How to Teach by Henry Kiddle
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Title:How to teach. A graded course of instruction and manual of methods for the use of teachers. By Henry Kiddle … Thomas F.

Harrison … N. A. Calkins.

Author:Kiddle, Henry, 1824-1891.

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Permission must be received for subsequent distribution in print or electronically. Please contact umdl-info@umich.edu for more information.

Print Source:How to teach. A graded course of instruction and manual of methods for the use of teachers. By Henry Kiddle … Thomas F.

Harrison … N. A. Calkins.

Kiddle, Henry, 1824-1891.

Rev. ed.: 269 p. illus. 20 cm.

Cincinnati,

New York,

Van Antwerp. Bragg & co.

[c1877]

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How TO TEACH. A GRADED COUIRSE OF INSTRUCTION AND MANUAL OF METHODS FOR

TIEHE: USE OF TEACHERS. BY HENRY KIDDLE, A.M., SUPERINTENDENT OF PUBLIC

INSTRUCTION, NEW YORK CITY. THOMAS F. HARRISON, FIRST ASSISTANT

SUPERINTENDENT OP (;RAM. SCHOOLS, N. Y. CITY, AND PI’ROF. Of’ METHODS AN1) PRINCIPLES OF TEACHING IN SATURDAY NORMAL SCHOOL. N. A. CALKINS, FIRST

ASSISTANT SUtPERINTENI)ENT OF PRIM. SCHOOLS, N. Y. CIT’fY, AND I’ROF. OlP

MIETHODS AND PRINCIPLES OF TEACHING IN SATURDAY NORMIAL SCIHOOL. REVISED

EDITION. VAN ANTWERP, BRAGG & CO., 28 BOND STREET, NEW YORK. 1,37 WALNUT

STRF-F,T, CINCINNATI.

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Eclectic Educational Series. TEACHERS’ MANUALS. KSuisi’s lzfe (f Pestaozzi. Hailiia’z’s Iifndei,airlen Culizrie. Haitliatn’s Leerzt-es on History of Pedas,‘qy. Tlhe Exaiiiner, or Teacizer’s Alid. Sflar-tls Afaozual of F)iee Gymnastics. Object Lessons, by Lilieztlal Izd1 A4iyzn.

Payne’s School Supervisio’n. :ow’s Good Aforzals and Gentle Alnzzze-s. *./
f Entered according to Act of Congress, in the year 1873, by J. W.

Schcrmer honri & Co., in the Office of the Librarian of Congress, at Washington. Copyright 1877 by VAN ANTWERPP, BRAGG & CO. ECLECTIC PRESS, VAN ANTWERP, BRAGG & CO., CINCINNATI.

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PREFACE. THE system of graded instruction, which has become so general in this country, requires for its successful application, the constant use, onl 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 established principles, so that the mind of the instructor may not be diverted firom that which should engage his immediate 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 practical business of teaching, but whose field of observation has been sufficiently 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 officers, is designed to afford such a guide as 373702 -k -i -A i –

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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 i’nlto which the course is divided. This difference is, however, rather nominal than real, since the number of glrades into which a course of study is divided is entirely arbitrary, except so far as it may be dictated by special circumstances. Where 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 necessity of constantly reorganizing classes, renders frequent promotions, or transfers from class to class, indispensable, and, hence, a large number of grades becomes a convenience.

In schools having a smaller and steadier attenldance, 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-corresponds, 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 performance of their professional duties-that is, in some degree, to show them what to ieach, as well as 7]ov 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 4

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PREFACE. 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 subjects and methods which, as they dispense to a considerable extent with the actual objects themselves, and appeal to the acquired ideas of the pupils, may be properly denominated cogiceptive. 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 and reasoning faculties, such las physiology, natural philosophy, and astronomy. By this kind of teaching, it is designed that the pupil shall acquire the ability to gain an experience 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 R’s” left the pupil’s mind in a condition of matured stolidity, and while, perhaps, a most ready talking’, writing, and p’Lrsing machine, sent him forth to go through this beautiful world, 5

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blind to its manifold wonders and glories, and fit only to become the easy prey of the demagogue and the bigot. It is an evidence 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 ill 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 various 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. Helence, references to more full and complete works on the subject have been given in connection with several of the grades, in order to aid teachers in finding the additional infornation which they may need in this direction. The demand for copies of the “Manual of Instruction and Discipline,” recently prepared by the authors of this work, for the use of the primary and grammar schools of the city of New 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 American pedagogy, now so scanty and insufficient. PREFA COE. 6

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CONTENTS. INTRODUCTION……………………………….. GRADED

COURSE.-TENTH GRADE (Outline)…….. HOW TO TEACH SUBJECTS OF THE TENTH

GRADE… Reading (23); Phonetics (27); Spelling (27); Aritlih metic (29); Object Lessons (34); Drawing and Writing (35); Management (36). NINTH

GRADE (Outline)………………………… How TO TEACH SUBJECTS OF THE

NINTHI GRADE… Reading (39); Plhonetics (40); Definitions (40); Spell ing (41); Arithmetic (41); Object Lessons (44); Drawing and Writing (45); Management (45). EIGHTH GRADE (Outline)……………………….. How TO TEACH SUBJECTS OF THE EIGHTH GRADE.. Reading (49); Punctuation (50); Phonetics (50); Def initions (51); Spelling (51); Arithmetic (52); Object Lessons (59); Drawing and Writing (61); Manage ment (62). PAGE 11 21 23 37

39 47 49

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CO1NJENTS. PAGE 63 HOW TO TEACH SUBJECTS OF THE SEVENTH GRADE. Reading (65); Phonetics (66); Definitions (66); Aritlh metic (67); Tables (73); Object Lessons (74); Ge ography-Preparatory Steps (80); Drawing and Writing (81). SIXTH GRADE (Outline)…………………………. HOW TO

TEACH SUBJECTS OF THIE SIXTHI GRADE… Reading (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)………………………… HOW TO TEACHI SUBJECTS OF THiiE FIFTIi GRADE… 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 (126); Outlines of Zoology (129). FOURTH GRADE (Outline)………………………. 137 H:OW

TO TEACHI SUBJECTS OF THE FOURTH GRADE.. Reading (139); Spelling (139); Definitions (140); Eng lish Grammar (140); Arithmetic (144); Syllabus of Topics for Common Fractions (147); Syllabus ~ 8 SEVENTH GRADE

(Outline)……………………… 65 83 86 105 107 139

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CONTENTS. PAGE for Decimal Fractions (158); Geography (163); Elementary Science-Botany (164); Mineralogy (168); Writing (172). THIRD GRADE

(Outline)………………………… 175 HOW TO TEACHI SUBJECTS OF THE

THIRD GRADE… 177 Reading (177); Spelling (178); English Grammar (179); Composition (179); Arithmetic (180); Sylla bus for Arithmetic (182); Geography (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 (194); Syllabus for Physiology (196).

SECOND GRADE (Outline)………………………. 199 ‘How TO TEACHI 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 SUBJECTS OF THE FIRST GRADE…. 225 English Grammar (225); Composition (226); Arith metic (226); Algebra (229); Geometry (232); Out lines of Physical Geographly (236); History, Ancient and Modern (238); Natural Philosophy (241); Astronomy (243); Chemistry (245); Bookkeeping (250); Constitutionl of the Unlited States (251). 9

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CO VTENTS. PAGE GENERAL SUGGESTIONS RELATIVE TO CLASSI FICATION AND

INSTRUCTION………………. 252 Reviews (252); Progress of Classes (252); Progress of Pupils (252); Recitations (253); Lessons for Home Study (254); Physical Training (255); Man ners and Morals (256). GOVERNMENT AND

DISCIPLINE……………….. 257 SCHOOL

LIBRARY…………………………….. 263 ~ 10

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INTRODUCTION. No task can be more responsible, or require the exercise of greater care than that which has for its object the proper education of the young. To perform it efficiently, special preparation and study are indispensably necessary, not onlv in regard to the branches of knowledge which may have been selected as a basis for the instruction, but also in respect to the proper methods and appliances to be employed, in order to render the instruction truly effective. These methods must be determined by a consideration of the faculties to be trained and educated, as well as the nature of the subject taught; hence, the teacher should be familiar with at least the outlines of mental science,-the office of each of the faculties of the mind, the order in which they are naturally developed, and the proper means of aiding in this development, so that the training and instruction given may result in that 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 mind are as definite, and as general in their application, as those which apply to the material universe; and it is evident that a true system of education must be based upon a knowledge and application of those l(aws.”

How important then that the teacher should make himself familiar with these laws! Certainly no true success can be obtained

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IJTROD UCTIO-V. without thiis knowledge; for destitute of it, the teacher is only an empiric, applying rules the reasonl of which he does not know, and nmechanically following methods, the rationale of which he does not understand. If the teacher have sufficiently mastered these elemelntary principles of his profession, it will not be difficult for him at all times rightly to understand his pupils’ menital condition and grade of adv-wLcemenlt-a matter of the greatest importance, especially at the first stage of school instruction. Failing in this respect, mainy 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 accolmplished. They do not seem to be aware of the extent to which the pupil’s mental faculties, more especially 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 regular tuition at all, or subjected to any of the manipulations 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 corresponding 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 nLtture lherself. Here is no senseless cramming of words, for words are only learned after the ideas which they represent have been acquired. Under the guidance of a teacher properly conversanit with the laws of the mind \ 12

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ITR OD UCTION. 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 uised, the effect of which is to counteract the work of nature, and cheek the mental activity of the young pupil. To learn A, B, C is, of course, necessary as one of the rudimental steps of primary instruction; but this, like everything else, should be so done, that the intelligence of the pupil may be fostered, not deadened, in the acquisitionl. In every stage of intellectual training, let the teacher always remember, that his pupil’s mind is not to be treated as a “p)assive 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 usefLl purposes. Let him constantly apply the principle, so tersely expressed by Sir William Hamilton: ” The pri)iary)principl)e of edcatioein is tlhe deteimiation of the I)tl)il to self-activity- (le doinq clottin for hiim)vl’iclil he is able to donoir li-se?.” This principle is equally applicable to every stage of the mind’s development, as well as to the different processes of instruction adapted to these stages; but it will be impossible accurately and effectively to apply it, without a complete knowledge of the order of mental development, and of the relation of that development to the study of each of the branches prescribed for the instruction and the cultivation of the mind. Knowledge is to be considered as the.food of the nii)il; since by the proper reception, digestion, and assimilation of it, the mind is to attain a nmaturity of strength and efficiency; and upon its quality and quantity it must depend whether that mind is to be healthy and vigorous, or puny, sickly, and imbecile. It is, therefore, of the greatest importance to ascertain the 13

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LINZ’ OD UCTI0.V. effecb produced 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 nlent consideration in selecting the subjects to be taught; but the teacher should, in the classification, 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 efficiency 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 pr)ocesses of teaching to the various subjects taught, as well as to the faculties which they call into exercise, should be a prominent object in the 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 observer, 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 verbatire the contents of a particular textbook, or to repeat with verbal accuracy and fluency certain rules, definitions, and formnule, 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 arbitrary association. The illjury, however, done to the mind by this continued process, is incalculable; since, 14

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INTi OD UCTION.. 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 presenting the subjects to be taught must depend upon the relations here referred to. Rules and methods may, indeed, 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 famniliarity with the subjects taught.

“A teacher,” says Edward 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 aspects, with its antecedents and consequents, or he cannot present it in just that shape in which the young mind can apprehend it. HIe 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 instruction, is designed to deal with this inquiry quite exhaust i5

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INTR OD UYCTION. ively, and it is in furnishing a guide to the teacher in this important part of his 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 shlould, as an essential )a’rt of his professional preparation, acquire.

In this connection, the auttom))atic te)dencies of the mind are to be studiedthe tendencies, that is, to fall into habits, these when depraved constituting what may be called the morbid growth of the minid. No part of the teacher’s duty is more important than the exercise of a constant vigilance, in order to arrest the formation of deleterious habits, or to aid in forming suchl 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 quantity of knowledge acquired that constitutes a criterion of mental advancement, but the mode of employing the mental faculties-the habits of thouytt 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 hab)its as to become a kind of “second nature.” 16

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INTR OD UCTION. How to use textbooks, as well as when and for what purposes to employ them, is at the present time particularly, a most important subject of’ study to the teaclher. 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 textbooks must always be among the most important instrumentalities 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 effective 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 tunaided 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 mature 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 instruments for affording this necessary aid and direction; but in doing this, the tendency should always be to stimulate, not repress, intellectual activityv-to bring into play the higher faculties of the mind, not to render its energies dormant by offering only the dry forms, the mniouldy skeletons of knowledge, instead of the vital germs of intelligence and thought. If, after the various grades of school study have been passed, the pupil is left with a torpid, vacant mind, the loss which he has 17

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I3 17ROD UGIJOV. sustained is too great to be compensated by even the ability to read, write, and cipher. On the other hand, a pupil that has not only mastered the elementary principles 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 educated than he could possibly be by an exclusive dependence upon oral instruction. One of the most serious abuses to which the employment of elementary textbooks is liable, is the practice of requiring the pupil to commit to memory, verbatim, 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 definitions first, and the reasoning based upon them afterward, but this is not the order of investigation. The definitions are the results of an induction based upon the facts obtained by observation; they are generalizations of those facts, and are 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 him to observe the phenomena-to collect an experience of his own; tell him, or let him learn from the book what has been discovered by the experience of others; and when the facts thus obtained form a sufficient groundwork, lead his mind to the proper induction, after which the definition, principle, or rule, based upon it, comes naturally, and will be thoroughly understood. The definitions thus taught should be brief and accutrate in language, and, as a general thing, should be 18

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INTROD UCTION. committed to memory verbalti; for great skill is required 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 textbooks, 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 Te(aching and Oral Instritclion have assumed a prominent place in every rational course of study. Both these terms necessarily exclude the use of textbooks.

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 appearances 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 instructionl; its lifeless representatives of ideas cannot dispense with those vivid expressions of thought which come fresh from the lips of the teacher. Besides, there is a language other than words a language to which the eye, the tones of the voice, the movements of the 19

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INTROD UCTIO-Y 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 conlduct-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 rather 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 wonder of the day.” 20

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GRiADED COURSE OF INSTRUCTION. GIRAI)E. (LOWEST PRIMAIrY.) Tive allowed, about five motth7s. LAN(GUAGE. Reading.-Words, anld wliat they represent; their sounats, and letters; also shlort sentences composed of familiar words. The alphabet, by review. Phonetics.-Sinple soLunds of letters for training thle organs of hearing and of speech. Spellinfg. -Words of regular formation-to be taught fiom tlhe blackboard, charts, etc.

ARITHMETIC. Counting and’Adclifng. Objects-as balls on the Numeral Frame, pebbles, etc. Figutres.-From 0 to 100, as symbols of the numbl)ers, taugit by counting objects. OBJECT LESSONS. Foi,m.-Collmoa shapes, as square, oblong, ball, cylinder, cube; different kinds of corners, and of lines.

TENTH 4

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22 GRADED COURSE OF ISTIRUCTION. Color. -Common colors, as red, yellow, blue, green, orange, purple, to be distinguished. Objects.-Names of common objects, their uses, and principal parts. Hu man Body.-Principal parts of the body. DRAWING AND WRITING. On Soates.-Making dots and small crosses in rows; drawing short lines, corners, etc. Printing or writing simple letters. MANAGEMENT. Length of Exercises.-Fiftcen minutes at one time.

Discip)ine.-Constant, but varied employment the best means.

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LA&G UAGE. HOow TEO TACTi SUBJECTS OF TIIE TENTII (Olt LOWEST PItIMAEY) GRADE. LANGUAGE. Rea(li,,g.- Clhildren learn worlds as ctad(ible signs or names of objects, actions, and qualities, 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 imanner young children gradually become familiar with 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 swords, 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 themselves 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 fors))s. The spoken words are first learned as wholes; the printed words should be learned first as wholes and associated with both the spoken words and the objects which they represent.

Therefore, teach first shiort 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 23

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21.O W TO TEA (‘l the first lesson in reading, priint the words onl the blackboard several times, and point them out on charts, etc. Let the pupils point out the words on the blackboard, and on charts; also let them print the words on their slates. Special pains should b)e taken to lead thle children to associate the printed words withl the objects which they represent, either by the use of the objects themselves, or by pictures. In teaching words that are not n1ames, care should be taken to illustrate their meaning by simple phrases, conversations, etc. D)uring the earlier lessons, omit words of irregular formation, having several sileni1
letters, such as togyite, knoe i, knot, thoygh, thou(yht, etc. This class of words may be presented 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 at sight, as a whole, and the sounds and names of the letters which coripose the word be taught afterward. After the chlildren have learned a few words at sight, they may be taught the sotncls, and the lette’s which form those words. For the purpose of teaching the sound-elemets of words, select those in which the sounds and letters are similar, as cat, rat, hat, mizat, ox, fox, box, etc. The teacher should sound the elements orI letters of the words first, then require the pupils to imitate the sounds thus made. But before this can be done suecessfiilly the pupils must ])e trained to distinq(ltish, and to proditce these sounds, as directed unnder the head of Phonetics 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 24

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LAIVG UAGE. words, and then taught the remaining ones 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 smitall letters are, of course, to be taught first. After the pupils have learned several single words, simple sentences may be presented, 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 fo)r2is of words, at first, is surprising. And no less astonishing is the readiness with which spelling is afterward learned. Let the order of teaching reading be, first, lthe idea; then), its sounid-symibol, or spoken word; next, the formisynmbol, or printed word; and sutbsequently, its represenitation by 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 objects and ideas to the minds of the pupils. Senise, and souind, and for)t, 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 lead, is constantly comparing the forms of new words wvith the forms and sounds of those previously mastered. The teacher mnay and,should aid the young pupils 2 25

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HOW TO TEA Htt in acquiring the ability to learn new words by arranging in groups, on the blackboard, those already learned, and showing them how to compare the forms and souinds 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: Paill tin, fin., ~i(( i. qen. (o. fn NVWhen the children have learned to pronounce the words in a column, at sight, let them learn to give the soundsofeach,as-k- t, cat; r t, rat; Li t, hat; etc., not as a s)pelli)iy 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: rake, make, cake, bake. lamiliar Words.-The list of familiar words taught in this grade should include those commonly used as names of articles of food, dress, furniture, utensils used in the house, in the garden, or on the farm, and 26 cat, rat, I liat, iiiat. I)egz, hell, tell, men. ox, fox, box, top. c2tl9,, gitn, rit-gi, .full. old, cold, told, scold. line, fine, 11 i i’l e, pine.

mule, rule, cube, tube. me, we, see, bee.

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LANG UAGE. different articles used in the schoolroom, also names of common animals, familiar qualities, actions, etc., such as, bread,fish, cap, vest, chair, bed, etc. Phonetics.-The object of teaching this subject should be, first-to train thle or,qyais of hieariny, so that the children may readily distinguish the sounds heard in speaking our language; secoind-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 words by sight-the teacher should herself make the sounds, and then require the pupils to imitate them, as: a4, (; b, 4(; o5,; 6, 0; e, e; e,e; b,ee;,, u,u; a,; 4,4.; a,aa; afterward, thus: G, O, a, a.; e, e; a, a; o, o, o; a, ~Y~, u When their organs of hearing and of speech have thus been trained, both to distinigtish and to imitate sounds, proceed to teach what sounds are represented by the letters of simple words, as-a)l e, in a t, c a t, n a n, to0, iot, pii, ceip, wet, cake, miake, late, sl a t e.

Should more definite directions relative to methods for giving the first lessons in Phonetics be desired for this and the following grades, see pages 297-308 in Nev Primcary Object Lessons, by N. A. Calkins.

Spelling.-After the words have been learned by sight and sound, let them be learned by spelling, and the children requested to observe that 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 27 I

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HOW TO TEA CHII on a preceding page, under the head of Readingi, 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 requested to pronounce the word, and name the letters composing it. Parts of words may also be erased, and the pupils 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 schoolroom, common animals, plants, names of familiar qualities, 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, therefore, 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 Train the pu1)ils to proniounce wvorcds readily tt sight. Never allots tkhemv to use uqnnattral tones in s)eakingy o0 reading. Correct their faults in the Use of tlaiy(uaye as tliey OCC?tit. 28

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AIII IJETIC. ARITHMETIC. Counting and Adding.-Tlle child’s knowl edge of,iluiber commences with counting objects. lHe cannot learn the value of.fi#ytres from 1 to 10 until he can count te)t objects. Therefore couti,rin should be attended to first. The Num)le)xa fralne 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 Framne for teaching counting. This mode of using it consists simply in holding the Frame before the pupils, and moving the balls on the first wire, one at a time, while the children count I “one, two, three, foulr, s five, six, seven, eight, nine, ten.”

The same counting -may be repeated on the second, x’, )P third, and on each succeeding wire. At first the counting should not extend be-COUNTING. yond ten. When all the balls on each wire have been counted in this manner, proceed to move one ball o0n each wire, and let the children count to ten, as before. Let this exercise be continued, from day to day, until each child can count from one to ten, alone. Afterward, the counting may be extended to t(venty, by moving the balls on t(vo wires; then to thirty, by moving the balls on three wires, and 29

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HOW TO TEACII so 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.

Adding.-When the pupils can count to one hundred 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 twos, as far as fifty, and have also learned to read and write figures as far as 20, the teacher may write a column of 2’s on the blackboard, and train the pupils to add the fiyqtres 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 tvo 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 balls, thus, the teacher may write a column of 2’s with a 1 under it, on the blackboard, so as to make the combinations produce the odd numbers. After sufficient training upon these combinations, both with the Numeral Frame, and the blackboard, require the pupils to write similar columns of 2’s with a 1 underneath, and add as before, writing the sum below the column. 30

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ARIl[lMEIETIC. Let the same process be pursued i teaching the addlition of tlrees; first, by balls onl the Numeral Frame, as three, six, nine, twelve, etc., then by figure 3’s onl 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 tihrees should be combined with one, next with two, so as to produce different combinations of numbers, as with the twos. During a still later stage, the pupils may be taught to add by alternating twos and ones; then threes and ones; then threes and twos; then threes, twos, and ones. Each of these steps should be taken first with objects, then with figyt)es onl 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 fours, fives, and sixes, and their combinations with ones, twos, threes, etc., in the next or Ninth Grade. The order of the steps is indicated by the objects employed in teaching, viz.: Numeral Frame, Blackboard, Slates. Of course, these exercises with columns of fyigures should not be introduced before the pupils have been taught to know figures as symbols, and to make them onl their slates. Value of NTum bers.-It is exceedingly important that the first ideas of the value of numbers, and of figures, be associated with numbers of objects counted. Both the valtue of ntnubers and the valute of figuyres should be taught in connection with counting objects. Here, again, the Numeral Framie is the most useful apparatus. When the pupils can readily count ten, th6 teacher may hold the Numeral Frame before the class, move onie ball on the second wire from the top, and 31

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IHOW TO TEACH request the pupils to say “o)ie ball.” Then the teacher may move two balls, one at a time, on the tlird wire, the pupils counting themn as moved, thus: “one, two; two balls.” Then move 7three balls, one at a time, on the fourth wire, the pupils counting thus: “one, two, thlree; three balls.” Then move foutr balls in the same manner; then five balls, and so on. The position of the balls on the wire while the pupils are counting, may be seen on the sixth wire in the accompanying illustration of the Vaida(u of N libe)-s. While the pupils are counting “one, two, three, four, five,” the teacher does not move the balls to thle 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 VALUE or NUMBERs. -Simll)le Vatle of Figqures-represents the teacher in the act of moving the five batls 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. 32

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ARITIIME IC. Next let the pupils tell the number 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 Niutibers will be learned thoroughly. _Figures.-Figure, bols of the number of first consecutively, in g Oto9; from 10 t o 1 9 etc. No succeeding group shouldl be presented until the preceding one has been thoroughly learned, so that the pupils cal read them at sight, ill order, and out of order. While teaching the Simple Value of Figures, the Numeral Frame will be found a most valuable aid. During this stage of instruction the teacher shouild make frequent use of the blackboard, and the pupils of slates. Additional suggestions relative to methods for teaching the First Ideas of Numbers and of Figures, may be found oni pages 194-209 of New Primary Object Lessons. 2*

33

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110 W TO TEA CII OBJECT LESSONS. ‘N. B.-E(tch exercise i)l object lessonis sh7ould be coiducte(d Uitlt a views to form-iny habits of atteitioei and careftlI observatio) th7ro’tl7 thle Utse of the senses. _orm.-In Nature’s school, children first learn to know things as wholes; they learn to know their parts afterward. The teacher who would be successftul must follow Nature’s plan of instruction. Present, therefore, conmmon objects, as wholes, and lead the pupils to lnotice resemblances in shape, first; afterward direct their attention to prominent differences. A Box of For)is a(zzd Solids, containing forty-eight plane Forms and fifteen Solids, has been prepared for the special purpose of Object Teac7hiny. 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 themn 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.-The pupils should be led to distinguish resemblances and differences in color from “colored cubes,” or cards, and to group together objects of like colors. They should also learn the namnes of the six principal colors. 34

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DRA WING AND WRITING. Objects.-The lessons on Comnion Objects in this grade should be simple and conversational, treating only of their most obvious parts and uses. Sutch common 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. iHtutan Body.-In this Grade the lessons on the H-umnan Body should lead the pupils to notice and name the parts, as head, nec, rk, Ttru nk’mis, hands, legs, feet; also parts of the head, as crown, face, forehead, cheeks, chin, mouth, nose, eyes, ears, etc. N. B.-If more explicit information be desired relative to methods for giving lessons on shlcl)es of linies, corniers, square, oblony, ball, cylindler, cube, and comimion objects; also on colors, and on the ht ma bo(ly, it may be found in New Prime ar y Object Lessons. DRAWING AND WRITING. Drawing on Slates, etc.-The exercises of D)raqwiniy and Prinitingi oi slates shoutld be introduced in such 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 witl 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 iseful. 35

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1 HOW TO TEA CH MANAGEMENT. Length of Exercises.-The exercises of this Grade should iot be continued upon the same subject longer than fifteen minutes at one time, without materially 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 frequent changes in the position of the body; also constant bnt 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 children should niever be coqmpelecl to sit wvithlioit eml)ploymlerit, either for the miniiil, the anids(1, or the bodv, 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. 36

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N INTH GRADE. (PIIMAIY.) Time allowed, about five moitths. LANGUAGE.

Reading.-In the First Reader. Phontetics.-Pupils to be taught to recognize and to make the sounds of the letters in words of one syllable.

Definitions.-Pupils to be practiced in illustrating the meaning of words by their use in short sentences; also in telling what the words mean.

Speling.-Words firom the reading lessons; also familiar words in common use. ARITHMETIC. Adding.-With objects, andl 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 fiom dictation. Romaj, Numbers.-I, V, X, L, with their combinations to sixty, inclusive; also their use on the face of the clock. OBJECT LESSONS.

Form.-Common shapes, continued; adding those of rhlomb, rhomboid, circle, semicircle, crescent, sphere, hemisphere, cone; also position of lines.

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38 GRADED GOURSE OFINS7‘1IUCTIOVN. Color.-Shades of common colors, as light and dark red, light and dark blue, etc. IItunan Body.-Names and uses of the limbs, and of their parts; also the names andl shapes of the principal bones. Objects.-The principal parts and chief uses of common objects. DRAWING AND WRITING. On Slates.-Connect dots by lines; draw squares, oblongs, rhomibs; divide lines into equal parts. Write simple words with small letters. MANAGEMENT. Doing.-Train children to see, to do, and to tell. Manners anel Morals.-Use the appropriate daily incidents -of school as occasions for giving instruction in Manners and Morals.

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LANG UAGE. How TO TEACH SUBJECTS OF THIE NINTII GRADIE. LANGUAGE.

Reading.-The manner of teaching Recadiny during the first term in which books are used by 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 ill reading from books, are, learning to kgowv the word(s at sihyit, so as to pronounce them readily; learning to k)towv what the fvords and se)te)ces mtecant; learning to readc in sutch a manner as to imitate good coenversation, 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. Secoind Ste).-Train the pupils to find out what each sentence means, and to tell the meaning in teil onus language. Thirdcl Step.-Train the pupils to read each sentence so that the reading mnay resemble good conversation. 39

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t IOW TO TEACH Finally, when the lesson has been read ill a proper mainher, the teacher should talk with the children about it, and encourage them to tell, in their owil language, what they have read. N. B.-Let the stantd)(lad for good rea(dily be its inear resemiblance in an e to good co)nvers(ttio). Further suggestions relative to first lessons in reading from books may be found on pages 333-337, of New Prii)iary 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 DnI. EDWIN LEIGI. Phonetics.-TThe object of exercises in Phonetics should be the same in this grade as in the precedingto 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 descriptions 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 oirgans of speech to flexibility and accIIuracy in producing sounds.

Deflnitions.-During the lessons of this grade, it is appropriate to teach the children to use the principal words of the lesson ini brief sentences, to enable themn to show readily that they understand what the words mean, as: “A horse can draw a cart.”-“I must be yood(.”-” I can hol(id a l)ook.”-” ioiv is white.” ” I will try to lears to read.”-” I imust obey my mother,” 40

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ARITIIMETICU. etc., etc. Such exercises will be found to be much more useful to young children thani teaching them formal definitions to be recited. The mneaning of diflicult or unusual words must, of course, be e.plained and illustrated by the teacher. SSp)lligJ. I1 oral spelling, the words should be distilncetly pronounced by the pupil before they are spelled, then each letter clearly uttered, (a )ause m7ade betiveeni 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 lessons, should include such appropriate words as the children most commnonly hear and use. These should be printed or written onl 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 writing 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 pelingy lessonis by copyiny the words o)t slates.

ARITHMETIC. Addinlg.-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 with tlhe Numeral Framne, do not allow the children to count and add by role. See that due attention is given to the objects counted.

When the pupils can add readily 41

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I0 IW TO T~A(II single columns, each composed of like inumbers, as all 2’s, all 3’s, 4’s, 5’s, etc., teach them to add single coltumns composed of different small numbers, as 2’s anid 3’s; 2’s, 3’s, and 4’s; also 2’s, 3’s, 4’s, and 5’s. 2 4 5 These combinations should be illustrated 3 3 4 on the Numeral Frame at first, then 2 2 3 taught with figures on the blackboard; 3 4 2 and subsequently copied by the pupils on 2 3 5 their slates, and added by them silently. 3 2 4 In adding, let the pupils be trained from 2 4 3 the first to name only the sums, thus: 3 3 2 3, 5, 8, 10, 13, 15, 18, 20, 23, 25;-4, 6, 2 2 5 9, 13, 15, 18, 22, 24, 27, 31;-4, 9, 11, 3 4 4 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 blackboard thus: 9 10 11 1 1 1 10 11 12 9‘10 2 2 11 12 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. 42 0 1 I 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 6 1 7

7 1 8 8 1 9 12 1 13 13 1 14 14 1 15 15 1 16 etc. 0 2 2 1 2 3 2 2 4 3 2 5 4

2 6 5 2 7 6 2 8 7 2 9 8 2 10 it 2 13 12 2 14 13 2 15 14 15 2 2 16 17

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ARII:tMETIC. Reading and IWiting Figures.-Both the reading and writing of numbers in figures can be taught most thoroughly in steps, or groups. The figures should be presented first in their order, in connection with counting; then out of their order. In this Grade the figures should be taught withiout num.eration. The following groups will indicate appropriate steps: First Step. 10 11 12 13 14 15 16 17 18 19 20 21 etc., to 99. FourthI Step. 200 201 202 203 204 205 206 207 208 209 210 211 etc., to 299. These steps maybe continued in this manner through 999. As mnuch time will be required to teach the first and third steps as for any four other steps. Let the children be trained to reactd and write the numbers contained 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. 43 TIti2,-d Step. 100 101 102 103 104 105 - 106 107

108 109 110 III etc., to 199. Second Step. 100 200 300 400 500 600 700 800

900. Fiftli Step. 300 . 301 302 303 304 305 306 307 308 309 310 311 etc., to 399.

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HOTW TO TEACH _?omazn, Numbers.-Besides teaching what numbers are represented by I, V, X, and L, and their combinations to sixty, 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 shape by means of its representative form in thle 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 was properly directed to their shapes only, as straight, crooked, curved, waved, spiral. When they are taught to recognize and name the 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 pupils 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,” “ColorChlarts,” and other colored objects for illustrating these lessons, and require the pupils to show, by placing in groups colors that nearly resemble each other, with what degree of accuracy they distinguish colors; and at the same time they should be taught to know common shades and tints by their names. 44

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DRAWING AND WRITING. HMuman Body.-In giving the lessons on the h?Glartib bo(ly, 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 information relative to methods for giving lessons on pZane foreist, solids, position of Iinies, shades of colors, the Human body, and on com?,gio} 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 Primiary 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 illustrations on the blackboard, relative to each point and step of the lessons. MANAGEMENT.

DDoing.-Childrenb learn wltucA faster by doing than by merely repeating what they have been told. Therefore, whenever possible, arrange the exercises of each subject so that the pupils may be called upon to do something which relates to that subject, willth their haniscl,; also so as to require them to tell what they see and d(o. 45

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t IOW TO TEA(‘1I. Regular Occupation for all the Pupils.A teacher who furnishes that regular and constant occupation which commands the attention of all the pupils during the several exercises of the day, thereby gives the best assurance of ability to manage a school successfully. Indeed, the secret of niaintaining good discipline chiefly lies inll this. Hlence the 9pa)tner of teac]igzy becomes an important element of good management as well as of good instruction, for it is this which chiefly determines the order of the class. Furthermore, habits of learning are acquired from the prevailing methods of teaching. To learn how to manage a class or school, so that all the pupils may have constant occupationl, 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 different lessons upon the same subject, and even changes in the manner of conducting the exercise of a single lesson will be useful to the teacher toward the attainment of this aim. In a class composed of young children, frequent alternations 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 e(aclt e s)oise by the class. 46

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EIGIHTH GRADE. (PRIMARY.) Time allowed,-about five months. LANGUAGE.

Readting. Fist Reader completed, and an easy Second Reader 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 distinguislhed.

Definitions.-Meaning of the words read to be shown by using them in short sentences. Spelling.-From reading lessons; and lists of other familiar words. ARITHMETIC. Adding.-Single columns of ten figures; adding by decades, through 9s’. Numeration and Notation.-Reading and writing figures through nine places (987, 654, 321). Mental.-Simple, practical questions which require the adding of numbers fiom 5 to 9 to numbers below 30; also, subtracting similar numbers. Multiptlicatio, table commenced. Roman Xumbers.-Their combinations through two hundreds. The Key to Roman Numbers to be taught.

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48 GRADED COURSE OF INSTRUCTION. OBJECT LESSONS. Form.- Parallel and perpendicular lines, angles, prisms, pyramids, surfaces, circumference, diameter, etc. Color.-Primary and secondary colors. ttuman Body.-Principal bones and their uses. Animals.-Names and uses of familiar animals; also where they live. Plants.-Names of trees, plants, flowers, fiuits, 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. MANAGEMENT. 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.

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LANG UA GE. How TO TEACH SUBJECTS OF THE EIGHTH GRADE. LANGUAGE.

Rea(ling.-The exercises for teaching Reacding in the Eighth Grade may be divided into three step)s, as in the Ninth Grade. First Step).-Training tile pupils to know the words at sight; also what the words mean. Second Stepl.-Attention to the thoughts expressed. Thiird Step.-Reading in easy, conversational tones. 1. The pupils may be trained to know the words at sight by writing them in columns on the blackboardby pronouncing them from their books, commencing with the last word of the paragraph and proceeding in an order the reverse of that pursued ill reading. 2. As soon as the words are known readily at sight, chief atte,tio~i should be givei to lthe tioutg7its expressed. The pupils may be led to attend to the thoughts expressed by requiring them to find out what the sentences tell, without reading them aloud. The teacher may aid them in this matter by proceeding in a manner similar to the following: Request the class to loolk 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 iii a similar manner with other sentences of the lesson, and 3 49

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10 OW 2‘0 TEA CIl require the pupils to tell what those sentences say. The teacher may ask: What does the first line tell us? What do the words ill the next sentence say? Who cal tell what the next paragraph is about? 3.

When the pupils have accomplished the first two steps in a given reading’

lesson, thev will be prepared to take the tIird stel), and will readily learn to read with easy, conversational 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 anl easy, speaking voice.

Faults in reading are most readily overcome wlhen the efforts 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. Punctuattion.-The time commonly spent in teaclhing children to recite definitions of punctuation-marks is wasted. Instead of this, lead the pupils to observe that a s0hort )(pat i.S ((e (is t at a comazc, a little lo)zyer )pause at a semnicolo)t, and still longer pa}tse) s act the questio/)-itcark and period. Lead the pupils to see that the questionl-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 quotation-marks, should first be explained from the blackboard, then examples of their use should be pointed out by the pupils in their reading books. Phonetics.- In this grade the pupils should be taught to distinguish the sounlds of given letters in words of one syllable, and to make these solunds, as, the sound of a inl a in ball U, o0 in cto/, o ill (0, it ill ftll, 50

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LANG UAGE. fin ftri, f in of, k in Cile, 9) in COI, C in co, etc. When the pupils can distingutiish 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 )cakel, 9)t-c-/C, make, a has its first sound, the e is silent; boi-gyi, b-a-t, bought; ott represents the fourth sound of ca, y and At are silent. As a method for training pupils to distinguish the silent letters, let them first soutz,ld a word, giving each sound as heard when the word is properly pronounced  then s)ell it, namning each letter in order-next tell which letters have no sound. Care needs to be taken, in each grade, to prevent the pupils from nmalking the short sounds of a, e, I, o, and it, too long, when sounded alone. Let each of these sounds be made very short, as heard in at, net, it, 9lot, 91U(.’ 2Definitions.-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 stattemeint 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 witi a sufficient variety and simplicity to secure a clear knowledge of the izeani)/qt of tle words. The practice of using the given words in sentences, so as to illustrate their meaning, should be continued in this grade. Spelin,i fl.-Care should be taken in oral spelling to have each pupil pronounce the word before spelling it, to name each letter distincitly, to mitake t1l)(i(tse bettween 51

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110 TIV TO TEACH the syll(bles, 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 friom dictation. In selecting familiar words it would be well to request 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. ARTITHMAETIC. Adding.-Continue tlhe exercise of adding single columns, in the same manner as ill the Ninthl 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 6 9 7 add readily, without 6 3 7

4 8 5 9 6 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 6 8 7 9 7 are composed of 6 3 7 5 8 6 9 6 7s, 8s, and 9s. 6 6 7 4 8 5 9 9 The progressive ar6 5 7 3 8 4 9 8 rangement of these 6 4 7 7 8 8 9 7 columns is illus6 3 7 6 8 7 9 6 trated here. When -.-….-.-.-.-.-~the pupils h ave learned to add a coluimn on the blackboa,rd, they shlould copy it on their slates, and then each add it singly, writing the sum underneath it. 592

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AR1TIiME YIC. will greatly facilitate learning to pidly. oward teaching pupils to add by by writing various combinations lackboard, in the following form nig the pupils to add the numbers to copy them on their slates and orally, and afterward add them again: 5 15 25 35 4 4 4 4 9 19

29 39 7‘7 7 14 24 34 44 54 6(4 etc. 49 7etc. etc. When the various combinations with eachl of the nine digits have been made thus in the form of decades, the pupils mray be required to review them by writing on their slates, in groups, combinations of two numbers 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 p)roduce a like figure when added, as that 9
and 7 always give the unit 6, 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 addiing single columns, they can readily acquire the habit of ((ldiicj qvitkhout co?(utti)jy. One of the most effectual means toward securing this habit, in addition to the adding by decades, 53 45 4 49 85 4 95 4 55

4 1)9 65 4 etc. 75 4 87 7 97 7 9 7 I ol 19 7 216 29 7 ,‘i 39 7 46 ,- 9 7

69 7 79 7 89 7 99 7

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110 TV TO TEA ACI1[ is to teach the pupils to give special attention to the figure representing the qtnits as each successive nunmber is added, i.

e., attention to caddiiny thle Ufnits. To explain this process, the teacher may write a columni of figures on the blackboard, as represented here Ca. b. by the one marked ac. Then the pupils may be 7 - 0 led to notice the qtnit 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 ueit figure; 7 and 5 will 8 - 0 give2; 2 and9 willgivel; l and 9 a 0; 5 7 - 2 and 7willgive 2; 2and 8 a 0; 6 and9 a 5; 5-5 and 8 a 3; 3 and 7 a 0o,” 9 - 0 During this explanatory process, the 9 - 1 teacher may write the qtzit figure opposite 5 - 2 the number added which produces it, as rep 9 - 7 resented in the column marked b. So soon 8 as the pupils understand this process of - adding and naming the Misit figures only, the 90 teacher should erase the coliumn, b, representing these units, and require the pupils to add by naming the units, as follows: 8, 7, 2, 1, O, 5, 2, 0, 6, 5, 3, 0. When they can do this readily from the blackboard, the pupils may copy the same column on their slates, anid add by naming the ~zils 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 sumi, 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 how to addl, that they may acquire correct habits.

Teachers may observe that the iztgmber of figures in the column marked b, corresponds with the number of 54

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ARI’YilJ[ETIC. tens in the sum of column a niiie-and that 9 tens, with the last unit figure, 0, gives the sum of column a. But this fact is not of sufficient practical importance to render it desirable that much prominence should be given to it. After pupils have been thoroughly trained in adding single columns, and understand Numeration and Notation, 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 both the length of the lines and of the columns.

Give many more examples with a few long columns than with long lines. Care should be taken not to embarrass children by giving them lo)gy and (laree examples in addition before thev 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. N_umeration.-On commencing Numeration, the three places in the unit’s period should be taught by the order of their places, and by their names; as, alit’s place, the first place on the right-hand side; te)l’s place, the seco)td place from the right-hand side; lzunzdre(‘s place, the t7lir(l place from the righlt-hland side. When 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 similar manner. The places in this period should be taught first as the 55

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tto JW TO TEA CEH fouLrth, fifth, and sixth places; then the pupils should be led to observe the similarity of iam)ies between the first, second, and third places of thle qt)iit’s period, and tihe first, second, and third places of the tIlo?,sa((1d’s period; as units, tels, hundreds of u ni/s; units, tenls, hundreds of thoutsand(Is. When the pupils can both read and write any number readilv, fi’om units to hundreds of thousands, proceed inl tihe same mannler to teach the mlillio)‘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 mentioned; also wvrite readily any nimmber through hundreds of millions, from dictation. Care should be taken to teach the pupils to write the figures neatly, tand in straight columns.

Two or three weeks may be spent on the unit’s period, before proceeding to the thousand’s period. 3l-ental Arithmetic.-In the iEighth Grade the answers to the questions in MAental Arithmetic should be simple and concise. The laniguage used should be sufficient to render the solution of the example, and tlhe answer to it, clearly intelligible to a listener, yet so brief as not to retard, unnecessarily, the process of menaltl calculation. Appropriate forms for answering questions in Mental Arithmetic, in tlle Eighthl Grade, may be seen in tlhe following examples: Howa many are six apples and three apples? Ans.-Six apples and tliree apples are nine apples. If a coat cost $15, and a hat $5, how much will both cost? Ais.- Both will cost the sum of 815 and $5, which is $20. Henry had 8 marbles anid bought 4 more; how many marbles had he then?

Ais.-THenry thlen had the sum of 8 marbles anid 4 marbles, which is 12
marbles. 56

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ARI IlyT[ETl TC. A boy had 9 apples and gave away 5 of them; how many apples had he left? AWNs.-He had 4 apples left; because, when 5 apples are taken from 9 apples, 4 apples will remain. JlultiJ)lication Table.-IIn presenting the Multiplicationl Table, it is very desirable that each step be thoroughly 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 twcos, thlien of threes. When tlie groups of twios have been illustrated by the balls, the teacher may write the table of twos on the blackboard, thus: 2 times 2 are 4 3 ” 2 ” 6 4 ” 2” 8 5 ” 2 “10, 6 ” 2

” 12 7 ” 2 “14,etc. On placing the Secoi(nd For before the class for the first time, the teacher should explain the use of the sins x and -. The pupils may be told to read the sign of multiplication the same as the word “times,” and the s?y) of equality the same as “are.” Let the pupils copy and learn the First Form), so as to repeat it, both forward and backward.

Afterward place the Second( For)) on the blackboard, and let the pupils give each answer orally; also copy the table and write the answers. When the table of wvos has been learned in both forms, teach the table of threes in the First Fori, then in the Secozd( Forni), and afterward review’ bothl of them, in combination, in a TYhird Form, somewliat as follows 57 First Fo}rm?. 2x3  6 3x3 9 4x3=12 5 x 3-15 6 x 3:18 7 x 3-=21, etc. 3x2= 6 6 x 2 1 9 x 2:18 4x2= 8 7 x 2= 14 5 x 2:10, etc.

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HO IV TO TEA CGI 8 x 3  5 x 2  7x3- = 6x2  All the tables may be taught on the same pla,n-first in order, then out of order, then by combin)iationI with the tables previously learned. New tables should not be presented before the pupils have learned thoroughly each preceding one through the three.o/brs. Roman _ntmbers.-In the Eighth Grade, the Key to Roman Numbers should be explained to the pupils, and numerous applications of it made to a variety of combinations, viz.: When letters representing equal values stand side by side, a(nd when a letter representing a smaller number stands on the ri.qt-hand side of one representing a larger nlumber, the values of each are to be added, as II tiwo, XX t’weytty, VI six, XV
fifl,een, LX sixty, XXX thirty. When the letter representing a smaller number stands on the left-hand side of one representing a larger numnber, the value of the left-hand letter is to be taken firom the value of the rigyit-hand letter, as, the valuec 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 firom the value of L in XL gives. folty as the number represented by XL, etc. Training the pupils in numerous applications of this Key will save muclh of the time usually spent in nmemorizing the Romin Numbers. 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. 58 Tltir-d Fo) rm1. 4x2= 5 x 3= 9 x — 2 x 3  9 x 3  8 x 22 x 6  3 x 4  4 x 3= 6 x 37x2  3 x 9 

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OBJECI’ LPESSO.NS. OBJECT LESSONS. Form.-Special care should be taken, in teaching various Forms and Solids, to cause the pupils to discover the given shape in other objects than those shown by the teacher from the set of’” Object-Teaching Forms.” For the accomplishment of this purpose frequent reviews should be had, without presenting the forms which represent the shapes that have already been learned, whenl the pupils may be requested to mention several objects of thle given shapes. Lead the pupils to observe that all prismis have oblong sides, and all )pyram))ids triangular sides; that prisms differ in the number of their sides, and in the shape of their ends; that pyramids differ in the number of their sides, and in the shape of their bases. Linies anid A, leS.-In teaching pupils what constitutes parallel lines, lead them to notice the fact that the lines are sid(le-by-si(de; that they are the s(am)te di,stanice aa)r (at atll opl))osite poin)ts; afterward, in a subsequent grade, they can easily be led to observe that both linlies extend inl tlhe same direction; also that they can never meet. In previous grades, the pupils have become familiar with the terms sharp, square, and blunt, as applied to corners; use this knowledge to illustrate the different kinds of angles, and give the terms ac?ute, rilght, 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 onl the blackboard, and the pupils also required to represent them onl their slates. 59

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HIOW TO TEA CII Color.-All tlhe lessons on Color should be illustrated with “Color-Charts,” “Color-Cubes,” “Colored Cards,” pieces of ribbon, silk, worsted, or other colored objects; also witl good water-colors. Care should be taken to make the pupils understand that by mixing two Primary colors, a Secondary color will be produced; also that no Primary color can be formed by mixing two Secondary colors. They should also be taught which 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 ill 1e?v P)riiiairy Object Lessots. Ii;tnman Body.-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 ulses. Anim,tals.-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, runnling, jumping, hopping, flying, swimminllg, etc.; so that they may be able to tell what 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 might be written 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 60

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OBJECT LESSON5. 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 efficient aid in preselnting this subject, by the use of ” PRANG’s Ncatltacl History Series, for Plants.” Objects.-PPupils 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 quaclities 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

AND WRITING. On Slates.-All necessary explanations and illustrations as to the manner of drawing figures, the foimation of small letters and capitals, should be made by the teacher from the blackboard, first to the whole class; afterward, attention may be directed more to the work of individuals of the class, for the purpose of giving special instruction.

61

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I)PA VIJNG AND WI?ITING. Let the teacher of the class select, each day, six slates from those pupils who have made the most coinmenidable improvement in drawing and writing, and place them on her desk for inspection by the class. If properly managed, this plan will prove a good incentive to improvement in neatness ill the dralwing and writing. (,se of Pe)cils. Tie pupils should not be allowed to write with lshort 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 drawilig, to avoid permanent curvature of the spine froiom bending sideways; and serious injury to the eyesight from inclining the head too far forward, and holding it too near the desk. MANAGEMENT. Physical Tr’aining.-The pupils in all the grades should be exercised daily in such a mannler 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 frequently, in simple changes of the position of the body, by requiring the school or class to stand and to sit together three or four times in succession, also to exercise the arms briskly, will do miuch for the physical comnfort of pupils, and even increase the progress in their studies. The necessity of pure air in a schoolroom is a matter too serious to be neglected by any teacher for a single hour. Yet quite too comnmonly, even where the means for securing it have bee]l provided, teachers carelessly neglect ventilatioii. 62

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SEVE1NTH GRADEo (PRlMARY.) Time allowed, about five month1s. LANGUAGE.

Reading.-In a Second Reader; with conversational tonesthe use of Italic letters to be explained. Phonetics.-Sounds of short words in commion use to be given by the pupils-exercises to be had for correcting indistinct enunciation. Deflinitionits.-The meaning of words to be given, chiefly by their use in short sentences. Spelling.-Oral and written-words from the reading lessons; 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 Arithinetic.-Practical questions in Addition, Subtraction, and Yfultiplteation. Also Oiral DrillU for rapid comibinations of numbers.

M]tltiplication Table Continued through 12 times 12. Romnan Numbers.-Reviewed. Tables of Measure.-United States money; time; liquid and dry measures.

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64 GRADED COURSE OF INSTRUGCTION. OBJECT LESSONS. Fornt.-The polygons, arc, radius, and other forms. Size.-Comiparative, and measured.

Color.-Harin()ny of colors. ltunmac LBo(ly.-Organs of the senses.

A1timnals.-Comparison and simple classification by groups, famnilies, etc.

Plants.-Slhapes of roots, leaves, flowers, etc. Plants used for food, etc.

Objects and Qualities.-Continued. Occup)ations.-Trades, tools, productions, commodities, etc. GEOGRAPHY-PREPARATORY STEPS. Place and Dicectioi.-First. Position of objects on a table. - Second. Position of objects in the classroom. Third. . Location and direction of streets and other objects near the sclhool. DRAWING AND WRITING. On Slates.-Words and short sentences to be written from dictation; Capitals to be used. Drawing simple figures. On Paper.-Simiple words of small letters. The pupils to be taught to write their names, witl their ages, and the date.

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LANG UAGE. How TO TEACH SUBJECTS OF TIIE SEVYENTII GRADE. LANGUAGE.

-Reading.-The methods given for teaching Readi)gy in the Eighth Grade should be continued in the Seventh Grade. It is exceedingly important that children be early trained to give attention to the subjectmatter 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 conversations..These may be used for training the pupils to read in easy, speaking tones. Afterwards, other selections 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 thle 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 m)a(xtter and,)ialgr,er of reading. The first extreme destroys the pupils’ interest in this exercise, and prevents them from acquiring the habit of reading to gain information; the second leads to carelessness in mannlier, and the habit of reading without sufficient attention to the subject of the lesson, and to what is related concerning it. 65

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HOW TO TEA CH The use of 1talics should be illustrated from the blackboard 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 k, a has its fourth sound, the first I has its own sound, the second I is silent. BOuIglht, b has its own sound, out represent the fourth sound of a, gh are silent, I has its own sound. Thintk, th are sounded together, i has its second sound, n has the sound of uy, k has its own sound.

Definitiots.-All modes of teaching that will allow pupils to give mere memorized definitions, without the ability to illustrate the meaning of the given words by their use in complete sentences should be avoided.

During the exercises in definitions, the pupils’ faults of language should be corrected. Spelling.-The exercises for teaching spelling in the Seventh Grade may be continued as in the Eighth Grade. 6

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ARI7IMETIC. 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 occurrence ill business, should be given. Exercises for training the pupils to add without counting should be continued in this grade in a manner similar to those described for the Eighth Grade, on pages 52, 53
and 54. Subtraction.-The processes of Subtraction mnay 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. Secoind Stel.-With examples in which it is necessary to take or “to borrow” from the column of a higher denomination. Tlird( Step.-With examples having naughts in the -minuend, making it necessary to take from the third or fourth column on the left. The Secoyed and Third Stel)s may be illustrated first by the use of bundles of sticks; also by the 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 I have only 2 cents, I must take one of the dimes 67

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HOW 2‘0 T’EA CI 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 will remain. I wish to take away 8 dimes, but find that I have only 3 dimes remaining; 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 uiits, (ens, and hundreds. The process of representing these illustrations may be shown on the blackboard, thus: 10 10 10 10 4 3 10 4 3 10 $0 4( 2c Oh. 4t. 2 units 2 8d 5c 2 8 5 $2 5d 7c 2 5 7 Afterward the process of the Second anld Third Steps may be further represented on the blackboard, with common examples in subtraction, by cancelling the figures fromt whichi one has been taken, and writing the remainder above it thus: 9 9 10 3 10 5 10

5 10 1.10 3t:0 10 4 10 4 2 0 3 1 0 3 2 0 2 A 0 0 0 1 4 4 5 1 5 4 1 5 1 3 5

4 5 3 2 8 1 8 9 0 5 1 0 4 5 9 7 After this process, commonly called “borrowing” (buit 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 68

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AP-IIMYIfVEI’IC. teacher, the pupils should be required to copy on their slates the same examples, also the process of taking fromt a figure representing a number of a higher denomination, by cancelling; then similar examples shoiuld be given them to write out in full, that they may become familiar with the process of takintg f it, by cancelling. IFormis of i/ll/utstrctioI for explaining a subject should be continued no longer than may be necessary to enable the pupils to understand the subject. The process of cancelling in illustrating subtraction should be used for a few days only. When it is first dropped, another plan mnay 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 onie less in the subtraction, thus: 240050 135453 104597 In subtracting these examples, the pupil might say: 3 lfrom 10 leave 7; 5 from 14 leave 9; 4 from 9 leave 5; 5 froln 9 leave 4; 3 from 3 leave 0; 1 from 2 leaves 1remainder 104,597.

This process is shorter and less liable to mistakes in practice than the common way of borrowing one” fIlom 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 ‘ CompounLd Numbers.”

ltiltiplication.-Instruction in regard to the processes of gmult~,i)licatio) may be presented in four steps, as follows: 69 4263 1445

2818 16320 15415 900

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; HOW TO TEA CII Fir-st Ste).-Give examples iii which no single prods uct will exceed nine, as 243 3,142 3,231 231,232 2 2 3 3 486 6,284!,693

693,696 Seconid Ste).-Give examples iii which it will be necessary “to carry ” to the next column, including multipliers of a single figure only, from 2 to 5, as: 345 4,583 2,435 32,563 2 3 4 5 690 13,749 9,740 162,815

Tlti-(d AStep).-Give examples, including naughlts in the multiplica(nd, a(nd use as multipliers 6, 7, 8 and 9. 2,034 3,102 14,020 10,050 6 7 8 9

12,204 21,714 112,160 90,450 Fourti Step.-Give examples with multiplicands, as in the third step, and use for multipliers 10, 11 and 12. Teach the pupils where to write the first fiture in each partial product. 24,065 3,108 40,207 40,207 12 80414 40207 482,484 10 240,650

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. 70 3,108 11 3108 3108 34,188

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ARITIIIMETIC. -Lentat Aritthmetic.-The forms of the answers, in this grade, may very properly employ more language than in the preceding grade.

The following examples and solutions of them will represent suitable forms: Exam)les:-A man paid $12 for a barrel of flour, $8 for a ton of coal, and $5 for a load of wood; how much did he pay for all? Anis. He paid for all the sum of $12, $8, and $5, which is $25. A farmer paid $40
for a cow, and sold her for $36; how much did he lose? Ans. He lost the difference between $36 and $40, 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. Or(al 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+4+2+4 + 5, are how many? In giving these examples for addition, 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 plus, 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 performed the addition correctly. JIlutiplication, Tctbles.-When all of these tables, through 12 times 12 have been taught by the 71

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HOW TO IEACH Ilh tee formns as described in the Eighth Grade, they may be reviewed from the blackboard ill 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. 5x 6 are 30; 6x5 are 30; 4x 8 are 32; 8 x 4 are 32. 9x5 “45; 5x9

“45; 6x8 ” 8x6 ” 7x6 “42; 6x7’” 42; 5x8” 8x5 ” 4x9 ” 9x4 ” 7x9 ” 9x7 ” Iln writing these tables on the blackboard for this review, the several products mnay 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. -Romnafn Nuiibe.s.  Review and give further applications of the key, as iindicated in the directions relative to this subject for the Eighth Grade. - Tables of feasure.-The tables of weights and measures should be introduced first, by talking with the pupils about their experience in the uLse of them, and by familiar illustrations given by this means. Thus the table of United States money may be illustrated 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 uhe hours marked on the clock, and 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 copy the items on slates, both 72

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ARITHMETIC. in the order of the table and in a different order. Continue the repetition and copying until the table is thoroughly learned. Each of the tab]les may be presented and learned in a similar manner. TABLES FOR

THE SEVENTH GRADE. UNITED STATES MONEY. 100 cents make one dollar. 50 ” “
onehalf dollar. 25 ” ” one quarter of a dollar. 75 cents makle three quarters of a dollar. 10 mills make 1 cent. 10 cents ” 1 dime. 10 dimes “

1 dollar. 10 dollars ” 1 eagle. LIQUID MEASURE. 4 gills make 1 pint. 2
pints ” 1 quart. 4 quartq ” 1 gallon. 31~ galls. ” 1 barrel. 2 pints make 1 quart. 2 quarts ” 1 small measure. 8quarts ” 1 peck. 4 pecks ” I bushel.

TIME MEASURE. 60 seconds make 1 minute. 60 minutes ” 1 hour. 24 hours ” 1
day. 7 days ” 1 week. 30 or 31 days” 1 month. 12 months ” I year. 52 weeks ” 1 year 365 days ” 1 year. 100 years ” 1 century Are the Summrer months.

Days of the Week. March,) April, Ar May, June, ) July, August, September, October, November, December, January, February, Sunday, Monday, Tuesday, N

Wednesday, Thursday, Friday, Saturday. 73 DITY MEASURF,. Sea-gons of ae, Year. Spring, Summer, Autumn, or Fall, Winter. Are the Autumn, or Fall months.

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tl OTW TO TEA CH Review.-IIn reviewing these tables, the teacher may question the pupils somewhat as follows: How many hours make a day? How many days make a year? How many days make a week? How many weeks make a year? How many minutes mnake an hour? How many months make a year? What is the shortest measure of time? What does it take to make the longest measure of time? How many quarts make a gallon? How many quarts in three gallons? How many quarts make a peck? How many pints in two 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 lessons 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 each succeeding grade, so as to avoid the possibility of memorizing 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. 74

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OBJEC’T LESSONS. By requiring the pupils to describe the shape of objects placed before the class, the teacher will be enabled to test their knowledge offormi. Size.-This subject may be illustrated by various objects, as strings of different sizes and lengths, slips of paper of different lengths and widths, and small pieces of wood. The pupils will 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. Drawing 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 green with blue and gyreeni; blue and oraune with yellow and oratnye; yellow and ])i(rple with blte and 1)2ur)le, or red and ptri)le. 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.

-tuman Body.-In teaching children the names and uses of the organs of sense, and their parts, special effort should be made to lead themn to understand the subject by means of observations made with their ovwn organs of sense. The actual seeing, hearing, feeling, tasting, and smelling of objects teach children facts 75

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110 W TO TEA CII which it is impossible to convey to their minds by means of the memorizing of language, however thorough and precise. Aninmals.-The lessons on this subject should lead the children to notice the most distinguishing poiuts ill the structure of ianimals, 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 cushion-like feet of the cat enable it to walk noiselessly about in search of its prey; how 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 substances. The chief aim of these lessons being to train the pupils in habits of observing nature, so that they may be enabled to gain therefrom the most useful knowledge, the exercises should be conducted il such a manner as to lead them to notice accurately the structure and habits of the various animals thaft come within itheir own observation. The facts thus learned should be, by the aid of the teacher, properly classified, as a foundation for subsequent study of fthe same subject. Prangq’s Natural Hlistory Series, with the ” Manual” vwhich accompanies it, will be found a valuable aid in giving instruction on Anicimalncs and Pl(tits. Plants. The lessons on plants, in this grade, mlay appropriately lead the pupils to learn the most common sha1)es of roots, as turnlip-shlaped, braniching, fibrous, 76

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OBJECT LESSONS. conical, tuberous, etc.; also the sha(es of leaves, as needle-shaped, arrow-shaped, egg-shaped, heart-shaped, hand-shaped, etc.; also the common shapes of floives, as fulnnel-shaped, bell-shaped, pinlk-shaped, butterflyshaped, 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, and lead them to observe their mode of growth, form, uses, etc. Objects and Qualities.-Two distinct classes of exercises may be given iunder this heading. One consists in training the pupils to distinguish given qualities, 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 theso classes of exercises, in their proper order. Observation and Conparison. - Habits of observing various objects, and noticing their several shapes, colors, qualities and miatcterials of which they are made, are exceedingly useful as a means of gaining knowledge; yet habits of conf)criny two or more objects, and observing what qualities, shapes, colors and materials they possess in common, constitutes an advanced stage of development which not only adds additionial power of gaining knowvledge, 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 forags, colors, 77

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HOW TO TEACII and most obvious qualities. It is therefore appropriate that they now should be trained to discover chlici 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 accomplish 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, quality, or material without aid. The teacher should aim to train the pupils to discover the principal characteristics 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:  Fiirst. Write on the blackboard the words, Mateerials, S/hapes, Colors, QuCalities, leaving room to write other words under each. Then place some object before the pupils, as a common slate, and request 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 blackboard under its appropriate heading. When the lesson is finished, the blackboard will contain something like the following: Materials. Stalapes. oblong, black. right angles. opaqu e, brittle, combustible. 78 C0107-8. Q?((Zlities. slate, woold, iron.

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OBJECT LESSONS. Occupations. Tlle exercises on this topic should cause the children to ascertain the names of tools used in different occupations, and what 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 blackboard, and the pupils copying them subsequently on their slates. These exercises will furnish an excellent opportunity for practice in observation, and in describing 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. Carpenter. { Saw, Plane, Chisel, Auger, Awl, Hammer, Mallet, Rule, Square. Shoemaker. Last, Knife, Awl, Pincers, Hammer. Painter. Pots, Brushes, Knife, Ladder. CABINET-MAKER. Tools Used. Saws, Planies, Chisels, Bits, Hand-screws, Squares, Scrapers, Mallet. Black-walnut, Mahogany, White Oak, Cherry, Pine, Glue, Varnish, etc. Articles Made. Tables, Stands, Bureaus, Sofas, Bedsteads, Desks, Book-cases, Sideboards. 79

Materials.

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tO IV TO TE,A CII GEOGRAPHY  PREPARATORY STEPS. Place an(d Di)irectiona.

The exercises in this subject must be objective ill their character; and thev should be conducted with a view to prepare the pupils f or understanding the elementary steps of Geography. The manner of giving the lessons in steps will prove most useful to the pupils. First Step.-Train the pupils to observe and describe 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. Theu 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.

Seconzd Ste. Train the pupils to notice and describe the I)ositions of the parts of the classroom, and of the principal articles in it, as: door, windows, blackboard, seats, table, chair, closet, etc. The teacher should draw the outlines of the classroom, 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 drawing it. Subsequently the pupils should copy the same on their slates.

Tiird Stel).-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. The terms of direction, as east, west, north, south, may be introduced in this step, and the 80

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DRAW.ING AND TVIiITING. Points of Co)2z)ass taug7t. Represent the locations of streets, buildings near the school, etc., on the blackboard, and let the pupils copy them, as before. DRAWING AND WRITING. Ont 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 trainimg should be made a prominent object. The blackboard 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 positions 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 ele))e)ils of letters; let them learn to write simple words as soon as practicable. It is not necessary that the pupils should write all thie 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 oe 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 iu writ 81

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IIO WV TO TEA CII. ing should be pointed out and illustrated on the blackboard, and such directions givein as will enable the pupils to correct those faults. Before leaving this grade, the pupils ought to be able to write simiple words neatly with the penl; and to write their ownl names, and their age; also the day of the month, and the year, in a proper form for dating a letter. They should also be able to write familiar words, and short sentences from dictation, readily and plainly. 82

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SIXTITH GRADE. (HIGIIEST PIMARY.) 1ime allowed, about five qnonths.

LANGUAGE. Reading. -Second Reader completed, or an easy Thiid lReader commenced. Phoitetics.-Words to be analyzed by sounds; names of the sounds to be stated; faults of enunciation to be corrected. Deflnitions.-The meaning of words to be given orally, and in writing. Spelling.-Words firom the reading lessons, also familiar words, and short sentences from dictation, both orally, and by writing on slates. ARITHMETIC. Addition afnd Subtraction reviewed. Multiplication 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 Arithmetic.-Practical examples in each of the four simple rules. Division, Table.-Taught in connection with a review of the Multiplication Table.

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IIO W TO TEACII Tables of IFeight an(l Measure.-The tables of Common or Avoirdupois Weighlt, of Long, Cloth, and Surface measure, also a miscellaneous table to be taught, and those of the Seventh Grade to be reviewed. OBJECT LESSONS. Forjn.- The shapl)es of obljects to )be compared and described, and their resemblances and differences stated. Hutman Body.-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 samne, and of differcnt falllilies of flowers. - Objects.-Various objects to be examined and their shape, color, most obvious qualities, and properties to be stated. The distinctions between miners vegetable, and animal substances to be taught.

Occupations.-Exercises to give the pupils lhabl)its of observing and describing common productions, commodities, etc.; also to give them ideas of the exchange and sale of these. GEOGRAPHY. -‘rst Stelp.-The location and direction firom the school of the most prominent objects near the school, and of the places in its vicinity. Second Step.-Definitions relating to the forms of land and water, fiom cards, blackboard, and outline maps. 84

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DRAWING ANLD TJF/lI1’ING. T/ird Step.-Teach the namne of the city or town, the county, and state in which the pupils live, and also of the places in the vicinity, showing their location on an outline map. Fourth Step.-Teach the shape of the Earth by means of a (globe and hemisphere maps. Fifthl 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 countries. DRAWING AND WRITING. O,n Slates.-Writing to be continued as in the Seventh Grade. 0,) Paper.-Writing in books, fiom copies, with necessary instructions in regard to the position of the body, hand, and paper. 85 I

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HtOW TO TEAUH HIow TO TEACH S UBJECTS OF TIEE SIXTHI GRADE. LANGUAGE.

Readinq.-Before a new lesson is read, the iunfamiliar 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 ill 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 exercise will train pupils to habits of attentive listening, and to a proper regard to the subjectmatter. In efforts to correct the faults of a class in readiyg, 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. Afterward 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, nclih more effectively than by trying to point out half a dozen different kinds of faults at once. 86

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LANG UAGE. Phonetics.-The phonic analysis of words should train the pupils readily to distinguish and make all the sounds in given words, also to determine which letters are silent. It should also lead the pupils to such habits of distinctness in articulation as will remove the fault of neglecting to sound the final con sonants, as d in and, send; r in fay, ca)r; i)ly in singing, eating, etc.; also the errors of sounding improperly both consonants and vowels in the pronunciation of common wor(is. No other means is so efficient for training the organs 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 successfully cultivated. and the mleans furnished to the pupils for determining what are the correct sounds of the language, how to produce them, and the ability to cultivate their own organs of speech and tones of voice. - - 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 similar character. It is desirable that an oral exercise of’ this kind, given as a lesson on one day, should be followed on the next day with the same words to be defined in a written exercise, thus training the pupils to write as well 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 pupil 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 87

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1HOW TO TIEA C~I of reciting formal, memorized definitions would be avoided by using thus several modes of giving the meaning of the same word, and the pupils would learn to define, and use words intelligently.

Spelling.-AMore attention should be given to written 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 pupils may be requested 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 that may be purchased 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 Subtraction.-It is intended that the pr)ocesses 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 accuracy. Now, special pains should be taken to teach the muses of Addition and Subtraction by means of practical examples. A brief review of these rules should be had at least once each week, during the entire term of the Sixth Grade. Ffultiplication.-Instruction may be arranged and presented in three steps, as follows: 88

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ARITtIMET’IC. First Step.-Give examples with multipliers of two figures only-12 to 99. Second Step.-Give examples with multipliers of three figures-100 to 999-including some with naughts in the multiplicand. Third Stel).-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 difficulties 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-un(der thefigture used as a nulij)lier. Review each step with practical examples, embracing transactions that come within the observation of the pupils.

1)-ivision.-This rule can be taught most thoroughly by commencing the instruction with the “Long Division” form, and using a small number for a divisor. Four Step)s will indicate the methods and order for teaching Diivision,. First Step.-Give examples in which each figure of the dividend will contain the divisor without a remainder, thus: 2) 486 (243 3) 963

(321 9 06 8 06 6 03 3 0 8) 4 08 6 0

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0 T OW TO TEACH Second Step. -Give examples with the divisor less than ten, in which remainders will occur during the partial divisions, thus: 8)9856(1232 8 18 16 25 24 16 16 0 Third Step.-Give examples with divisors from 10 to 15, then teachi the ” Short Division) ” form; and subsequently require the pupils to use the Short form for all examples where the divisor does not exceed 12. 10)2540(254 11)3564 (324 15) 345 (23 20 33 30

54 26 45 50 22 45 40 44 0 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 Loniy and the Shtort forms, taking care to arrange the two modes so that the difference in their lengths shall readily illustrate why one formn is called “Long Division,” and the other onie “Short Division.” Fourth7 Step.-Give examples with divisors embracing numbers from 15 to 50. Arrange these examples so 90 0 0

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ARITI[METI’O.0 that different quotients shall contain naughts in various positions. Each step should be amply illustrated on the blackboard, by the teacher, then a sufficient number of examples given to furnish the practice necessary to enable the pupils to understand it, before proceeding to the succeeding step. Teaclhers should aim first to cause their pupils to understand the processes of the several rules, then to ease 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. IAENTAL

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 will 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 between 8 cents and 18 cents, which is 10 cents. Division. How many tops at 3 cents each can be bought for 12
cents? Anis.-As many tops as 3 cents, the price of one top, is contained times in 12 cents, which is four times; therefore four tops can be bought.

If 2 apples cost 4 cents, what will one apple cost? Ans.-If 2 apples cost 4 cents, one apple will cost onehalf of four cents, which is two cents. 91

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tIO W TO TEAC1 Division Tables.-The Multiplication Table may be so reviewed as to enable the pupil to learn the Divisionl Table easily. The following form will illustrate methods for accomplishing this: 4 x 7 are 28; 4 in 28 seven times. 7 x 4 “28; 7 in 28 four ” 6 x 7 ” 42; 6in42seven ” 7 x 6 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 322? How many sevens in 56? How many nienes in 45? IHow many twelves in 108? How many eigy7its in 96? How many fives in 60? Hlow many sixes in 54? etc. - Tables of Weight anid Measure.-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 thoroughly during this grade. TABLES FOR THE

SIXTH GRADE. Co.ImoN, OR AVOIRDUPOIS WEIGIIT. 16 ounces make 1 pound. 8 “

” 1 half pound. 4 ” I 1 quarterof apotiund. 100 pounds ” 1 hundred weight.

20 hundred weight make 1 ton. 2000 pounds make 1 ton. LONG MEASURE. 12
inches make 1 foot. 3 feet’ 1 yard. ~ 161 feet “1 1 rod. 51 yards ” 1 rod.

40 rods ” 1 furlong. 8 furlongs ” 1 mile. 320 rods ” 1 mile. 3 miles ” 1
league. 92

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ARIINJlI[EIU’IC. SITSURFACE MEASURE. 144 square inchces make I square foot. 9 ” feet ” 1 ” yard. 30i ” yards ” 1 ” rod. 160 ” rods ” I acre. 640
acres ” 1 square mile. CLOTII MEASURE. 3 feet make 1 yard. 36 inches ” l “

18.. 11 i” 9… 1~” 41 11 11 i 1; 4quarters” 1 ” MISCELLANEOUS TABLE. 48
pounds make 1 bushel of l)arley, [or buckwheat. 58 ” ” 1 bushel of corn.

60 ” ” 1’ ” wheat. 196 ” ” 1 barrel of flour. 200 ” “. 1 ” ” pork, [beef, or fish. 250 ” ” 1 ” of salt. lRevie. A-After these tables have been thoroughly learned in order, the teacher may conduct brief reviews of those of both the Sevelnth and Sixth Grades, by questions somewhat like the following: HIow manay inches in three-quarters of a yard? JIow many yards in one rod? How many rods in a mnile? Hown many squareinjches 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?

93 12 things make 1 dozen. 144 ” “. 1 gross. 12 dozen ” 1 ” 12 gross ” 1
great gross. ‘20 things ” 1 score. 24 sheets ” 1 quire of paper. 20 quires ” 1 ream. 32 pounds ” 1 bushel of oats.

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HOW l’O TEA CHII 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 exclusively 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, will 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 prominently 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 teachers to regard, as of much importance, the manner of givinzy the lesson. Form.-The character of the instruction in this subject, especially so far as it pertains to learning to recognize and describe the valious forms 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 provided for this purpose, the time given to this topic should be chiefly devoted to comparing and describing other objects by their shape, stating wherein those compared resemble each other, and wherein they differ. 94

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OBJECT LESSON,S. I/uman -Body.-TThe lessons in this grade should be conducted so as to review the fiacts learned in previous grades, and also so as to extend the pupils’ knowledge of the laws of health, especially so far as these pertain to the condition of the skin, habits of cleanliness, and the mainner of eating. Aniinals.-The manner of conducting the lessons on this topic for the Sixth Grade classes may be nearly the same as that for the Seventh Grade; but the pupils in this grade should be led to consider a greater number of animals than those in the previous one, and to observe more carefully the peculiarities of structure, etc., with a view to extending their knowledge of classification. To aid the pupils in making groups of animals, by simple classification, let the teacher write on the blackboard the following and similar names for groups: Swvimmingy Birds, Wadin) Birds, Climbing Birds, Kcratch7iny Birds, F1esh-eating B
irds, Perching Birds. Then request the Ipupils to give the names of animals to be written under each heading. These lessons relative to animals should lead the chlildren to make comnparisons as to form, structure, habits, size, etc., and to learn in what countries and localities the various birds and quadrupeds may be found. PRANG’s Natural Htistory Series will be found adapted to giving this instruction. 95

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10OW TO TEA CI Planits. 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 conmparison of pinks, lilies, fruit-blossoms, etc., with a view to noticing resemblances 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, and copied by the pupils on their slates, as a spelling execise. The names of fruits and glasses used for food, etc., may be written in groups. Like the lessons on animals, these exercises should be so conducted as to lead the pupils to form habits of carefully studying nature, as a means of pleasure and as a source of knowvledge; 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. GRAY-Hov Plcatnts Growv; and How Plants Behave. Objects.-In the Sixth Grade the lessons on objects should include their descriptions as to forml, color, and most obvious quaities. In this connection, it is desirable 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, what qnality 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? What qualities give value to glass?

What to steel? to iron? Why will not lead make good springs, or knives?

9(;

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OBJECI’ LESSONS. 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 tlree steps. 1irst Stel).-P-Request the pupils to observe slate-pencils, 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 plaints do. When the most obvious differences between these two classes of substances have been perceived by the pupils, give the term inzeral as the name for one class, and Veyetable as the name for the other. - Secoizd Step.-The teacher may next call attention to thle three great classes of substances-mineral, vegetable, and animal-anld lead the pupils to observe, and to tell what animals and vegetables can do (as take food, breathe, grow, die), which minerals cannot do. T1hird Step.-Let the pupils be led to notice what animals generally can do which vegetables generally cannot do (as move from place to place by their own power); also to observe the differences between the food of plants and that of animals; as that plants feed on miiierals, or simple substances from the earth and air, while 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 aniimal substances; that wood, 5 97

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HOW TO TEACH bark, gum, sugar, that oince formed a part of a vegctable, are called veygetable substances. Occupations.-The exercises on this topic should not only lead the pupils to observe and describe common 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 Poinlts of ComIi)ass, ill trainung the pupils, until they are able to name any direction, 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 buildings, 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 represenit on the blackboard the situation of the school-house, and the location and directionl 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 the 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, 9)R

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GEOGRAPHY. lake, bay, river, etc.; then show how the same or a similar oblject 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 surrounded by wvater 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 w-yL to teach all the definitions. GCeograph1ical Cardls, containing pictorial and map representations, will be found of great assistance in illustrating these definitions. During this step the instruction has for its chief object training children to recogize the various forms of land and water, 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 Step.-Commence the instruction relative to the names and location of particular places 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 knowledge of those pupils whose personal visitations have made them acquainted with the locations of the greatest number of places, as to extend the knowledge of the other pupils.: co.:**: 6 o s 99

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HO V TO TEAC.H 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 taught, and their location shown on a map. Fourth Step.-In teaching the shape of the earthi 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 shape only; also that each differs from the other in size. By this means prepare them for lunderstanding that the globe represents the earth only in shape. Follow this with some simple illustrations as to the comnparative 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 represenltations upon hemisphere maps. F?thf Step.-Talk with the pupils about people of different races and nations, and point out on the globe, also on outline maps, the locatihon 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 t-h3 Nhite bear; Africa as the home of the lion, zebra, ~ *.. 100

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GEOGRAPH}Y. ostrich and camel; Australia as the home of the kangaroo; Spailn as the country where cork and raisins are 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 bananas, etc. By means similar to that herein described the pupils may be made to realize that Geoyraphy 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 siap)e of’ thle Earth, of the different portions of it as the ihomes of races of ne)t, 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 textbooks on Geography, to be examined by the children ufter the lesson has been given orally by the teacher; but in no case should the pu})ils in this grade be required to study a lesson in the book before the subject of it has been p)resented 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 presented, and the general character of the facts taught should conform to the directions given here, without regard to the order of presentation in the textbooks in common use. After completing the course of objective instruction in Geography, as indicated in the preceding steps, the 101

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I -IOW IO TEA CII. pupils will be prepared to commence the study of this subject ill an intelligent manner from good textbooks. 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 allowed to write, they should be t(uqght and trained how to write by the teacher. Children need something besides copy-books, to become good writers. GENERAL SUGGESTIONS. Reviews.-Such a review of the previous lesson, as an introduction to, and in connection with, each new lesson 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 these occasions the leading facts learned in previous grades, upon that subject, should be included. These remarks are intended especially for the first five grades of this course of instruction. Progress of Classes.-Whenever it is found that a class has advanced further in one or two subjects of its grade than it has in others, 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. 102

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GENERAL SbTUGGESTIONS. No study of a succeeding grade should be introduced into a class of a lower grade before that class has completed 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 they 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 coInductinrg class exercises, are necessary to furnish the opportunities for needed rest during school hours, besides the usual recesses of school.

- Vocal 1fusic.-Instruction in vocal music ought to be given to the pupils of all the grades in every school. Principles of Education Applied.-Teachers who learn to apply principles of Education in the order of presenting knowledge, and in their methods of teaching, will rarely fail of becoming successful in their work. They will early acquire 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. Principle.-Commence 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 kindred unknown which forms the subject of the lesson. 103

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HOW TO I!EACH. To ascertain the known, or the related unknown, the teacher must consider what previous opportunities the children have had for obtaining knowledge of the subject, and then by questions determine the true attainments of the pupils relative to the matter for the proposed lesson. The next point for the teacher to decide is, how can that which the pupils already know, concerning the subject of the lesson, be used in the best manner to aid them in learning that which they do not yet knowof it. For illustration, let this principle be applied to teaching Reading 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 sulfficientprogress 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 teaching that unknown which forms the main object of the lesson? [See pages 39, 40. After this mainner the subjects of instruction should be examined by the teacher, in each of the grades; and, as a mlost important part of the process of teaching, 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. 104

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FIFTIH G RA D E. (LOWEST GRAMMAR SCHOOL.) Tine allowed, about five mont7ts. OUTLINE COURSE. LANGUAGE. Readinff.-Of the grade of a Third Reader (first half), with a review of p)unctuation, Roman numbers, and elementary sounds; and with exercises on the subject-mnatter of tile lessonls. Spelting.-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. Defltitions.-From the realding lessons, to teaclh the meianing of the words, with illustrations l)y forlming seuteinces; in nc case to be committed to memovy and mechanically recited. Grammar.-Correction of Langiiage. ARITHMETIC. Mental Arithmetic.-As far as in written aritlhmetic, to include exercises in the analysis of operations and examples, and in rapid calculation without analysis. IVrittecn Arithmetic.-Through the simple rules and Federal money, with practical examples. Tables of weights, measures, etc., completed anld reviewed, with practical illustrations and simple applications. 5*

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HOW TO T’EACII GEOGRAPHY. Eir.st Stage.-Simplest elementary and systelmatic g(ncral out. line of the geographly of the world as a wlhole witlh (efinlitions and illustrations by means of the globe, of the form, loni.gnitude, iotions of the earth, zones, latitude, longitude, etc.

Second Sttge. Outlines of North America and the West Indies, including local and descriptive geography. ELEMENTARY SCIENCE. i,oocd, Clothing, andl Btil(ling lIaterial.s Zoolo()fy,f -By or7(l instriction, to develop the powers of observation and reflection, and to cultivate facility in oral description. DRAWING AND WRITING. 0if,Slates.-Continued. On Paper.-Writing in books, with particular attention to position, holding pen, etc., etc., as in Sixth Grade. 1. Words containing easy coml)binations; as man, name, noon, soon, etc. 2. Words containing long and short letters; as heart, long, youth, etc. 3. Words with easy capitals; as Ape, Cold, Ink, Lamb, Time, Useful, Vanquish, etc. 106

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LANG UA GE. How TO TEACH SUBJECTS OF THIIE FIFTTI GRtADE. LANGUAVGE.

Readiitg.-In teaching reading in this grade and in the two or three others immediately succeeding, the chief difficulties to be overcome mnay be classed under the following heads: First.-Hesitaction over, or 1tze wiscaZli,y of famniliar words. This arises from want of practice, and where strongly marked should claim the chief attention. Second.

lfisp)rotnuiciatio) of’ recoynized wor-ds, as stiU, for stone, winder for window, thedter for theater, etc. Thircd.-New word-s of which the meaning and pronunciation are not yet known to the pupil. New and difficult words should be carefully pronounced, and, if necessary, explained, before the piece or paragraph is read by the pupils. Foutrlh.-Faunlty 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 omiss;on 107

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HOTw TO TEACH or slurring of syllables, should receive careful and constanit attention. Lists of common words liable to be mispronounced, such as length and strenyth, should be made by the teacher, and the class exercised upon them. The elementary sounds and their more difficult combinations in words and phrases requiring great mobility of the vocal organs, and especially fintal conlsonzants, should receive 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 importance of mobility of the muscles of the lips, let the teacher read a paragraph with the lips almost motionless, and then read it again, giving as much play as possible to these muscles. The great contrast in distinctness of articulation will be at once manifest. Among 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 sentence(s twice or thrice repeated, and withl the greatest rapidity consistent with perfect distinctness. Particular attention should be given to pupils of foreign birth or parentage, so as to insure their masterv of the principal difficulties of English pronhunciation. Phonetic drills are very useful for this purpose. fiftM.. iafrshi 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 108

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LANG UAGE. 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.  Vgzyue or e)rroneous coflcel)tion of the subjectmatter 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 lesson will permit it, the pupils should be accustomed to state, in their own language, the important facts, principles, and moral lessons therein taught. Words, phrases, or allusions should be briefly explained, whenever necessary for the proper understanding of the piece read.

Seventh.- Want of rhetorical training. Should a large number of consecutive lessons in the Reader be of the same general character, a part should be omitted, so as to give variety of style and subject. No selection, other than the best English poetry, should be so long dwelt upon and so frequently repeated as to render the exercise a mere recitation. As a test of the general condition of the reading, classes should occasionally be called upon to read unfamiliar pieces of the same grade. Where thel)rimary 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 reference. 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 iunavoid 109

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ItO W TO TEA CII ably endeavor to pronounce correctly, enunciate distinctly, and emphasize naturally. Additionial effect will be given to the exercise by requiring the pupils to reproduce, in their owln language, the substance of what is read to them. Where a simple systern of diacritical marks is used in the Reading Book, the pupils should be taught to understand alnd apply them. An occasional brief review of the Rom,an numbers, and of the names and signification of the marks used in punctuation, should be required. The successfui application of these suggestions involves 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. TIlE exercises in spelling should be bothl oral and written, but principally written. The selections of words from the reading lessons should be so made that the class will not l)e prevented from advancing from onie reading lessomi 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 spelling 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. 110

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SPELLING. 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 “d’blee” for “d ouble-e,”

“d’blowv ” for “1 double-o,” etc. “Misceilaneous 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 commoijest conversational use. They may be readily obtained by calling upon the class to suggest them. The mnodifications of the primitives required in order to form themn should be taught. The written exercises should be as neat as possible, eare being taken to train pupils to habits of orderly arrangement of their work. Whlen sentences are given, particular attention should be paid to the ordinary troublesome monosyllables, to the proper use of capitals, the sign of the possessive case, the period, the interrogationl mark, and the use of the hyphenl iii a word divided at the end of a line. DEFINITIONS.

In selecting words for definition, two leading pirposes 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 ownl vocabulary. Very simple words, such asfatller, water, k-)fe, knee, book, cli,ilcl, etc., the v)ea)ii~ of which every child already understands, should not, in the lower grades at least, 111

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o 110W TO TEA CII be assigned for definition. Properly to define such words requires a nice discrimination in the use of laiinguage atnd a minuteness of analysis beyond the power of a young child. Teachers are apt to go astr ay in tlis direction. It is principally on this account that the limitation, “to teach the mealning of the words,” has been introduced in prescribing this part of the grade. The written exercises will necessarily contain many such words, and thus the child will learn to spell them. WThere 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 pronunlciation, a separate construction should be required for each in the written exercises. Defining one part of speech by giving another parti 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 iand 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 mnere committing of dictionary definitions to memory, or the substitution 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 112

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ARITII[METIC,. words, these being most clearly comprehended when the words are put into sentences or phrases. At this stage of the pupil’s advancement, a full exercise on a given word should comprise the fo]llowing: 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 defi)titio]zs 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 forl the exercises in conraposition 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 invariably insisted upon. ARITHMETIC. Mental Arithmetic.-

The mental arithmetic shouill both precede and accompany the written aritlmetic, 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 written arithmetic, and the results obtained be written upon the slates, promptly, and at a given signal. The analysis can then be separately required of as many pupils as may seem expedient. 113

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l HOTV TO T’EACIH Illtstratio).-Oine method of conductiing such.tn exercise is subjoined. Teachers fertile in expedients will devise others equally good, and involving the following important elements: 1. The exercise to be simnultan,eous; 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 hluids. 2. Teacher gives question with distinctness. 3. Pupils work silently, remaining in position until the answer is found, when each silently raises the riglht hand, or stands. 4.

When sufficient time has been given, teacher says “Ready Write,” wvith a pause between the wvords. At the last word the answer is inst(antly written in large fioe;ies, 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 usinig four light taps of the peicil, meaning, “JReady,” “Write,” “As you were,” “Show.” 5. Teacher calls upon some one to read the answer, usually upon one whose res.ults 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. 6. 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 character consistent with clearness, and all nunnecessary repe ]14

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ARIIIIME[EIC. titions of formula be carefully 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 atrithmnetical combinations necessary to the solution. Besides simple examples in the four fundamental rules and Federal money, very simple operations involving practical applications of the selected tables of money, weight, and measure, should constitute a portion of the exercises in mental arithmetic. In the explanation or analysis of examples in mental as well as written arithmetic, the pupils should generally be called upon, before solving, to state the question. AIental exercises in arithmetic should be conducted in a spirited manner. They should always have the character of extemporized exercises, and ill no case form a part of the home-work of the pupil.

Writte, Ai,ithmetic.-The slates should be kept in the best condition as to cleanness; the figures should be distinctly and neatly made, and written in lines parallel to the upper edge of the slate. A reasonable allowanice should be made for imperfections in the forms of figures in those exercises where haste is required; yet every effort should be made to fix in the pupils habits of care, neatness, and system in all that pertains to the written exercises. Exercises in adding columns of figures should be given with such frequency as may be found necessary to produce and retain accuracy and rapidity. They should be in both forms-the silent and the oral. Every form of counlting, whether by fingers, dots, marks, or other devices, should be strictly prohibited, and the class should be frequently tested for this special purpose. 115

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H OW TO I’EA CA, The ptipil should be allowed to name only the successive results arising from the addition of the several successive figures, avoiding all that oral or mental repetition of the tables which is known as the “spelling process,” and all other unnecessary formulae.

Illtustration. 789 457 632 17S Correct ilfethod.-8, 10, 17, 26; 9, 12, 17, 25, etc., etc. lZcorrect Methlod.-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 d(lifficult to change it. I.t acts as a clog to the menetal activity of the pupil, who finds hinmself unable to think out the result ill any other way. It is as if he should spell aloud every word as he reads. The above remark, in regard to the oral or mental repetitionof 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 the 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 way as to cultivate the intelligence of the pupil. Examples requiring a very large number of figures 116

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ARITHM,ETIC. for their solution should be avoided, except as far as they may be necessary in order to give practical expert1ess. Examples should be given to test +the pupils’ accuracy in writing numbers requiring O’s, and their knowled(lge of the proper methods where the multiplier or divisor contains O’s. Exercises should be given to insure facility in reading and writing Federai moniey, nlid in reducing, by i-ispectio)i and withliout aitlysis, dollars, or dollars and cents, to cents or to mills, etc., etc., and conversely. This reduction beconmes important i certain cases in division of Federal money. (See Analysis B.) Analog,ous exercises in Federal money should be substituted for those in the simple rules referred to in the preceding sections, -Is soon is may be found expedient. In all practical examples, instead of tellinig pupils to add, subtract, multiply, or divide, give the question in suchl a manner as to oblige them to exercise their own judgment as to the method and principle to be employedl. No detailed analysis is necessary in addition or subtraction.

Give short examples of bills of purchase or sale involviiig 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 flirtliler till he has thoroughly mastered them. Write 30,003,050-700,500,00i 117

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118 HOW’TO TEA CH Multiply 30850 by 307; by 4070; by 2009. Divide 732427
by 200; by 40000, etc.-Sliould of course only be done by short division.

Divide 732427 by 100; by 10000, etc.-Should only be done by pointing off.

Write 3 dollars and 5 cents; 10 dollars and 7 cents, etc. Bought for $2095.07, sold for $2500. How much d(lid I gain or lose? Sold 320 bushels for $176. How much a bushel? Analyze. Spent $42 for tea at 87L 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 similar to the last two, they may be rejected in the second stage in this grade. The following are all the forms of arithmetical analysis necessary to the fifth grade; FORMS OF ARITHMETICAL ANALYSIS FOR BOTH MENTAL AND

WRITTEN ARITHMETIC. A. ( Fundamental)-iVtultiplication. Question.-If one yard cost $3, what will 4 yards cost? Anialysis.-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.-If one yard cost $3, how many yards may be bought for $12?

Analysis.-If one yard cost $3, $12 will buy 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.-Spent $42 for tea, at 87ic. a pound. How many pounds did I buy?

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ALU]‘rnwEi’]U 119 Analysis.-$42 are 42000 mills, and 87A cents are 875
mills. I c.ti buy as many pounds as 875 mills are contained, etc. See preceding “Suggestions” for remark about reducing Federal money without analysis. C. (De)eived)-Division. (2.) Questio?t.-If 4 yards cost $12, what will one yard cost? Analysis.-If 4 yards cost $12, onle yard will cost i of $12, ~which is $3. NOTE.-Avoid the very faulty forms “as much as 4 is contained in $12,” or ” times in $12,” or ” 4 is contained in 12.”

Question.-If 5 lbs. cost $3, what will I lb. cost? Analysis.-If 5 lbs.

cost $3 or 300 cents, 1 lb. will cost 1 of 300 cents, wlich is 60 cents.

COMBINATIONS OF A, B, AND C. Cand A. Division and Multiplication.

Question.-If 4 yards cost $12, what will 9 yards cost? Analysis.-First l)y 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 $12, how many yards may be bought for $27? Analysis.-First by C for price of 1 yard, then by B for inuimber of yards. NOTE 1.-Avoid setforms 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 quotient. NOTE 3. It is frequently an assistance to some pupils to have them divide each question into conditions andl demand-as 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 be sparingly used. NOTE 4.-Analysis A and B apply to questions in the tables, substituting the word since for if. Examples: I-low many quarts in five pecks? Since one peck contains eight quarts, five pecks contain, etc., etc. How many feet in 84 inches’? Since 12 inches make 1 foot, 84 inches contain as many feet, etc., etc. 119

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HOW TO TEACH TABLES. In this grade, the tables of the preceding grade should be thoroughly reviewed, with the following additions: Time.’ Teach about leap-year. Avoirdupois JVeight.-7000 grains -= 1 pound; 2240 pounds - 1 old toll; 62 p)ounds, or 1000 ounces = 1 cubic foot of water. Troy IVeight.-Explain its use, the great difference between its pound and ounce, and those of Avoirdupois Weight, the grain being the only identical element. 24 grains = 1 pennyweight; 20 pennyweights = 1 ounce; 12 ounces, or 5760 grains = pound. Apothecaries’ IFreight.-Explain its use. Show that it differs fronm Troy Weight in nothing but the method of subdividing the ounce. Teach that thle 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.-4 rods, or 66 feet, or 100 links = 1 chain; 80
chains 1 mile. Surveyors’ Square Measure.-Explain 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 towvnship.

Solid or Cubic M1easure.-Explain its use, and the difference in kAind 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 inches 1 bushel; 231 cubic inches =  1 gallon.

Angular Measutre.-Teach the following terms: Circle, 12)0

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GEOGRAPHY. oircumference, quadr)ant, radius, diameter. Teach the notation.

Give examples in reading, as 16~ 17’ 45”. 60” = 1 minute; 60’ = 1 degree; 90~ = 1 quadrant; 360~ = 1 circle; 360~ = circumf. of the Earth; 69+ miles = 1 degree of latitude; circumference of a circle = 3-1 times the diameter. English Money, etc.-Tlie usual table. Teach the value of a pountd ste-lin7g-$4.866+. Teachl the value of a franc-18 cents 6 mills; also of the mark of the German Empire-23 cents 8 mills. If any foreign dollar is taught, let it be the thaler of Germalny -71 cents 4 mills.

GEOGRAPHY. Gefneral Suggestions for all Grades.-!T 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 relationl or dependence. On the contrary, lie should, from the first, be led to consider the ear2l as man’s dwelling-place-its 9miotions as bringing him the necessary vicissitudes of day and night, and the changes of the seasons-its lagid-surface as the chief theater of animal and vegetable life-the oceai as the world’s broad highway, and the exhaustless source of clouds and rains, so necessary to every form of life on the land-surfacethe great permanent air-cY)’)e.zits 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 springs and rivers, with their branches, as carrying back again, and over the land, the ever-circulating water of the ocean-and of cities and towins, not as black dots on a map, in colored patches, which he has learned to call countries, perhaps near some crooked black streaks Which he has learned to call rivers, but as the 6 121

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HOWTV TO TEACH centers of social life and development, the seats of government, and the crowded, busy hives of human industry 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 formule, of long lists of rivers, capes, peninsulas, boundaries, etc., supplemented, perhaps, by a precise, verbatim repetition of the descriptive geography, as contained in even the very best textbook, it is one of the dullest and most unprofitable of studies. The textbook is a most important, and even indispensable auxiliayil, but there is no more common and pernicious error, than that of substituting it in place of the teacher, who thus is degraded into a mere stupid, profitless, and mechanical heatrer of lessons. The requlisites for successful teaching are a globe, a blackboard, an outline map and pointer, and a good textbook. The pupil’s first impressions should be formed firom the globe, rather than from the flat and distorted representation of the map. When the textbook 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, by the teacher. If this be done in a spirited manner, and the results carefully tested, the detailed study of the textbook will be greatly assisted and unified by the comprehensive view thus imparted, and the important details more surely remembered. Geography of the -Fifth Gr(ade.-In the preceding grade, the pupil has been taught the leading elementary ideas upon which geography is founded; in 122

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GEOGRAPHY. the present grade, these are to be reviewed, explained, anid systematized, begiinning with a general view of the world. The following is a syllabus of the points which should claim attention: Syllabus for the Fifth Grade. Part lst.-Thle form of the earth, its magnitude, thie continents and grand divisions, their relative positions, their connecting istlhmuses, and a few of their most important projections-the oceans, their positions, and prin cipal arms and islands-five or six of the great mountain systems of America, and fiom eight to ten in the rest of theworld; three or four well-known volcanoes-about a dozen each of the chief 2-ivers and straits, and about half as many great lakes-fiom ten to a dozen of the most important cities of the world, and, ia a very general way, the location of the most important countries, such as the United States, Great Britain, Germany, Japan, Clina, etc. With each of these cities and countries some interesting or importantfact 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 hlypothleses 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 direction, temperature, and use, pointing out only the equatorial current, one Arctic current, one Antarctic currenrt, and the Gulf stream-the trade wieds (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 climnate, as affected by distance fiom the equator, and by elevation-the motions of thle ear?tht, and the inclination of its axis-the zonzes, their limits, and a very few of their well-known and characteristic plants and animals, arnd, in a very general way, the location of the chief races of mankind. ‘ Outlines of lrorth A merica-.”-First: Treat the continent as a whote, pointing out its separate countries, most inportant capes, peninsulas, islands, and arms of the sea; its divisions into mountains, plateaux, and lowland plains, naming only a few of the most important of each. - 123

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HOW TO TEACH Iceland, Greenland, Alaska, and all other Arctic Geoqgraphy to be treated very briefly, and chiefly with reference to climate, resources, and people.-Newfoundland; the Donmiaion of Canad(a, 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 importance 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 a section of the country roughly drawn in chalk upon the blackboard will be found efficient]; the high western plain; the low central plain; the eastern slope, and the California basin; about a dozen ofthe chief rivers, with the great branches; about five or six each of the great lakes,’ bays, and capes; about twenty of the principal cities. - Descriptive Geography will include a very brief description of the highlands, lowlands, and drainage system already pointed out; the climate and its gradual modifications by latitude, elevation, and distance from the sea; and a general statement of the leading agricultural staples in the order of their latitude-rice, sugar, cotton, tobacco, corn, and wheat. Mexico.-Its surface, climate, resources, and people; their language, government, and social condition; about five or six of the principal cities. Central Amterica 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. 124

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LAXG UA GE. LANGUAGE. Correction, of Language.-In all the grades the pupils should be trained in the correction of lca)guage, aud taught to avoid common errors of speech. This is best accomplished in connection with the dcictation exercises required in the several grades; also by oral exercises specially adapted to this purpose, and by iinci(le)tal ist -tclion 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 instrucetion, the object being to impart the habit of qtsigl 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 themselves. On this account, teachers cannot be too careful themselves 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 following suggestions are made: Write on the blackboard such faults in expression as are liable to be committed, including-1.

Ungrammatical expressions: as I have)n’t no book; I haven’t got my p)encil; Iseers Atim do it, etc. 2. Slang: Thlis is an aiqful easy lesson, etc. The faulty expressions written in this 125

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HO W TO TEA CH 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 contaminated 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 expressionIs 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 fact 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 correction will have a permanent effect in improvimg 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 previous suggestion is to make the pupils critics on themselves and others, most of the inaccuracies committed resulting rather from carelessness and inattention than firom a want of knowledge. The teacher will, of course, often find it necessary to give direct instruction in relation to certain expressions. Of course, no instruction in technical grammar, or in any grammatical rules, is required until the next grade. ELEMENTARY SCIENCE. (By Oral Instruction.) GENERAL

SUGGESTIONS FOR ALL GRADES. The lecdin#l object in this branch of instruction is to ctltivate habits of observalion anid refiection, and to give 126

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ELEMiENTARY SCIENCE. facility in oral description. Avoid everything tending 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.

“Familiair obj/ects,” and familiar animals, plants, and minerals take precedence 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.

No topic should be treated exhaustively, nor should the topics selected be so few, or so frequently reviewed, as to narrow down or suspend the discipline of the observing ficulty. The selection and limitation must be left to the good sense of the teacher. The objective mnetiod of teaching presents two distinct, though intimately related departments. Perceptive teachinig, in which the object, as an acorn or an egg, 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. T/le ulse of l)ictitres, 9,iodels,‘or other sensible representations of objects, constitutes an important combination and modification of the two principal methods, and should be often employed.

Definitions should be very sparingly introduced, an d never in the first stage of a subject. If given at all, they should sum up knowledge already attained. The terms oryanic, in)organic, veyelctable, aniual, and minzeral, are prominent among the very few terms requiring defi 127

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HOW TO TEACH nition. 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.

Imipo(rtant facts not readily derived firom the pupil’s own observation, must, of course, be supplied by the teacher. Avoid overloading a topic by details. No topic should be selected in which the numlber of facts to be told bears a large proportion to those which the pupil may be led to discover for himself. Thle laiyguaye used by tlie pupil should be enztirely his own, excepting, of course, the few indispensable definitionls. The process employed will present two distinct stages: First, the analytical or preparatory, in which the teache’ 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 responses by the pupil will be, of course, in his own words; and the additional statements which the teacher himself may find ilecessary to 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 thle facts thus stated should be written upon the blackboard in the briefest possible synoptical form, but each only after it has been considered. While some such synopsis is indispensable to the teachlier as the first step of preparation for giving the lesson, it should never be presented to the pupil except by the gradual process above indicated. The second or review stn(ge of the process is based upon the results of the first, and furnishes the principal discipline of the powers of description or oral statement. The facts already considered should be rearranged, if 328

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ELEMEiY TAR Y SCIENCE. necessary, into an orderly synopsis upon the blackboard, the pupils being called upon to assist in this arrangement.

They should then be required, in turli, to state what they can recall of each item of the synopsis, then of each group of items, and, lastly, of the whole subject. Theni the synopsis may be wlholly or in part removed or hidden, and the oral process of review repeated. As afitnal stage, and before dismissing the subject, an extempore conpositi(o), with or without the aid of the synopsis upon the board, should be written by each pupil upon his slate. OUTLINES OF ZOOLOGY. In relation to this part of the fifth grade, the following suggestions are made: Zoology being a science of classification, it is indispeinsably requisite to teach the distinctions upon which the classification depends. Only the simap)lest outtline need be taught, with such facts and details as seem most naturally appropriate to illustrate the subject. The process of classification being naturally objective, that is, animals being classified by their obvious peculiarities, the 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 the four great types or sub-kingdoms. Write upon the blackboard the names of a sufficient number of familiarly known animals without classification. If he have their pictures in books, or on chlarts, let each be shown before asking and writing its name. Let the 6* 129

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1-10 W TO Ty,A CH pupils spell each name before the teacher writes it.

Suppose them to be lobster, ox, oyster, dlog, beetle, stafish, 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 their 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 faniliarly known; but these may readily be overcome by the use of pictures or even rough sketches on the board. Having thus grouped the names upon the l)lackboard, a few questions will lead to the perception that the animnals of one group have a backbone, composed of many pieces, and an internal bony skeleton; those of another are made up of distinct r ings andjoi)nts; and so on of the other groups, each of which may now be readily expanrded, by asking the pupils for the names of other animals, 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., carefiully 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 resemblances aind differences. The terms m))ine)ral, vegetable, azniial, organic, and iniorganic, should be previously taught or reviewed in a similar mainner, through the perceptions of the pupil, guided by the questions of the teacher. 130

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ELEMENTARY SCIENCE. Renme))ber that the skillful use of interrogatioz is thle teachler’s chie meas of awakening thought, and producintg lastiiq imzpr-essions. Well-known typical animals should be taken as the objective basis of the classification; such as n )i, mionkey, bat, cat, rat, horse, deer, cow, and whale;eayle, parrot, cana?ry, rooster, ostrich7, snipe, and dluck;turtle, alligator, racttlesniake, and frog;-perch7, codl, shicrk, etc.;-bee, biutterfly, 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 preparatory thereto; thus, it is better to use the term fourhanded than qnadrunmana; gnawers than } odetiia; scratchers than raso)-es; twqo-winiged tihan dilp)era, etc. A few scientific terms, such as giiolltsc 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 peculiarities and habits-which the pupils themselves may have observed, will forma 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 should not be attempted at first. Some system of diagram)s, roughly sketched in chalk, will be found of great service in assisting the pupils to 131

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I0 HOW TO’ TEA CII remember the classification. The best and simplest is, probably, that used in the ordinary “genealogical tree.” The diagramn 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 “outliine” without having first, by careful study, acquired it. This can be readily acconmplished by means of any good school manutal 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: kinydom)), branc71 or type, class, or(ler, fam),ily, yen?s, sj)ecies, 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, which is here presented for the guidance of the teacher. This synopsis comprehends three successive outlines, each complete in itself, or taken wiith that preceding it: FIRST GENERAL

OUTLINE. Distinction of organic and inorganic objects taught objectively.

Differences between animals and plants. What is an organ? An animal? Four great types of animals (Cuvier’s, and omiitting the protozoa). Exercises in classifying, by types only, such animals as the dog, lobsters, elam, coral, lad, asp, g’oose, starfish, garter-snake, shrimp, toad, tortoise, oyster, etc. The reasons for the classification shouldbe given in each case. Each type to be then briefly defined. Why vertebrates are placed first. 132

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ELEMENTARY SCIENCE. SECOND GENERAL OUTLINE. Classes of Vertebrates.-(Tenney’s arrangement is here selected as beiing, 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 with milk), birds, reptiles, batrachians (frog kind), fishes; brief description of each class to be given. Name common vertebrates to be classified, occasionally mentioning an animal not a vertebrate, in order to test the attention and accuracy of the pupils; for example: alligator, robins, mouse, worm, herring, toad, lion, jelly-fis7, rattlesnake, elephtant, flea, hawk, turttle, etc., etc. Classes of Articulates to be treated very briefly, but in the same manner as the vertebrates. Simplest division, as insects, crustacea, and wormns, to be employed. Classes of MoloUuscs.-Treat also briefly, by referring only to their general characteristics. Teach the meaning of the terms univalve and bivalve. Specimens of shells will be useful for illustration;. but it must be remembered that the structure of the animnal 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 containing a few of the small molluscs found in every pond, will give clear ideas. A small aquarium will )be found very useful.

Classes of Radiates, probably treated withl sufficient fulllness in connection with types. Review if necessary. Here it would be well to mention the grouping of animals as herbivorous, carnivorous, and omnivorouls; also the general relations of the teeth of animals to other peculiarities, such as feet, forms, food, digestive apparatus, and habits; also, as fear as may be possible, illustrations of the importance of their several flinctions in nature. THIRD GENERAL OUTLINE. In this outline some orders slhould be omitted, or but briefly considered, because not readily treated objectively. If all the prescribed classes cannot readily be taught, owing to the limited 133

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11) iV 1‘0 I’ lACH 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 geographical distribution of each to be also briefly referred to.

Fourhanded (Quadrumana.)-A few examples, according to the experience of the pupils. Refer to the geographical distribution. Hand-winged (Cheiroptera).-Use 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 (Insectivora).-Treat very briefly. The mnole, its habits-refer to its small, hidden eyes, etc. Fesh-eate.rs (Carnivora).-To be treated more fully. Refer to general structure of teeth, feet, and stomach. Refer to catfamily, using colmmon cat as type; dog famnily, 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 (Miarsupials). Refer to the geographical distribution. The exception of the opossum. Gnawers (Rodents).-Use the rat or squirrel as a type. Refer to peculiarity of teeth, and the provision for their continued growth. Teachl about the rat, mouse, squirr?el, beaver, rabbit. Refer to the woodchuck, porcupine, and guinea-pig. Titick-skizned( (Pachyderms).-Treat briefly of the elephant, the rhinoceros, and swinie families; more fully of the horse family, includinghorse, ass, and zebra. Geographiical origin of the horse, its dispersion, and its influence in human affairs. Cud-chewers (Puminants).-Relations of food to teethl, stomach, feet, etc., etc. Teach three families: 1. Deer family, horns solid, deciduous; 2.

Hollow-hor’nedfamily (hliorns permanent); 3. Camel family(hornless).

Refeir to llama and vicuna. VWhale-like (Cetaeea).-Refer to the fish-like character of the 134

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ELElfENIA4R Y SCIENCE. whale; how it differs from a fish; its uses. The porpoise and the dolphin. NOTE.-Two of the preceding orders (8th and 9th), are sometimes classified under the following 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-Rumiuants).

These are again divided into the following groups of families: A.

(Hollow-horned) ox, sheep, and antelope families. (Solid-liorned) deer, giraffe families. (Hornless) camel family. B. (Solid-hoofed) horse family.

(Thick-skinned or Pachyderms) elephant, swine, hippopotamus, rhinoceros, and tapir families. BIRDS. Birds of Prey (Raptores).-Vulture, falcon, owl, condor, hawk, eagle. Cliinbers (Scansores).-Palrrot, woodpecker, etc.

Perchers (lnisessores).-Humming bird, swallow, kingbird, thrush, sparrow, canary, etc. Scratchers (Rasores).-Galliuaceous birds and dove family.

Runners (Cttrsores).-Ostrichl; its habits. WTaders (Grallatores).-Cran e, stork, snipe, etc. Swimmers (Natatores).-Duck family: Swan, petrel, penguin, albatross, etc. Refer to nests of birds, also their migrations, instinct, etc. REPTILES AND FROG FAMILY. Treat very briefly, teaching something of turtles, crocodiles, and alligators; serpents and their fangs; the flog and its transformations. FISHES. Treat the classification very briefly; show distinction between the two groups, bony and cartilaginous fishles, with the orders spine-finned and soft-finned; also the shark and the sturgeon. ARTICULATES. These present many advantages forthe schoolroom. They alre small, and easily procured for perceptive teaching. A simple I 135

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iHOW TO TEACII 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 explained-their structure and the functions of their chief organs. Their wonderful transformations should be explained and exemplified; also the difference between insects proper, spiders, and many-footed artitculates (myriapods).

The following orders should be taught and exemplified: 1. Membrane-wiged (Ilymnenopterea).-Including the bee family, the ant family, the wasp family, the ic7tneumon family, their peculiarities, habits, and instinct.

2. Scale-winged (Lepidoptera).-Moths and butterflies, how distinguished; caterpillars, etc., clothes-moth, geometer. 3. Tiwo-winged (Diptera).

Mosquito filmily, wvheat-fly, housefly, etc. 4. Case-winged (Coleoptera).-Beetle, fire-fly, weevil, etc. 5. Ilalf-winged (Hemipteera); or bugs, cicadas or harvest-flies, tree-hopper, cochllineal, boat-fly, etc. 6. Straiglht-winged (Orthlopteta).-Cricket, katydid, locust, grasshopper. 7. Net-winged l!Neuroptera).-Dragon-fly, May-fly. Refer to the white ants. Spiders (Arac7thida). Mcany-footed Insect.s (Myriapods).-Centipedes. Crustacea.-Crab, lobster. Woirms.-Earth-worm.

NOTE.-It is important to distinguish carefully the three terms, insect (i.

e., six-footed [hexapod]. or true insects), arachnids, or eight-footed spiders and scorpions, and myriapods, 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 ol)vious 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 hind-body (or abdomen). The head is furnished with feelers, (antenne); 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 arachnids, the head and body are consolidated into one division, which has no antennee, supports four pairs of legs, but no wings. In the inyriapods, the entire body consists of a series of very similar joints, not grouped into divisions separated (inserted) from one another, but of which the first serves as a head, whfiilst each ot the others, however numerous, supports either one or two pairs of more or less imperfect legs. 136

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FOURTH GRADEo OUTLINE COURSE. Time allowed, about five mont7s. LANGUAGE.

Readitg.-Of the grade of a Thlird Reader (latter 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 Grammar.-To include the analysis, parsing, and construction of simple sentences, and with such definitions only as pertain to the parts of the subject studied. ARITHMETIC. M’ental Arithmnetic.-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 Arithmetic.-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.-Of the United States in detail. Local and descriptive geography treated as in the Fifth Grade.

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110W T’O TEA CII ELEMENTARY SCIENCE FOR ORAL INSTRUCTION. Botany.-An outline knowledge of Botany, including the general structure and common uses of such plants as most pupils may readily observe. This sliould, if possible, be taught during the spring and summer months, in order to make it in the highest degree objective by the use of specimens. Mineralogy.-A simple outline knowledge of Mineralogy, illustrated b)y specimens. This may constitute the fall 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. On Paper.-Review of the elementary forms; their combination 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. On Slate or Paper.-Review of the Fifth Grade as far as may be necessary, and drawing curve lines, and figures formed fromni tlhem, as the circle, ellipse, etc.; also simple designs containing, straight and curved lines. 138

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SPELLING. HOW TO TEACH SUBJECTS OF THE FOURTH GRADE. LANGUAGE.

Reading.-See directions and suggestions given for the Fifth Grade. The latter half of a Third Reader usually comprises selections appropriate to this grade. Particular attention should be given to clearness of articulation, to naturalness of intonation, and to general style.

Spelling.-The exercises in spelling, both oral and written, should be the samne 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 mniscellanzeouts words taught in this grade; also, familiar personal names. An excellent occasional modification of this exercise is, to have the pupils draw the outline of a letter-envelope upon the slate, or use a neatlytrimmed piece of writing paper of the same shape, and direct 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. 139

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1O HW JO TEACII Definitions.-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” should be with Enylish primitives at first, without regard to the etymology of those primitives. The affixes of Anglo-Saxon origin will therefore be taught first; afterward the meaning of such as ab, con, pre, pro, sub, io), eat, etc., may be taught as illustrative of the diversity of meaning of such words as abstract, subl)‘act, concede, accede, precede, etc. Also as showing that, for example, all words having the prefix sltb convey the signification of un)der, aid all having the suffix ion meau the act of. 2.

Each group, with its common radical or primitive, after being written on the slate or blackboard, should be made-thle subject of an oral exercise in definitions, in order to impress upon the pupils’ minds the modifications of meaning produced by the affixes. The exemplification of the words in sentences should be also carefully attended to. English Grammar. Thle instruction in this subject required for the Fourth (Grade includes analysis, parsixig, and construction, and in the order mentioned.

Grammar is the science of thle sentence; and, therefore, the fundamental idea to be imparted is, wh1at constitutes a sentence. Oral lessons should precede the study of the textbook, as a preparation for it. The ideas involved in the definitions should first be developed, before the pupils are required to commit these definitions to memory. The contrary practice, once so common, is 140

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LANG UAGE. very discouraging and injurious to the pupil, since it conmpels 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 blackboard; and then, by analysis, let the pupils be made familiar with the relations of the words used as subject, verb or predicate, and adjuicts, or )l od ifie)s. The distinctions comprehended in the pa2t.s of speech can all be successively taught in this way, and the pupil enabled 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 ill what relation the words used in the sentence stand to one a]lother (general grammar); the object of the paarsinig (only another kind of analysis) is to apply the principles and rules proper to these relations (particular grammar); the object of the constructions is to impart practical skll 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-suzbject and verb, or si)il)le predicate; next, that indcdustriouts is added to pupils, rapidly to learnz, and very to rc)pi(ly. The pupil then knows that industrious, being an adjunct of a noun, is an adjective; that rap)idly, 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 adjtuncts with a simple predicate,-sentences containing a 141

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HOW 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 invention of the pupil is brought into play in connection with his knowledge of grammar; and the exercises glide progressively 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, especially in the use of the apostrophe as the sign of the possessive case-in the proper plural termination of niiouns-the proper forms of the.pronouns, etc. This is a point of considerable importance. The sentences required to be studied in this grade include: 1. Sentences with a simple subject and a simple predicate; 2. Those with simple word adjuncts of either subject or predicate, or both; 3. Those with simple phrase adjuncts (so as to teach the prepositiont); 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, looked, 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 should not be allowed to degenerate into the 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 142

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LANG UAGE. 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 curriculum would be complete without it. It should, however, be carefully kept within propelr limits, both as to time and place, and should not be permitted to encroach upon other branches of equal importance. Each department 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 either etymological or syntactical, according to the technical discrimination followed in most textbooks 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 I, thou, hlie, and she, long before the application of any syntactical rule, the diversities of inflection and their proper use may be observed and studied by the pupil in connection with the ordinary analysis of simple sentences, and consequently at a quite elementary stage of the study. The transformation of “John can see James”’ into ” I can see him,” will teach him the nature of a pronoun, how to distiniguish it, and then how to defize 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 I to me. Similar exercises upon the other pronouns, used in 143

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HO W 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 object. He will then be ready to use intelligently the terms siJiyzelar, 2)lural, nominative, and objective, as applied to varied inflections, and to correct such errors as, “Who saw him? Me.” “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, repeat, and explaing the declensions of the pronouns. A similar plan should be followed in the comparison of adjectives and the conjugation of verbs. A few common errors are subjoined as a further illustration of the kind of work proper to this grade. ERRoRs IN ETYMOLOGY.-1. The Possessive Stgn. A goos’es foot. Three geeses’ heads. Two fox’s tails. A moans hlat. 2.

Improper formn of tenses. They done it. We seen him. He would have went.

If I had have seen it. 3. Imnproper utse of verbs. He must set still. The book lays on the desk. He laid still. ElRRoRs IN SYNTAX. -1. Subject. Me and her can sew 2. Predicate. We was there. He don’t know. She dare not do it. 3. Obect. He struck my brother and I. Who did you see? Attribute. If I were him. She looks beautifully. ARITHMETIC. Mental A’rithmetic.-TThe character of the examples 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 3 of a pound of sugar, how many ounces?” “18 quarts are what part of a bushel?” etc., etc. 144

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ARITHM[ETIC. Written Arithinetic.-Federal Money should also form a part of the regular work of this grade at least once a week, Lnd should be frequently reviewed. Particular care should be taken ill the selection of examples that no one of them be so intricate and prolix as to consume a large amount of time, without affording sufficient exercise of thought in the application of arithmetical principles. Too much importance, nevertheless, can scarcely be given to the requirement of “practice for rap)id(ity and (accuzracy” in Federal money, as well as the simple rules of Arithmetic. To this should invariably 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 performing 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 taught, their value, as a mental discipline, is of the highest order. When taught merely, or chiefly, by memorized formulae, called “rules,” they are, for the greater part, a waste of precious time.

No prlciple shozutd be presenled nti the pup[il s 145

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HOW TO T’EA Cl-I about to a)i(ke use of it, (aicd gio defgiitiooi slhoild be yivenz or required before tlie ideas ivhicl it e)-ibod(ies lave beeti deduced, andl clearly pJrese)ted(l by preliiniary ilushra(ion and questioniny. No rules should be given until a sufficient number of examples for practice have made them a succinct statement of principles previously understood, or the results of the application of principles, rather than mere mechanical formulae 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 ou(tlinie 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 ithe first stagyes, be wrought upon the slates, in order to secure correctness in notation, and to allow the pupil more easily to give the necessary analysis without the additional mental tax required by the effort to retain the numbers. In the written exercises pupils should use the signs of operation, + - x +, and the sign of equality, to indicate the work performed, and its result. This outline should then be followed by a full course, in which the substance of the first constitutes the exercises in mental arithmetic, while the written arithmetic comprises the more difficult portions of the general subject, 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 apparently long, is in reality the most expeditious. The pupil soon obtains a clear, comprehensive, and connected view of the essential principles, and 146 I

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A RITIIHMEY IC. the expanded review which constitutes the second course will then require but little time. SYLLABUS OF TOPICS Fo]n OUTLINES OF

COMMON Fp’ACTIONS. (WITH SUGGESTIONS AND EXAMPLES.) I.-The idea of a fiaction developed objectively. The equality of the parts to be very carefully illustrated. Tile relativen value of various fractional parts, as greater or less, as ~, l -2, Xetc. The definition of a fraction. One or more of the equal parts of a unit. The terms of a fiaction (lefined and the order of statement. The notation of fractions and location of termls, or order of writing. Exercises in writing and explaining fractions.

Fractional expressions less than a unit. Proper fractions defined, and examples. A proper firaction is one that is less than a unit. Fractional expressions equal to or,qeater thIan a unit. Improper fractions defined and illustrated. An improper firaction 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 lunits to improper firactions.

-Analysis A. (Page 152.) Pteduction of mixed numbers to improper fractions.-Analysis A. - Deftinition of mixed numbers. Exercises in mixed numbers, limnited to small denominators. Reduction of improper fractions to mived nutmbers.-Analysis B. (PaIge 152.) 147

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li 10 1 O’EA CH III.- IReduction of fractions to greater denoinitators-or higher terms. [What may halves, thirds, etc., be changed ilnto? 4’s? etc.]

To be illustrated objectively. Examples with greater denominators than can readily be solved by inspectiont. Analysis C. (Page 152). (Begin with fundamental axiom.) Term D)ivisor or Factor, with exercises in finding, by inspection only,. a Common Divisor or Commn,on Ftcto-. Definition to be given. NOTE.-Too great importance can hardly be given to this exercise of inspection. The application of the principle is indispensable in many of the arithmetical exercises in every succeeding grade. With proper training, it will become, within reasonable limits, a fixed mental habit, requiring no conscious effort. Reduction of Fractions to Lower Terms or Less DenominatorsExamples-Analysis 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 inispection.

Reduction to Common Denominator-use two fractions only. Application of common multiple in reducing to common denominator. Distinction between common multiple and common denominator. Definition of common denominator.

” ” least common denominator. Examples in reducing to least common denominators.Analysis C. Examples involving previous reduction to lowest terms, by inspection. Reduce 3 and  65 to their least common denomi nator. Use of common denominator as the simple but indispensable basis for the working and explanation of Addition, Subtraction, and Division of Fractions. 148

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ARITlIMETIC. V.-Impossibility of adding quantities with unlike names, illustrated: Add 3 elmns and 4 oaks; add 3 trees and 4 trees = 7 trees. In teaching the 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 5-by 23, or find 23 timnes. Adding things of like names. Adding fractions of the samie denominator-Examples. Adding fraictions of different denominators-ExamplesAnalysis C. (P,age 152). Necessity of reducing to common denominator. The numerators only 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-Analysis C.

NOTE.-See that the sign of operation and the equality sign are not omitted. Avoid reducing to improper fractions. Rule. lst. 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. R?ule.-lst. See that the fiactions are in their lowest terms; 2d. Reduce to common denominator; 3d. Subtract the less nlumerator 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?” 1st. Reducing to improper fractions. NOTE.-In mixed numbers avoid 2d. The difficult case, 73-2s (deferred to review.) VI.-” Multiplication of fractions” and ” compound fiactions” identical. Such expressions as -2L of 2}, 3 of 7, etc., only involve the finding of a fractional part, and should be treated at first as such, rather than as a special kind of fiactions. It must not be forgotten by the teacther that fiom the nature and definition of a fraction, every example in fractions must involve or relate to division in some way. 149

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HOW TO TEACH There are two cases in the so-called multiplication of fractions: 1st. Where a fraction or mixed number is to be aetually multiplied. In this case the multiplier must be a qvwole h1umtibe’ as 3
himes 2, or 3 tinmes 42. 2d. Where a fraclionalpart is to be taken of either a qvfole numbder, or of a fraction, or of both; as 2 of 17, or 2 of {, or 23 of 71-. NOTE.-MMutliplication by a mixed number is a combination of the 1st and 2d cases. Only in the first case should the expression “
times” be secd. In the second case the expression “of” only should be use(l. In the case of multiplying by a mixed number, the expression “timnes” is used for conciseness, though not logically correct. The proper expression is too cumbersome in practice-” 4 times the eumber and 2 of the nurnber.” Only the two varieties of the first case, and the first two varieties of tho second case should be required until the subject is reviewed. ‘7 times 3-Analysis as in simple x, then B. (Page 152). 7 times 4. Analysis as in simple x, tlhen B. (Page 152). (~ of 24;‘it-of $24. No analysis, except reducing to lowest term-s. J of 25; S-4 of $25. Anatlysis E. i (Page 152). of 75; 28 of e. Analysis F. (Page 152). Multiplicat diion (P Fr actions = 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 firaction of a dollar. Occasional examples involving preliminary reduction to lowest terms. R?le.-lst. See that the fractions are in their lowest terms; 2d. Multiply the numerators for new numerator, and the denominaters for a new denominator. Solutions by direct cancellation should not be required until the review. 150 Examples: Multiplication oF

Fractions

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ARITHEVElYIC. VII. There are, theoretically, two cases iii the Division of F~lacioas: 1st. Divisioni OF a FRACTIOXNAL NUMBER by an integral nunmber, as -3- + 7, and 4-3 + 7; evidently identical with I} of 3, and 7-of 4-3
in the so-called multiplication of fractions. 2d. Division of any nnumber, integral or fractional, BY A FRACTIONAL NUMIBER, as 5 +. i,.- 8 — — 85

-. 98 8’ 6’ 8 6 8’, s6 - 9 The form of putting the questions should be varied as much as possible, so as to train pupils to select and apply the right principle and method. Sometimes the divisor, sometimes the dividend, should be first named. “How nmany tines are 43-contained in 9?” Use this form of questioning at least as fiequently as the more technical form, Divide 9 by 48. 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) Divisiob of and by Fractions-Analysis: The method and analysis to be l)y commnon divisor. The first case may also be analyzed by Analysis F (page 152), if desired. The miietliod by inverting the diviso) is deferred to the review. See Note 1 under Analysis G (page 153.) Rule.-lst. See that the fiactions 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 what part of 8? 8 what part of 11? (Analyze from the unit, 1 is 8 of 8, 5 are -‘ of 8, etc., etc.) -3-are what part of x? a are what part of —? etc., etc. 151

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O110W TO TEAG CI PracticalExamples: 5 If 7 yards cost $, wlhat will a yard cost? 1st Group. ” 8yards” $49,’ ” ” (If a yard cost $ l, how much cain be 2d Group. bought for $8? 2d Group. I bogtfr$If a yard cost l}, ow mtuchi cani be [ bought for $;? 3d Group If: yard cost $5, wlat will a yard cost?

,, l ” i $,, ” FORMS OF ANALYSIS FOR TIIE OUTLINES OF COMMON FRACTIONS.

Analysis A.-Exanmple. Reducc 51L to halves, or to an improper fraction:-1

-.; 5 — 5 times 2- = 1; 20 + -= LI. Analysis B.-Examrple. Reduce %” to units, or to a mixed number:-1 -=2: lience, in 1-,- the re i as many units as - are contained times in 125, equal to 7.. Analysis C.-Examnple.-Reduce to niniths:-In a unit there are-; hence-3,and-2 2 x 39=_ NOTE.-Avoid saying “a whole number,” or “one whole number,” when speaking of a unit.

Analysis D.-E.-ample.-Recluce 1L2 to its lowest terms:-By inspection the greatest common divisor is 6, hence it may be reduced to thirds; -‘- = ; hence there are as many thtir(1s as 4-4 are contained times in,or two-thirds-!]. Analysis E.-E.xample.-Find 3 of 25. of 25 is 3L; — of 25
are 3 times 3- = 9-1; or (using as a basis the Axiom 3 of a unit = ~ of 3
units; 3 -= of 3, first illustrating objectively by lines divided into parts), - of 25 =- of 3 times 25 = I of 75 = 93, The former process is, in many respects, preferable. Analysis F.-Examnple.-Find 3 of’. (First, as a basis, show OBJECTIYELY that Of of - =; ~ of ~f 4, etc., etc.) of =$-; of 5 tim s= -; of o  3 times -  =1. NOTE lst. Make the same question “practical,” and apply the same analysis. If a yard cost $-, how mucb will 1} of a yard cost? It will cost 3 of — of a dollar, etc., etc., as before. NOTE 2d.-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 following Rule for the Multiplication of Fractions: 1st. See that the fractions are in their lowest terms; 2d. Mul 152

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ARITIIME7’ C. tiply the numerators for the numerator of the product; and multiply the denominators for the denominator of the product. Analysis G.-E.vamnple.-If a yard costs $3, how much can be bought for $1? (See Aualysis B, 5th Grade, to be combined withl reduction to Common Denominator.) If a yard cost $3, $, will buy as many yards as $3-are contained limes in $7-, or, reducing to Common Denominator, 3 = 72, 9 = -

5, as miny yards as 171 are contained tilnes in 5-, or 2-e7yards. NOTE
lst.-To “invert the divisor an( proceed as in multiplication,” is much more concise as a method, hut it is not in any sense an ctnalysis, but a condensed and valuable rule, which is to be both taught and analy3zed in the review. When this concise rule is taught b)elfore the analysis by redlucing 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 alw ays 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 much more difficutlt 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 nrental discipline, any course which practically excludes the fundamental principle of division by a fraction should bc carefully avoided. NOTE 2d.-It will be perceived that the analysis of the division of one fraction by another by the process of reducing to a common denominator, is essentially identical with the analysis of reducing an improper fraction to a whole or mixed number.

Analysis H.-Example.-If 4-of at yard cost $3;, what will a yard cost?

(See Analysiq C, in 5th Grade, with which the following is essentially identical.) If 47 of a yard cost $ , l of a yard will cost ~ of $3- (note that this division by the numerator is the vital step in the process), which is $-e%-; and a yard or -7I will cost 7 times $,,, or $5-L, equal to $1-,2L. NOTE lst. Tbis is one of the most important analyses in the entire range of the arithmetic of the grammar-school grades. If neglected, or badlytaught, it seriously deranges the work of the teachers of more advanced grades, where it must be so frequtently applied. If the teacher will present it immediately after, and then in connection with, 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. 7* 153

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HOW O TI,A CII NOTE 2.-It is, of course, understood that the examnples 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 $-3 purchase 4 of a yard, how much will a dollar buy? SYLLABUS OF TOPICS FOR EXPANDED REVIEW OF COMIMON FRACTIONS. I.

Systematic Review of D)efititions of terms used in fractions, wit h illustrat ive exantples. Omit complex fractions having fractions i n th e denominator. Complex fractions hlaving an integral de nominator, such as 2, read 23 fiftlls, are to be ” reduced to higher terms.” See Aiatlysis C, page 152. The multiplier to be used is evidently the denominator of the fraction found in the numerator. All other cases of “complex fractions,”

so called, should )be 7 l treated as indicatedl divis,ion. Such expressions as are not to be explained as firactions. A unit cannot be divided into 9} equtal parts. Examnples in finding the Greatest Comnmon F’actor of numbers by inspection.-Mental. ERamples where the factor cannot be readily found by inspection, as 292 and 365;-315 and 572. The SPECIAL

METIIOD required is too difficult fori 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.

Ea(mnyples to li)e reduced by inspection; A12tas, 7, Anlyss D, page 152.

Examnples involving the special method offinding the Greatest Common Factor; as 32, 1 etc., etc. Not too long.-Analysts D, page 152. Reduction of Improper Fractions and Mixed Xumbers. 1st. Examples solved mentally or by inspection. 2d. Examples witli larger numbers.-AAnalyses A and B.

Examples in finding tihe Least Comnmol Mlultiple of two or more numbers-and definition. 154

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APITHMVETI C. 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, 36, alndcl 48. Statement of Method or rule. Relation of Least Conmmon Multiple to Least Common Denominator. 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 3fixed unumbers. Say “Reduce to Least Comnmion Denominator,” rather t1han, “Find the Least Comnmont Miultiple of the Denominators. Of course the latter forms a part of the process of the former. Ex.amples in Subtraction; asI -__5_; 87 29. 5. 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 important devices, maniy, or miost, of which have been already taught, and their principles explained. These devices, such as reducing to lowest terms, cancellation, rejecting terminal O’s of a divisor, should not be at any time lost sighlt 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.-Show its identity with dividing by common factors, and with reducing -to lowest ter,ms. Show this by examples in firactions. Examples of simple applications of cancellation to whole numbers. IV. Multiplicationr of Fractions Give examples whiere callerllthlioi caluno,t be applied.Analysis F. 3-2; z X 49; 23-7 x 144; x63 x1247; abstract and practical. Give examples that slhould be done by cancellation.-Analysis. Lowest terms, 155

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HOW TO TEACH 125 x sa; 246 of $17.38;;-if 39 barrels cost $84, what will 26 barrels cost? If a ton of hay cost $17-5, what will 2!, ton cost? If 1
acre cost $23-,, what will 19-l- 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. 3-of a number are equal to I of 3 times the number, etc., etc. 3 of 40 - 8 of 3 times 40. V. Division of Fractions. 1st. Review and apply the miethod by common clenominators. 2d. Review thoroughly its analysis.

Analysis G, page 153. 3d. 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 tle divisor, but in no case let the analysis of the rule be forgotten. Let it be given by the pupils as often as maybe 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 7:L are what part of 9-? $4 , what part of $72? - what part of -2 9?-See Analysis I, page 157. Give examples where cancellation cannot be applied: 17 * 25. 2 .33 — 49; 133 +. 1. At $17 a yard, how many yards can be bought for $133? If 5]- bushels cost $18-, what will 1 bushel cost? Give examples where cancellation is to be applied 23-12-ill-; 213-.2L, etc. Give short examples involving simple combinations of the multiplication and division of fractions; also addition or subtraction, with multiplication or division, like the following: Bought 723 yards and 31 yards at $1-a yard; what is cost of thle whole? Bought 36 yards; kept 9~ yards, sold the remainder at $] a yard; how much did I get for it? If I had sold it for $7L, how much a yard would that be? If ] yard cost $5-, what will,If yard cost? If 3 yard cost $7, how much can be bought for $;,5? 156

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ARIII’MEI~C. FoRMs OF AN ALYSIS. The following is the simplest form of the analysis of the important practical rule of inverting the divisor,” etc.

The introductory step of using a unit as the dividend, is only a case of dividing one fraction by another. Analysis I.-Exnample.-Divide - by -.

(Begint with a unit for thle dividend, and apply the principle of comg?ion divisor.) 1st Step.-A unit divided by -, or 7 + — 7 (which quotient, it will be observed, is the divisor inverted). 2d Step.-TlTherefore 3 of a unit divided by - =3 of - = a. Conidensed form.-(1 + 61) = (77 +*) = -; therefore (-3- + 5) = - of — _. 5 -4 0 Ex.rample.-If - of a yard cost $-3, how much can be bought for 7-7 W8 Analysis.-Combination of H and G.

Page 153. Exanzple.-If -7 of a yard cost $-, what will 9 of a yard cost?

Combination of H and F. NOTE.-Give a thorough review of analyses F, G, and H, before attempting the above combinations. Decimal Fractions.-The exact nature of decimal fractions should be explained and illustrated; also the meaning of the word decial)t. Show that decimal fractions may be used like common fractions by writing the denominator. Illustrate by the decimal notation, showing that whole numbers greater than 9 are also expressed 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. 157

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HOW TO TIEACH The illustrations may embrace the following:-1. How to write decimals, as 7-tenths, 7-ihundredths, 7thousandths, 7-ten-thousandths, etc. 2. Show that the enumerator is FIRST written, as ill common fractions. 3. Show that the “decimal point” and the ciphers, when used, are only required to indicate the tdenominator. 4. In readizily decimal fractions, the pupils should be cautioned to avoid such expressions as “tens of thotusands” for ten-thoitsa(dlhtks, ” hundreds of thousands” for hundred-thousadlths, 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 apl)oximate value of decimals as compared with simple common fractions; as, that.7634
is a little more than 3; that.8741 is somewhat less than’, etc.

Previous’to this, however, it is well to teach the exact value of certain decimal expressions: as.75-3,.125 =, 4’ 8) .375-3, etc. These exercises will serve to render the subsequent work of the pupil intelligible.

SYLLABIUS 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 fiactions. Reduction of decimal fractions: 1st. By T)ispection, with analysis as in common fractions.

Examples, mental, oral, and written. .3 to.00’s, to.000’s, etc.;.15
to.00000’s. To higher tc.‘mrS, Analysis C, common fractions. Page 152. 3
to.O’s, to.00’s, to.000’s, etc.; 7.3 to.O’s, to.000’s, etc.; to improper-fractions, Analysis A, Page 152. Reduce.700 to lowestDECIMAL terms. Give Analysis D, Page 152. 158

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ARITHMETIC. NOTE:.-Avoid saying “the ciphers to the right are crossed off because they are of no use.” The statement that “they do not affect the value,” is not satisfactory unless the pupils show why they do not. II.

Reduce common fiactions to decinmal fractions. Give Analysis E. Use axiom 3 of a unit = of 3 units; 3 -_ of 3. Make this definite by objective illustration, using lines divided into parts. Examnple. -] to tenths; to hundredths; 4 of 1 = of 3 of 30 tenths = 7 tenths- =.71 =.75. NOTE.

Pnpils should be accustomed to read decimal fractions, especially hundredths (in subsequent grades applied to per ceut.), so as to include outstanding fractional parts, where there are any. It is generally better to state what denominator is required, instead of the more indefinite requirement to “reduce to a decimal fraction.” Exaiiple.-Reduce -, to a decimal fraction of two places, or reduce ], to hundredths. Ans. Two places will give hundredths for the denominator. 4 1 1 14.0 =-of i-of four-hundre d hundredths =- 11)- 41 11 11 11.36 4-11 240 240 24 3 )3.00

Reduce -to a decimal:  =- = - = Y of 3 = M4 of 300 hundredths =43 320 320

32 4.75 Riule 1. 1st. Reduce the numerator, considered as a whole number, to an improper fiaction with the required denolminator. 2d, Divide by the given denominator. Or, Ruile 2. Divide the numerator by the denominiator,.

NOTE.-Give examples to show what common fractions in their lowest terms can be made entirely decimal, and wvhich can not. In the general work of the class, pupils should rarely be required to continue the division beyond three or four places. Reducing Decimal Fractions to Common Fractions in their Lowest Terms. Rule.-Writc the fraction as a common fraction and reduce to lowest terms. Analysis D, common fractions. k Evamples:.625.4125.87500 14.125 “.07~.3L.662 5.11L.871, NOTE.-Pupils should be made tlhoroughly familiar by rapid mental exercise, usually without analysis, with the decimal expressions for halves, 3ds, 4ths, 5ths, 6ths, 7ths, 8this, 9ths, llths, 12tlils, and vice versa, using preliminary reduction to lowest terms whenever possible, as in -1-, 9l, etc., etc. 159

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EHOW TO TEACH III. Addition of Decim(al Fractions. Exanples: Add.2,.05,.008,.7283. Addl.0005,.97..0101, etc. ” Give mixed numbers.

Analysis as in common fractions, by principle of reducing to lowest terms.

The necessary additional ciphers miay be” untderstood” in the solution, but not in the oral analysis, 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 thle brief rtule of common fractions. Cases as in common fractions.

1st. When a fraction or a mixed number is to be multiplied, as 4 times.75, 17 times 8.047. Value of 13 barrels at $8.375 a barrel. 2d. When afractional part is to be taken, as: .4 of.83,.4 of 75,.4 of 8.75. How much is.7 of $38.45?.079 of $120?.90Y, of $160.48? Value.179 of ton 9 $92
a ton? at $92.87: 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. 3 $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 “1 Oths by 10ths, how many places?” “O1000ths 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, 100Oths by 100ths = 100.00OOOths, or 5 decimal places for denominator. Ans..00360 = in lowest decimal terms.0036. Why cross off the last 0? 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 $14.83=.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: 160

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ARITHLVEZIYC. 1st. When the divisor is an integer: 7. 8, 8. 7, 6-5, 6 -

120, 7.2 - 6, 3.6. 120, etc. Put ques tion in several ways: 1st, Divide 7.2 by 6; 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. When the divisor is or contains a decimal fractioii 6 +.03;.8 +.005;.004..8;.0036 —.024; 7.2 .009; 8.5.45; 3 +

7.203;.2 . 8.75;.3006 -.- 7.4; 8.5. 9.78; 8.638. 9.5; 8.638 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 greate?r, (.003).6,) INCREASE the denominator of the dividend to.000’s. 2d. Whiere the denominator ofthe divisor is the less, (.12).17286,) DIMINISH the denominator of the dividend to.00’s (lhundredths) by cutting off the last three figures. A Gene}ral Rule.-lst.

Reduce the denominator of the dividend to the denominator of the divisor; 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 fiactional portion of the quotient.

Applications.-Thlle applications of decimal fractions will be principally found in Federal Money. Simple combinations with common fractions should occasionally be used; also simple combinations of two or more of the rules of decimal fractions. Use the principles of cancellation arid reduction to common fractions whenever they will simplify the operation. Examples in finding what decimalfraction one decimal fraction is of another; especially how many hundredths-use ONLY small amounts or very simple examples: 8 cents, how many hundredths of 64 cents? $7.25, how many hundredths of $9.75? 161

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SUPPLEMIENTARY NOTE TO THE ARITHMETIC OF THE FOURTHI GRADE. Particular attention is directed to the three following elementary and mutually related problems, and to their importance as the essential preparation for the commercial arithmetic of the higher grades. 1st. To take a fractional part of a given number: Fundamental. Common Fractions. I)ecimal Fractions.

Percentage. How much are 3 of 15? How much are.75 of 15? Find 75 per cent.

of 15? How much are 7L times 9L? How much are 3.48 times 7.53? Find 62’

per cent. of 8.75? Value of 4} yards 0 $52 a yard? Value of 8,47 tons 6

$3.45 a ton? Find 872 per cent. of $48.37’? 2d. To find what (fractional) part one given nuimber is of another given number: Derived. 6 is what dec.

fi’act. of 15? 6 is what com. fract. of 15? 6 is t of 15? 6 is what per cent. of 15? 6 is how many 100tl’s of 15? 7~ is what com. fract. of 9‘3? 3

72 7 is what per cent. of 9 2? 3 $4~~~~2~ 7~ is how many lOOthis of 9l? 3

$42 are what dec. fract. of $5-5? 4 $4} is what com. fract. of $594?h $4a3 are how many lOOtlis of $5-4~? $ is what per cent. of $514? 3d. To find the number of which a given number is a given fractional part: Derived. 85 is ~ of what number? So85 is.625 ofwhat number? 85 is 62 per cent. of what number? 21 is - of what number? 18.75 is 1.3 of what number?

or is 11 per cent. of what number? $8+ ale9 4of a u$. re12ofwasu? $1. 845
per cent. of what n? $8! are -1 of what sum? $9.25 are 1.25 of what sum?

$12.60 are 87-sy per cent. of what sum? ~5 a

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GEOGRAPHIY. GEOGRAPHIIY. Geography of the United States ic detail.-IN
teaching the geography of the United States, it is particularly important that the time of the pupil be not exclusively taken up with the study of niere local details-with learning the several courses, etc., of lollng lists of rivers, and the exact situation of still longer lists of towns. A certain, but carefully limited, amount of local geography is indispensable as a basis for the more important descriptive geography. The necessary local yeograph7y 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, lakes, 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 portions of the study. Ti,e descri)tive georapihy should include the simplest physical outlines of the country as a whole; the elevations, the great mountain ranges, plateaux, an(l plains; the drainage by single rivers onl the Atlantic slope, and by extensive complex river systems in the remainder of the country; the clim?zate, with its modifications in the several sections, as cold or hot, wet 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 163

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IOW TV O TEACII routes, natural or artificial, and the cities, as the centers of manufacturing and commercial industry. The descriptive geography of individucatl SAtates or Territories may then, in great part at least, be deduced from a consideration of these general facts. All tiresome sameness and repetitions will thus be avoided, and the pupil will be made to appreciate the real importance of the study. ELIEMENTARY

SCIENCE. (By Oral Instruction.) BOTANY. THE general suggestions relating to the object of this branch of instruction, given in connection with tihe subject of zoology, in the preceding grade, and the remarks there made in regard to the extent of classification, 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 attaches to so many objects of the animal kingdom. Au 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 distinctions often very minute, must, for the purposes designed to be accomplished in these simple lessons, be 164

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EL FMEN TAR Y SCIENCE. carefully limited. Only common plants need to be classified. The limitations of the classification to be taught are indicated below. The first fewv lessons should show the strutcture of plants and the general functions of each of their parts, -the root, the stemni, the leaf, the.flower, the seed; the growth 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, shirubs, and trees; also between a(lznals, biennials, and perennials. Examples of each to be given. Classification of leaves-a beautiful and very usefil department of the subject, especially as at means of training the powers of observation may then be taught, the children being encouraged to gather specimens for careful scrutiny. The vocabulary employed to indicate the peculiarities is very interesting, and will serve to teach something of etymology-as ovate, cordate, palbiate, digitate, serrate, etc., etc.

Give the pupils for,?i(la for methodical examination and description.

(kbee Jfiss Youiiaizs’s “First Boole of Botany.”) Clctss’ification of roots an)d stemt)s, to be taught in a similar manner, but much more briefly Next, that of blosso)Is. First, show the parts of a blossom, taking a regular one to begin with as of a lily, a morninyglory, or a butter-cup. Analyze so that the pupils can see the parts, showing the calyx and sepals, the corolla and petals, the stamens and the pistil with its ovary. Give a sufficient number of exercises to make this familiar, and let the pupils analyze for themselves. The principal forms of flowers, as bell-shaped, wheel-shiaped, salver-sha])e(l, cross-sha)aped, buttterfly-sh-aped, etc., etc., may then be shown. The arrangemnent of the blossoms on the stem (inflorescence), as far as it can be exempli 165

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II0 W TO TEA CII1 fled by actual specimens, as heleacl, race7)e, spike, qltmbel, etc., may also be learned. The following outline of classification may be taught: A. (Series.) Flowering (p7cenogamous) plants. B. (Series.) Flowerless (cryplogamotus) plants. At first use only the familiar terms. The scientific may often be dispensed with entirely.

Give examples of plants in each series; as Rose. Lily, Geani; Fer), Moss, Muslhroom). A, including a (class). Outside-growing (exogenous) plants b (class). Inside-growing (enidooye)iouis) plants. Illustrate by stems, showing the rings or annual layers of growth in the former, with bark, wood, and pilih, and their absence in the latter. Teachl the coincident peculiarities of the leaves, as neetted-veinied and parallelvei)ecl, affording a ready method (approximate) of distinguishing these plants, and thus giving opportunity for useful exercises; also those of the seeds, as of two seed leaves (cotyledons) or only one (dicotyleldonous and izlonocotyledonzous). Familiar examples to be found by the pupils; such as Rose, Buttercup, Geranium, Pea, Potato, Grape-vile, etc., etc., and Lily, Indian Coli, Common Grass, etc. (a), Including 1. Orders or families of plants, wvith blossoms of many petals (polypetalo?ts); and, 2. Orders, or families, of those, withl blossoms of one petal (onoopetalous). The pupils will readily find specimens of each, the names of which they have already learned. The orders of (b) should not be taught. Nor need any instruction be given in relation to the classification of cryptoganmous plants, ferns, mosses, etc., this being 166

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ELEMENTARY SCIENCE. too difficult, and depending upon distinctions not sufficiently obvious for the purpose of these lessons. Attention, however, may, if occasion offers, be called to the fructlfication) of ferns. Such of the ordel)s or fag)ilies, should be taught as are very familiar, and depend upon quite obvious distinctions, familiar names being exclusively used. Thlus the MfuIstar(d Fay)ily, the Pilse Fa)zily, the Cioltfoot ~amily, the Rose gam)ily, the Lily Famiiily, etc., etc., may be taught as far as the collection and presentation of specilmens render it desirable; that is, not the mere fact that there are such families, but in connection wvithl an actual object, and when the i)qtquiry 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 bott2zisfts, 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 CO)nf’o)t u?ses of planzts’ may be taught to some extent incidentally with some of the above instruction, but more fully at this stage. This will embrace tlteir uses for food, clothin)y, mzedicine, etc. Take our own plants first. Show that the roots of some plants are useful; of others, the seeds; others, the leaves; others, the fruit; others, the bark, etc.

Some few plants of other climates and countries may then be referred to, as cotton, rice, suyar, tea, cofee, etc., etc. The relation 167

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HOW TO I’EACH ship of these plants to our own nmay then be shown; that is, the faitilies to which they belong’. MIINERALOGY. Before commencing instruction in this branlch, the teacher should again read the general remarks on teacl)ing elementary science in the Fifth Grade. This subject 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 immediate perception of the pupils in the classroom, 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 gnetlhod 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 imI)arted information. This, however, should be given not arbitrarily, 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 mind to self-activity being the great desideratuti’in this kind of teaching; hence, the important principle should be kept steadily in view that notlhing 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 yreparation for it without being practically familiar with at least -the outline facts of the science. This preparation may readily be made with the assistance of even a small 168

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ELEMENTARY SCIENCE. cabinet of minerals, properly labeled (Day’s Grammncar School C,abinet, for example), and ally of the smaller manuals of Mineralogy (Dana’s, for instance). What has been said in the preceding grade, as to the pro)rietv or necessity of attempting only a part of the subject, is equally applicable here. What is done should, however, be systematic not miscellaneous and unilrelated. Do not attempt to treat any of the topics exlhatstively. 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 should be guided by the teacher by means of a regular formula, considering in a fixed order its f[obrms, structure, cleavage, fracture, tardness, wveighit, colori, luster, etc., etc. These special characteristics and their proper order will be readilv remembered after a little practice. Each term thus used should be carefully illustrated and explained as soon as its introduction becomes necessary. Begin with Mi)ieerals-Rocks to be afterwards considered as mineral aggregates. A clear conception of the general properties 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, rockcandy, etc. Use only the term crystal, withlout giving the namies of substances. 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 needlelike 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 8 169

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0HOW TO TEA CGI ice, or a snow bank, must 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 crystallization, and draw attention to the mysterious and inldestructible 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, some 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 niot at first named, and should be compared first as to the resemblances, 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 importance, economic uses, etc., etc. Be particular siot to introod?ce an unexplained term such as the f?ame of any rock or mineral, as gneiss, or gypsum. The name means nlothing until explained as quartz has been. Other forms 170

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ELE,MENPAR PY SCIE_E.NC: 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. Eniconr age the pupils to look for and bring in specimens which they think to be of the same character as those studied.

Let tIieri tell why they think they are the same. Let othiers tell why they think they are not. Having thus treated of quartz, next consider, in the same way, feldsl)par and mica. The pupils will now 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 kornblende 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 iml)ortant, mostly from Dana, is subjoined, from which the teacher can make such selections as will conform essentially to the above plan. MINERALS. Water; carbon, diamond, coal and coal-mining, anthracite, bituminous, jet, plumbago, amber, petroleum, asphalt; sulphur; saltpeter, salt, borax; lime, gypsum, alabaster, selenite, calcite spar, chalk, stalagmites, limestones (crystalline and compact), marbles, quicklime, hydraulic lime, dolomite; alum; talc, soap-stone, (French chalk), meerschaum, pyroxene and hoirnblende, 171

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110 W TO TEA CI corundum and emery, feldspar, albite, orthoclase, garnet, mnica. METALS. Mineralized [ores] or native-Ores of tin, iron, nickel, zinc, lead, mercury, copper, gold, silver, platinum. Enter into no details of Mietallurgy; a few simple 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. ROCKS. As single minerals-example pure limestone. As compounds-granite or conglomerate. Rocks as crystalline and uncrystalline, stratified and unstratified, aqueous, igneous and metamorphic. Thie relative position of important rocks-granite, syenite, gneiss, mica-slate, steatite, trap, basalt, lava, pumice, slate, shale, schist, quartz-rock, burr-stone, sandstonres, grits, conglomerates, limestones, marbles, saud, clay. Such of these rocks as are found in the vicinity of the school, or are frequently seen by the pupils when used for paving, flagging, building, etc., should receive particular attention. WRITING. Penmanship and Slate-Writing.- Penmanship should be carefully taught in each grade of the Course, in addition to the constant practice which is required in slate-wr) iting. 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 1672

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WRITING. careless habits, his style of writing, both with pen and pencil, will be almost incurably vitiated. The exercises in spelling firom dictation, etc., should be performed with punctilious accuracy, even if some sacerifice of rapidity be at first required. Of course, there should be a constant effort to improve both in rapidity and accilracy-quiantity 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 permitted 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 2encil, which should be sufficiently long to be held as a pen. The lessons in penmanship 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 possible. Hie should be permitted to write 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 p_apers 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 he can do it; but perfection in details should not be expected in the rudimental stages. It should, from t lte fitrst, be deemed essential (at least mzeritorious) to execute the work prescribed with dispatch, provided there is no want of care or attention. Westina lente, however, 1‘6‘3

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HOW TO TEACH is a motto that applies to the acquisition of this art, as well as others, in 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 illustratingl 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 7and and the eye as well as the giiid of the pupil are to be trained in this branch of instruction,-the hand to execute,-the eye to discern, the qvi)zd 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 execute the dictates of mind and eye. HIence 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 indispensable pre-requisites to the acquisition of a good hand-writing.

The first of these demands especial attention, and every lesson should, for some time, be introduced by distinct directions as to the proper method 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. 174

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THIRD GRADE. OUTLINE COURSE. Time allowed, Jrom eight to ten months.

LANGUAGE. Reading.-Of the grade of a Fourth Reader, with attention to the elocutionary principles, rutes, and exercises required to teach expression; also special exercises in vocal culture. Spelling.-From the reading lessons, with additional exercises, both oral and written; careful attention to syllabication. Definitions.-In connection with the reading lessons; also a review of the prefixes and stuffixes taught in the preceding grade,-and exercises in their combination with various easy roots. Fnqyish Grammar and Composition.- Continued, with the analysis, parsing, and construction of easy complex and compound sentences; also the writing of short compositions under the inspection of the teacher.

ARITHMETIC. Mental Arithmetic.-Through 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. IFritten Arithmetic.-As far as in mental arithmetic, with similar processes and methods of analysis; also with exercises to give practical expertness in simple computation.

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[HOW TO TEACH GEOGRAPHY AND HISTORY. Geography.-Of Sout7i Amnerica and Etropve, both local and descriptive; the topics of the preceding grades to be occasionally reviewed in outline. Hi,story.-Of the United States, including an account of the early discoveries, and the outlines of the Colonial History to 1763, only such dates to be taught as are essential to a clear understanding of the narrative. ELEMENTARY SCIENCE (FOR ORAL

INSTRUCTION.) A review, as far as possible, of the topics of the preceding grades, and, in addition thereto, the simple outlines of Physiology and Hygiene. WRITING. On Stlates.-Continued as in the preceding grades. On Paper.-Words containing difficult elementary forms; also phrases and short 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, such as the cube and parallelopiped, in various positions; also the cylinder, cone, pyramnid, and prism. The drawings of simple objects, domestic utensils, etc., may also, occasionally, be copied from cards. Exercises in vinelike, vertical, and horizontal repetition of conventional forms, and in drawing designs from them, may now be given. 176

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IiEADIl-VG. How TO TEACH SU]BJECTS OF THIE TTIIRD GIADE. LANGUAGE.

Readinf/.-In the preceding grades, due attention is required to be given to e)p1ctsis and anod ulation; but in this grade the exercises should take thle 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 articulation ahid proper inflections of the voice; they should be taught exFression-to comprehend tle character of the piece read, to enter into its spirit, anid, to some extent, at least, communicate it justly and forcibly. Considerable attention should also be given to vocal culture.

For this purpose exercises should be employed with the view to impart the pljiysical as well as ietuila capabilities required for this purpose. The pupils should be taught the proper position of the body, and the right mode of using the lungs and the vocal organs so as to make their utterance effective. 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* 177

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HOW TO TEACH portion of each reading-lesson being devoted to this kinid of instruction and practice. It is essential that the 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 mallnner 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 shoulid be read and re-read, until an approximation, at least, to correctness has been attained by one or more pupils. Concert reading and declamation may be resorted to occasionally, with very beneficial results. Spellinig.-Oral spelling, except for the purpose of teacliing syllabicatio)n, should be discontinued. The proper division of words into syllables is an important matter, and should receive due attention. In this connection the correct use of the kyphegi in compounds should be taught, and the pupils exercised therein. The ivritte)t 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 commnon test-words, iucluding proper names, both of persons and places, so as to impress the orthographly of such terms firmly on the pupils’ minds.

1)eflnitions.-For suggestions, see the preceding grade. 178

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GRAMM[fAR. English i,Gramnar.  alysis,_parsing and constutctio)t 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 sentences, 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 si)plest_.phraseoloqy should be used. The exercises in tconstructio 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 instruction in the other portions of the subject. Thev should be required to analyze and parse the defective sentences which occur in their own compositions, so as to discover the inaccuracies and to alply the necessary principles and rules for their correction. The exercises for the special purpose of accustoming tille pupils to care and criticism in the use of language should be continued. Complosition.-The compositions should, as far as possible, be i,mprom?6)tt, and written 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 179

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HOW TO TEACH writing of compositions is assigned as a home task. To manmy pupils 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 themnes assigned by the teacher. The compositions proper for this grade should be brief, and on sim2l-)e subjects, which should be either selected by the pupils themselves, or, whenL prescribed by the teacher, should be of such a character as to interest 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 they 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 simply, but language as the vehicle of thoughit. ARITHMETIC. Mental Arithmetic. -For the purpose of review, brief examples in fractions, both common slrd 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 accuracy 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 therefore should be carefully tested in the mental work. 180

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ARTIItIE[T. C. The special province of this grade being D)enominate Nu7lbers, the exercises, both in mental and written arithmetic, should deal largely with the applications of fractions to that class of numbers, including Federal 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 textbook. If the questions given out to the pupils to be solved instanter are spontaneously constructed 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 classroom to read from a book questions in mental arithmetic, of little variety, hackneyed in form and character, anLd 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 than in any other subject. For suggestions in relation 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. W,itten 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 181

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HOW TO TEACH is strictly utilitarian. Practical utility should, therefore, be the controlling element in all the exercises employed. The daily necessities of the house, the shop, the market, etc., indicate the general character of the selections 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 indispensable basis, should be thoroughly reviewed, and not only nmemorized, but understood. Pupils should be trained to work with reasonable rapidity, and all long and complex examples, as well as those involving obsolete weights, measures, or money, should be carefully avoided. Reduction shlould 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 methodically kept to be used as a basis c(f the necessary reviews.

SYLLABUS. Reduction Descending.-Shlow why it is so called. The denominations should always be written with the exam, Pupils should not be allowed to “add in” by a separate line; it greatly increases the work, absorbs the time unprofitably, and indicates mental feebleness. The explanation or analysis should be given by processes which make the multiplier an abstract number. The impossibility of multiplying by a concrete number should be carefully shlown. As an illustration of the above, suppose the question to be, 182

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ARITHMETIC. ” 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 75 3 00 quarts; 300 quarts and 3 quarts are 303 4 quarts; and since 2 pints make 1 quart, there are 303 qts. twice as many pints as there are quarts (803), 2 62 pts. which are 600( pints. 606
pts. In this analysis the work done on the slates is directly explained, the multipliers 4 and 2 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, which is concise, and perhaps more clear than the other, the work done on the slate is indirectly explained, the multipliers 75 and 803 not being those actually used. When this method is employed, an illustration of the following principle should be occasionally required: “The product of two or more abstract numbers is the same, whatever may be 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. Tile 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. Reduction Ascending.-Tliis is best taught and understood 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 off O’s will change to short division. 183

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O0 W TO0 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 examlples in Re(lduction be ill the first of the three. They should be few and very short in the last. Remember that the quarter of a lhundredwyelght is seldom.n used now, excepting in textbooks-the Avoirdupois drain nowhere else. In addition and subtraction, give only Avoirdupois weight. 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 may be written upon the board or read firom the text. book if pupils have one. Then require 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 mentioned may be taken in multiplication and division as wvell 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 muich a pound, hundredweight or ton, or vice versa.

Such examples may involve preliminary addition or subtraction, or both Linzear Measui-e. - Reduction.- Employ the denominations most in use-the inch, the foot, the yard, the rod, and the mile -very rarely, if ever, all in the same example. Omit cloth measure, or if briefly referred to, use only -s -, -s, ths and i6thls. 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 thie other. One may be employed to advantage in the classroom. To convert feet or yards into nmiles, and ,ice versa, use only 5,280 and 1,760; 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, multiplication and division. Surface Measure.-(Of very great practical importance.)-Treat briefly in reduction.

When 30-4 is used as a divisor let it be in. very short examples. Give examples in addition and subtrac 184

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ARITHMIETIC. 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, bricks, carpets, dress-lininlgs, etc.; also very simple questions in finding the area, circumference, or di ameter of a circle wqoen square root tis not involved, using I or 3.1416 for ratio. Solid Measure.-Employ only the inch, the foot, the yard, and the cord; use the last but little. See that pupils understand the mutual relations of lineal’, surface, and solid measures, and that they are not convertible, the units being of totally different natures. 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 of board neasurwe, giving very simple practical examples involving cost. -Dry and Liquid Meafsures.-Use no obsolete denominations. Omit beer measure.

Remember that the barrel and the hogshead 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,,ats, cisterns, etc., using 231 and 2150 cubic inches, and omitting fiactions. No other multiplication or division should be required. Circularleasure.-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 very important.) Treat reductions very briefly. Do not involve more than two or three denominations in one example. Leap-year. Addition and subtraction. Diffiirence of dates-by days, and by years, months and days. Relations of difference of longitudes to time. Explanations and examples. Conversion of longitude into time and vice versa. Mliscel’,aneous.- Practical examples in values, involving dozen, gross, quire, ream, quintal, barrels of flour, fish, etc., making out simple bills, receipts, etc. 185

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tt W TO TEA CIt iVo1tey.-Reduction and other simple exercises in Federal money are always in order firom 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 reference to the percentage of exchange.

Pupils should know soimething of the money of Canadaidentical with our own-the value of the franc, and of the German mark. Fractional Compound Numbers.-The consideration of this subject has been deferred to avoid complicating it with simpler and more important matters. Reject all examples in addition, sulbtraction, 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 fractionii 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. A. 37 3 of a bT)ushel to pecks, quarts, etc. Examples: Case 1st. B..673 of a ~, how many shillings, pence, etc., or dollars and cents. A. 7ft. 95 in., what common fraction of a B -
cubic yard? Case 2d.” B. 15 cwt. 38 lbs. are what decimal frac Case 2d.

tioni of a ton? ~8 14s. 9Ld are how many dollars and [ cents (at $4.866j-)? GEO]GRAPHY. SOUTH AMERICA. Local Geography.-Begin with the continent of South America, as a whole, its boundaries, the nainm(s and relative positions, or boundaries, of its political divisions-a few of the chief capes and islands, the position 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 186

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GEOGRIAPIIY. drainage, only two or three lakes, thie courses of the Orinoco, the Amazon, the San Francisco, and the Parana described, and their great branches named and pointed out as systems, but not described.

The local geographly of the several countries taken separately should be very brief, and should include a review of the matter previously considered in the study of the continent-that is, the relative positions or boundaries, the positions of the mountains and plateaux, 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 Geography.-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 s,tif(ce of the country as mountain, plateau, or plain; the zo)ues; the climzate as modified by latitude, elevation, and the prevalent winds; the leading characteristics of the great plains and plateaux; a brief notice of volccanoes and eartlquakes; a few of the principal plants and anzima~ls; the three races, their distribittion, and their principal occupations, and the influence of the physical geography thereon; the European Ictlguages spoken; the chief productiozns ald exports, vegetable, animal, and mineral, and the forms of governmnient. EUROPE. Local Geography.-The geography of Europe should le so taught as to avoid the presentation of a 187

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HOW TO TEACHIT large amount of minute detail. In local geography the boundaries of the continent, the names and relative positions 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 important lakes, including two or three in Switzerland; from twenty to twenty-five of the important rivers, specifving those which are important as commercial waterways; the names and positions of the capitals of the several countries, and from fifty to seventy of the other important cities.

Descriptive Ceograph?y.-The descriptive geography 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, together with their relations of blood, language, commerce, etc., with the people of the United States. In reviewing the chief cities, state any important or interesting facts in relation to each. Review.-The topics of the preceding grades should now be reviewed in outline. This important requirement may best be met by making the exercise a comparative one. It should not be a home-lesson, but a vigorous classroom exercise, discarding for the time the textbook, and using the outline 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 constitute one lesson; all the mountain systems, plateaux, plains, and volcanoes, another; the climate and productions, a third; and so on. iss

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IISIl’O RY. HISTORY OF THE UNITED STATES. General Suggestions. -Thie l(ctdij purp)ose of 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 definite. To this end a simple preliinacy outline sketc7h should be carefully fixed in the-minds of the pupils of this grade, and firequently reverted to in the reviews of all the grades in which the subject is taught. The geography already learned will greatly simplify the process. This outline can be given most expeditiously and efficiently by means of oral instruction and the use of the map. It should be very brief, and, if it be thought expedient, should be reduced to writing by the pupil for reference. Aill detail should be reserved for the study of the textbook. The following sketch is presented only as illustrative of this suggestion. Its modification byre-arralngement or otherwise, or the substitution of another in its place, may be found desirable. OUTLINE SKETC-H. 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. 189

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.HOW TO TEACH 3d. Spain, guided by Italian genius, led the way to its discov ery, exploration, and colonization. 4th. The first permanent English settlement witlhin our 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. 5thl. For a century and a half the English colonies were confined to a narrow strip east of the Alleghanies. 6th.

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. 7thl. The colonies had wars with the Indians min whose country 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 developed il the English colonies a spirit of selfreliance and political freedom, and a system of local and elective self-government. 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 colonies 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 immigration and emigration. 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 Engla2d in defense of naturalized citizens and in vindication of the rights of neutrals; 2. A war with Mexico, resulting fiom our annexation of Texas; 3. A great 190

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civil war, arising in part from questions originating in our colonial history and in part firom more recent causes. Lessonis aid Rlecitations.

-Lessons in history should be assigned by topics and not by pages. All verbatim recitations of sentences and paragraphs should 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 seqtence of events, rather than the precise date of each, is what is chiefly necessary. Mlaps, especially those of the textbooks, should be used whenever the subject may require it. Historic episodes, however interesting, should not receive the careful study given to the essential narrative. The stories of Juan Ponce de Leon, the Conquest of MexicQ, 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 teacher, 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 the facts in such a manner as not to wound the religious or political sensibilities of any. Reviews.-Reviews of the portion already taught with frequent references to the preliminary sketch, are of the highest importance. These reviews should take three distinct forms: the Clirortoloqic(al, the method 1tISiTOll Jr 191

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HO W 1‘0 T’EA CE usually followed in the textbook; the Biographical, requiring the pupil to state all that has been learned in regard to particular individuals; and the Geoqral)tical, requiring a statement of all important facts relating to the history of a locality. Many of the topics treated by the second and third of these methods necessarily become cumulative. For instance, the facts relating directly to George Washington will be gathered from at least three distinct and important periods in our history. A connected statement of the important events that have taken place in Philadelphia, or in the valleys of the Hulldsonr and of Lake Champlain, or in the State of Virginia, will necessarily cover a large part of the gelieral subject in the higher grades. Such statements must, of course, be brief, and will often be a mere chronological table. Many of these reviews and certain parts of the regular 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 important individuals, etc., are instances., The narrative reviews will necessarily 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. Suggestions for the Third 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 textbooks 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. 192

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HISTOREY. SYLLABUS OF TOPICS. The voyage of Columbus; the naming of America; the occupation of the West India Islands and all the neighboring portions 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 Novwt Scotia by the French. Vijrinia. The settlement of Jamestown and the events directly leading to it. The cultivation of tobacco; the introduction of slavery; the navigation acts and Bacon’s rebellion. Maryland.-The Calverts; religious freedom; Clayborne. .Yew Entgland.-Tie 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. The 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. -Yew Netteirla,nds.-Henry Hudson; the settlement on the Delaware; at Fort Orange; at Manhattan Island; the Dutch Governors; Kieft’s conduct: Stuyvesant. iNew 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; union 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 Caroli’a.-Charleston settled; Carolina divided into two separate governments in 1729. Georgia.-Savanuah settled; character and purposes of Ogle-tho1p. a’ 9 193

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HO W TO TEA CH 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, biographically, referring to Columbus, De Soto, Cortez, Cartier, Raleigh, etc., etc. The Frenchi and indian TVar.-This should be taught in outline, the principal points being:-The gradual extension of the English 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 nearly all other 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. Read, but do not memorize, the details of military movements and events; fix the se quence of events; use the smap. In the biographical review, let the pupil tell very briefly of Washington, Braddock, Johnson, Monckton, Amherst, Abercrombie, Howe, Wolfe, Dieskau, and Montcalm. ELEMENTARY SCIENCE. (For Oral Instruction.) PHYSIOLOGY AND HIYGIENE. The chief purpose of this study as a branch of Common -School instruction is, to give useful practical knowledge of the laws of health. As the subject can 194

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ELEIVENTARY SCIENCE. 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 esseln tial to the main purpose. Anatomy, which occupies so much space in many textbooks, should not take ip 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 conseqtuence 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. Oa(fl (desc’ilptio)t of structure or function should take the place of defti)iliols. 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 putpil’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 diaplbiagm, the heart and part of the great tubes leading to and fromn it; the brain and the bony cavity which contains it; the eye; portions of the spinal cord and nerves; small glands; (and portions of limbs, showing the relations of muscles, telndonls, 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 interesting and profitable. Where it would not be expedient to iresort to this means of illustrationll, preparations (simi 195

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HOW’O TEA CH lar to those manufactured by Auzout) could be used, if procurable, and in their absence, diagrams and clarLts. A syllabus of leading points is subjoined. It should not be expected that all these.can be taiiglht 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 mind.

To know that it consists primarily of First, a bony frame-work (the skeleton); second, a motor apparatus attached to the frame (the muscular system); third, a directing apparatus by which the mind controls the body (the brain, the nervous system, and the sensory organs); fourthi, 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 whether voluntary or involuntary, requires the destruction? of a minute part of the organism and the removal of the destroyed part from the system; that this constant destruction and removal make necessary a corresponding reconstruction and renewal, by means of new material; and that for these purposes there are provided, fifth, a circulatory apparatus (the blood-vessels), to carry away old material and to distribute the new; sixth, an aerating appalratus (the respiratory 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 material (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 mnuscles (al teidlotns,-their uses; tlheir tariranLgeent in 196

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ELE,MENTAR Y SCIENCE. pairs, and why; how attached; how able to contract; effects of exercise; use of calisthenics. 3. The nerivouis system,-the means of becoming conscious of the external world; the spinal cordl; its importance and protection; its ramifications; effects of severing or injuring the spinal cord; care of infants in this respect. Tile sympathetic system; the nerves as telegraph wires; the brain and its principal functions; uses of sleep; late hours, stimulants, etc. Tile org,ans 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. Tile skin, its structure and uses; the perspiratory glands and tubes; uses of perspiration; importance of 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 circulatory system,-the general relations of the heart, arteries, veins, and capillaries; the valves; the pulse; its rate; the rapidity of circulation. Effects of firesh air and exercise on the circulation; limits of exercise; dangers of excessive rope-jumping, etc.

Effects of sleep on the circulation; effects of tight garments; of insufficient or improper 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 apparatus; how protected; arrangement 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; exosmosis and endosmnosis as concerned in respiration; intimate relations of the capillaries and air vessels; frequent full inspirations ameans of increasing the capacity of the lungs; pernicious effects of tight lacing on the capacity and action of the lungs. The air,-its composition; relations of oxygen to the carbon and the hydrogen introduced with the food; products of respiration all invisible excepting watery vapor; the poisonous nature of carbonic acid; danger from it in wells, aid in vats; 197

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EHOW TO TEACH. the effects of smaller quantities; the other substances thrown off by the lungs and the skin; the ventilation of classrooms and of sleeping-rooms; effects of foul air fiom cellars, sewers, sinks, water-pipes, garbage, gas-lighlts, stoves, etc.; simple and cheap disinfectants; chloride of lime; chlorine; sulphlate 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. The 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. Dyspepsia, its preventable causes and terrible consequences; common errors to be avoided in the preparation of food; common poisons and their antidotes. 198 o

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SECOND GRADE. OUTLINE COURSE. Time allowed, about ten montls. LANGUAGE.

Reading.-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 Grammnar.-Analysis, parsing, and construction continued; also the correction of false syntax. Comnposition.-Continued. ARITHMETIC. Menta, and Written. -Commercial rules, through per. centage, including profit and loss, commission, insurance, stocks, interest, discount, etc.; with carefully graded exercises in analysis and calculation. The problems, to teach and illustrate the methods of computation employed in ordinary business transactions. GEOGRAPHY AND HISTORY. Geography.-Of Asia, Africa, and Oceanica, both local and descriptive; an outline review of the topics of he preceding grades.

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HOW TO TEA CI History.-Of the United States, fiom 1763 to the present time, includting the outlines of the Revolutionary War, the formation of the Union, the chief events of the national history, including also a brief outline of the great Civil War of 1861-5, and its results.

ELEMENTARY SCIENCE. BY ORAL INSTRUCTION OR WITH A SIMIPLE TEXTBOOK.

Natural Ph,ilosophy. The outlines of mechanics, hlydrostatics, and pneumatics. Astrononty.-Elementary astronomy, to include an explaaation of the ordinary phenomena, and a brief account Of the bodies constituting the Solar System. WRITING AND DRAWING. Penmanship.-Instruction and exercises of a similar character to those of the preceding grade, but more advanced.

Drawing. Continued practice in the work prescribed for the preceding grades, to which should be added the sphere, the oblate and oblong spheroids, the hemisphere, with first lessons in shading; also the drawing of rectangular solids from blocks in various positions, with a few simple directions as to perspective. Drawing from objects, natural fruit and plant forms, also con ventional forms, and the composition of designs. 200

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201 HoW TO TEACH SUBJECTS OF THE SECOND GRADE LANGUAGE. Reatlin.q.-In this grade, the simple principles of elocution, taught in the preceding grades, should be carefully reviewed, and exercises to cultivate the voice, and confirmn habits of distinct articulation should be continued to some extent. The ratio)ale of good reading should, as occasion offers, be more fully explained, particularlyas regards emphasis and mniodulation.

Emotional 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 subjectmatter, and enable them to obtain all the i forrmation and cultutre of mind which they may be made the vehicle of imparting. Much time is apt to be misspent in this grade by simply permitting the pupils to read mechlanically 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 earnestness and skill of a teacher are so thorough as the teaching of reading in this grade and the next. The READING.

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OW _0 TEACH subject, the style, the difficult or unusual words, the allusionls, 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 sufficielnt variety, both as to style and subject, to afford scope for what is above suggested. They should include didactic, nlarrative, argumentative and oratorical selections; extracts from distinguished writers ini history, biographly, popular science, etc., as well as the various departments of poetry; an important object of the instruction being to give a taste for reading more fully the works or compositions from which the extracts are made. Some account of the authors should be giveni in connection with the lessons.

Definitions and Word Analysis.-The p)refixes and suffixes learned in the preceding grades should be reviewed by means of appropriate exercises involving the application of easy roots. For this purpose such words as the following may be used - Drunkard, Thralldom)i, Depthi, Abduct, Versioni, Local,-involving English, or Anglo-Saxon, and Latin affixes only. Next, the exercises should involve the use of easy Latint roots, such words as the following being used: Avert, Advert, Convert, Pervert etc.-verse, version, diverse, etc. The application of various affixes, so as to form several words from the same root, will serve to impress the meaning of the root, i,l its various forrizs, on the mind of the pupil, as well as to review the affixes. Latin wiords need not be’taught. After a few exercises of this kind, words containing miscellaneous roots may be used; as, Predict, Subm)?it, Reject, Invade, etc.; then words containing prefixes and suffixes, as, Submiission, Objection, Confluent, Procedure, 202

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DEFIN17IONS 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: Abduct, -formed from the root duct which means to lead, and the prefix ab, which means away. Henlce, abclduct means to lead away. Actual meaning, to take away by stealth; as, “They tried to abduct the child from his parents.” In this form of analysis, the root and its meaning are first stated; next, the suffx; then, the prefix, and then the literal meaning of the word, to be followed in all eases 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. Tile 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 the formatioez of words from given roots should form a prominent part of the exercises used to fanmiliarize the pupils with the mneaninlg of the roots, as well aothe 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. Tlhus, after analyzing the word dentist, the pupil gives, as far as he can recall to mind, the words derived from the

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O110W TO TEA CLI root cdent; as dental, dentate, denloid, dentition, dentifrice, dentiform, indent, etc. Words such as dentistry are to be considered as of secondary formation, and to be analyzed by considering dentist 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 significations with 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 half is the Anglo-Saxon healf, home the Anglo-Saxon 7idm, and the German heim, etc., etc., are interesting and useful for a very different purpose, and should occupy a more advanced place in an educational scheme. English Grammar.-In this grade, the pupils should be exercised in the antalysis and parsing of selntences of a higher grade of difficulty; but those of anomalous 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 relationf the clauses or members. This is essential to a correct and definite understanding of the nzeaning of the sentence, as well as for the application of rules having reference to the construction of sentences. Some knowledge of pu?nctuation should be imparted in this connection. 204

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GRAMMAR. The following sentence analyzed will illustrate the requirements of this grade in this respect: “Pay the debts whichi tliou owest; for lie w/ho gave thee credit irelied U)oi thy ihonor, and to wtv7z/holdfroyu hiimt h/is due is both )niean anid unjust.” zlnaiysis.-This sentence consists of two members: 1. “Pay the cldeblts,” etc., to “ovest;” 2. “He vho/ gave thee,” etc., to ” unjust.” These members are connected by “for.”

The first member contains the clause 1”w/iich tho’t owest,” used as an adjunct of ” debts.” The second member consists of the two clauses: “IIe who gave thee,” etc., to “ihonzor,” and ” To witlhocl,” etc., to “ulj.ust.” This should be followed by the parsing of the most important words, which will show whether a more minulte analysis of the sentence should be required of the pupil or not. . As far as may be necessary, the strtucture of the sentence, discovered by analysis, should be made the subject of rhetorical criticism, with reference to its cleaniiness in expressing the meaning intended to be conveyed, its})ropriety, iunity, harm-)ioniy, etc. The thought itself may be, to some extent, analyzed, and subjected to critical remark. The parsinzg, as an application of the rules and principles peculiar to our own language, should also, as fa[r 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 discovering inaccuracies, as well as by impressing more deeply upon their minds a knowledge of thle rules by which they should be guided in expression. Exercises in the corr)ection) of false syntax should be. abtunldantly used in this grade. * ‘:,I 205

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HOW TO TEA H Compositiot,.-The construction of sentences should assume thile character of extended composition, the themes being selected by the pupils themselves or assigned by the teacher. Of course, care shoulld be taken that the themes are of a simple character-appropriate 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. ARITHMETIC. 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 lowing order: First, simple percentage, in four cases one fundamental and three derived; second, the apl)i cations of simple percentage, technically known as Co mission, Brokeraye, and Profi atid 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 bead of “percentage not in volving time.” The third division of the subject is interest, or “per centage involving time.” It has five cases-one ftunda 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.”o this course there is no ol) jection, provi(led( tat the formule be not employed in :…tl mental arithmetic, anid that they ecompanll)aiy the I: 206C

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ARITHMETIC. usual analysis and be not used as a stibstitute for it. With this exception, the 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, percentage, etc., are employed in the following syllabus of topics in the usual technical sense of the textbooks. SYLLABUS OF

TOPICS. The term percentage-exercises in reading per cent. Examples-Read the following, exemplified and defined first as decimal fiactions, and then as per cent.:.75,.8,.605,.003, .08-,.001, etc. Exercises in changing common fractions to per cent. and vice versa e: Examples 3, z, 4.o,~,, 138, 21, 1t,, ~-, etc., how many hundredths? what per cent.? Examples-25
per cent., 75 per cent., 33~ per cent., 147 per cent., 88-per cent., 325
per cent., 137. per cent., etc., are equivalent 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 (Fcndamental).-To find the perce)itage, the base and ratLe being given. See table, page 162.-To find a given fractional part of a given number. 207

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0HOW TO TEA CH 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 fiactions. NOTE.-When this lbform of the case has been taught, its mnodificaltions should immediately follow.

Example-Had $750; paid out 9 per cent. How much had I left? Example-Had $750; earned 9 per cent. more. How mnuch had I then? 2D CASE (Derived).-To find the rate when the percentage and base are given. See table, page 162.-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 fraction 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 i’%% 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 amountt (or difference) and rate are given. To-find a number which differs by a given fractional part of itself from a given number. 208

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AITIl’HfETIC. Example-What number is by 8 per cent. of itself more than 351? or 351 is 8 per cent. more than what number? Examiple-My flock of sheep increased 8 per cent.; I then had 351. How many had I at first?

Example-I lost 8 per cent. of my sheep, and had 299 remainimg. How many had I at first? NOTE.-Axiom.-The base is 100 per cent. of itself. This is only a form of the fundamental axiom of fractions, 1  [First, find the per cent. of the base, represented by the given number; 100 per cent. + 8
per cent. Of Aalstis w =-108 per cent. of the base; 100 per cent.-S8 per examples. cent. =92 per cent. of the base. Second, proceed as in 3d case-351 is‘0 a of what number?-299 is r%-% of what number? As a part of the general review, give an example in the fundamental case, and let the pupils derive the other three cases from it, and then their modifications.

Commission and Brokerage and Profit and Loss are but applications 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.-Teachl 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 cxamnples in interest, will be found to give better results than twvo or more. Whatever method be employed, the pupils should, from the first, be carefuilly 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-alff”-one-sixth of 24 days is 3 mills, etc., etc. As a preliminary to applying this method, the class should have a thorough trining on such questions as the following: FintI .207 of $185.75; -find.0685 of $36.25; (see preceding grade).-In 2 years, 3 months, and 20
days, at 6 per cent. per annlum, w7tat decimal fraction of the principctl is equal to the interest? at 7 per cent? at 5? at 8? at 7L? etc. 209

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O0W 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 fundamental case, and from that derive the others in their order, being particularly 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 principal for 1
yea?; to find the principal, by the interest of a principal of $1; and that, in the fifth case, the given amount is to be divided by the amount of $1. 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 with 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. Geography.-Complete the local and descriptive geography of one continent or grand division before beginning thai 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 geography of the individual countries will involve but little labor, and will be easily rememnbered. 210

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HISTORY. The geography of Asia is by far the most important and interesting; that of Africa and Oceanica is comparatively simple, and should be reduced, in teachiing, 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, together with a knowledge of the leading productions and exports, and the location of the principal cities. The whole subject of geography is embraced in this and the preceding grades; but, instead of a continuous course as is here indicated, some prefer al outline or primary course at the first, followed by an advanced course, presenting the subject in full detail. This is the plan usually followed in geographical textbooks, most series embracing a primary geography, and a higher geography for grammar schools or for the advanced classes of district schools; and this plan affords, especially in large graded schools, many advantages over a continuous course.

IUistory.-The teacher is particularly referred to the General Suggestions in regard to U. S. History, in the preceding grade. The Outlines of the Revolutionary War.(Teach as in the French and Indian War.) Causes of the Revolution.-Navigation Acts-Restriction of Colonial manufactures-effects of war on the national debt of England-taxation without representation-the Stamp Act, 1765; 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 Congress at Philadelphia-its measures-Lexington, April 19,1775-its effects upon the country-Bunker Hill-siege of Boston-Waslhing,ton appointed Commander-in-Clhief-evacuation of Boston, 211

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HOW TO TEA{CII and subsequent general drift of military events towards the west and soutli 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 FayetteBritish move on Philadelphia, 1777-Chlad’s Ford-its consequences -Burgoyne’s invasion, its route and purpose, 1777Scliuyler-Burgoyne’s disasters-Gates-the two battles of Stillwater-Clinton’s miovements-Buryoyne’s sutrrender, Octobeir, 1777-its far-reacliing consequences-the French alliance and assistance-British retreat fiom Philadelphia-Battle of Monmouth, 1778-New York the base of the British destruction along the coasts of Connecticut andVirg,inia-Wyoming battle of the Chemung, 1779-it breaks forever the power of the Iroquois-Paul Jones-Charleston captured, 1780-large numbers of Tories in the south-consequent years of guerrilla warfare-Surmter-Marion-Gates at Camden-destruction of hLis army, and of Sumter’s force-Arnold’s treason-the mutiny at Morristown, 1781-its causes-condition of the army-Robert Morris-Arnold’s ravages-Greene’s retreat-battles in Carolina and their consequences-Cornwallis at Yorktown-combination of the Frencdh and American forces-Sturrender of Co)}nwallis, 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 convention to revise the Articles-a, new Constitution devised instead, 1787-adopted by the States-,qoes into operation, 1780. In the biographical review include a brief notice of Henry, Hancock, Franklin, Lee, Jay, Livingston.

1789-1797.- TVaihitngton’s Administration-Domestic history; the cabinet-leadling measures States admitted-ltheir former relations.

Foreign relations-Trouble with France, and its causes. NOT’E 1.-Read the Indian war. The teacher will give a brief statement concerning Boone, Clark, the original extent of Virginia, and the Ordinanice of 178.. NOTE

2. Give, orally, a very brief outline account of the French Revolultion, the resulting relations of France and England and of Europe generally; the continhiance of these wars to 181.5. Refer particularly to the fact that political differences in the United States were, to a great extent, based upon onr foreign 212

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IIISTOR Y. policy, and that we were at last drawn into the vortex of the great European wars in 1812. Refer also to Washington’s Farewell Address, and give, briefly, a very few of its leading poinlts. 1797-1801.-Ad(ams’s Administ)ations. -Foreign relationscontinued troubles with France.-D)omestic history;-unpopular measures-the death of Washlington-removal of the Capital. 1801-1809.-Jefferson’s Adlniaistratioi. -Domnestic lhistory;admission of Ohio-its previous relations-the Louisiana purchase-its immediate antd 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.-(Read the detail.) The state of Europe, and the importance of our carrying-trade-extraordinary measures of France and England in relation to the rights of neutrals-English claims of right of search and impressmnent-bearing of the impressment claim upon our naturalized citizens, and our national honor-” Once a subl)ject, always a subject “-affair of the Leopard and Chesapeake, 1807 Orders in Council and the Milan Decree, 1807-Embargo, 18071809-Non-intercourse Act, 1809.

1809-1817.-AMadison’s Administration. The entire interest centers in the Foreign relations thley control the Domestic history. Berlin Decree abolished, 1810. NOTE.- Read the affair of the Little Belt Indian War.

War declared June 19, 1812 its two chief causes. NOTE.-l-ead the detail of the military and naval operations; show briefly, in outline, first, the several aggressive expeditions into Canada, from Detroit to the St.

Lawrence-tltheir general failure; second, the smallness of the navy-its brilliant success, but little direct influence,on the fortunes of the war, excepting on the lakes-utter destruction of American commerce; third, the aggressive expeditions of the British, tlhe Americans being chiefly on the defensive after 1812-IIndian war in the West and Southtlwest-invasions from Canadablockade of all important ports-naval and military expedition against Washington and Baltimore-invasion by the way of Lake Champlain-expedition against New Orleans, and its purposes fiinal repulse of all these attempts, and similar fate of renewed aggressions of the Americans against Canadadestruction of the Indian power. Give the sequence of leading events, omitting the dates, except as to years. The Hartford Convention-its alleged purp)oses-its effectstreaty of peace, December, 1814-a pailt of the general pacifi 213

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H0 W TO T’EA CIt cation of Europe upon the fall of Napoleon-the causes of the war not even alluded to in the treaty-have these questions ever been settled? If so, when and how? NOTE. Read the second Barbary war, 1812-1815-its causes and results. In the biographical review include a brief notice of Hamilton, Burl, Randolph, Fulton, Whitney, De Witt Clinton. 1817-1825.-Monr-oe’s Administration.-Domnestic history;-MIissouri Compromise, 1820-formation of new parties on questions of commerce and finance-Whigs and Democrats-the leading questions until 1845.-Foreign relations; purchase of Floridathe Monroe Doctrine, 1822, its origin and importance. 1825-1829.-Johrn Quincy Adams’s Administration.-Tariff of 1828-leads to the defeat of the Whigs and the election of Jackson.

1829-1837.-Jacksont’s Administiationi.-‘Domestic history;United States Bank-nullification, 1832-Clay’s Compromise. Foreign relations;-the French indemnity. 1837-1841.- Van Buren’s Admninist)ation.-Panic of 1837-SubTreasury Bill, 1840-political revolution.

1841-1845.-Hamreison-Tyler’s Admninistration.-Domestic history;-the Bankrupt Law-Dorr’s Rebellion.-Foreigq? relations;-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 Mexican war-boundary claimed by Texas-M-exican war, May, 1846, to Feb., 1848. NoTE.-Read the details; give the leading military events in sequence, omitting all dates, excepting years. Teach with the following grouping. Northe?n operations-Taylor east of the Rio Grande-west of it Wool-Keao ney-Doniphan-Fremont. Southern ope)eations-Scott’s campaign. Treaty of Guadalupe Hiclalgo-its terms-discovery of California gold in 1848-its important subsequent influence upon the national development. 1850-1853.-Taylor and Fillmore’s Administration.-The Slavery 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.-Pierce’s Administration.-Effects of the Fugitive Slave Bill-the Kansas-Nebraska Bill, 1854-it annuls the Mis 214

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IIISTOI? Y. souri Compromise-rise of a new party, “Free-soil” or Republican-civil war in Kansas, its causes-flow of immigrants into that territory. 1857-1861.-Buchtanan’s Adminizstration. Continuation of the Kansas troubl)le-Jolhn 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 Ca’olina, Dec., 1860-Fort Sumter more States secedeConfederate government formed, Feb., 1861.

1861-1865. Lincoln’s Administration.-Civil war-Fort Sumter, April 12, 1861-effects upon the Northl-thle President’s proclamation-more States secede, making eleven in all. NOTE.-Pead the details of the war; show the importance of the question of foreign intervention, and the eflobrts on )both sides 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 Chambersbhrg-all of which were repelled. That the main objects of the aggressive movements of the Union troops were, 1st, the destruction of Leers army; 2d, The opening of the Mississipl)pi-that after the opening of that river by the fall of Forts hIenry and Donelson, and the subsequent cap)ture of New Orleans and Vicksburg, the lines were contracted by a movement from the northwest to the. southeast, ending in Sherman’s march from Atlanta to Savannah and Goldsboro’. The leading incidents will then readily fall into place.-Showv the importance of the blockade, the chief function of the fleet also, but very briefly, the enormous expcnditore of men and money on both sides, and the measures by which they were obtained.

1865-1869.-Jo7hnson’s Administration.-Death of Lincoln-the two subjects of leading importance-Ist. Providing for the pi)blic debt - 2d.

Reconstruction - the 13th Amendment — the President and Congress quarrel-impeachment-tlithe French in Mexico, and the demand of the Uiited States Governmentpurchase of Alaska-laying of the first Atlantic telegraph cable. 1869-1873.-Geant’s Adginistratioii.-Pacific Railway-14th and 15thl Amendments-the Alabama question-leading provisions of the treaty of Washington thle 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 andl tlhe Lakes as the great water - 215

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HO W.‘O TEA> CII way-steanm and steamboats-lrailways-telegraphs. In the liograpllical review include a notice of prominient men, such as Calhoun, Clay, Webster, Seward, Greeley,:Morse, etc., etc. ELEMENTARY SCIENCE.

Ncatural Philosojphy.-The suggestion to use “a simple textbook” should not be initerpreted as a recommendation to dispense with oral instruction ill this branch. On the contrary, the, proper use of the textbook is as an auxiliary, as a general guide to the teacher ill the selection of subjects, and as an important help to the pupil ill preparing at home for the recitationI of a lesson which has been previously explained and illustrated inll the classroom. Any system of procedure which omnits this preliminary oral instruction is certainly not worthy of the name of teachli?ny. The textbook 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 encouraged and led to report such instances of the applications of the principles they have been taught, as they can themselves discover in the phenomena and incidents 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 teacher will find a wide difference in the readiness with which individual pupils will conceive and apply scientific principles. With a few, the bare statemenlt of a principle will often enable them to point out 21(,

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ELEEMENTARY SCIENCE. 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 interpret the facts presented, be clearly apprehended. In all experiments the pupils themselves slhould be made as far as possible participants. 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 encouraged to try further experiments for themselves at home, and to furnish an account or a repetition of them in the classroom, 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 textbook. The teacher, and’not the book, should be the master. An intelligent pupil will not be long in finding out whether or not the statements in the text are the limit of his teacher’s acquisitions. The great majority of young minds are hungry for this sort of knowledge, and it will unquestionbly 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 i n which th is w ill be found necessary, the terms porosity, })orous, solid, a nd im peeetra7bility may be taken as instances. It is by no means necessary that the pupil should be abl e t o give a n exact and comprehensive scientific definition of such terms; a few analytical ques 10 217

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HOW TO TEA CGII tions by the teacher will readily show if the subject is understood. Whelka lesson from the textbook is to be given 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 explanations the pupil 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 experiment to a knowledge of the facts. The facts once ascertained, the prin)ciples underlying them may be deduced. A limit will, sooner or later, be reached, where the more recondite parts of the subject, so far as they may be entered upon, must be taught empirically, 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 yravity” 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-]et a pupil pull, and at the same time notice that lie is exerting a force, that the position of the index will vary with the degree or amount of force, that the miotion 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 the effects are identical with those produced by his muscular force. He will no longer vaguely conceive that the effect produced 218

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ELEMENTARY SCIENCE. upon the scale is because the body is hieavy (which was to him a vague term), but because the earth actually pulls it as lhe did, though no connecting bond is visible, as when ie pulled. A knitting-needle suspended ault balanced upon a thread and acted upon by a simple mag’net, will clearly convince him thls,t a force may be 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 attraction upon it.” If now you wish to teach the law of the variation of tIle weight of a body of invariable mass, as should indeed be done, the next step must be empiricacl. The pupil’s deficiency in mathematics forbids any other course of procedure. The “Law of Gravitation” must be stated to him, together with the reason for so doing without proof. It will develop inll 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 problems 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 complicatedl 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 element and evidence of a teacher’s success-experimentimg at home by the pupils themselves. The principles of thie lever may be just as well developed by means of a pen-handle, a pointer, or a window-pole, as by a polished brass or steel bar; a large spool makes an excel 219

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HOW TO TEACH lent wi,eel and axle; a ribbon-block a good single p11lley, fixed or movable; a slate, a book, or a, shlingle, an i)tclinedplaiae; a pocket-knife will soon furnish a good wvedge from a little piece of board, while the use of the blade itself is an excellent illustration of the application of the principle; and a large screw or a discarded auger-bit, with a knitting-nleedle or a pen-holder for a lever, makes an efficient siiiqle screw. And so through every department of the subject. Nothing marks more fully the ability of a teacher than fertility in such resources. Strings, tops, balls, and marbles; pop-guns, p)otato-mills, bean-shooters, and putty-blowers, and the thousand and one nameless articles to be found in pupils’ pockets, furnish an exhaustless mine of apparatus, and good apparatus too, for the skillful teacher. The immortal Dalton wvrought out his atomnic 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 “whlere there is a will there is a way.”

SYLLABUS OF TOPICS. (To be illustrated asfar as possible objectively.) CONSTITUTION, FORMS, AND PROPERTIES OF MATTER.-Ilustrate the following terms-body or mass, molecule, atomn; 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, compressibility and expansibility, inertia, mobility. FORCE AND ITS FOIMS.-A ttraction and repulsion: refer briefly to the fact that atoms and atomic forces are treated of in clhemistry. Indestructibility of matter to be briefly explained. MOLEcULAR FORCES.-Colhe8sve foc’e: the properties of matter which are dependent upon cohesion; tenacity, flexibility, brittleness, hardness, ductility, malleability; the properties depend 220

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ELEMENl’AR Y SCIENCE. ent upon cohesion and molecular repulsion; elasticity. Illustrate the elasticity of flexure; of compression; of expansion; of torsionI. Relations of solids, liquids, and gases to molecular attraction and repulsion. Adhesive force: properties dependent upon adhesion; capillary attraction and its uses in organic and inorganic nature. Divisibility of matter-into particles by mechanical force; into molecules by heat, solution, etc.-Whlat forces are overcome in each case, and by what other force. MECHANICAL FORCE.-Gravity-why called universal gravitation; its simplest phenomena; its law; weight, a measure of gravity. MECHANICS OF SOLIDS.-Center of gravity; line of direction, plumb-line; stable, unstable, and indifferent equilibrium.

Simple.Jfackines.-Lever, with simple problems in mental arithmetic; pulley, wlheel-and-axle, inclined plane, wedge, screw. MECHANICS OF

LIQUIDS (Hyd?rostatics).-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 hlydrant water flows fiom the open tap; at what height it ceases to flow, and why; other illustrations of the same principle; what that principle is; the hydrostatic paradox; the hydraulic press; specific gravity; the hydrometer; why iron ships float. MECHANICS OF CASES (Pneumatics).-Air-its compressibility, expansibility, and elasticity; chief mechanical difference fiom liquids; its weight; its pressure in.all directions; upward press-Lre and how shown; the mercurial barometer, its construction, principle, and uses; Torricelli’s experiment; P-ascal’s experiment; the 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 the most impressive and beautiful phenomena connected witlh the sun, the moee, the stars, planets, 221

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tHOW TO TEA OIL comets, and meteors. iHe should endeavor to induce the pupils to observe more attentively these phenomena, and to excite their curiosity to know about them. Encourage them to ask questions in relation to what they observe; as, Why does the moon change its appearance? Why does the sun rise sG far from the east point, or set so far fi’om 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 heavens 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 Eartk, its form, magnitude, motions, etc. Circles, and angular distanices on the Earth and in the heavens; Dcty and i~ight; the Seasons, etc: these topics should be illustrated by the use of a Tellurian, and Problems for tie Globe should be used for the purpose of exercise and illustration.

Next, teach the general arrangement of the Solar Syste)m. Inferior and superior planets-their magnitudes, revolutions, position of orbits, periodic times, and apparent motions. The niat kenatical defizitions necessary for the proper understanding of this portion of the subject should be taught incidentally thereto. 222

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FIRST GRAD)E. Time allowed, about twelve monlths. OUTLINE COURSE.

LANGUAGE. . Reading, Spelling, Definitions, and Word Analy.sis, continued as in thIe preceding grade. ELglislh Gramnnar.-Analysis, Parsing, and Syntactical criticism and correction, continued; the anomalous and icliomatic forms to be taught and explained. Composition.-Exercises on selected themes; Practice in Letter Writing, commercial and social.

MATHEMATICS. Mental and Written Arithmetic.-Continued and reviewed, including the rules pertaining to the mensuration of regular plane surfaces and solid bodies; with exercises in analysis and calculation, continued. Algebra.-Through equations of the first degree. Geometry.-The geometry of plane figures, with practical applications. GEOGRAPHY AND

HISTORY. Geography.-The Outlines of Physical Geography. Hiistory.-The Outlines of Ancient and Modern.

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HOW TO TEA CH ELEMENTARY SCIENCE. BY ORAL INSTRUCTION, OR WITH A SIMPLE

TEXT BOOK. Natural Philosophy.-Simple outlines completed, to include Acoustics, Pyronomics, Optics, Magnetism, and Electricity.

Astrooiomy.-Elementary, continued and completed. Chemistry.-Elementary principles and facts. WRITING AND DRAWING. Penmans hip.-Instruction I0 be continued as in the preceding grade, with practice in the writing of paragraphs, verses, business forms, notes, superscriptions, etc.

Drawing.-Drawing objects of regular form in perspective, block combinations, etc., with shading; copying pictures offamiliar objects, animals, etc., with easy landscapes, as far as the time may permit; also (for males) simple architectural and mechanical drawing. The drawing of designs to be continued. MISCELLANEOUS BRANCHES. Bookkeeping.-Single and double entry; with careful instruction in the principles of the latter.

Constitution of the United StaItes.-History of its adoption; its various provisions and amendments; the reasons for the same to be explained as far as may be necessary or appropriate. 224

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225 How TO TEACI SUBJECTS OF THIIE FIRST GRADE. LANGUAGE. Reading, Spelling, and Definitions.-See the preceding grade. English Grainmar.-The exercises of this grade comprise those of analysis, parsing, and conposition. Sentences of an irregular or idiomatic coHstruction, should be presented to the pupil, with the view to-show how far their analysis can i)e made to harmnonize 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 contravenes well-established rules and principles-shlould 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 Addisoii, Johnson, Irving, 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 is 10* GRAMMAR.

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HO W TO TEA CHI 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 auxiliary in carrying on the instruction here suggested. Composition.-The exercises in composition in this grade, as in those preceding it, should be, to some extent, im’prom2ltu, 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 ill the outline course, should receive a very careful attention at this stage of the pupils’ progress. MIATTHEMATICS. Arithmetic.-In this grade, the teaching of arithmetic consists in large part of a review of what has gone before, with exercises sufficient in number and difficulty 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: Excha)ngye, Eqvoatio) of’ Paymnents, Proportions, Partnersh)i2, SqAcare Root, and Cutbe Rloot, with their simple applications, and Menstration. The exercises employed 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 226 l

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ARITII[ElY~IC. being in all cases deduced fiom the analysis. A careful explanation of the business transactions involved in any of the rules or their applications, should always be given before the pupils are required to solve the problems. Failure more frequently arises from a want of this knowledge 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. EXCiANGE. Its nature; bills of exchange; par of exchange; acceptance; domestic exchange-to include two cases:-I. 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.-Rememnber that the old par value of the pound sterling is now prohibited by law, and that the new legal value is $4.866X. EQUTION 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 del)its and credits. Analysis, on the principal of interest, reducing each principal concerned to $1.

PItOPORTION. Ratio; proportion defined; relation of antecedents and consequents; ratio of 4 to 12, 4: 12=-l-; method of finding the missing term; simple and compound proportion distinguished; 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. PARTNERSIiP. Terms definled. Cases:-1. To find each partner’s share when the profit or loss is divided according 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 227

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HOW 7O TEA CH square root. Illustrate by simp7le powers, integral and fractionalcommon fractions and decimals (the latter carefully). Problems in which the root contains denominations other than units. Illustrate by geometrical construction (square of the sum of two lines). The following arc 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 detot.,inate numbers.

Show that the numll)cr of supe:ficial units corresponding to the liraear units of the length, is tmulliplied by the number (abstract) of linear units in the width. Thus, if the lei,ngth 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. Teachl and illustrate the geometrical theorem on which this problem depends. Give various questions requiring 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 formuta representing the cube of the sum of two quantities, will enable the pupil to remember clearly the details of the rule. Thle applications of the’Cube Root should include the computation of the contents of similar solids. MENSURATION. This should at least include the following cases:-1.

To find the area of a parallelogram when the base and altitude are given; 2. To find the area of other quadrilaterals, 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 contents 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 mienital exercises, the slate being used only when the numbers 228

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ALGEBR-,A. involved are too large to be readily retained in the mind. The pupils should be very frequently practiced in this mental work. The textbook in mental arithmetic should be sparingly used, and great care should be exercised in assigning lessons for liome-study in this branch.

Algebra.-TlThis subject should be taught as a peculiar Xathematical la()quagye, by means of which the relations of quantities and the results of their combinations may be expressed, and thus the reasoning in regard to them facilitated. The symbols, both of quantities and relations, or operations, should at first be carefully taught and illustrated. The simple operations of addition, subtraction, multiplication, 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 what the proposition is to ordinary language. It is the means of definitely expressing a mathematical truth, either particular or general. Inequations (technically so called) express truths, but not exactly; as, when we say, x+y75, we do not indicate holw mc,?tc7 the suim of x and y exceeds 5; but if we say, x+y 6, 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 textbooks, for mental solution; as, What number is that, to the half of which if 5 be added-the sum will be 11? Even thie dullest pupil can be easily made to perceive the use of expressing that 229

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H0 W TO TEACH condition so that it can be clearly kept in view; as (x representing the unknown number) x +5-11. In solving such a problem, the successive steps or processes of reasouin)y should be kept in view. Thus, subtracting 5 from each member, the result (expressed by a secoild equation) is, x-6; and, multiplying by 2 the result (expressed by a third equation) is x=12, which gives the solution. (Applied axionm 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 Mulltiply x 3x + 5 by x’-x’+ 2; Divide x3-y3 by x-y, etc., etc. These exercises are proper in their place, but of themselves they hlave but little,- if any, educational or practical value. SYLLABUS Ol’ TOPICS. 1.

Preliminary explanation of symbols, both 16tters, as representatives 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 in such a way as at once to indicate their meaning; as, a 4 b. the the stim of a and b: a-b, the diffelenca between a and b; a x b, the product of a and b, etc. Exercises in finding the numierical value of expressions, whien particular values are attributed to the representative letters, will greatly aid in accomplishing this result.

Thus, find the value of a2b-b3 when a=3, b=2, c= 1, etc. c 2. Easy problems in arithmetic, the solutions of which may be facilitated by the 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 equations. Most of the textbooks in use will afford a sufficient variety. 230

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ALGEBRA. 4. Practice in solving equations of this character; 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 processes of analytical reasoning. Thus in the equation above given, the pupil will easily be made to perceive, that the nmultiplication of both members by 24 will produce an equation without firactions. 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 expertness 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 =xd’ (1.) = d b c x -a x -‘b (2.) - 4 — =2 b a x-a2 x -b2 (3.) - = 0 b a x x (4.) - -1 a-b a+b (a + b) x (a - b) x 1 (5.) _-a-b a+b -4 231

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110 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-iinvolving the various methods ofelimziJtation -should follow this, and sufficient practice in the solution, of paoblems should also be afforded. The latter, with the preparation herein indicated, may be made a most important aid in training the mind to carefuil 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 afford hints as to the order and method of presentiing the most important topics. Geometry.-This subject, from its extremely abstract character, is quite difficult for young students fully to comprehend. It is essential that the abstract ideas with which it is concerned should be developed in the minds of.the pupils at the preliminary stage of the study. Unless this is done, they cannot be benefited 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 nature of the truths to be proved, as well as of those assumed 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 twvo dimensions; next, that of a line, abstracted from the surface, involving one dime)sio); and, lastly, that of a point, as indicative of a position in the line, or at either of its extremities, and involving no diienisions.

These terms, reversing the order, should then be defined; namely, point, line, sbut;face, solid. 21,312

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GEO~E TR Y. LTUnless these fundamental conceptions are clearly and thoroughly impressed upon the minds of the pupils, no true progress can be made. The classjificationt of lines and surfaces may then be taught, the fundamental idea used being that of direction; as of a straight line, never ch7anyi)y its direction; a curve line, clhanging it at every pointt; of a broken line, changing it at certain points. The classification of surfaces into plane, ctrved, and broken may be made in an analogous manner. With this, the idea of parallel lines may be made to harmonize by conceiving them as lying si(de by side (literal meaning of parallel), and all in the same direction, i. e., tending to a point at an infinite dlistance, or tending to points, at a finite distance, iwhich, wherever assumed, are at the same distance from each other (the latter may be tlie easier to develop at first). The idea of a plane annyle should be made to harmonize with these conceptions of a straight line and parallel lines, being conceived as expressing the di#‘erenzce in diriectiont of two straight lines that meet at a point. NOTE-This, it will be seen, harmonizes with the idea of parallel lines, which tend to a point at an infinite distance, and hence never meet, and cannot form an angle; while the straight lines that form an angle tend to a point at afinite 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 reasonzihg should be carefully explained, and that they should, to some extent, be exercised in the same. Tlhis can easily be done by bearing in mind that geometrical truths 233

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HOW TO TEACH have reference to a comparison of magnitude, and hence involve the idea of equality as a definite fact, anl iniequality 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 which lies opposite to the greater angle is greater (not how much greater). Hence, as a preliminary exercise, the following might be given:Quzestion-If A is equal to B, and B is equal to C, how does A compare with C? Answeve They are equal. Question-Why is A equal to C? Answer-Because they are both equal to B. Question How does that prove it? Aniswe,i-Because things that are equal to the same thing are equal to each other. QuestioinCan that be proved? Angswer-It cainnot; it is selfevident. Qutestio)i-What are selfevident truths called? Ansvwer They are called axiom)s. A variety of such exercises may be employed; and, in this way, the pupil, before beginning formal demonstrations, may be made clearly to apprehend the nature of geometrical reasoning-so different from that which he has generally employed during all his previous studies, 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 geometrv. and to learn it by } eadi)tg (not rolto 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 entirely the possibility of any rote study, or merely verbal recitation. For this purpose, the figures employed should be different firom those in the text book, the letters used in connection with the figures should be changed, or numerals used in their stead. The demail 234

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GEOM[ETRY. strations should sometimes be given without using either letters or numerals; and, in the case of such as are very easy, the figures themselves may be dispensed with. Ili 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 following Syllabus (intended to be only suggestive) embraces everything required. SYLLAB:S o0 Topics. I. Elementary decfinitions-axioms-symbols. II. Theorems relating to straight lines, angles, and polygons 1. The sum of any two adjacent angles is equal to two right angles. 2. Vertical angles are equal to each othter-. 3. The various theorems 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. Triangles are equal, (a) when they have two sides and the included angle in each respectively equal; (b) when they have two angles and the interjacent side in each respectively equal; (c) when they have three sides in each respectively equal. 6. The sumI of the three angles of a triangle is equal to two righlt 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. 13. Any problem, either after, or in connection with, these theorems, which can readily be performed; as, to construct an equilateral triangle, 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 mnay also be profitably interspersed 235

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HOW TO TEACH III. Ratio and Proportion. IV. Tile Circle:-1. ~elations of angles to cthords. 2. Relations of angles to arcs. V. Area: 1.

Comnparative areas of parallelograms and of trialgles. 2. Measure of areas, of a parallelogram, of a triangle, of a tra(pezoid, etc. 3. Of squa)es 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 Physical Geograp)hy.-Some departments of physical geography, tloughl perhaps not knownil 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 direction of a mountain chain, or the boundaries of a continent, 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-cuLrrents. 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 planetary conditions, of the mutual relations of all its parts, internal and external-the land, the sea, and the atmnosphere,-together with the geographical distribution and conditions of the various forms of vegetable and animial life, and of the various races of mankind. In the brief time that can be allowed to so comprehensive 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. 236

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PHYSICAL GEOGRIAPHY. A synopsis of the points included in the grade is here appended. If a textbook is used, Ithe teacher should first be thoroughlily familiar witli its contents, so that it may be employed principally as a reading or referencebook from which appropriate selections may be read in the class. If any other course be pursued, most of the textbooks 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 OF TOPICS. The Earthi as a Globe-its form and dimensions, and how ascertained. The Earth7 as a Planet the zones. and their causes. The Interior of the Earth-its probable condition, and how infelrred. (Treat briefly.) The Su:face of the Earth-its division into land, water, and atmospheric envelope; the land divided; the ocean not; co parative extent of land and water. Thle Land Surface (Omit Geology). Comparison of the continents in their direction, contour, elevations, andarea; comparison of the great mountain systems of the continents; volcanoes; distribution of; theories of volcanic and earthquake plienomena (very brief); comparison ofthe plateau belts; of the great plains; the great islands and archipelagoes, their distribution and arrangement. NOTE.-To illustrate the comparison of the continents by the several classes of elevations, give upon the blackboard rough chalk diagrams of sections o’f the continents. The 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 effects. (Both very brief.) The Atmosp7here-its constituents; vital importance of its watery vapor and its carbonic acid to plants and animals; eval)poration fiom the ocean surface, especially in the torrid zone; the almosphere and the watery vapor as the Earth’s blanket. 2113 7

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HOW TO TEACH The Winds-the trades, and counter-trades; theory of (very brief); region of variable winds (very brief); the winds as carriers of ocean vapor; solar heat the great cause of oceanic and atmosplheric circulation. Thte Great Rain-belt-its annual oscillations; tropical, rainy, and dry seasons; the mountains as condensers-illustrations.

Dainage-the river systems of the several continents compared; 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); icebergs, their origin. Vegetation (very brief)-warmth and-moisture necessary to; general characteristics of tropical vegetation; examples of tropical plants; examples of plants of subtropical and temperate regions; 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 t)rief)-comparison of the characteristics of the several zones and continents as to animal life; examples. Matfi-thie various races, their numerical proportion, leading peculiarities, and distribution. The pictures and illustrative diagrams and maps of any good textbook will, if properly used, very greatly simplify and expedite the study of nearly every department of the subject, and will render definite ideas that might be otherwise vague. HIistory (Outtliiies of A?icieit ancd Moddri).-The genieral” syggestionis given iii relation to the history of the United States (see Third Grade) are, to a very great extent, applicable to this grade. The much greater extent of time to be covered in teaching ancient and modern history, together with the vast number 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 minnute study of the subject. 238

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HISTORY. This outline should be brief, but should show clearly the chronological and geographical relations of the nations, 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 firmly 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, medieval, 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 or2der of tine 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 historv of different nations has been studied, the leading events of each should be arranged in synchronous tables. The reigns of contemporaneous sovereigns, for example, should be compared, and the connection of events in each carefully studied. Reviews, sucl as are suggested in connection with thie United States history, by a chronological, geographical, and biographical arrangement of topics, should be given with sufficient firequency. The following syllabus presents thie topics which should be embraced il the outline above suggested: 239

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HOW TO T’EA CH SYLLABUS OF TOPICS. 1. The nations and countries of the most remote antiquityEgypt and Ethiopi(, Babylonia and Assyria, Lydia, Medi(, Syria anld Palestine, Persia. Of these only a brief sketch need be learnied. 2. GREECE-tile mytlholoic 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 Republic in its various stages, including the contests between the orders of Patricians and Plebeians; the successive wars with the Samnites, Carthlaginians, etc.; the civil wars, including the triumvirates; the fall of the Republic, and the foundation of the Em. pire under Augustus. Thle territorial conquests should be shown in connection with tlhis. 4. THE ROMAN EMPIRE-its territorial acquisitions and clian-lges firom Augustus to the division of the Empire at the death of Theodosius, including a brief sketch of the principal reigning emnperors, 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. 6. 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 fall. 8. FRiANCE-the invasion of Gaul by the Franks, and foundlation of the Me?rovinqan Dynasty; a brief sketch of it; thle Carlovingian Dynas.ty, inceluding Chlarlemagne’s conquests. and the revival of the Western Empire; the Capetian Dyinasty to the end of the Reio-n of Louis XI. This will include the Crusaddes. 9. ENGLAND-a brief sketch of British History before the time of Egbert; from Egbert to the Tudors. (England may be 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 the leading nations; other nations, including Germany, Prussia, Russia, etc. 240

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ELEMEATARY SCIENCE. 12. AMEnRICAN 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 wiiters upon the most importaut topics.

The instruction should embrace advice and direction as to the best writers in each period and nation. Historicactl selections will be found valuable for this purpose. ELEMENTARY SCIENCE (BY ORAL INSTRUCTION OR A SIMPLE

TEXTBOOK.) Xatural Philosophy.-For general suggestions, see preceding grade. SYLLABUS OF TOPICS. Acoustics.-Preliminary-a general idea of the transmission of vibrations illustrated-the nature of sound-sounding bodies-a medium necessary-the air as a medium-other medialimits 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-forksspeaking-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.

Pyronornics.-Heat-known only by its effects-effect on the nerves-effect upon the constitution of bodies-transmission of heat-the three methods of transmission illustrated-air a bad conductor and worse radiator important relation of this fact to clothing, to vegetation, etc.-liheat as a sensation-rela 11 241

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HOW TO TEA CH tion of terms hot and cold-sources of heat-quantity and effects of solar heat-its relations to physical geography - source of the heat developed l)y friction-motion of mass converted into molecular motion-heat only a mode of vibratory motion -force as indestructible as matter-source of heat in combustion-the thermometer-principles employed in its construction-nature and determination of the zero-evaporation-its causes-effects on temperature of bodies-phenomena of boiling-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-engineits 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-photometry by shadows-non-luminous bodies-how seen-reflectionits 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 thlermic 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 artificial magnets-polarity-attraction and repulsion-imagnietic induction-temporary and permanent magnets-the Earth a magnet-magnetic needle, and why it points to the north.

Electricity.-Frictional electricity-conductors and non-conductors-electricity not a fluid but a polarizing force, related to magnetism-attraction and repulsion electric induction-insulators-effects of points-atmospheric electricity-its originlightning-rods-the flash the white hot air-the thunder-popular fallacies as to electric fluids, thunder-bolts, heat-lighltning, and the cause of thunder-current electricity fiom chemical actiona battery, its wires and poles-polarized condition of the parts hlow to develop heat and light uses made of thesesim. ple helix-simple galvanometer-magnetism developed by electric current-temiporary magnet and magnetic telegraph. 242

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ASTIYON~OXY. Astronomny.-The topics embraced in the preced ing grade should be carefully reviewed in this grade, as far as may be necessary to secure thorough preparation for the advanced portions of the subject, which consti tute the special work of the grade. The use of the globes should be continued, ill order more fully to fa miliarize the pupils with the Doctriile of the Sphlere so important to a clear understanding of astronomical facts. The interest of the pupils in the observation of astronomical phenomena should be sustained by calling their attention as frequently as possible to facts whllich.they can verify in this way. 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 furniish valuable aid in the accomplishment of this. The positions of thile planets Jupiter, Saturn, Mars, Veinus, and Mercury, among the stars, should be kept constantly in view, together witl their apparent mnotions, 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 earth (give a genieral idea of the manner of finding this, altlough a minute knowledge of parallax may be reserved for the more advanced part of the subject); solar spots-theory with regard to their cause, their apparent miotions, what is deduced. firom this. The Zodiacal ligiht may be briefly referred to in connection with the Sun. 2. TiHE

PEIAtARY PI,ANETs-in succession, commencing with 243

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IO W TO TEACII 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 subjiuct more attractive. 3.

THE MooN-in a similar manner, teaching about its phases and their cause, its revolutions, periods, Harvest Mioon, Librations, and a brief general description of the lunar surface (Selenogialahy). 4. ECLIPSES-solar and lunar; total and partial, how caused; comparative frequency-ecliptic limits. Transits, their causewhy important. 5. TIDES flood and ebb, spring and neap, how caused; principal facts connected with them; the tidal wave; heighlt of tide 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 the orbits, size, mnass, density, and apparent magnitude of conspicuous comets. 7. A brief account of Meteors, their supposed nature and origin  cause of the periodic displays of meteors. 8. STARS-classification the constellations na-mes, classification of, brightest stars ineach-apparent chlange in position due to precession; cause of precession; exercises in finding the constellations visible at any time; the galaxy; proper motion of the stars; multiple stars; variable and temporary stars; distances of stars, how found; parallax, diurnal and annual. 9. NEBULa-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 unequal; equation of time; tropical, sidereal, and civil years, how and why they differ in length. 11. ASTRONOMICAL REFRACTION-its effect upon the apparent positions of the heavenly bodies; variation at different altitudes. 12. GE1NERAL REVIEW. 244

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UIIFEMIS)TR Y. In giving instruction in this subject, its special office as a means of training the cogzcep()ive.faculty. sbouild be kept steadily in view. Facts of observation and facts of inference should be carefully distinguished. Apparatus and diagrams will afforld some aid ill enabling the mind to grasp the more difficult facts of inference; but the actual observction of the phenomena to be illustrated should precede, as far as possible, the use of these. Thus, a good telluriah 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 conmplicated machinery, without the attentive observation of the natural phenomena, and the conceptions based upon them, rather serve to give false niotions than to impart clear ideas of the actual facts. A good planlisphere will prove a valuable aid in the study of uranography. 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, hlie is contemplating the works of a beneficent Creator, infinite in wisdom and power. No subject is so well qualified as astronomy to give just ideas in this respect, and, while performing a peculiar and most important office it the training and development of the intellectual powers, to exalt the understanding and give elevation and tone to the whole character. Chemistry.-The instruction given in chemistry in the common schools, like that given in physics and 245

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IOW TO TEA C’I. ill the natural sciences, must necessarily be at the most only rudimental. Whole sections of each subject must be omitted. Ill every department of oral instruction ill science, the principal object should be to form the mind to proper habits of observation. This, together with the knowledge of the facts and principles of science incidentally thus imparted, is a )repcratttiou1 for the systematic study of these sciences, rather than a formal attempt to impart a knowledge of their complete outlines. Yet this knowledge of the facts and principles thus obtained, is in itself of so great practical importance 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 chemistry 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 within his own power to acquire. As iii 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, perhaps more than anything else, insure the further prosecution of the subject by the pupils themselves. There are so many excellent textbooks in the rudiments of this science, all abounding with practical hints and illustrations, in relation to the construction of suclt 246

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CHEM[IST11R } apparatus, that 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 objiective process of instrulction may be applied to the study of facts in chemistry, the subject being quite as profitably and easily approached from any one of a dozen starting-points, other than the one here selected. No other department of science can be made to showv the value of this process more clearly, or to furnish more important mental discipline. Experiment nmust 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 tihe subject can here be sufficiently expanded to illustrate the process, the furither details being necessarily left to the ingenuity of the teacher. SYLLABUS OF TOPICS. FoncEs.-(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 ph,ysical forces, in pulverizing, solution, fusion, polarization, etc., in which the substance remains unchanged in composition and general properties. Chiemical 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 common names as far as possible at first, such as sulphur, copper, blue vitriol, alcohol, etc.) E,xp. 1st. Show copper filings and pulverized sulphur; let the properties of each be objectively noted; melt them together slowly; notice the iheat 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.

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HOW VTO TEA CU Exp. 2d. Burn sulphur in air; the sulphur disappears, and an invisible sour gas is formed, perceived by the lulgs and the smell; has been made from the sulphur and the air. Exp. 3d. Burn alcohol or kerosene in air: slhow water as a product; heat given out in all these changes of substance. Chemical attraction: such changes are produced by a force known as chemical attraction or chemical affinity: the atoms of sulphur and copper attracted each other and formed a new substance; (omit its name); this force frequently breaks old combinations to form new and stronger ones. Exp. 4th7. 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 tihe 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. Sth. 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; compare 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. Exp. 6th. Burn a piece of marble or chalk in a charcoal fire; lime kilns; marble changed to lime; properties different; tell that the great heat lias driven off the gas. 248

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CII[EMISTRY. Exp. 7tl. Make and filter lime-water; agitate some of the gas of Exp, 5 with lime-water in a bottle; water becomnes milky; the gas has united with the lime as before burning; chalky sediment settles; lime water a test for this gas; meaning of the term test. Exp. 8t7t. Agitate the gas from soda-water with lime-water: result identical with the last; therefore the gas in soda-water is the same as that from the marble. E.rp.

9th. 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; therefore the same gas. Exp.

loth. 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. 1tit.

Burn ordinary charcoal; it seems to have dissolved in the air; gather the air firom 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 fats, coal, bread, wood, etc. Show by over-)aked l)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. 13th. 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. Hydrogen, 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 the atmosphere: combustion; nitrogen; carbonic acid; its relations to plants and to animals; illuminating gas. Chemistry of rocks anid soils: limestone and lime; quartz, 11* 249 lb

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ti0 W TO TEA Ct[ sandstones, and silica; clay, slate, and alumina; granite, feldspar, potash, soda, etc.; common salt. Chiemistry of plants and animals: starch, gum, sugar, lignin, vegetable and animal oils, albumen, gluten, etc. Special topics: bread-making, soap-making, glass-making, fermentation, distillation, photography, etc., etc.

MISCELLANEOUS BRANCHES. Book - keepintg.-After the forms required in single-entry bookkeeping have been taught, whlich should be quite brief, the nature of double-eu try bookkeeping should be explained, by showing the relation of debit and credit, and how the former in one accounIt 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 clcssificatio)t of accounts should be followed by an explanation of the three books-Day-book, Journal, and Ledger. Jourlnalizing simple entries in the Day-book should then be taught; aind sufficient exercises given to impart readiness and accuracy in the process. The keeping of a simple and brief set of accounts will then render the whole process and theory intelligible to the pupils’ minds, aiid will also render them sufficiently expert in their application. 3. All the common bitsiness forinis should be taught; as the form of bills, receipts, bank checks, promissory notes, bills of exchange, invoices, etc., etc. Bitsivless correspoildenice 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 250

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MISCEL L ANEOUS BRA NCIIES. carefully attended to. Quantity and qutclity should both be insisted on in this respect. Constitttion of the United States.-The recommendation to teach the Constsitulion of the United(

>States applies 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 requiremenits of the organic law of the nation-the distribution 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 carefully elucidated, such as ex-I)ost-facto lavs, bills of atta(in(de-, habeas corpus, etc., etc. The history, English 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 various times, during the past history of the country, would prove, in boys’ classes especially, as far as time and opportunity may admit, very beneficial for discussion, as tending to impart readiness in speech, as well as selfreliance and freedom in thought and opinion. i 251

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IO HW T’O TEA CII. GENERAL SUGGESTIONS RIELATIVE TO THE CLASSIFICATIOX AND

INSTRUCTION OF PUPILS IN SCHOOLS. Reviews.-Such a review of previous lessons, in connection with each new lesson ou the same subject, should bc given as will cause the pupils properly to associate together the facts learned in all of them, and thus lead them to acquire a comprehensive as well as a famnliliar knowledge of each subject contained ill the grade or the course. General reviews of subljects should be had at least as often as once during each month; and in these the leading facts learned in previous grades should be included. Progress 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.

Progress of P:upits.-It often happens that a few of the pupils of a class wvill so far outstrip their fellows in a single month,,iS to render it necessary to transfer these rapid learners to a class of the next higlier grade. While great care should be exercised not to stimulate the excessive mental activity or precocity of young pupils, yet the disparity of progress in pupils of tie samiie class may sometimes be used as an incentive to 252

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i GENEPAL SUGGESTIONS. urg,e forwvard those who are extremely sluggish or inert. This may be done by promotinlg in a public manner, at the end of eachi month, two or three of the pupils 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 permittillg 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. Recitations.-No class in the primary grades should be required to spend more than 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 claige in the mnanner of conducting class exercises, are both necessary in order to furnish opportunities for rest during school hours. Thie recitations should be spirited exercises. The questions should be as definite as possible. The teacher should carefully avoid implying in the question any of the facts or principles that should be 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 assisted to fix. Unless thoroughly familiar with the details of the textbook, the teacher needs special and renewed preparation quite as muich as the pupils. Without this, he will not succeed. In hearing the recitations, he should carefully discriminate between the statements 203 II I I -A

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IHOW TO TEACH. found in the textbook 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. Lessostsfor Htome Study.-IIn every class, however well graded, the pupils will differ much in age, health, mental capacity, and home advantages. A correct and judicious classification will reduce this inequality 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 inferior mental capacity or opportunities for home stiudy. Teachers must bear in mind that the one great object of homne study is to train the pupils to self-exertion,to give them the ability to depend upon their own efforts as students, and by degrees, to dispense with the aid of a teachler. It is, therefore, of supreme import~‘ce to avoid everything that would discourage, or deprive of selfreliance; and nothing has a stronger tendenicy il this direction than the imposition of excessive tasks. Teachers are especially admonished to be considerate toward pupils of a delicate constitution, an over-excitable brain and nervous system, or in temporary ill-health. MIany 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 bI)y an inordinate devotion to books and study. The lenytt7 of the tasks imposed should, therefore, be 254

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GENERAL SUGGESl’IONS. most carefully scrutinized and adjusted. The practice of assigning a fixecd number of words, lines, paragraphs, pages, or examples, without a minute inspection of their nature or contents, is often accompanied with disastrous results. The pupils are wearied and discouraged; and the parents, finding the work of the schoolroom trans ferred to the home circle, lose all confidence in tie 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 written upon the blackboard, and made the basis of the recita tion. This will do much to induce a rational method ill study, and prevent a slavish adherence to the text. The teacher should advise with his pupils as to their time 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 firom home lessons on account of its tendency to produce myopy, when studied by artificial light. Many hours of confinement in a crowded classroom, 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. Physical Training.-The pupils should be exercised, as much as may be practicable, in such a way as to expand the lungs, develop the muscular system, t 1 3 255

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HOW TO TEACII. and impart an easy and graceful carriage to the body. In schools for boys, the marching drill should be employed in the ordinary evolutions of the schools, with such instruction as may be requisite to make it effective. Light gymnastic and calisthenic exercises should be employed as far as may be necessary or suitable for tlhe 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 exercise of the mental powers. Whlen pupils are under 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 classroom work. In the case of young pupils, even while in the classroom, it is desirable that they rise at intervals for a few minutes, to exercise, by varied movements, both the upper and lower limbs. -lanners and l[orals.-Such instruction should r be given daily to the pupils of all the grades as will foster a spirit of kindness and courtesy towards eachl other, a feeling of respect toward parent and teacher, and a love for cleanliness, order, law, and truth. The reading lessons and the ordinary incidents of the schoolroom may be made the means of inculcating the great moral truths common to all well-ordered minds. Children learn to love and practice kindness, neatness, truthfulness, and politeness by observing these traits in those around them. It is, therefore, exceedingly important that the teacher should present living 256

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GEPFRAL SUG GESTIOIYS. illustrations of these qualities, by her owu conduct before the pupils, during all her intercourse with the class.

Social relations, the dependence of each individual upon his neighbor-the necessity of labor the beniiefits 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 development of the moral nature is of greater importance to the welfare of the individutal and the community than ally other part of education, i1o opportunity should be omitted for training children in such habits as will cause them to grow up trutllful, honest, self-governing, and law-abiding citizens. ii .

GOVERNMENT AND DISCIPLINE. In all the rules and methods of discipline employed, the true object of discipline should steadily be kept ini view; namely, to train the pupils so that they may form rigt1 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 punishment which, whether that species of coercion be permitted or not, should be most carefully avoided. Modes of punishment especially painful to the corporeal system, such as the sustaining of wearisome biurdens, unlnatural and long-continued attitudes of restraint, standing, kneeling, etc., are exceedingly wrongful andcl injurious. Equally so is the confining of de i 25,7 I

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HOW TO TEA CH. linquents, by tying them or shutting them inl closets.

These are all a resort to mere physical force, instead of moral incentives, and involve 1o appeal to a sense of honor or duty in the child. Thley do not properly assert the at7hloriit*y of the teacher, nor do they really produce obedience on the part of the pupil. When corporal punishment is resorted to, it should be of a proper claracter never partaking of that continuous infliction of pain which we denominate torture, and never administered except in a spirit of mildness, and deep regret at its necessity. Whlen all those persuasive incentives and a,gencies vwhlich constitute mzor)al suasio)n have been appealed to without avail, and there is no other recourse, corporal punishment may be resorted to in order to save the }u}il, but for no other reason. The necessities of discipline may seem to require 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. Inl directinlg the various movements required of the pupils, care should be taken never to touch t hem). The teacher should take such a position 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 commands but once, and that they must be obeyed at once. Harsh tones of the voice are unnecessary and improper.

Words of disapprobation may be uttered by the teacher in a tone of decisio), wiithout the use of any severity that would imply resentment, anger, or antipa thy on the part of the teacher. On the contrary, the language used, and the tones of the voice, should al 258

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GENERAL SUGGESI IONS. ways express a feeling of synpalty 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 tagonlize it, and prevent all real submission, securing only a temporary semnblance 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 fiLr as may be proper 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 sufferingacutelyv; 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 per manently, impairs its respect and regard for the teacher. The cultivation of a due feeling of symp)atly 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 inspires 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, 2iD9

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HOW TO’EA CII. eager to tell what they know, and in an audible tone of voice. Encouragement has a peculiar influence in promoting both melntal and moral improvement. Public exj)o.sutes ad(l badgyes of disygace belong to a class of punishments which, if ever resorted to, shlould be employed under careful limitations, and with great circumspection and prudence, for it requires a skillful, discreet, and conscientious teacher to use them safely and wvith advantage. Ii thle discipline of girls, they should be avoided altogether, as destructive of that niCe sense of slhame and tlhat delicate sensibility to reputation which are to be most carefully fostered in the fenmale character. Cleanli)ness, qnetho(t, aid regul(rity 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 tlle dictates of morality and social refinement. Children should be taiughit how to sit, to stand, to move, to walk. Rules are required for this; but they need to be only fewv and simple, and the nice and watchful observation of children renders it quite easy to’enforce them, provided they are not capriciously applied. Children must first be taught them, and then niever permitted to violate them without admonition or correction. Teachers should never forget that their pupils are constantly tand closely watching their conduct, and that they are prone to imitate whatever they observe. Tlley should, therefore, see nothing that they mniay 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 260

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GENERAL SUGGESTIO-0S. suLroundings. These should, therefore, be neat and orderly. The rooms in which they assemble should be clean, the desks and other furniture, as far as possible, without injury or defacement, and everything giving evidence of constanlt and punctilious attention.

Children, firom the contemplation of these things, unconsciously acquire habits of order, neatness, and regularity, which hlave an important bearing upon their usefu’lness and happiness in after life. The basis of goo(l 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 Lunnatuiral; and whatever is Lunnattural is really disorder1l!y. The postures should be graceful, easy, andl uniform, but should be frequently chlangoed; the movements, while as simultaneous as perfect attention would necessarily produce, should also be easy and naLtural. Goo(l order involves impression rather thlan repression; it does not consist in a coercion fromn wlhich result merely silence, and a vacant gaze of painful restraint, but it results from the steady action of awakened and interested intellect,-the kindling of an earnest purpose and an ambition to excel. Hellce by making punishment the first; instead of the last, resort, the true object of educational discipline is defeated. The prevailing atmosphere of the classroom 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 everything essential to effective discipline will sprilng firom an interchange of confidence and regard between teachers and the pupils committed to their instruction. ./ 261 i I J I

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HOW TO TEACII. 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 teachtiny, let the kind of knowledge and the mnode 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 simply Cat 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 regardest him?” Thus may 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 religious character of our age.and country, and must render our Common School educa tion, as a means of fostering and slpporting the free institutions of our Republic, unworthy of support or vindication. 262 k!

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GEI~ERAL SUGGESTIOINS. A SCHOOL LIBRARY. Its Necessity.-Of all the means necessary to a tea.cher’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 coin mnent. Its enormous quantity shows thatit is extensively read, and it is well known that it finds its chief market among the youLng. An enfeebled mnind and avitiated taste, as shown iiin 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 j jurious results of an uncheckea indulgence in thle men tal dissipation which this trash induces. Its darker shaides and more injurious and debasing consequences need not here be dwelt upon. The proper antidote and substitute for this wide-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 paragraphs illustrating the lesson, a brief 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 I) i I }1 263 iI I

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HOW TO TEACILI many a valuable work that might otherwise remain 1untouclhed upon the shelves. Once introduced into the world of good books, and fairly interested in even one of its many departments,once tastin,g and enjoying the wholesome sweets of a sound and ennobling lite(rature, a young man or a young woman, it may be safely trusted, will not abandon it for that to which allusion has been made. Ateacher has failed in one of the most important of all of his functions, 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 Ch,arPtcter.-Great care and discretion are necessary in the selection of books for a school library. As far as possible they should be subcll books. 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, Chaillt’s works, the Rollo books, etc., togethler with a fair proportion of good stan dard works, such as those of Prescott, Bancroft, Lossing, Hume, and Macaulay, the Student’s Series of Histories, Translations of Jos-phus, Herodotus, Thucydides, etc. In selecting from the great number of works of imaginary travel and adventure, written with the professed purpose of giving to youth instruction in the physical geography, natural history, and social condition of various countries, all those in which the narrative is overdrawn, and therefore 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 2,64 ‘i I I

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GENERAL SUGGESI’IONS. erence to their moral purity and their permanent value as additions to litera_ture, rather than because they are new and are advertise as popular. Many a school library has been filled with Ephemeral trash and made the instrument of mental degradation rather than of elevation, by want of care in this respect. Such old classics as Robinsoni Crusoe, Paul and Virginia, anld the Vicar of Wakefield, should not be wanting. A few of the leading popular poets should also be represented by small volumes. In their selection of books, pupils should be advised by their teacher, so that they may not attempt works beyond their 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 -Rolanld, 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 inlg points in relation to France and Europe at the period referred to, then reads a brief but inter esting 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 the pupils because they have none of the preliminary conceptions relating to the subject which the method above indicated supplies. Ti 265

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HOW TO TEA CH. Books of travel present peculiar advantages for this method, and are among the most instructive portions of current literature.

Anl excellent plan with individual and advanced pupils is for the teacher to select some interesting book, sufficiently brief and simple, and in place of the usual exercise 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. I I.I “I’l 266

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ECLECTIC SERIES-LANGUAGES. ECLECTIC CLASSICAL SERIES. By G. K.

BARTHOLOMEW, M. A. Bartholomew’s Latin Grammar. I 2m0, 276 pp.

Bartholomew’s Latin Gradual. I 21m0, 150 pp. Among the features that please me, I may specify the natural order of arrangement and scientific treatment of subjects; the unusually full and careful analysis and derivation of words; the principles and practice of analyzing sentences; the excellent manner in which the modes and tenses are handled, particularly the subjunctive mode; and the pains taken to bring the Grammar upl) to the present state of the science of language.”-Pi-Prf. W.

S. TYLER, ,4Aiiherst College. … The whole foice of reason lies on the side of this Romoani method of proniunciation…. This is the first effort of which we are aware to put the system forward as a preferred one in a school hand-book. Once adopted generally, its alleged harshness-which, after all, is no greater than that of Greek-will cease to be thought of.

The absurdity of objection on that ground will appear to any one whose ear has ever caught the mellifluous flow of lIomier’s grand old Greek, or of Anacreon’s lyrics, polished, perfect, and musical.” -Newu York Evening, Post, WM. CULLEN BRYANT, Editor. DUFFET’S FRENCH METHOD. A,4 Progressive and Practical ffethodfor the Study of the Fiench Lan guage, by F. DUFFET, Paris, France, author of a PoIultir Method for Zearninzg En,glish.

D1)uffet’s French Method, Part L 12mO, I92 pp., limp clothl Duffet’s Frenoh Method, Part IL 12mO, 192 pp., limp cloth. “Prof. Duffet has been a very successful teacher in the English, Spanish, and French languages, and there is scarcely a city of any importance in the United States but contains his students, whose facility in reading and speaking French is the best testimonial to the excellence of his methods of instruction…..

By patient and lalorious comparisons and corrections [of methods heretofore in use] he has at last completed a book which many competent French linguists and students pronounce the very best of all methods of instruction in French.”-St. Louis Democrat. t I

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ECLECTIC EDUCATIONAL SERIES. BOOKS FOR TEACHERS’ LIBRARIES. Pestalozzi: His Life, Work, and Infuience. By HERMAN KRUSI, A. M., Instructor in Philosophy of Education at the Oswego Normal and Training School. 8vo, cloth. 248 pp. Illustrated. ” Probably no man living has more thorouglylv investigated Pestalozzianismi than Prof. Krusi. The son of his first associate, a hearty admirer of his system, early traine(l in its methods, having had an experience of thirty years as instructor in Normal Schools in Switzerland, Germany, England, and America, he has had ample opportunities to test these principles and processes in a great variety of ways and in widely different circumstances. I heartily recommend the volume to the earnest teachers of our country.”-B. G. NORTHROP, Sec’y Coizui. Board of Educaioll. History of Pedagogy. Twelve Lectures on the History of Pedagogy, delivered before tlhe Cincinnati Teaclhers’

Association. By W. N. HAILMAN, A.M. 12mo, cloth. i20 pp. Illustrated.

Kindergarten Culture, in the Famtily and Kindergarten. A Complete Sketch of Froebel’s System of Early Edu cation, adapted to American Institutions.

For the use of Mothers and Teachers. I2mo, cloth. I20 pp. Uni formn with History of]Pedagogy, and by the same author. Illustrated. The Examiner, or Teacher’s Aid. By ALEXANDER DUNCAN, A. M. Designed to assist Candidates for Teachers’ Certificates in preparing for Examination; Pupils in Reviewing their Studies; Teachers in Examining their Classes; and for the use of Normal Schools and Teachers’ Institutes. THE EXAMINER embraces, in concise form and systematically arrainged, questions upon Orthography, Re(eadin,o-, Grammar, Aiihretic, Geography, Uizited States Histor),, T/eosy anzd Praclice qf Teaching, Physiology,, and Algebra. i i i I I

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ECLECTIC EDUCATIONAL SERIES. DI)IAILOG(UES AND ELIOCUTION. The School Stage. A new collection of Juvenile Acting Plays. By W. H. VENABLE. For Little Children. Plain and full direc tions relating to Costume, Properties, an(l Stare Busi ness. Illustrated. The Amateur Actor~ Over twenty choice Acting Plays, selected from stand ard English authors. By W.

H. VENABLE. For Young People. Full and lucid descriptions and explanations. Illustrated. Dramas and Dramatic Scenes. Edited by W. H.

VENABLE. Twenty Plays, selected from the writings of standard authors.

Adapted to school and home exhlibitions, and to the use of advanced classes in reading. Illustrations by FARNY. I2m0o, cloth, 236 pp.

Elocution and Vocal Culture. With numerous Exercises in Reading and Speaking. By ROBERT KIDD, A. M. I 2mo, cloth, 480 pp. MceGuffey’s New Juvenile Eclectic Speaker. Improved edition. 200 easy and animated Exercises for Reading or Speaking. 228 pp. -McGuffey’s New Eclectic Speaker. 300 master-pieces from the very best sources of Amnerican and English Literature. i2mno, cloth, 504 pp. l

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ECLECTIC EDUCATIONAL SERIES. SPECIAL READING Kidd’s Rhetorieal Reader. For Class Drill and Private Instruction in Elocution. By ROBT. KIDD, A. M. I 2mO, cloth, 360 pp. Institute Reader and Nornial Class-Book. For the use of Teachers’ Institutes and Normal Schools, and for Self-Training in the Art of Reading. By W. H. COLE. 12mo, cloth, 360 pp. Part I. contains practical directions to,primary teachers, followed by exercises from the Primer and First and Second Readers. Part II. continues the directions, and contains a Maoiial of Articulation for drill purposes, and a series of leading lessons from the Third, Fourth, and Fifth Readers. Part III. is intended to be a complete Reader for advanced classes, andl to furnish those who desire to pursue the study of Elocution w ithlout a master, with the necessary instructions and exercises. Part IV. is added to enable those who have little or no experience in such organizations, to form and conduct a successful Institute. The Hemans Reader. For Female Schools.

Extracts in Prose and Poetry, selected from the writings of more than I30
different authors. By T. S. PINNEO, A. M., M.D. i2mo, cloth, 480 pp.

MeCGuffey’s New High School Reader. For Advanced Classes. Embracing about two hundred Classic Exercises for general practice in Reading. I 2mo, cloth, 480 pp. It MceGuffey’s Rhetorical (Guide. Fifth Reader of the fc/eccic Series, by the late WVM. H. McGUFFEY, LL. D. Elegant extracts. in Prose and Poetry, with copious Rules and Rhetorical Exercises. I2mo, cloth, 480 pp. -I i f

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ECLECTIC SERIES-SCIENBE. The Elemenets of Physios. By SIDNEY A. NORTON, A.

M., Prof. in Ohio Agricultural and Mechanical College, and author of ElementJ of vatural Pli/losopz/y. For Academies and Commoni Schools. i2mo, cloth. 286 pp. Illustrated. Elements of Natural Philosophy. By S. A.

NORTON, A. M., Professor of General and Applied Chemistry in Ohio Agricultural and Mechanical College. 360 illustrations. Problems and Copious Index. Principles of Logic. By A. SCHUYLER, M. A., Professor of Mathematics and Logic in Baldwin University. I21mo, cloth. I68 pp., including Analysis of Contents. Manual of English Rhetoric. By A. HEPBURN, Professor in Davidson College, N. C. The Principles and Rules of English Rhetoric, for the use of classes in High Schools and Colleges. i2mo, cloth. 280 pp. Manual of Physiology and ygiene. By R. T. BROWN, M. D., late Chemist-in-Chlief in the Department of Agriculture, Washington, D. C.

50 Lessons, adapted to the use of Common and High Schlools. 288 pp.

Illustrated. Manual of the Constitution of the t. S. Designed for the Instruction of American Youth in the Duties, Obligations, and Rights of Citizenship. By ISRAEL WARD ANDREWS, D. D., President of Marietta College.

408 pp. Library edition, 8vo, full slheep. School edition, i2mo, cloth.

Good Morals and Gentle Manners. By ALEX. M. Gow, A. M. A systematic TextBook on Moral and Social Law. “Practical Ethics for the training of the true Gentleman and Lady.” 12mo0, cloth.

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ECLECTIC EDUCATIONAL SERIES. HISTORY. Manual of Ancient History. From the earliest times to the fall of the Western Em pire. By M. E. THALHEIMER, formerly Teacher of History and Composition in Packer Collegiate Institute. 8vo, 378 pp. Handsomely illustrated with full-page engravings of Ancient Temples and other historical ob jects, charts of the principal cities, and accurate and finely executed double-page maps of the various coun tries considered in the text. Complete Index and pro nouncing Vocabulary. Mediaeval and Modern History. By the same author. 480 pp., full 8vo. I2 beautiful and accurate double-page maps. Voluminous Index. Ij ~ The above are companion volumes, uniform in size, binding, and price, the two-together forming a valuable, concise, and complete History of tle World, from the earliest times to the present. History of England. A History of England, for the use of schools, by M. E. THALHEIMER, author of Ancient and Medieval and Modern History. i2mo., cloth, 288 pp.

Illustrated. An admirable work written in the entertaining style of the author’s A/,.cie/it History and Medkeval and Modern History, which have been pronounced unrivaled by the press and leading educators. Spirited illustrations by FARNY. Double-page maps, and numerous sketch-maps, skillfully drawn and engraved, and giving all needed assistance in this direction. Eoleetio Historical Atlas. Full 8vo., cloth. 18 double-page maps, accurately drawn and engraved. A hand-book for general readers and students in-Ancient and Modern History. I’ A Sehool History of the United States. By W. H. VENABLE. I2m0., 270 pp. Finely illustrated, and accompanied with carefully drawn maps and charts. I I i

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ECLECTIC EDUCATIONAL SERIES. RAY’S MATHEMATICS. A,4 Thoroughl, Pri-ogressive, and Complete Course it Ari/imeziic, Algebra, and the Hii,her Mathematics. Ray’s Primary Arithmetic. Ray’s Intellectual Arithmetic. Ray’s Practical Arithmetic. Key to Ray’s Practical. Ray’s Test Examples in Arith. Ray’s Higher Arithmetic. Key to Ray’s Higher. Ray’s New Elementary Algebra. Ray’s New Higher Algebra. Key to Ray’s New Algebras.

Ray’s Plane and Solid Geometry. By ELI T. TAPPAN, A. M., Pres’t Kenzyon College. I2mo., cloth, 276 pp. Ray’s Geometry and Trigonometry. By -ELI T.

TAPPAN, A. M., Pres’t Kenyon College. 8vo., sheep, 420 pp. RaIy’s Analytic Geometry. By GEO. HI. HOWISON, A. M., Prof in Mfass. Instilitze of Technot/og,. Treatise on Analytic Geometry, especially as applied to the prop erties of Conics: including the Modern Methods of Abridged Notation.

8vo., sheep, 574 pp. Ray’s Elements of Astronomy. By S. H. PEABODY, A. M., Pi-of. of Physics and Civil Ezingintteering, Mass..4,‘zic. Colle,e.

Handsomely and profusely Illustrated. 8vo., sheep, 336 pp. Ray’s Suryeying and Navigation. With a Pi-eliminary Treatise on Trigonometry and Mensuration. By A. SCHUYLER, Pi-of of Appblied Mathemiatics anzd Logic in Bald omJii Universily. 8vo., sheep, 403 pp. Ray’s Differential and Integral Calculus. Elements of the Infinitesimal Calculus, with numerous examples and applications to Analysis and Geometry. By JAS. G. CIARK, A.

M., Prof. in W4illitam e(uell Coll/e-e. 8vo., sheep, 440 PI) DESCRIPTIVE

CIRCULARS ON APPLICATION. APR 2 6 1921 EMBRACING

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