is a comparative science. It considers the world 
 as an organic whole, and includes the study of its plane- 
 tary conditions, of the mutual relations of all its parts, in- 
 ternal and external — the land, the sea, and the atmos- 
 phere, — together with the geographical distribution and 
 conditions of the various forms of vegetable and animal 
 life, and of the various races of mankind. 
 
 In the brief time that can be allowed to so comjire- 
 liensive a subject in a single grade, it is obvious that 
 only the simplest outline can be presented. The work 
 has been carefully prepared for in the geography of the 
 preceding grades, to which attention is here specially 
 invited. 
 
PHYSICAL GEOGRAPHY. 237 
 
 A synopsis of the points included in the grade is here 
 appended. If a text-book is used, the teacher should 
 first be thoroughly familiar with its contents, so that it 
 may be employed principally as a reading or reference- 
 book from which appropriate selections may be read in 
 the class. If any other course be pursued, most of the 
 text-books treat the subject so extensively that the pupil 
 will necessarily leave it, at the end of the term, with 
 only an unfinished foundation and no superstructure. 
 
 Syllabus op Topics. 
 
 Ttie Earth as a Globe — its form and dimensions, and how as- 
 certained. 
 
 The Eartli as a Planet — the zones, and their causes. 
 
 The Interior of the Earth — its probable condition, and how in- 
 ferred. (Treat briefly.) 
 
 The Surface of the Earth — its division into land, water, and 
 atmospheric envelope ; the land divided ; the ocean not ; co 
 parative extent of land and water. 
 
 The Land Surface — (Omit Geology). Comparison of the con- 
 tinents in their direction, contour, elevations, and area ; compari- 
 son of the great mountain systems of the continents ; volca- 
 noes ; distribution of; theories of volcanic and earthquake phe- 
 nomena (very brief) ; comparison of the plateau belts; of the great 
 plains ; the great islands and archipelagoes, their distribution and 
 arrangement. 
 
 Note.— To illustrate the coraparison of the continents by the several classes 
 of elevations, give upon the blackboard rough chalk diagrams of sections of the 
 continents. 
 
 Tlie Ocean — its subdivisions and great areas compared ; its 
 level ; its great currents, their function and some one theory of 
 their origin (very brief) ; its tides and waves, and their efi"ect3. 
 (Both very brief.) 
 
 The Atmosphere — its constituents ; vital importance of its 
 watery vapor and its carbonic acid to plants and animals ; evap- 
 oration from the ocean surfixce, especially in the torrid zone ; 
 the atmosphere and the watery vapor as the Earth's blanket. 
 
238 HOW TO TEACH 
 
 TJie Winds — the trades, and counter-trades ; theory of (very 
 brief) ; region of variable winds — (very brief) ; the winds as car- 
 riers of ocean vapor ; solar heat the great cause of oceanic and 
 atmospheric circulation. 
 
 The Great Bain-belt— its annual oscillations; tropical, rainy, 
 and dry seasons ; the mountains as condensers — illustrations. 
 
 Drainage — the river systems of the several continents com- 
 pared ; their existence and direction in relation to the winds and 
 mountain ranges ; causes and location of deserts — illustration ; 
 lakes ; snow in the frigid zone, and on lofty mountains in the 
 torrid zone; glaciers, their origin and motion (very brief); ice- 
 bergs, their origin. 
 
 Vegetation (very brief) — warmth and moisture necessary to ; 
 general characteristics of tropical vegetation ; examples of tropi- 
 cal plants ; examples of plants of subtropical and temperate re- 
 gions; of arctic regions; the great forest belts, their location 
 and causes ; prairie belts ; desert belts ; effects of certain plants 
 on human industries and development (very brief). 
 
 Animals (very brief) — comparison of the characteristics of the 
 several zones and continents as to animal life ; examples. 
 
 Ifan — the various races, their numerical proportion, leading 
 peculiarities, and distribution. 
 
 T7ie pictures and illustrative diagrams and maps of any good 
 text-book will, if properly used, very greatly simplify and expe- 
 dite the study of nearly every department of the subject, and 
 will render definite ideas that might be otherwise vague. 
 
 History (OutUnes of Ancient and Modern). — The 
 general suggestions given in relation to the history of 
 the United States (see Third Grade) are, to a very great 
 extent, applicable to this grade. The much greater ex- 
 tent of time to be covered in teaching ancient and mod- 
 ern history, together with the vast nnmber and diversity 
 of nations which it embraces, necessitates, in a much 
 greater degree, the fixing of a good outline in the mind 
 of the pupil, as preliminary to a more minute study of 
 the subject. 
 
JUS TOBY. 239 
 
 This outline should be brief, but should show clearly 
 the chronological and geographical relations of the na- 
 tions, the history of which is to be studied, and, to 
 some extent, their ethnological relations. When this 
 has been done, it will be perfectly easy to take up the 
 history of any nation comprehended in the outline, and 
 to treat it intelligibly. 
 
 The use of maps, charts, and synchronous tables, will 
 aid very much in impressing hrmly upon the pupil's 
 mind such an outline as is here suggested. The maps 
 used should show clearly and accurately the territorial 
 extent and relations of the various nations generally 
 treated of in ancient, medieeval, and modern history. 
 All names of places referred to should be carefully 
 pointed out on the map, so that their exact location 
 may be constantly kept in view. This will aid the 
 memory very much, as it brings into play the faculty of 
 conception. 
 
 In the arrangement of topics the oi'cler of time should 
 be carefully followed at first, and the date (year) of 
 each important event kept before the mind of the pupil. 
 A few leading dates should be carefully memorized. 
 After the history of different nations has been studied, 
 the leading events of each should be arranged in syn- 
 chronous tables. The reigns of contemporaneous sove- 
 reigns, for example, should be comjiared, and the con- 
 nection of events in each carefully studied. 
 
 Keviews, such as are suggested in connection with 
 the United States history, by a chronological, geographi- 
 cal, and biographical arrangement of topics, should be 
 given with sufficient frequency. 
 
 The following syllabus presents the topics which 
 should be embraced in the outline above suggested : 
 
240 SOW TO TEACH 
 
 SyIiLABus of Topics. 
 
 1. The nations and countries of the most remote antiquity — 
 Ugypt and Ethiopia, Babylonia and Assyria, Lydia, Media, Syria 
 and Palestine, Persia. Of these only a brief sketch need be learned. 
 
 2. Greece— the mythologic period (very brief) ; the period 
 from the beginning of the Persian war to the Roman conquest of 
 Greece. This will include the rise and fall of the Macedonian 
 Empire, with its divisions under Alexander's successors. 
 
 3. Rome— the legendary period ; the foundation of the Re- 
 public in its various stages, including the contests between the 
 orders of Patricians and Plebeians ; the successive wars with the 
 Samnites, Carthaginians, etc. ; the civil wars, including the trium- 
 virates ; the ftiU of the Republic, and the foundation of the Em- 
 pire under Augustus. The territorial conquests should be shown 
 in connection with this. 
 
 4. TiiE Roman Empire— its territorial acquisitions and chan- 
 ges from Augustus to the division of the Empire at the death of 
 Theodosius, including a brief sketch of the principal reiguing 
 emperors, and the invasions by the Goths, Huns, and Vandals. 
 
 5. The Western Empire, from Honorius to its fall under 
 Augustuius (brief), including the barbaric invasions, 
 
 G. The Eastern Empire — from Arcadius to the taking of 
 Constantinople by the Ottomans ; a brief sketch, including the 
 wars with the Goths, Saracens, Seljuks, Mongols, and Ottomans. 
 
 7. The Saracenic Empire — a brief sketch of its foundation, 
 its territorial conquests and extent, its divisions, and its f;ill. 
 
 8. France— the invasion of Gaul by the Franks, and founda- 
 tion of the Merovingian Dynasty ; a brief sketch of it; the Car- 
 lovingian Dynasty, including Charlemagne's conquests, and the 
 revival of the Western Empire ; tlic Capetian Dynasty to the end 
 of the Reign of Louis XI. This will include the Crusades. 
 
 9. England— a brief sketch of British History before the 
 time of Egbert ; from Egbert to the Tudors. (England maybe 
 studied first, if it is preferred.) 
 
 10. Other nations contemporaneous with England and France. 
 (Very briefly.) 
 
 11. Modern History— in a similar manner; England and 
 France, as tJie leading nations ; other nations, including Ger- 
 many, Prussia, Russia, etc. 
 
ELEMK^TART SCIENCE. 34I 
 
 13. A>rERic.vN History — not immediately connected with 
 U. S. History. 
 
 Other parts of the world as China, India, etc., may be omitted 
 in this preliminary outline — which is all that can generally be 
 pursued in the Common Schools. 
 
 This history should be so studied as to induce the 
 pupils to read standard writers upon the most impor- 
 tant topics. The instruction should embrace advice 
 and direction as to the best writers in each period and 
 nation. Historical selections will be found yaluable for 
 this purpose. 
 
 ELE^IENTARY SCIENCE 
 (by deal instruction or a simple text-book.) 
 
 Natural I^hilosojyli y» — For general suggestions, 
 see preceding grade. 
 
 Syllabus op Topics. 
 
 ^coMsiics.— Preliminary — a general idea of the transmission 
 of vibrations illustrated — the nature of sound — sounding bod- 
 ies — a medium necessary — the ah* as a medium — oUier media — 
 limits of audibility of vibrations — velocity in air and other 
 media — loudness does not alter the velocity — reflection of 
 sound — echo, its causes and limits— physical distinction of 
 noise from music — pitch in music— effects of tension upon 
 vibrating wires — influence of sound boards— tuning-forks — 
 speaking-trumpets, speaking-tubes — resonance — murmur of 
 shell — the ear, its construction and action — the wonderful 
 physical condition of the tympanum when listening to a full 
 orchestra. 
 
 Pyronomics. — Heat — known only by its efi'ects — efi'ect on the 
 nerves — eff"ect upon the constitution of bodies— transmission 
 of heat — the three methods of transmission illustrated— air a 
 bad conductoi- and worse radiator— important relation of this 
 fact to clothing, to vegetation, etc. — heat as a sensation — rela- 
 11 
 
242 J^OW TO TEACH 
 
 tion of terms hot and cold— sources of heat— qiiantity and effects 
 of solar heat— its relations to physical geography — source 
 of the heat developed by friction — motion of mass converted 
 into molecular motion — heat only a mode of vibratory motion 
 —force as indestructible as matter— source of heat in combus- 
 tion — the thermometer — principles employed in its construc- 
 tion — nature and determination of the zero — evaporation — its 
 causes— effects on temperature of bodies — pheuomena of boil- 
 ing—temperature of boiling water— why invariable at a given 
 elevation— economic applications — why the boiling point varies 
 with elevation — boiling in a closed vessel — the steam-engine — 
 its essential elements and general principles— high-pressure and 
 low-pressure engines. 
 
 Optics. — Light— moves in straight lines — shadows — sources 
 of light— vibratory nature of light (only refer to it)— velocity 
 of light — how known — law of intensity illustrated — photome- 
 try by shadows — non-luminous bodies— how seen — reflection — 
 its law— mirrors, and their uses (treat more fully of the plane 
 mirror than of the others)— refraction— its simplest phenomena 
 
 its law — lenses — uses of, especially the convex lens— color 
 
 the prism and the solar spectrum — the order of the colors 
 
 (refer very briefly to thermic and actinic rays)— Frauenhofer's 
 lines (brief )— phenomena of the rainbow — the colors of objects 
 — primary colors — the eye and vision. 
 
 Magnetism. — Magnets, natural and artificial— forms of artifi- 
 cial magnets— polarity— attraction and repulsion— magnetic in- 
 duction—temporary and permanent magnets — the Earth a mag- 
 net — magnetic needle, and why it points to the north. 
 
 Electricity. — Frictional electricity — conductors and non-con- 
 ductors—electricity not a fluid but a polarizing force, related 
 to magnetism— attraction and repulsion— electric induction— in- 
 sulators— effects of points— atmospheric electricity— its origin— 
 lightning-rods— the flash— the white hot air— the thunder— pop- 
 ular fallacies as to electric fluids, thunder-bolts, heat-lightning, 
 and the cause of thunder — current electricity from chemical 
 action — a batteiy, its wires and poles — polarized condition of the 
 parts how to develop heat and light — uses made of these — sim- 
 ple helix — simple galvanometer — magnetism developed by elec- 
 tric current — temporary magnet and magnetic telegraph. 
 
AS^BO^''OMr. - 2i:] 
 
 Asfi'Onomp, — The topics embraced in the jn-eced- 
 ing grade should be carefully reviewed in this grade, as 
 far as may be necessary to secure thorough preparation 
 for the advanced jjortions of the subject, which consti- 
 tute the special work of the grade. The use of the 
 globes should be continued, in order more fully to fa- 
 miliarize the pupils with the Doctrine of the Sphere — so 
 important to a clear understanding of astronomical facts. 
 
 The interest of the pupils in the observation of astro- 
 nomical phenomena should be sustained by calling their 
 attention as frequently as possible to facts which they 
 can verify in this Avay. By degrees, the pupils should 
 be induced to familiarize themselves with the locations, 
 at different seasons of the year, at a given time by the 
 clock, of the most conspicuous constellations and stars. 
 The use of the Celestial Globe, or a planisphere, will 
 furnish valuable aid in the accomplishment of this. 
 The positions of the planets Jupiter, Saturn, Mars, 
 Venus, and Mercury, among the stars, should be kept 
 constantly in view, together with their apparent mo- 
 tions, and general progress eastward. The use of a 
 good almanac will afford assistance in accomplishing 
 what is here suggested ; also in calling attention to 
 the more unusual phenomena connected with eclipses. 
 
 The following topics should be specially treated in 
 this grade : 
 
 Syllabus of Topics. 
 
 1. The Sun — its magnitude, real and apparent ; distance from 
 the eartli (give a general idea of tlie manner of finding tliis, al- 
 tliougli a minute knowledge of parallax may be reserved for the 
 more advanced part of the subject); sobir spots — theory with 
 regard to their cause, their apparent motions, what is deduced, 
 from this. The Zodiacal light may be briefly referred to in connec- 
 tion with the Sun. 
 
 2. The Primary Planets — in succession, commencing with. 
 
244 HOW TO TEACH 
 
 Mercury, the pupil to learn the most important facts in relation 
 to their orbits, magnitudes, telescopic appearance, synodic and 
 sidereal periods, axial rotations, apparent motions, seasons, 
 satellites, etc. The Asteroids, their orbits, etc. Any interesting 
 facts in relation to the history of astronomical discovery should 
 be communicated incidentally, as this will serve to make the 
 subject more attractive. 
 
 3. The Moon — in a similar manner, teaching about its phases 
 and their cause, its revolutions, periods. Harvest Moon, Librations, 
 and a brief general description of the lunar surface {Selenog- 
 raphy). 
 
 4. Eclipses — solar and lunar ; total and partial, how caused ; 
 comparative frequency — ecliptic limits. Transits, their cause — 
 why important. 
 
 5. Tides — flood and ebb, spring and neap, how caused ; prin- 
 cipal facts connected with them ; the tidal wave ; height of tido 
 at different places — primitive and derivative tides. 
 
 6. Comets — their peculiar appearance, the different parts of 
 which they are composed ; different kinds of comets ; periodic 
 times of the comets of short period — interesting facts in relation 
 to WiQorbits, size, mass, density, and apparent magnitude of con- 
 spicuous comets. 
 
 7. A brief account of Meteors, their supposed nature and origin 
 — cause of the periodic displays of meteors. 
 
 8. Stars — classification — the constellations — names, classifica- 
 tion of, brightest stars in each — apparent change in position due 
 to precession; cause of precession ; exercises in finding tlie con- 
 stellations visible at anytime ; the gakuy ; proper motion of the 
 stars; multiple stars ; variable and temporary stars; distances of 
 stars, how found ; parallax, diurnal and annual. 
 
 9. Nebul.e — classification of; their nature and appearance; 
 general location and appearance ; the location and appearance of 
 the most noted. 
 
 10. Time — how measured ; solar, sidereal, and civil day ; why 
 the solar exceeds the sidereal day ; why the solar days are un- 
 equal ; equation of time ; tropical, sidereal, and civil years, how 
 and why they diflFer in length. 
 
 11. Astronomical, Refraction— its effect upon the apparent 
 positions of the heavenly bodies ; variation at different altitudes. 
 
 13. General Review. 
 
VEEMISTBY. 245 
 
 In giving instruction in this subject, its special office 
 as a means of training the conceptive faculty, should be 
 kept steadily in view. Facts of observation and facts of 
 inference should be carefully distinguished. Apparatus 
 and diagrams will afford some aid in enabling the mind, 
 to grasp the more difficult facts of inference ; but tlie 
 actual ohservation of the phenomena to be illustrated 
 should precede, as far as possible, the use of these. 
 Thus, a good tellurian will illustrate clearly the causes 
 of the change of the seasons, and a diagram may be 
 made to show the reason of their unequal duration ; but 
 the facts of these changes and inequalities must first be 
 clearly apprehended by the mind. If this is done, the 
 natural curiosity to know the cause will make the pupils 
 more attentive to the instruction given. Cumbrous 
 and complicated machinery, without the attentive ob- 
 servation of the natural phenomena, and the conceptions 
 based upon them, rather serve to give false notions than 
 to impart clear ideas of the actual facts. A good plani- 
 sphere will prove a valuable aid in the study of uranog- 
 raphy. 
 
 Nor should the teacher fail, in connection with the 
 instruction, incidentally to impress upon the pupil's 
 mind that, in studying the laws of the universe, he is 
 contemplating the works of a beneficent Creator, infi- 
 nite in wisdom and power. No subject is so well quali- 
 fied as astronomy to give just ideas in this respect, and, 
 while performing a peculiar and most important oftice 
 in the training and development of the intellectual pow- 
 ers, to exalt the understanding and give elevation and 
 tone to the whole character. 
 
 CJieniistry.— The instruction given in chemistry 
 in the common schools, like that given in physics and 
 
24G no W TO TEACH 
 
 in the natural sciences, must necessarily be at the most 
 only ruclimental. Whole sections of each subject must 
 be omitted. In every department of oral instruction in 
 science, the principal object should be to form the mind 
 to proper habits of observation. Tliis, togetlier with 
 the knowledge of the facts and principles of science 
 incidentally thus imparted, is a prejmration for the 
 systematic study of these sciences, rather than a formal 
 attempt to impart a knowledge of their complete out- 
 lines. Yet this knowledge of the facts and principles 
 thus obtained, is in itself of so great practical import- 
 ance as to render it an indispensable part of any proper 
 scheme of common school education. 
 
 The process employed should, as far as practicable, 
 be the same as that suggested for the instruction in 
 natural philosophy. The lesson, when not a review, 
 should usually begin with an experiment. The facts 
 to which the attention of the pupils is particularly 
 directed, should, as far as possible, relate to the chemis- 
 try of common things or of every-day life. They should 
 be so taught as to leave in the mind of the pupil a 
 determination and a conscious ability to know more of 
 a science so highly practical, so intensely interesting, 
 and so obviously Avithin his own power to acquire. 
 
 As in Natural Philosophy, the greater part, or 
 even the whole, of the necessary apparatus may, with 
 a little ingenuity, be extemporized. As a stimulus to 
 the inventive powers of the pupils, this is in itself an 
 important matter in practical training, and will, per- 
 haps more than anything else, insure the further prose- 
 cution of the subject by the pupils themselves. There 
 are so many excellent text-books in the rudiments of 
 this science, all abounding Avith practical hints and 
 illustrations, in relation to the construction of such 
 
CHEMISTRY. 247 
 
 apparatus, tliat it is not necessary here to do more than 
 refer to tliem. 
 
 The following syllabus of topics, together with a few 
 experimental illustrations therein introduced, is chiefly 
 intended to show how the objective process of instruc- 
 tion may be api)lied to the study of facts in chemistry, 
 the subject being quite as profitably and easily approach- 
 ed from any one of a dozen starting-points, other than 
 the one here selected. No other department of science 
 can be made to show the value of this process more 
 clearly, or to furnish more important mental discipline. 
 Experiment must be made to raise questions in the 
 mind of the pupil, only to be answered by deductions 
 from further experiment. 
 
 A small portion only of the subject can here be suffi- 
 ciently expanded to illustrate the process, the further 
 details being necessarily left to the ingenuity of the 
 teacher. 
 
 SYLiiABus OF Topics. 
 
 Forces. — (Begin with a very brief review of the following 
 points in Natural Philosophy.) All changes in matter are 
 effected by forces ; examples of 'physical changes wrought by 
 •physical forces, in pulverizing, solution, fusion, polarization, etc., 
 in -wliich the substance remains unchanged in composition and 
 general properties. 
 
 Chemical changes ; those in which the substance has changed 
 its properties ; experimental illustrations : (use no chemical 
 names or terms at this stage of the work ; use well-known com- 
 mon names as far as possible at first, such as sulphur, copper, 
 blue vitriol, alcohol, etc.) 
 
 E.rp. 1st. Show copper filings and pulverized sulphur ; let the 
 properties of each be objectively noted; melt them together 
 slowly ; notice the heat given out in the process ; examine the 
 substance produced by the combination ; it is neither copper 
 nor sulphur ; compare with a similar mixture of melted sugar 
 and sand ; solution will show these last unchanged. 
 
248 HOW TO TEACH 
 
 Exp. 2d. Burn sulphur in air ; the sulphur disappears, and an 
 invisible sour gas is formed, perceived by the lungs and the 
 smell ; has been made from the sulphur and the air. 
 
 E.vp. M. Burn alcohol or kerosene in air: show -water as a 
 product ; heat given out in all these changes of substance. 
 
 Chemical attraction: such changes are produced by si, force 
 known as chemical attraction or chemical affinity : the atoms of 
 sulphur and copper attracted each other and formed a new sub- 
 stance ; (omit its name) ; this force frequently breaks old combi- 
 nations to form new and stronger ones. 
 
 E.vp. ^th. Make a solution of blue vitriol (copper sulphate), in 
 a small vial, dip a clean knife-blade into it ; copper is deposited 
 on the blade ; ask what substance must have been contained in 
 the transparent blue vitriol ; tell that this copper was combined 
 with another substance which has taken up some of the iron, 
 at the same time rejecting or throwing down a part of the 
 copper. 
 
 Elements (nearly all to be told) ; iron and sulphur called 
 elements ; why ; there are many elements (65) ; some, like iron 
 and copper are metals ; therefore called metallic elements ; all the 
 rest, like sulphur, are called non-metallic elements; about a 
 dozen elements compose the greater part of the material of all 
 known substances ; nearly every substance, water, rocks, plants, 
 and animals consists of chemical compounds. 
 
 Carbonic acid (carbonic dioxide ; carbonic anhydride ; use none 
 of the names at first). What is it that bubbles in soda-water? 
 How do you know that it is not air ? Its taste ; its smell ; why 
 called acid (reserve the scientific definition of an acid). 
 
 Exp. 5th. Show marble fragments, or chalk (not the plaster 
 cylinders used upon the blackboard). Show muriatic acid ; 
 dilute a little with water ; taste it ; an acid ; pour the dilute 
 acid upon the marble or chalk. (A small bottle, bent tube, and 
 receiving-bottle for the gas are necessary.) Smell the gas ; com- 
 pare changes which have taken place with those of copper and 
 the iron in Exp. 4 ; one acid has taken the place of the other ; 
 the acid gas must have been solid ; the force which held it so 
 compressed. 
 
 Exj). Gih. Biorn a piece of marble or chalk in a charcoal fire ; 
 lime kilns ; marble changed to lime ; properties different ; tell 
 that the great heat has driven off the gas. 
 
CHEMISTRY. 249 
 
 Exp. 7ih. Make and filter lime-water ; agitate some of tlie gas 
 of Exp, 5 with lime-water in a bottle ; water becomes milky ; 
 the gas has united with the lime as before burning ; challvy 
 sediment settles ; lime water a test for this gas ; meaning of the 
 term test. 
 
 Ei-p. Sth. Agitate the gas from soda-water with lime-water: 
 result identical witli the last; therefore the gas in soda-water is 
 the same as that from the marble. 
 
 Exp. Q(h. Burn a candle in an open wide-mouthed jar ; close 
 the jar tightly; candle soon goes out; a part of the candle has 
 disappeared; test, as before, the air that is left in the jar; there- 
 fore the same gas. 
 
 Exp. 10th. Let the burning candle smoke or smut white 
 paper; tell and show that the smut or lamp-black is charcoal ; 
 its better name, carbon. 
 
 Exp. 11th. Burn ordinary charcoal ; it seems to have dissolved 
 in the air; gather the air from it ; test it; now use the popular 
 name, carbonic acid gas (other and better names to be learned 
 hereafter) ; therefore carbon in the candle ; in kerosene ; in all 
 fots, coal, bread, wood, etc. Show by over-baked bread, meat, 
 by wood, etc. 
 
 Exp. 12th. Blow breath through a straw or a pipe stem into 
 lime-water; test shows abundant carbonic acid; from bread, 
 vegetables, and other food. 
 
 Exp. 13ih. Collect from marble a quantity of the gas ; show 
 that it will not support combustion ; fatal to life ; the gas in 
 mines, wells, vats, etc. ; suicide with charcoal ; necessity of 
 thorough ventilation. 
 
 In the same manner oxygen may now be considered, its 
 properties and functions shown, and its principal compounds, 
 including the carbonic acid of the preceding experiments. Hy- 
 drogen, chlorine, and nitrogen may be next in order. 
 
 Review. At this stage it is desirable to review, rearrange, and 
 explain the knowledge already acquired, under the following 
 heads : 
 
 Chemistry of water : hydrogen, oxygen; solution of solids and 
 gases in water ; hard and soft waters ; mineral waters. 
 
 Chemistry of tlie atmosphere : combustion; nitrogen; carbonic 
 acid ; its relations to plants and to animals; illuminating gas. 
 
 Chemistry of rocks and soils: limestone and lime; quartz, 
 
 11* 
 
250 - HOW TO TEACH 
 
 sandstones, and silica ; clay, slate, and alumina ; granite, feld- 
 spar, potash, soda, etc. ; common salt. 
 
 ChemMry of plants and animals : starch, gum, sugar, lignin, 
 vegetable and animal oils, albumen, gluten, etc. 
 
 Special topics : bread-making, soap-making, glass-making, fer- 
 mentation, distillation, photography, etc., etc. 
 
 MISCELLANEOUS BRANCHES. 
 
 JBooIv -h'ee2)i^if/- — After the forms required in 
 single-entry book-keeping have been taught, which 
 should be quite brief, the nature of double-entry book- 
 keeping should be explained, by showing the relation of 
 debit and credit, and how the former in one account 
 may be exactly balanced in another, so that one set of 
 entries may be made to verify the accuracy of another, 
 and thus prevent the admission of any errors which 
 may not be readily discovered and rectified. 
 
 2. The classification of accounts should be followed 
 by an explanation of the three books — Day-book, Jour- 
 nal, and Ledger. Journalizing simple entries in the 
 Day-book should then be taught; and sufficient exer- 
 cises given to impart readiness and accuracy in the pro- 
 cess. The keeping of a simple and brief set of accounts 
 will then render the whole process and theory intelli- 
 gible to the pupils' minds, and will also render them 
 sufficiently expert in their application. 
 
 3. All the common business forms should be taught ; 
 as the form of bills, receipts, bank checks, promissory 
 notes, bills of exchange, invoices, etc., etc. Business 
 correspondence should also receive some attention. It 
 is of great importance to render the pupils expert in 
 writing a good business letter. In every exercise 
 fluency, legibility, and grace in penmanship should be 
 
MISCELLANEOUS BRANCnSS. 251 
 
 carefully attended to. Quantity and quality should both 
 be insisted on in this respect. 
 
 Constitution of the United States,— The 
 recommendation to teach the Co7istitution of the United 
 States appHes to pupils of both sexes in this grade. It 
 would appear to be essential that those who pass 
 through a full course for common schools should have 
 some knowledge of the simple principles and require- 
 ments of the organic law of the nation — the distri- 
 bution of the powers of the general government, and 
 the rights, duties, and obligations of an American 
 citizen. 
 
 The Constitution itself should be the text studied, 
 the pupils being made familiar, as far as possible, with 
 the language of the instrument, and also instructed in 
 the meaning and intention of the several provisions. 
 Several matters, purely technical, will need to be care- 
 fully elucidated, such as ex-postfacto laws, bills of at- 
 tainder, habeas corpus, etc., etc. The history, Englisli 
 and American, particularly the former, with which 
 these are connected, will prove a most instructive and 
 interesting subject for comment by the teacher. 
 
 Questions as to the construction of certain points in 
 the Constitution, which have been in agitation at vari- 
 ous times, during the past history of the country, would 
 prove, in boys' classes especially, as far as time and op- 
 portunity may admit, very beneficial for discussion, as 
 tending to impart readiness in speech, as well as self- 
 reliance and freedom in thought and opinion. 
 
252 now TO TEA OIL 
 
 GENERAL SUGGESTIONS 
 
 Eelative to the Classificatiozst an"d Instruction 
 OF Pupils in Schools. 
 
 Meviews. — Such a review of pi-evious lessons, in 
 connection with each new lesson on the same subject, 
 should be given as will cause the pupils properly to asso- 
 ciate together the facts learned in all of them, and thus 
 lead them to acquire a comprehensive as well as a famil- 
 iar knowledge of each subject contained in the grade or 
 the course. 
 
 General reviews of subjects should be had at least as 
 often as once during each month ; and in these the lead- 
 ing facts learned in previous grades should be included. 
 
 Proffvess of Classes, — Whenever it is found that a 
 class has advanced further in one or more subjects of its 
 grade than it has in others, less time should be devoted 
 to these subjects, and more to others, so that the grade 
 of the class may be equalized in all its studies. No 
 study of a succeeding grade should be introduced into 
 a class of a lower grade until the class has completed the 
 requirements of the grade in all the branches of study 
 included therein. 
 
 J*7^ogr€SS of JPtijiils. — It often happens that a 
 few of the pupils of a class will so far outstrip their fel- 
 lows in a single month, as to render it necessary to trans- 
 fer these rapid learners to a class of the next higher 
 grade. While great care should be exercised not to stimu- 
 late the excessive mental activity or precocity of young 
 pupils, yet the disparity of progress in pupils of the 
 same class may sometimes be used as an incentive to 
 
OENEBAL SUGGESTIONS. 053 
 
 urge forward those who are extremely sluggish or inert. 
 This may be done by promoting in a public manner, at 
 the end of each montb, two or three of the j)upils who 
 are found to have made the greatest improvement, into a 
 higher class of the same grade. In doing this, however, 
 care must be taken not to disturb the gradation by per- 
 mitting pupils to omit important branches of study. As 
 a general thing every pupil should be required to spend 
 the whole time which may be prescribed for the grade. 
 
 Hecitations, — No class in the primary grades 
 should be required to spend more tlian half an hour, 
 at one time, in the same exercise. The mind, as well 
 as the body, needs rest. A change of subject, and a 
 change in the manner of conducting class exercises, 
 are both necessary in order to furnish opportunities for 
 rest during school hours. 
 
 The recitations should be spirited exercises. The 
 questions should be as definite as 2>ossible. The teacher 
 should carefully avoid implying in the question any of 
 the facts or principles that should .bo stated directly by 
 the pupil. The habit of repeating the pupil's answer 
 should also be avoided. Pupils should be invariably 
 required to use natural and proper tones in recitation, 
 to enunciate distinctly, and to avoid grammatical errors. 
 If this be not done, the lessons in reading and grammar 
 will be of little avail to break up pernicious habits of 
 speech, which the teacher, by his neglect, will have as- 
 sisted to fix. 
 
 Unless thoroughly familiar with the details of the 
 text-book, the teacher needs special and renewed prep- 
 aration quite as much as the pupils. Without this, 
 he will not succeed. In hearing the recitations, he 
 should carefully discriminate between the statements 
 
254 EOW TO TEACH. 
 
 • 
 
 found in tlie text-book and additional ones which he 
 may have found necessary to make in the preparatory 
 explanation of the lesson, and which the pupil may have 
 had no opportunity to con over. 
 
 Lessons for Home Study. — In every class, how- 
 ever well graded, the pupils will differ much in age, 
 health, mental capacity, and home advantages. A cor- 
 rect and judicious classification will reduce this inequal- 
 ity to a minimum; but there will still remain a wide 
 field for the exercise of discrimination, care, and caution 
 on the part of the class teacher. The lessons should, in 
 all respects, be adapted to the average ability of the pupils 
 of the class ; but, even beyond this, some allowance will 
 often have to be made in the case of pupils of quite in- 
 ferior mental capacity or opportunities for home study. 
 Teachers must bear in mind that the one great object 
 of home study is to train the pupils to self-exertion, — 
 to give them the ability to dejoend upon their own 
 efforts as students, and by degrees, to dispense with the 
 aid of a teacher. It is, therefore, of supreme impor- 
 tance to avoid everything that would discourage, or de- 
 prive of self-reliance; and nothing has a stronger ten- 
 dency in this direction than the imposition of excessive 
 tasks. 
 
 Teachers are especially admonished to be considerate 
 toward pupils of a delicate constitution, an over-excita- 
 ble brain and nervous system, or in temporary ill-health. 
 Many children of this class are precocious in mental 
 activity and exceedingly ambitious to excel; and the 
 greatest care is required to prevent them from injuring 
 themselves by an inordinate devotion to books and 
 study. 
 
 The length of the tasks imposed should, therefore, be 
 
OENEBAL SUGGESTIONS. 255 
 
 most carefully scrutinized and adjusted. The practice 
 of assigning a fixed numher of words, lines, paragraphs, 
 pages, or examples, without a minute inspection of their 
 nature or contents, is often accompanied with disastrous 
 results. TJie pupils are wearied and discouraged; and 
 the parents, finding the work of tlie school-room trans- 
 ferred to the home circle, lose all confidence in the 
 judgment and ability of the teacher. 
 
 The teacher should ascertain the methods which 
 pupils employ in home-study. Verbatim study, except- 
 ing in case of important definitions, is to be discouraged. 
 While making the necessary preliminary explanations, 
 a brief abstract of the leading points should be Avritten 
 upon the blackboard, and made the basis of the recita- 
 tion. This will do much to induce a rational method 
 in study, and prevent a slavish adherence to the text. 
 
 The teacher should advise with his pupils as to their 
 l;ime and opportunities for home study. Household 
 duties, cramped and noisy homes, and deficient light, 
 no doubt greatly obstruct, in many cases, the pupils' 
 efforts. These should be, as far as possible, ascertained 
 and allowed' for. Very small print should be entirely 
 excluded from home lessons on account of its tendency 
 to produce myopy, when studied by artificial liglit. 
 Many hours of confinement in a crowded class-room, 
 with the long-continued and close attention required 
 there, renders rest and relaxation, with some kind of 
 physical exercise, indispensable to growing boys and 
 girls. The teacher should, at least, advise that these 
 come before home-study. 
 
 JPhysical Trainlnf/. — The ]uipils should be ex- 
 ercised, as much as may be practicable, in such a way 
 as to expand the lungs, develop the muscular system, 
 
256 SOW TO TEACU. 
 
 and impart an easy and graceful carriage to the body. 
 In schools for boys, the marching drill should be em- 
 ployed in the ordinary evolutions of the schools, with 
 such instruction as may be requisite to make it effec- 
 tive. Light gymnastic and calisthenic exercises should be 
 employed as far as may be necessary or suitable for the 
 general objects of physical training, or as a pleasant and 
 beneficial relaxation after the severer mental exercises. 
 
 Where formal exercises in calisthenics, etc., are not 
 employed, the pupils should have sufficient intermission 
 for recreation in the play-ground. Time thus given to 
 physical exercise will always prove a gain in the exer- 
 cise of the mental powers. When pupils are nnder 
 efficient discipline, their performances, at their lessons, 
 are always better after exercise in the play-ground,— 
 for the excitement, as it subsides, leaves the intellect 
 more active and hence readier for class-room work. 
 
 In the case of young pupils, even while in the class- 
 room, it is desirable that they rise at intervals for a few 
 minutes, to exercise, by varied movements, both the up- 
 per and lower limbs. 
 
 llanners and 3Iorals. — Such instruction should 
 be given daily to the pupils of all the grades as will fos- 
 ter a spirit of kindness and courtesy towards each other, 
 a feeling of respect toward parent and teacher, and a 
 love for cleanliness, order, law, and truth. The read- 
 ing lessons and the ordinary incidents of the school- 
 room may be made the means of inculcating the great 
 moral truths common to all well-ordered minds. 
 
 Children learn to love and practice kindness, neat- 
 ness, truthfulness, and politeness by observing these 
 traits in those around them. It is, therefore, exceed- 
 ingly important that the teacher should present living 
 
OEMERAL SUGOESTIOj^s^S. 357 
 
 illustrations of these qualities, by her own conduct be- 
 fore the pupils, (luring all her intercourse with the 
 class. 
 
 Social relations, the dependence of each individual 
 upon his neighbor — the necessity of labor — the benefits 
 of society and government, should be illustrated and 
 taught by means of easy and familiar lessons suited to 
 the age and capacity of the children. As the develop- 
 ment of the moral nature is of greater importance to 
 the welfare of the individual and the community than 
 any other part of education, no opportunity should be 
 omitted for training children in such habits as will 
 cause them to grow up truthful, honest, self-governing, 
 and law-abiding citizens. 
 
 GOYERX:^IEXT AXD DISCIPLINE. 
 
 In all the rules and methods of discipline employed, 
 the true object of discipline should steadily be kept in 
 view ; namely, to train the pupils so that they may form 
 right habits. 
 
 Firmness, vigilance, and uniformity, in dealing with 
 children, are of the first importance. The teacher should 
 never resort to violent means, as pushing, pulling, or 
 shaking the children, in order to obtain their attention. 
 All such practices constitute a kind of corporal punisli- 
 ment which, whether that species of coercion be per- 
 mitted or not, should be most carefully avoided. 
 
 Modes of punishment especially painful to the cor- 
 poreal system, such as the sustaining of wearisome bur- 
 dens, unnatural and long-continued attitudes of re- 
 straint, standing, kneeling, etc., are exceedingly wrong- 
 ful and injurious. Equally so is the confining of de- 
 
258 SOW TO TEACH. 
 
 linquents, by tying them or shutting them in closets. 
 These are all a resort to mere physical force, instead of 
 moral incentives, and involve no appeal to a sense of 
 honor or duty in the child. They do not properly as- 
 sert the autliority of the teacher, nor do they really pro- 
 duce obedience on the part of the pupil. 
 
 When corporal punishment is resorted to, it should 
 be of a proper character — never partaking of that con- 
 tinuous infliction of j)ain which we denominate torture, 
 and never administered except in a spirit of mildness, 
 and deep regret at its necessity. When all those per- 
 suasive incentives and agencies which constitute 
 moral suasion have been appealed to without avail, and 
 there is no other recourse, corporal jDunishment may be 
 resorted to in order to save the inqnl, but for no other 
 reason. The necessities of discipline may seem to re- 
 quire it, and they certainly do, if in order to meet them 
 the teacher must choose between chastising his pupil in 
 this way and depriving him of the benefits of the school 
 instruction and training, and thus insuring his moral 
 destruction. 
 
 In directing the various movements required of the 
 pupils, care should be taken never to touch them. The 
 teacher should take such a i)osition before the class as 
 will command the eye of every pupil, and thence direct 
 by the voice, or by a signal. Pupils must be habituated 
 to the impression that the teacher will give his com- 
 mands but once, and that they must be obeyed at once. 
 
 Harsh tones of the voice are unnecessary and im- 
 proper. Words of disapprobation may be uttered by 
 the teacher in a tone of decision, without the use of any 
 severity that would imply resentment, anger, or antipa- 
 thy on the part of the teacher. On the contrarv, the 
 language used, and the tones of the voice, should al- 
 
GENERAL SUGGESTIONS. 259 
 
 ways express a feeling of symiKitliy with the child. This 
 is the way to win the youthful mind, and to bend the 
 will, through the affections ; a different course will an- 
 tagonize it, and prevent all real submission, securing 
 only a temporary semblance of obedience. 
 
 "As is the teacher, so will be the school." It is, there- 
 fore, requisite that teachers should rigidly discipline 
 themselves by carefully cultivating habits of neatness, 
 cleanliness, and order, gentleness of manner, a watchful 
 self-control, and a cheerful spirit. In speaking, let the 
 rising inflection of the voice prevail ; then, the falling in- 
 flection of reproof will be more impressive and effectual. 
 
 Teachers should seek to obtain the sympathetic regard 
 of the children by giving a due attention to their wants 
 and requests, which should be fulfilled as far as may be 
 prpper and reasonable. Children are quick to perceive 
 and to resent injury or injustice. The child who asks 
 for the privilege of a drink of water, for instance, may be 
 suffering acutely ; and, if not accorded relief, when this 
 seems to be perfectly practicable on the part of the teach- 
 er, feels a sense of outrage which, for a time, if not j)er- 
 manently, imj)airs its respectand regard for the teacher. 
 The cultivation of a due feeling of sympathy for the 
 children will wholly prevent this. The possession of 
 this feeling in its fullness is the best foundation for suc- 
 cess in both discipline and instruction. 
 
 Encouragement insjiires confidence; and children, 
 more than others, need it. Let it be given in all cases 
 where this can be honestly done. To a want of this in 
 the discipline of classes, are to be ascribed the timidity 
 and reserve so often manifested among pupils by a hes- 
 itating manner, a low voice, and a tone of inquiry in 
 response, especially to strangers. A proper degree of 
 encouragement renders them confident and spirited. 
 
2G0 BOW TO TEACH. 
 
 eager to tell what they know, and in an audible tone of 
 voice. Encouragement has a peculiar influence in pro- 
 moting both mental and moral imj)rovement. 
 
 Public exposures and hadges of disgrace belong to a 
 class of punishments which, if ever resorted to, should 
 be employed under careful limitations, and with great 
 circumspection and prudence, for it I'equires a skillfuh 
 discreet, and conscientious teacher to use them safely 
 and with advantage. In the discipline of girls, they 
 should be avoided altogether, as destructive of that nice 
 eense of shame and that delicate sensibility to reputa- 
 tion which are to be most carefully fostered in the fe- 
 male character. 
 
 Cleanliness, metUocl, and regularity are among the 
 first and most necessary elements of popular education. 
 Every rule requisite to maintain or impart these should 
 be diligently and punctiliously enforced. 
 
 Education is unfinished until the physical powers are 
 brought into subjection to the understanding and the 
 dictates of morality and social refinement. Children 
 should be taught how to sit, to stand, to move, to walk. 
 Eules are required for this ; but they need to be only few 
 and simple, and the nice and watcliful observation of 
 children renders it quite easy to enforce them, provided 
 they are not capriciously applied. Children must first 
 be taught tliem, and then never permitted to violate 
 them without admonition or correction. 
 
 Teachers should never forget that their pupils are 
 constantly and closely watching their conduct, and that 
 they are prone to imitate whatever they observe. They 
 should, therefore, see nothing that they may not safely 
 imitate. There is an " unconscious tuition," the silent 
 influence of which produces the most permanent effects. 
 
 The character of children is greatly affected by their 
 
GENERAL SUGGESTIONS. 261 
 
 suiToundings. These should, therefore, be neat and or- 
 derly. The rooms in which they assemble should bo 
 clean, the desks and other furniture, as far as possible, 
 without injury or defacement, and everything giving 
 evidence of constant and punctilious attention. Chil- 
 dren, from the contemplation of these things, uncon- 
 sciously acquire habits of order, neatness, and regular- 
 ity, which have an important bearing upon their useful- 
 ness and happiness in after life. 
 
 The basis of good order is attention. It does not 
 require that the pupils should occupy, for any certain 
 time, a fixed position; that they should be compelled 
 to strain their glances upon a given point; that they 
 should be as motionless as statues. All this is unnatu- 
 ral ; and whatever is unnatural is really disorderly. 
 The postures should be graceful, easy, and uniform, but 
 should be frequently changed ; the movements, while 
 as simultaneous as perfect attention would necessarily 
 produce, should also be easy and natural. 
 
 Good order involves impression rather than repres- 
 sion ; it does not consist in a coercion from which 
 result merely silence, and a vacant gaze of painful re- 
 straint, but it results from the steady action of awa- 
 kened and interested intellect, — the kindling of an 
 earnest purpose and an ambition to excel. Hence by 
 making punishment the first, instead of tlie last, resort, 
 the true object of educational discipline is defeated. 
 The prevailing atmosphere of the class-room should be 
 always that of kindness and love, equal to that of a 
 parent, in whose place indeed the teacher is for the 
 time; and it will be almost invariably found that every- 
 thing essential to effective discipline will spring from 
 an interchange of confidence and regard between teach- 
 ers and the pupils committed to their instruction. 
 
262 now TO TEACH. 
 
 Those who have the management and instruction of 
 our Common Schools should exercise the greatest care 
 that their teachings and influence be not exclusively in- 
 tellectual, — that they tend not merely to inform the 
 mind, but to form the character, — not only filling the 
 head, but impressing likewise the heart. Even where 
 the operations of these schools are confined to teaching, 
 let the kind of knowledge and the mode of imparting 
 it be dictated by considerations having in view moral 
 and religious, as well as intellectual, improvement. Let 
 the knowledge imparted be always such as will refine, 
 ennoble, elevate. When scientific truth is presented, 
 let the pupil be led to look not simj^ly at nature, but 
 *' through nature up to nature's God ; " let him learn 
 the laws and phenomena of the physical universe with 
 the spirit of the Psalmist, when he exclaimed, " When 
 I consider the heavens, the work of thy fingers, the 
 moon and the stars which thou hast ordained, what is 
 man, that thou art mindful of him, and the son of man 
 that thou reo-ardest him ? " Thus mav instruction in 
 every class and grade be made effectual, without the 
 dogmatic teaching of sectarian tenets, in subserving and 
 promoting the best interests of its pupils, both temporal 
 and eternal. Any scope or intention short of this would 
 certainly be inconsistent with the intelligence, as well 
 as the moral and relio-ious character of our age and 
 country, and must render our Common School educa- 
 tion, as a means of fostering and supporting the free 
 institutions of our Eepublic, unworthy of support or 
 vindication. 
 
GENERAL ISULiaEiSTIOJSS. 0(33 
 
 A SCHOOL LIBRARY. 
 
 Its Necessity, — Of all the means necessary to a 
 teacher's true and lasting success in the mental and 
 moral training of his pupils, few, if any, are equal in 
 importance to a proper school library, — not necessarily 
 a large library, or an expensive one, but a library con- 
 sisting of interesting and instructive books, such as boys 
 and girls may readily be led to love to read. 
 
 The pernicious character of the greater part of the 
 cheap literature found in many so-called newspapers and 
 in other cheap forms of publication, needs but little com- 
 ment. Its enormous quantity shows that it is extensively 
 read, and it is well known that it finds its chief market 
 among the young. An enfeebled mind and a vitiated 
 taste, as shown in a craving for exciting and unnatural 
 stories, and in a positive dislike for instructive and truly 
 interesting reading, as being too tame and insipid to 
 hold the attention, are among the common and least 
 injurious results of an unchecked indulgence in the men- 
 tal dissipation which this trash induces. Its darker 
 shades and more injurious and debasing consequences 
 need not here be dwelt upon. The proper antidote and 
 substitute for this Avide-spread poison is good reading. 
 
 Such a library is also the indispensable supplement to 
 the systematic mental instruction given in the class- 
 room. If, for instance, care be taken and opportunities 
 sought during the lessons in geography, history, or in 
 any of the departments of science, to introduce some 
 little book from the library, and to read a few interesting 
 l)aragraphs illustrating the lesson, a Ijrief notice and 
 commendation of the book at the close of the exercise, 
 with a few hints as to how best to read it, will utilize 
 
264 BOW TO TEACH. 
 
 many a valuable "work that miglit otherwise remain un- 
 touched upon the shelves. 
 
 Once introduced into the world of good books, and 
 fairly interested in even one of its many departments, — 
 once tasting and enjoying the wholesome sweets of a 
 sound and ennobling literature, a young man or a young 
 woman, it may be safely trusted, will not abandon it for 
 that to which allusion has been made. A teacher has 
 failed in one of the most important of all of his func- 
 tions, if, being in possession of a good school library, he 
 has not fixed, in at least some of his pupils, the habits 
 and love of self-culture, by leading them to become 
 habitual readers. 
 
 Its Char'acter. — Great care and discretion are ne- 
 cessary in the selection of books for a school library. As 
 far as possible they should be small bools. The greater 
 part of the suitable works in history, biography, travels, 
 etc., are readily selected, and should include such works 
 as Abbott's Histories, Scribner's Library of "Wonders and 
 Library of Travel, Chaillu's works, the Rollo books, etc., 
 together with a fair proportion of good standard works, 
 such as those of Prescott, Bancroft, Lossing, Hume, and 
 Macaulay, the Student's Series of Histories, Translations 
 of Josephus, Herodotus, Thucydides, etc. In selecting 
 from tlie great number of works of imaginary travel and 
 adventure, written with the professed purpose of giving 
 to youth instruction in the physical geograpliy, natural 
 history, and social condition of various countries, all 
 those in which the narrative is overdrawn, and tliere- 
 fore teaches error, should be rejected. Natural history 
 and the other subjects treated of in the oral instruction 
 in science, should be abundantly represented. If works 
 of fiction are admitted they should be selected with ref- 
 
GENERAL SUGGESTIONS. 265 
 
 crence to their moral purity and their permanent vahie 
 as additions to literature, rather than because they are 
 new and are advertised as popular. Many a school li- 
 brary has been tilled witli ephemeral trash and made the 
 instrument of mental degradation rather than of eleva- 
 tion, by want of care -in this respect. Such old classics 
 as Eobinson Crusoe, Paul and Virginia, and the Vicar 
 of Wakefield, should not be wanting. A few of the lead- 
 ing popular poets sliould also be represented by small 
 volumes. In their selection of books, pupils should be 
 advised by tlieir teacher, so that they may not attempt 
 works beyond tlieir present ability to read with profit. 
 
 Uses, — Among the many ways which may be sug- 
 gested for making a systematic use of the library as a 
 means of culture, the following is given as an illustration: 
 
 Let us suppose that some new books have been pur- 
 chased, and that one of them is Abbott's Life of Madame 
 Eoland, and that the teacher has himself first read it, or at 
 least looked over it, and marked a few short but inter- 
 esting passages. Before the class or before several of 
 the higher grades assembled for the purpose, the teacher 
 hangs the map of Europe. In a brief conversational 
 lecture he states to the cLass or school a few of the lead- 
 ing points in relation to France and Europe at the 
 period referred to, then reads a brief but inteiesting 
 selection or two from the first portion of the book, and 
 commends the book to their notice. "With such an 
 introduction many pupils will read the work, while 
 without it they would not have thought of so doing. 
 It will generally be found that history and biography 
 are usually not read by tlie pupils because they have 
 none of the preliminary conceptions relating to the 
 
 subject which the method above indicated supplies. 
 13 
 
266 n^OW TO TEACE. 
 
 Books of travel present peculiar advantages for this 
 method, and are among the most instructive portions of 
 current literature. 
 
 An excellent plan with individual and advanced pupils 
 is for the teacher to select some interesting book, suffi- 
 ciently brief and simple, and in place of the iisiial exer- 
 cise in composition, to require of the pupil an abstract 
 of limited length, with the selection of a page or two of 
 peculiar interest or importance, to be read aloud, with 
 such explanation or remarks as the subject may suggest. 
 
TABLE OF PRIMARY SCHOOL GRADES.. 267 
 
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 e 
 
 
NUMERAL FRAMES, 
 
 The Abacus, or Numeral Frame, has come down to us from 
 ancient times. Although long disused, it is now not only a very popu- 
 lar, but an almost indispensable aid in teaching Children 
 
 to count, and in giving them 
 correct ideas of numbers and of 
 their first lessons in addition, 
 subtraction, multiplication, etc. 
 
 The balls, nicely and smoothly 
 turned from wood, are painted 
 four different durable colors and 
 varnished. The handles enter 
 the frame with a screw, and are 
 taken out for safe shipment. 
 
 In strength and style of finish, 
 our Numeral Frames are not 
 equaled by any others made. 
 
 IFE MAKE THREE SIZES: 
 
 No. I — size, 9 in. by ii in., with lOO balls Price, $1.25 
 
 No. 2 — size, 10 in. by 12 in., with 144 balls " 1.50 
 
 No. 3— size, 20 in. by 27 in., with 144 balls " 5.00 
 
 The balls of Nos. I and 2 are about a half-inch in diameter, and those 
 of No. 3 are i3^ inch. No. 3 has a different handle, a place being cut out 
 of the frame for grasping, or for hanging it up in view of the school. 
 
NEW FORMS AND SOLIDS. 
 
 Containing sixty four pieces — there being forty -eight Plane Forms, 
 
 fifteen Solids, and a six-inch Rule, among which are 
 
 several NEW Forms and Solids, not 
 
 included in any other set. 
 
 Each Form is stamped with its Number in th« List. 
 
 1. Equilateral Triangle. 
 
 16. Hexagon. 
 
 31. 
 
 Hemi-Sphere. 
 
 2. Right Angled " 
 
 17. Heptagon, 
 
 32. 
 
 Prolate-Spheroid. 
 
 O (i (fc tt 
 
 18. Octagon. 
 
 33. 
 
 Oblate. 
 
 4. Obtuse " 
 
 19. Nonagon. 
 
 34. 
 
 Ovoid. 
 
 5. Carved " 
 
 20. Decagon, 
 
 35. 
 
 Cylinder, 
 
 6. Triangle— 1 curved side 2 1 . Circle. 
 
 36. 
 
 Cone. 
 
 t. Isosceles Triangle. 
 
 22. Semi-Circle. 
 
 37. 
 
 Conoid. 
 
 8. Scalene 
 
 23. Quadrant. 
 
 38. 
 
 Cube. 
 
 9. Square. 
 
 24. Segment. 
 
 39. 
 
 Square Prism. 
 
 10. Oblong. 
 
 25. Sector. 
 
 40 
 
 Triangular Prism, 
 
 11. Rhomb. 
 
 26. Ring. 
 
 41. 
 
 Hexagon;,! " 
 
 12. Rhomboid. 
 
 27. Crescent. 
 
 42. 
 
 Square Pyramid. 
 
 13. Trapezium. 
 
 28. Ellipse. 
 
 43. 
 
 Trianguliir. 
 
 14. Trapezoid. 
 
 29. Oval. 
 
 44. 
 
 Six-inch Rule. 
 
 15. Pentagon. 
 
 30. Sphere, 
 
 
 
 This is the only set which is accurately and scientifically made. It 
 is the only set which is approved for use in the schools of New York 
 City. 
 
 PRICE, (neatly put up in substantial wood box), $2.75» 
 
 Also, Geometrical Forms and Arithmetical Solids. 
 
 26 Pieces, in box, . , , $2.sa 
 
SCHOOL GLOEES. 
 
 Our New School Globe. Probably the reason why so few of 
 
 our schools are supplied with a globe 
 is that there has been no good 
 globe to be obtained at a mod- 
 erate price. 
 
 Our New Five-Inch Terres- 
 trial Globe will precisely supply 
 this want. The map is new — clearly 
 and finely engraved — prepared ex- 
 pressly for taking the place of the 
 large and expensive globes. The 
 " Grand Divisions" are boldly colored. 
 The water is white, distinctly show- 
 ing the principal Islands, Peninsulas, 
 Capes, Gulfs, Bays, etc., etc. 
 
 It is mounted in a light and dura- 
 ble manner, with strong brass mountings, inclined axis, on a neat black 
 walnut stand. 
 
 Securely packed in box with sliding cover. 
 
 PRIGE^ 
 
 $2.25. 
 
 A Hemisphere Globe, (made by cutting a solid five-inch globe 
 through the Poles,) showing also the two Hemispheres on 
 a flat surface, will be found a great convenience to the teacher. 
 The two parts are united by a brass hinge. Price, - - $2.00. 
 
 Our Complete List of Globes comprises all the Globes, large and 
 small, which are known. It will be mailed on receipt of stamp. 
 
 J.W.Schermerhorn& Co., Manufacturers 
 
 14. Bond Street, New York. 
 
OUR GYMNASTIC APPARATUS. 
 
 " Mens Sana in Corpore Sano." 
 
 It is made of well-seasoned wood, varnished and polished. Dumb-bells 
 and Indian Clubs are made of maple ; Wands of white ash or black 
 walnut ; Hand-rings are very strongly made of three sections — black 
 walnut, cherry, and maple. Besides great strength, they have the merit of 
 beautiful appearance. 
 
 Dumb-bells — four sizes : price list. 
 
 Nos. I and 2, for children per pair, $0 60 
 
 Nos. 3 and 4, for youths and adults " 75 
 
 Rings — two sizes: 
 
 No. I, for children " 75 
 
 No. 2, for youths and adults " VS 
 
 Wands — in required lengths, nicely turned each, 30 
 
 same, with metallic balls " 75 
 
 Indian Clubs — five sizes of short clubs : 
 
 No. I, weight per pair about 2 pounds per pair, 1 585 
 
 No. 2, " " " 3 " " 1 50 
 
 No. 3, " " " 4 " " 1 75 
 
 No. 4, " " " 5 " " 2 00 
 
 No. 5, " '• " 6 " " 2 50 
 
 Six sizes of long clubs : 
 
 No. I, weight per pair, 7 to 8 pounds " 3 OO 
 
 .*. . " 4 00 
 
 " 4 50 
 
 " 500 
 
 " 5 50 
 
 " 6 00 
 
 Any size or style to order. Liberal discount on quantities. 
 
 Kehoe's Book on use of Clubs, ilUistrated 1 00 
 
 Manual of Calisthenics, ilhistrated, Watson 1 25 
 
 Hand-Book of Gymnastics, highly illustrated, Watson 2 00 
 
 J. W. Schermerhorn & Co., 
 
 Mamifacturcrs and Ptcbliskers, 
 
 14 Bond Street, New York, 
 
 No. 2, 
 
 10 
 
 No. 3, 
 
 12 
 
 No. 4, 
 
 " 14 
 
 No. 5, 
 
 16 
 
 No. 6, 
 
 20 
 
The Great Events of History, 
 
 FROM THE 
 
 Creation of Man to the Present Time. 
 
 Tnis work is based upon the famous book of Dr. Collier, so widely used ju 
 the School:- of Great Britain, and favorably known over the world. Wherever used, 
 the book has been found to materially abridge the labor of the learner and sweeten 
 his toil. 
 
 The American Editor, who is an experienced Teacher, has added to Dr. 
 Collier's book, the events from the Creation of Man down to the opening of the 
 Christian Era, the articles on the Settlement of America, the Indian wars, the war 
 between Great Britain and her Colonies in North America, the War of 1812, the 
 American Rebellion, and the French and Prussian War. The original plan of the 
 book has not been disturbed. 
 
 Features of " The Great Events of History." 
 
 1. The "Great Events of Histort " gives a connected view of the 
 entire Historic Period from the Creation of Man to the present time, 
 
 2. It is not too full to weary the pupil— nor tOO brief to be 
 
 uninteresting. 
 
 3. Its attractive style interests the pupil in General Facts, and thus 
 induces him to study particular History. 
 
 4. Each chapter is headed by its central point of interest, which is thus 
 fixed in the mind of the learner. 
 
 5. It describes briefly, but accurately, Life and Manners 
 
 in the leading countries. 
 
 6. It is brought down to the latest Historical Events.— The 
 
 American War of the Rebellion— the Seven Weeks' War between Austria and 
 Prussia, and closes with the Franco-Prussian war. 
 
 7- The Appendix contains a concise geographical account 
 
 of the most important places mentioned in the book. 
 
 8. It is a pleasant, readable work which may be used as a 
 Manual of History-a Class-reader, <« a book of reference. 
 
 9. Thronichout it is accurate, tcnching no absurdities— too 
 common with too many of our Modern School-Histories. 
 
 It contains .377 pages, in good clear type, and makes a very handy volume, 
 bound in cloth. 
 
 Price, (at which it will be mailed) ------ $1.50 
 
 First lots for introduction for Class use, by Express - I .OO 
 
 J 
 
 J. W. Schermerhorn & Co., fpubUshers, 
 
 H Bond Street, New York, 
 
($2.00 2>er Annum.) {Single NoSo 20 cts.) 
 
 THE 
 
 ^ii»!a» #.IItiatt0ial |U0atItI|, 
 
 A MAGAZINE OF 
 
 POPULAR INSTRUCTION AND LITERATURE. 
 
 An Independent magazine, designed to be : 
 
 1. A faithful record of educational progress at home and abroad. 
 
 2. A medium for tlie candid discussion of all matters relating to 
 instruction and school management. 
 
 3. An advocate of free public education, unrestricted by sectarian 
 bar. 
 
 4. An advocate of a wider and more efficient course of instruction, a 
 higher order of school books, and all measures for elevating the 
 rank, remuneration and intelligence of teachers. 
 
 Fearless and impartial criticism of quackery in school books and school 
 supervision will continue to be made a special feature. The freest ex- 
 pression of opinion, consistent with justice and propriety, is earnestly 
 invited. Original articles on educational topics are solicited, to be paid 
 for when used. 
 
 " It is always gooAy—Commomcealth. 
 
 " A lively and independent >Iontlily." — American Naturalist. 
 
 " The leading Educational Journal in America."— iO!/i.sri/?e Journal. 
 
 "The articles are short and comprehensive. Its notices of books and criticisms 
 
 arc just and intelligent."— i\'«<iowa; Intelligencer. 
 
 "It is iavaluable to all who have children to educate or school taxes to pay." 
 
 Club Rates: — 5 Subscribers for $8.00; 10 Subscribers, $15.00; 
 20 Subscribers, $30.00. (Club Subscribers may be at different offices.) 
 
 8^" Agents wanted in every locality. Circulars sent on receipt of 
 postag-e. Specimens, 20 cents each. 
 
 J, W. Schermerhorn & Co., fpublishers, 
 
 14 Bond Street, Ne%v TorJc. 
 
UNIVERSITY OF CALIFORNIA LIBRARY 
 BERKELEY 
 
 Return to desk from which borrowed. 
 This book is DUE on the last date stamped below. 
 
 iiilflfiiipf 
 
 JUL i; 195C 
 
 APR - '^" 
 
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 LOAN 
 
 MAY 14 REC'D-9 
 
 e:ived 
 
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