PEDAGOGICS. 
 
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PEDAGOGICS 
 
 A MONOGRAPH. 
 
 A New Theory and Practice in Teaching. 
 
 BY 
 
 R. D. ALLEN and J. T. GAINES. 
 
 EEEATA. 
 
 At bottom of page 28 read " 81 " for " 8'." 
 In Prin. 16, page 25, for "6^" read "a'." 
 
 LOUISVILLE: 
 
 PUBLISHED BY J. T. GAINES 
 
 1889 
 
PEDAGOGJGS 
 
 A MONOGRAPH. 
 
 t 
 
 A New Theory and Practice in Teaching. 
 
 . BY 
 
 R. D. ALLEN and J. T. GAINES. 
 
 LOUISVILLE: 
 
 PUBLISHED BY J. T. GAINES 
 1889 
 
COPYRIGHTED 1889 BY 
 
 R. D ALLEN and J. T. GAINES. 
 
 SDUCATION DEPr. 
 
PREFACE. 
 
 The authors believe that in this little volume they have 
 presented sometiiing new on the subject of education. 
 
 Associated in normal school work in the summer of 1878, 
 they first exchanged views upon the art of teaching. Begin- 
 ning with substantial agreement in theory and in methods, each 
 has ever found profit and pleasure in hearing the experiences 
 of the other in, to him, a strange field of labor — the one being 
 in the public school work, and the other in charge of a select 
 private school for boys. 
 
 The fact observed by both, that a method devised for use 
 in one field could be successfully applied in the other, sug- 
 gested the possibility of systematizing all teaching. 
 
 Frequent consultations and exchanges of experiences with 
 this end in view have taken place. Many things have trans- 
 pired to delay the accomplishment of their plans. They do 
 not now claim to have discovered all or to have devised a 
 perfect system. But some principles are now clear that were 
 once dark ; others are growing clearer as experiment burnishes 
 them. Enough has been completed to justify submitting 
 their views to the great brotherhood of teachers. 
 
 They ask for and ardently desire criticism, both favorable 
 and adverse ; the Empire would not have been had no ene- 
 mies opposed Napoleon, nor would the Lieutenant have been 
 the Emperor had no friends upheld him. 
 
 The chief concern of the authors has been to be under- 
 stood. Pestalozzi, Froebel, and Horace Mann were not under- 
 stood by their cotemporaries, nor is Parker fully understood 
 to-day. And why? No one can learn a fad by reading it or by 
 hearing it unless he knows it already in its elements. It is by tlie 
 
 544290 
 
4 ' . PREFACE. 
 
 'light of our experience as teachers that we must read the 
 
 words of a brother. Practical lessons are given within these 
 
 pages. Begin by trying these, and with the light they shed 
 
 seek to know the truths contained herein. That they are 
 
 f valuable may well be claimed, for they are the assimilations 
 
 ; from observations and comparisons upon more than twenty 
 
 ( years of active school- room work. 
 
 The postulates for teaching, on page 17 and following, were 
 first noted down as indnctions from observations of work in 
 teaching. After they were agreed upon, a theory was sought 
 jthat would satisfy them. That theory has been found, and it 
 is the mission of this Monograph to expound it. It is believed 
 that it will satisfy all experiences, from that of the mother- 
 teacher to that of the university professor ; that it will meet 
 the wants of all grades and kinds of teaching. 
 
 No such absurd claim is set up as that there has been no 
 effective teaching heretofore ; it is only asserted that often 
 where good teaching has been done it has resulted from pur- 
 suing the line of least resistance, and has not been dictated 
 by principle. 
 
 It is a fact, which no one can deny, that the majority of 
 teachers do adhere to definitions and make them the basis for 
 their work. 
 
 Believing it to be true, that there is not a principle or 
 truth to be found in any department of knowledge which 
 can not be so presented that the pupil shall himself discover 
 it, the authors submit the result of their labors to their col- 
 leagues in the hope that many who are now working in dark- 
 ness may thereafter walk in the light. 
 
 Thanks are due to Prof. F. E. Spaulding, of Louisville 
 Military Academy, to Hiram Roberts, of the Louisville 
 Training School, and to Messrs. Wm. J. McConathy, Wm. 
 Marriner, W. O. Cross, and O. B. Theiss, of the Public 
 Schools of Louisville, for valuable suggestions. 
 
 R. D. ALLEN, 
 J. T. GAINES. 
 
 Louisville, Ky., November, 1889. 
 
THEORY. 
 
 The practice of teaching set forth in this Monograph is 
 based on tlie theory that " The primary attributes of in- 
 tellect are, (1) Consciousness of Differences; (2) Conscious- 
 ness of Agreement, and (3) Ketentiveness. Every properly 
 intellectual function involves one or more of these attributes, 
 and nothing else." [Bain's Mental Science.] 
 
 If it ai)pears that Abstraction, Judgment, Reason, Mem- 
 ory, and Imagination.* the so-called faculties of the Intellect, 
 can be adequately explained on this theory, then it must be evi- 
 dent that a correct practice in teaching must ever engage the 
 powers of the intellect in "Differences," in ''Agreements," 
 and in " Rstentiveness," and also that any practice in teaching 
 which is not founded on the three attributes mentioned is 
 wrong, and therefore injurious in proportion to its departure 
 from these essentials to all healthful activities of the intellect. 
 . No one can question the proposition that agreement of 
 objects in qualities is the foundation of all classification. This 
 action of the intellect (originating classes) is called Ab. traction 
 by some ; by others it is called the Notion-forming Power. 
 
 Observe the mind at work assigning an object to a class 
 already formed. Does the intellect not discover the resem- 
 blance or agreement of the object with the notion, which is 
 the basis for the class ? Is not this Judgment f 
 
 If an intellect, without bringing two objects, A and B, in 
 conjunction, perceives their agreement by virtue of perceived 
 
 '•'Intelleclual Consciousness and Sense have not been included in this analy- 
 sis of the faculties, as some prefer, because they are conceived to be merely the 
 acts of intellect in separating objects internal and external. In either case, if 
 the classification be retained, the act named by the term is better expressed by 
 the first attribute— Consciousness of Differences. 
 
b PEDA(lOGIt;s. 
 
 resemblances in each to C, with which it in turn has been 
 compared, and again discovers agreement in D and E by vir- 
 tue of resemblances in each to F, and thus continues multi- 
 plying its experiences, will it not at length perceive the agree- 
 ment in these experiences and be able to arrive at the law : 
 *'In so far as two things resemble a third they resemble each 
 other?" And is not this an exercise of the intellect in that 
 mode of its existence called Reason f And is any thing else 
 involved in the whole j:)rocess, except agreements, differences, 
 and retentiveness? 
 
 In all these acts, in abstraction, in judgment, and in rea- 
 son, does not the Memory repeatedly exhibit itself? What 
 is memory if it be not a recurrence of a preceding state of 
 the intellect because of its agreement or disagreement with a 
 present state ? 
 
 Examine the following product of the Imagination: " The 
 cataracts blow their trumpets from the steep." What is it 
 but a blending founded upon the agreement of the emotions 
 produced by the trumpets and falling waters? 
 
 Thus far in the discussion agreements have had promi- 
 nence in reconciling the so-called faculties of the intellect to 
 the theory of three attributes, and three alone. But is not 
 the intellect engaged as well in each exercise with perception 
 of differences? Is not discrimination the foundation of a 
 perception of agreement? Can a resemblance be perceived 
 except by the light of differences already perceived ? And 
 does not the intellect after each exercise retain what it has 
 acquired, just as a plant retains the elements it has stored 
 from the air and earth? ■ Could the intellect abstract without 
 retaining the objects to be compared ? Would there be any 
 thing to abstract unless they were thus held ? Could the in- 
 tellect judge without retaining the notion of the class as a 
 basis with which to compare the new object? Could the in- 
 tellect make tJie successive steps required to reach the act 
 known as reason without holding over the fruitage of each 
 effort to serve as the basis for the succeeding comparison ? 
 
THEORY. 7 
 
 An evident corollary of thig theory is that a certain order 
 must exist in the recurring occasions for the exercise of the 
 three attributes. Reflection upon what has been said in 
 respect to Reason will reveal clearly the order of progression 
 to the assimilation of any principle. 
 
 Observing narrowly an intellect in its advance to assimila- 
 tion of truth, three steps* are apparent, viz: (1) perceiving 
 objects; (2) distinguishing resemblances and differences, and 
 (3) discovering the truth which is a content of the resem- 
 blances. During this process the sense-objects have become 
 thought-objects, and the intellect, retaining only those parts 
 which are essential to the truth assimilated, perceives the 
 objects more clearly than at first. 
 
 Assimilated j^f^'^^^^^P^^^ are retained by the intellect as 
 thought-objects, and these, as occasion arises for an exercise of 
 the will by an individual, are, (1) perceived, (2) compared 
 with reference to their fitness to the occasion, and some con- 
 tent of their relations (3) taken as a law for action. 
 
 That every man in every important act of his life does 
 exercise his intelli^ct in deciding as to his course in that case, 
 before exercising his will, can be illustrated by an occurrence 
 in every-day life : One sees a man leave his house prepared 
 to go to his daily work, sees him pause, look round carefully, 
 return, and shortly after reappear carrying an umbrella. 
 What has passed in his mind? The sultry state of the 
 atmosphere, the direction of the wind, the distinctness of 
 sounds, the presence or absence of this or that, many things, 
 in fact, which are retained by his intellect as thought-objects, 
 by the sensations which their representatives in nature pro- 
 duce, have aroused his attention. His intellect at once insti- 
 tuted a comparison among them, extending its view to embrace 
 others with which they were linked, concerning rain, its effects, 
 the value of life, the worth of an umbrella as protection, etc. 
 From this comprehensive group his intellect was able promptly 
 
 * The three acts of the intellect here pointed out will, for convenience, 
 hereafter in the text be called (1) perceiving, (2) comparing, and (3) assimi- 
 lating. 
 
8 PEDAGOGICS. 
 
 to make a law for his guidance. He probably foresaw it 
 would be necessary for him to be exposed during the day, 
 and he prepared himself. 
 
 Suppose, now, that after pausing and noting the appear- 
 ance of things, he had gone on, how can we account for it? 
 He has simply taken other links of the chain as his law. He 
 remembers, perhaps, that he will not have to leave his office 
 during the day, and sees that he can reach there before the 
 rain. Or perhaps he recalls that he has another umbrella at 
 his office for such contingencies. 
 
 To illustrate the relations of these intellect-acts, viz., 
 Perceiving, Comparing, and Assimilating to mind growth, 
 two simple examples are here given. 
 
 Suppose the task be to classify a number of marbles. 
 (1) Perceiving takes place. (2) Comparing follows, which 
 brings to view certain resemblances, as color, size, value, etc. 
 (3) Selection of one, as " color," for the guiding principle, the 
 classification is readily made. For the Second illustration, 
 suppose the task be to discover the prii|cipl^» upon which 
 depends the form of axle-nuts of a buggy? (1) By perceiv- 
 ing, the student is able to distinguish the nuts and their pjfrts, 
 viz., threads, form, motion, orifices, etc., and also to dis- 
 tinguish the wheels and their parts to which the nuts are 
 closely related. (2) By comparing, he perceives certain re- 
 semblances, viz., fastenings, covers for holding grease, which 
 extend throughout. Persisting, he finds a resemblance in the 
 direction of the threads in two of them. (3) With this 
 principle the nuts are classified as left-handed and right- 
 handed. Seeking to reconcile this diflference to the resem- 
 blance '* fastenings," he arrives at the principle. 
 
 The work of the teacher in these two illustrations (if we 
 impose the condition of the learner having a teacher) would 
 manifestly be to let the mirfd act alone and for itself in arriv- 
 ing at the principle. When he has supplied the material, his 
 after-work should be simply to direct the learner in his in- 
 vestigation by proper questions. These modes of existence 
 
^ THEORY. \) 
 
 of the intellect correspond to the questions ivhat, how, and 
 why, and the teacher is in his proper sphere when he supplies 
 the stimulus in each mode indicated by these interrogatories. 
 
 The remarkable parallelism in the three examples noted 
 above, in that the action of the intellect in each is the same, 
 leads to the conclusion that the acts resulting from the will 
 taking the assimilated truth as its guide in each case are alike 
 in kind, and are therefore phenomena of the same thing. If 
 the acts of the man in the first illustration are phenomena of 
 character — and who can deny that they are? — then, proceed- 
 ing to classify the marbles in the second case, or doing any 
 thing guided by the truth assimilated in the third illustration, 
 are also phenomena, of character. 
 
 ) And if this conclusion is true, then is it not clear that in- 
 tellect-culture is the greatest factor in producing marked 
 character both in individuals and in peoples? 
 
 Intellect development (on true principles) and character 
 education are so related that they go forward together ; or, in I 
 other words, that a weak or vicious character in a man [in / 
 the sense in which these terms are generally understo(>d] re- 
 sults from deficient or misdirected intellectual training, and / 
 that a strong or a virtuous character is the direct effect of en- / 
 larged intellectual teaching that neglects no relation man sus- / 
 tains either to the Supreme, to his fellows, or to the world of \ / 
 organic and inorganic objects that constitutes his environment. ) 
 
 The only intellect to w'hich one has full access is his own, 
 and this discussion will h» better understood if the reader 
 make careful tests of what is claimed to be true by close ob- 
 servations on his own mental processes in learning. 
 
 Observation upon the workings of one's own mind discov- 
 ers that it forms thought-objects which correspond to sense- 
 objects, that thought-unities are created that represent groups 
 or families of sense-objects, and that thought-verities (princi- 
 ples) are apprehended that represent the relations of sense- 
 objects and groups of sense-objects. 
 
10 PEDAGOGICS. 
 
 Furthermore, the observer of his own mind will see that 
 in the affairs of life he is constantly deciding as to his action 
 in this or that by means of thought-verities acting as laws 
 established by his reason for the government of his conduct. 
 
 Self-observation will -convince a candid mind that the art 
 of teaching intellect aright consists in conducting it successfully 
 and consciously through the three processes, viz : Intellect- 
 perceiving, intellect-comparing, and intellect-assimilating, and 
 in the order named.* 
 
 If truth and not error is assinvlated, then the teaching has 
 been successful; if the learner knows that he is assimilat'mg 
 new truths day by day, then his teaching has been conscious. 
 The pupil whose intellect has been successfully and consciously 
 taught will consciously and successfully — so benign is the in- 
 fluence of truth — apply these same processes in the affiiirs of 
 life ; he will be able to perceive more clearly, compare more 
 correctly, and to assimilate more advantageously than one who . 
 has been taught in a haphazard way, or who is self-taught. 
 He will, in consequence, attain success more readily (having 
 fewer things to learn anew) than his confreres, the self-taught 
 and wrong-taught. 
 
 These processes utilized by the educated man become his 
 character; the measure of character is power in utilization. 
 
 It follow^s, then, that the teacher who leads a pupil success- 
 fully and consciously along the pathway of his development 
 adds intensity to his character. 
 
 Now if this is true, viz: that intellect-education and char- 
 acter-development are the same in kind, i. e. , that what develoj)s 
 (intensifies) the one develops the other, it follows that the 
 problem of right moral training is solved if the true relations 
 of like entities (man to man, brother to brother, citizen to 
 
 *Itis not intended to assert that a period of life, say of years in (hiration, 
 should be devoted to each. The truth is, that in a very short interval of tinae 
 the intellect may act in each phase of its existence: it does so from the begin- 
 ning. The "order named'' is important, because the completed act, i. e., 
 assimilation, is the result of the other two. In the phenomena of character, 
 which is largely the fruitage of intellectual effort, these same processes manifest 
 themselves almost instantaneously. 
 
THEORY. 1 1 
 
 citizen, etc., etc.) be made a part of the intellectual equip- 
 ment of every pupil. This conclusion, which in effect puts 
 the teacher in the attitude of being the greatest factor in the 
 formation of moral character, brings up naturally the ques- 
 tion of his responsibility. In determining this, other data 
 €nter into the problem ; the natural bias of the child, the pre- 
 vious treatment he has had, and like considerations varying 
 in each case. If the natural bent of a child is to the right,\ 
 it is a good thing to make him strong in intellect and char-( 
 acter by education; if, on the contrary, his natural bias is tO| 
 the wrong, it would be hetter, perhaps, to leave him unedu- 
 cated. It would certainly be better to leave him so if his evil 
 tendencies are not destroyed or greatly modified by his course 
 of training. But who is to judge? Clearly it is no man's 
 province to say who shall or who shall not be educated. It 
 follows, then, that society owes to each of its members a 
 training adequate to make him self-sustaining; and in order 
 that no natural thief shall be endowed with power to prey 
 more successfully upon his fellows, the further duty is entailed 
 of making general education moral as well as intellectual. 
 This can be done only by putting into the curriculum those 
 dements which are the foundation for correct principles. 
 
 The conclusions based upon self-observation thus far drawn 
 will be apparent to any one who makes a careful study of his 
 own intellect. * 
 
 But are they true, and can they be confirmed by observa- 
 tions upon actual teaching? The argument following is based 
 upon observations made in teaching, and can be verified by 
 any one who has had sufficient experience as a teacher. 
 
 In the sphere of teacher one must assume that his pupil 
 has an intellect like in kind to his own, but differing in 
 degree, and proceed accordingly. He must treat it also as a 
 complex whole. As is the body, so is the mind. One sees a 
 man start from home to his place of business ; his body 
 moves, but at the same time his heart is beating, his blood is 
 
12 
 
 PEDAGOGICS. 
 
 coursing, his feet are stepping, his hands are swinging, his 
 muscles alternately tensing and relaxing, and his eyes are 
 turning here and there. His whole physical being, in fact, is 
 in action, each part contributing to make up the grand phe- 
 nomenon called walking. A very simple thing is this, upon 
 a cursory view, but a very complex thing when it is analyzed. 
 Such is the mind the teacher undertakes to train, equally 
 complex, and more difficult to analyze because its phenomena 
 are intangible; and especially to teachers, because they are 
 wont, in this, as in all things (such is the influence of our 
 system of education), to take what some one says for the 
 truth instead of striving each for himself, through observa- 
 tions on himself and his pupils, to assimilate the true laws of 
 teaching. 
 
 To be the cause of a healthful, positive expression of the 
 intellect in the consciousness of the learner, the teacher must 
 be able to command the atteiition of that learner so as to 
 cause him to know one thought-object from another, and to 
 know numbers of them ; he must be able, by directing the 
 memory, to lead the learner to perceive the relations between 
 his thought-objects, i. e., their resemblances, their differences, 
 and their capabilities for combination; he must also be able 
 to inspire the imagination of the learner to work out combi- 
 nations for himself; and lastly, he must be able to direct the 
 will of the learner by making him cognizant of the fact that 
 what new combinations he has made are a part of his mental 
 structure, and are to be used for his own good. (What is for 
 his good being what 'is good for society, of which he is but a 
 part, the good of society itself at the same time being the 
 all-wise will of the Infinite.) Truly, a healthful movement 
 of the intellect is a complex and sublime spectacle ! And 
 verily, he who brings it about in "one of these little ones" 
 hath his reward in the approving smile of the Father of All ! 
 
 To summarize what has just been elaborated is to say : 
 The mind is a complex whole, and must be treated as such if 
 healthfully trained. The teacher fails in his aim if he fails 
 
THEORY. 13 
 
 to know that atfentvn, memory, and imagination are but the 
 tools by which the pupil does his work, and that intellect- 
 culture and character are the completed products of that w^jrk. 
 He fails also to healthfully educate if he fails to discern his 
 true relations to his pupils. He can not give the pupil the tools, 
 but he can and he must keep them sharpened; he can not 
 build the structure, but he can and ought to draw the plan. 
 
 There is in no case a healthful action of the intellect of 
 the learner unless the three modes of action defined and 
 illustrated heretofore exist at the same time.^ 
 
 When the human being through reflection begins to ap- 
 propriate principles he has learned as laws for his guidance 
 in the affairs of life, he is developing character. That char- 
 acter is intensified in the same degree as his power to apply 
 his intellect in the discovery of truth is intensified. In other 
 words, strength of character and intellectual power exist to- 
 gether. Teaching the intellect affects the character in degree 
 in all cases. But it can be made to affect it in kind as well 
 by a judicious selection of thought-objects for the pupil. 
 And herein lies the responsibility of the teacher. He must, 
 by a proper choice of material, exercise those emotions of his 
 pupil that w^ill cause him to make a wise choice in principles 
 for his guidance. Now, if principles are selected (for the 
 pupil to discover) that are inherent in relations of himself to 
 his fellow pupils, they will in time become fixed as laws with 
 him, and he will have been educated morally. 
 
 It is to be observed that the will of the pupil becomes a 
 factor in such results; that it is a factor and an important one 
 
 <•" Time " is not here used in the sense of moment or instant, for it may be 
 a much longer period. Anj' one who has reflected after the discovery of a truth 
 or principle will observe that his thought-objects appear with a new force, and 
 the thought-unities resulting shine with a new luster. They are, in fact, the 
 data of the complete intellectual assimilation. It may be remarked here that 
 the difference between man and the lower animals consists in this, tnat they 
 never abstract a principle out of their thought-unities, nor is it certain that they 
 even perceive the thought-verities existing as relations of thought-objects; re- 
 flection shows that man does all this and does it as one act. And this is what 
 is meant by the phrase "at the same time." 
 
14 ' PEi^Aooaics. 
 
 in the education of character. It is a factor because it in- 
 fluences the choice in principles discovered, and it is impor- 
 tant because, unless the pupil is allowed unhampered to ex- 
 ercise it, his education is unhealthful. His will must be 
 guided, not broken. But how is the will to be guided ? 
 Evidently by exercising the emotions that are healthful in 
 tendency. But how is this to be done ? One evident answer 
 is, that it must be done systematically ; this refers to the 
 theory that should govern the practice. 
 
 But there is another answer that should shape the method 
 to be used, and this answer is paramount. If this effort to 
 improve the art of teaching succeeds in doing good, it will be 
 because the great lesson it shall convey is, that the welfare of 
 le pupil in after life is dependent to a very great degree 
 upon the method used in training him. Method, not methods, 
 is the term used, and the fact can not be too much empha- 
 sized that the one method should control in all efforts of the 
 teacher in ethics as well as in science. 
 
 Given the proper data, the manner of proceeding is easily 
 determined. Now the proper data for correct moral develop- 
 ment are found in the happenings of every-day life at school 
 and at home, in the history of individuals, of neighborhoods, 
 and of nations, and also in stories. 
 
 The theory and practice of schools in the sphere of moral 
 training has inclined too much to story telling^and story read- 
 ing. This is erroneous, for the reason that a story is a work 
 of art. The author is not a teacher, and has not the sole end 
 in view of engrafting a true principle upon the moral nature 
 of a responsible human being. His art requires certain cli- 
 maxes to be wrought in as part of the woof of his story. Re- 
 wards and punishments are an invariable accompaniment to 
 the happy ending of a story. For unless it does end well it 
 will never go to press for a second edition. This utilitarian 
 consideration largely shapes the form of stories. 
 
 But tl\ere is another and a graver objection to the sole use 
 of this as a method. It is this : In stories the motives of the 
 
THEORY. 15 
 
 actors and their choice of courses of action are rarely brought 
 out fully. For obvious reasons the full details of environ- 
 ment are never brought to the view of the reader-pupil, and 
 hence his principles are only approximately true. The char- 
 acter resulting from a course of training through stories will 
 always lack in force and independence, for the very apparent 
 reason that the pupil in acquiring it was a passive imitator. 
 He is a fit subject, when turned free, for the wiles of the po- 
 litical demagogue, inasmuch as he has never thought for 
 himself in assimilating principles. 
 
 The objection to making history alone the basis of moral 
 training is, that it is barren of material for all grades of 
 schools. Tiie great lessons of policy in governmental affairs 
 and in affairs of like magnitude are of such gravity that 
 they do not command the attention of young pupils. They 
 are of great value in high-school work, and their use with 
 such pupils as are just ready to struggle with the problems 
 of citizenship can not be too highly commended. But things 
 nearer home, things within the world of the little ones, are 
 needed for primary schools. 
 
 Hypothetical cases, and cases of real happening where the 
 names of the parties concerned can be withheld, are the best 
 possible material for this work. A good story made hypo- 
 thetical may be used for moral lessons. It is important 
 that the instruction in every case, whatever the material, 
 should be hypothetical, as by this means only can all the 
 thought- objects and thought-unities, which constitute the whole 
 environment of the thought-verity (principle) it is designed to 
 cause the pupil at that particular lesson to assimilate, be 
 brought together. 
 
 As to conduct of lesson : Principles, as they shape them- 
 selves in the minds of pupils, ought to be announced by those 
 who conceive them. These ought to be taken up and dis- 
 cussed by the teacher and pupils. If erroneous, the miss- 
 ing data which will make them true can be supplied by any 
 one who has discovered them. 
 
16 PEDAGOGICS. 
 
 Moral lessons conducted in this way, after the hypothet- 
 ical method, universal in scientific investigation, give exercise 
 to the will and leave it free to act. 
 
 This latter consideration is of great importance, because 
 no fact is clearer than that the will must be left unfettered in 
 order to the development of a character that will do right for 
 the right's sake. We all applaud the immortal sentiment 
 expressed by Clay in the utterance, "I would rather be right 
 than President," and we despise any other groundwork as 
 the motive for our actions. The teacher should prayerfully 
 lead his pupils to reach this noble ideal. 
 
POSTULATES. 
 
 In the formulated expression of the postulates and expla- 
 nations attaclud, presented in this section, the word " whole" 
 is used to name all the thought ohjects contributing to any 
 complete intellectual action. These thoiigJd-objcc's through 
 their relations disclose a truth; they are in this sense a 
 separate group ; they are spoken of as a " whole." 
 
 Where " repetition " Is enjoined in the explanations it is 
 meant not to use the same sense-objects or whatever else 
 constitutes the "whole" for that lesson, but others for each 
 repetition. Many repetitions are sometimes necessary to 
 enable all membfers of a class to grasp a truth. 
 
 I. It is only through a "whole" as a medium 
 that the intellect assimilates any truth. 
 
 This postulate assumes that the work of the teacher in- 
 volves (1) a comprehension of the truth it is his intention to 
 impress at any given lesson ; (2) a knowledge of all the ele- 
 ments (thought-objects) whose relations hold this truth as a 
 content, and (3) the bringing of these elements within the 
 mental view of the pn})il. 
 
 After placing the data, which must be a " whole," before 
 the pupil, questioning in the domain of "what" will lead 
 him to perceive all the elements. Questioning in the domain 
 of ''how," which includes " when" and " where," will cause 
 him to see differences and agreements. The question *' why " 
 will lead to the discovery of the truth, which is the objective 
 point of the lesson. For practical illustrations of the appli- 
 cation of this postulate see pages 26 and 47. 
 
 2 
 
18 PEDAGOGICS. 
 
 II. Assimilation of truth is a self-act, and is on 
 occasion. 
 
 This postulate assumes that the learning of every truth is 
 accidental to the intellect assimilating it. Let the conditions 
 exist of an intellect sufficiently developed to receive it and a 
 " whole" comprehensive enough to contain it, and the truth 
 is born upon their conjunction. The teacher is only one 
 of the circumstances that combine to bring the proper condi- 
 tions into existence. 
 
 This postulate accounts for the fact, often mentioned as 
 singular, that many of our greatest inventions were the re- 
 sults of accidental combinations. 
 
 As inferences from it may be mentioned the following: 
 The will of the learner does not cause him to learn ; neither 
 can the will of the teacher operate to cause assimilation of 
 truth ; excessive exertions of the will by either toward this 
 end tend to defeat it ; the will of the pupil should be exer- 
 cised in giving attention, the will of the teacher in building, 
 repairing, and enlarging the *' whole," or in exchanging it for 
 another. • 
 
 III. Formulating truth (language) follows the 
 assimilation of it. 
 
 IV. Language is necessary, and must become 
 generic in order to any great intellectual 
 development. 
 
 These two postulates are important, inasmuch as there are 
 many mistakes made by teachers growing out of ignorance or 
 disregard of what is assumed in them. It seems to be true 
 that the mind is content to hold a truth without language 
 so long as it sees it in the relations of one group or '* whole." 
 But as soon as it perceives the same truth in another group 
 a demand is born for symbols, as associations, by which to 
 retain the enlarged view now given to it. This demand and 
 its application are illustrated by lessons on pages 27 and 41. 
 That repetition is necessary in teaching is an inference from 
 
POSTULATES. 19 
 
 these postulates. It is necessary (1) in order to create the 
 demand for symbols, thereby securing their retention with 
 the proper meanings, and (2) to fix them in the memory with 
 their generic meanings. 
 
 V. The intellect is primarily analytical, and 
 secondarily synthetical in tendency. 
 
 The intellect of a learner looks out upon nature or upon a 
 ** whole" contrived by his teacher, and all at first glance is 
 chaos. Soon his intellect-perceiving enables him to separate 
 the various objects in view. These objects in nature or in 
 the artificial grouping are themselves units. If the atten- 
 tion is fixed upon one of them, the intellect separates it into 
 its parts, and so on for the others. This process is analysis, 
 and is the primary act of intellect. Transferring the atten- 
 tion from one to the many brings resemblances and differences 
 to consciousness. These relations hold truths as contents 
 which are seized by the intellect. Operating under con- 
 ceived principles, the intellect proceeds to make new units 
 which it did not apprehend at first glance. This grouping 
 act of the intellect, which seems historically to follow analy- 
 sis, is synthesis. It begins with the first seizure of a princi- 
 ple ; it is that factor which distinguishes the mind of man 
 from that of a lower animal ; it is the parent of language. 
 
 With this postulate governing him, a teacher can so ques- 
 tion his pupil as to lead him far enough in analysis to pre- 
 pare him for certain success on the other road. When syn- 
 thesis has accomplished its purpose of making a new " whole" 
 for subsequent analysis, the teacher's work is done for that 
 stage of development. 
 
 In any science principles taught are necessarily related to 
 each other, and at every stage it will be necessary for the 
 teacher to group facts that have been learned as species out 
 of which the intellect of the learner shall be made to con- 
 struct new generalizations. This fact, that truths learned are 
 species of higher genera of truths, makes it apparent that the 
 
20 PEDAGOGICS. 
 
 human intellect is capable of endless development. The other 
 fact noted, that the principles of a science are related, not 
 detached, suggests with a force not to be questioned that there 
 is a law of identity in every science which contains all others. 
 
 VI. All intellectual processes are at first un- 
 conscious. 
 
 This postulate requires the most delicate management on 
 the part of the teacher, in order to prevent doing irreparable 
 injury to those pupils who' need encouragement in their 
 efforts. The period of unconsciousness after the discovery of 
 a truth varies in different individuals, and herein lies the 
 danger. The teacher should exercise the greatest caie in ob- 
 serving, to prevent mistakes in judgment, which will lead him 
 to censure where it is not deserved. 
 
 VII. Intellects differ in degree, not in kind. 
 
 This postulate demands the same groupings of "wholes" 
 for all grades of intellect. Since repetition is enjoined by 
 postulates III and IV, as essential to successful teaching, 
 the opportunity is here afforded the teacher to so adapt his 
 exercises as to tax the various grades of intellect in the class 
 each to its limit, by making the first *' whole" probable to the 
 highest grade only. The lower grades will not be injured, 
 but be helped by their efforts to assimilate through a *•' whole" 
 not adapted to them. A subsequent effort will more surely 
 succeed after the same truth has been assimilated through 
 an easier "whole." 
 
 VIII. The mind, having assimilated a truth by 
 intellectual action, has an innate tendency 
 to apply it. 
 
 This postulate announces a fact which is important to the 
 teacher, inasmuch as it indicates that he is largely responsi- 
 ble for the moral training of his pupil. Its phenomena are 
 seen chiefly in the development of character. 
 
POSTULATES. 21 
 
 Now, how can the teacher bring about the recall by the 
 pupil of the principle or law that should govern his will in 
 any ca?e with such authority as will give it domination ? 
 
 1. The pupil must assimilate it under such circumstances 
 originally as are parallel to finding a treasure in a hollow 
 tree : no hint of its existence must be given him. 
 
 2. The teacher must invest the finding with a multiplic- 
 ity of associations, in order to provide for its recall in any 
 contingency in which it may be needed by the individual. 
 
 Take the principle, "Thou shalt not steal," for example. 
 Suppose a pupil's teaching only covers cases of taking money, 
 clothing, watermelons, etc., when he could get along without 
 them, or the owner could well spare them. Suppose, now, 
 that individual to be starving or naked, or to have a hungry 
 family dependent on him, and an opportunity is offered to 
 steal, would he have a principle that would dominate his 
 will? Assuredly not. Can we not account for those cases 
 of embezzlement and official stealing, now so common, by 
 there having been some hypotheses left out of the *' whole," 
 through which the embezzler assimilated his '*Thou shalt not 
 steal." 
 
 A curriculum of moral lessons might be contrived, taking 
 such abstractions as honesty, friendship, politeness, candor, 
 charity, kindness, etc., etc., as its basis. To teach any word 
 so that it will go into the vocabulary is to follow Postulate 
 IV. Now, when these words have been made generic by teach- 
 ing, has the pupil not also [possibly] been caused to assim- 
 ilate a law that will tend to dominate his will when necessary? 
 
PRACTICAL LESSONS. 
 
 The three primary attributes of the Intellect, viz., a Con- 
 sciousness of DiffeienC'S. a Consciousness of Agreement, and 
 Conscious or Unconscious lietentiveness, must ever be kept in 
 memory by the teacher in reading this section. And he must 
 also bear in mind the fact that the products of mind action 
 resulting from these are: (1) Thought-objects; (2) JRchtions 
 of ThougJit-ohjects, founded on Agreements and Differences; 
 and (3) Tiuihs, as contents of these relations. And a third 
 fact, without which all teaching would be purposeless, must 
 ever guide him, viz : A Truth once existent, the mind by a 
 natural bias tends to apply it, and thus becomes self-active. 
 
 The eight postulates given, while originally discovered 
 and formulated from observations made on experiments and 
 tests with classes, will be found to give full and logical ex- 
 pression to the tacts of mind noticed above. 
 
 It is not desirable to separate this work into lessons, for it 
 is not to be imitated. The intention is to give more forcible 
 expression to what has been already said, and to make clear 
 that tlie theory of this Monograph admits of easy practice. 
 Yet, if any one attempts from one reading alone to apply 
 these postulates, he will almost surely fail. It will require 
 much study, much reflection, and repeated trials to succeed. 
 It is the very simplicity of the whole thing that will puzzle 
 the one who tries it. 
 
 The reader will find the word "repetition" often used. 
 Let it be understood that this system forbids sameness in rep- 
 etition ; the same objects are in tlie kaleidoscope, but as it is 
 turned slowly around there is endless variety of beautiful col- 
 ors and symmetrical forms. Kepetition refers alone to the 
 
PRA(rriCAL LESSONS. 23 
 
 truth or principle ; Nature's resources for the expression 
 of the same j^rinciple are apparently infinite ; the teacher 
 must, in teaching principles, become as Nature is, tlie parent 
 of variety. The particular method must change with the 
 number, the advancement and the character of the pupils, 
 and with the subject-matter. The esprit de corps also has 
 much to do with deciding details. 
 
 Illustrations' are given in Arithmetic, Language, Geogra- 
 phy, Ethic.=:, Algebra, and Geometry; but it is believed that 
 a like application of the Theory may be made in any and 
 every science. 
 
 AKITHMETIC. 
 
 Nearly all the principles of arithmetic are emhraced in 
 this outline. Each is a species of some following one, and a 
 genus of some one that precedes it. It is not pretended that 
 this series of principles is the only method for arithmetic. 
 Other species and genera may be used. This is the best so far 
 discovered. Each principle is to be taught with distinct 
 ** wholes." [See Post. I.] With primary pupils the objects 
 at first used should be blocks, or similar things, which in 
 manipulation remain separated to the eye. Later, objects 
 like straws, which in part lose their identity in handling', and 
 still later, cards or sheets of paper, which in a greater degree 
 are obscured, should be used. Finally, objects, as cups of 
 water, which entirely disappear as separate units, ought to be 
 used. 
 
 In all the work the pupil must be led to discover the prin- 
 ciple, the teacher guiding by proper questions. In formu- 
 lating the principle for future use the teacher must perfect 
 the crude expressioti given to it by the pupil. It is not im- 
 portant to have the exact language used in this presentation 
 of principles. 
 
 When the figures are the objects usc'l, as in Prin. 8^ no 
 other objects can be used. 
 
24 PEDAGOGICS. 
 
 PRINCIPLES. 
 
 (1) Totals or Wholes are the same when all their parts 
 are the same. 
 
 (2) A whole is all its parts put together. 
 
 (3) A whole is increased by the increase of any part. 
 
 (4) A whole is decreased by the decrease of any part. 
 
 (5) A whole is multiplied by multiplying every part. 
 
 (6) A whole is divided by dividing every part. 
 
 (7) When all the parts of any whole are of the same size 
 or equal, the part is a unit, and the number of equal paits is 
 a coefficient, and the total is a named-whole, or a measured 
 quantity. 
 
 (8) A named-whole is multiplied either by multiplying 
 the coefficient or unit. 
 
 (9) A named-whole is divided either by ;ividing the co- 
 efficient or unit. 
 
 (10) Interchanging the coefficient and the number of 
 things ill the unit gives same named-whole. 
 
 In other relations, by change of names, the coefficient be- 
 comes the multiplier, the unit becomes the multiplicand, and 
 the named-whole becomes the product, and the 8th and 9th 
 principles become : 
 
 (8/ Multiply either the multiplier or multiplicand and the 
 product i« multij^lied. 
 
 (9)^ Divide either the multiplier or multiplicand and the 
 product i^ divided. 
 
 Omitting the objects, the multiplier and multiplicand be- 
 come factors, and principles (8)^ and (9)^ become : 
 
 (8)5 To multiply either of two factors multiplies their 
 product. 
 
 (9){ To divide either of two factors divides their product. 
 
 Applying 10th principle to (8){ and (9)J, and repeating the 
 application, gives: 
 
 (10)^ Any order of the same factors gives the same product. 
 
PRACTICAL LESSONS. 25 
 
 (10)" The prime factors of the product of any number of 
 composite factors are all the prime factors of the composite 
 numbers put together. 
 
 (10)"^ The factors of the H. C. D. are all the common 
 factors. 
 
 (10)^^ The factors of the L. C. M. are all the factors, 
 common and not common. 
 
 (8)" To multiply any factor multiplies the product. 
 
 (9)5^ To divide any factor divides the product. 
 
 (11) The how much larger or smaller two quantities taken 
 separately are than a third quantity, determines the how much 
 larger or smaller one quantity is than the other. 
 
 (12) The subtraction of one quantity from another, and 
 of the remainder from the smaller, repeating till nothing re- 
 mains, the last subtrahend used is the highest unit common 
 to both. 
 
 If the condition be imposed that a variable product of two 
 factors shall have one factor constant, (8)" and (9)" give : 
 
 (13) The direct proportion. 
 
 If the condition be imposed that a product of two factors 
 be constant, (8)" and (9)" give: 
 
 (14) The indirect projiortion. 
 
 If conditions be imposed that a given number of things of 
 one kind are to be put together in a whole every time a given 
 number of things of another kind are put together in a 
 whole, then to find a new whole of the latter kind for a given 
 whole of the former kind, gives : 
 
 (15) If a =C= h 
 
 then a^ =C= {a} -i- a) x 6 or, 
 
 (16) If a. =3= 6 
 
 then a^ --C= (6 -=- a) x 6^ 
 
 Suggestions follow as to practice in teaching these principles. 
 
 Prin. 1. Except this principle be thoroughly assimilated 
 
 by the pupil, failure in all the otiiers is quite sure. Take a 
 
26 PEDAGOGICS. 
 
 number of objects (blocks or straws, etc.), without counting, 
 and ask the pupil to make a pile with as many in it, also- 
 without counting. Repeat the process a number of times. 
 If the pupil can write, let him try to write on his pad or slate 
 what he has been doing; * if he can not write, let him state 
 what he has done. When he thoroughly apprehends wliat he 
 has done, then ask him how the piles are alike. When he 
 has discovered that they are alike in kind and number, then 
 ask him to state Jiow he knows they are alike in number and 
 kind. When he can answer this question, then ask iiim to 
 write down, with figures, the name of the first pile. To this 
 end he must count it. When he has written the name of the 
 first pile, ask him to write the name of the second pile. He 
 will start to count that pile also. This must be prevented. 
 Let him read over what he has discovered as to the respects 
 in which the piles are alike. When he has written down the 
 second })ile, then put on the blackboard the results thus : 
 8 blocks 8 blocks. 
 Now ask him to write between the names in what re- 
 spects they are alike. When he has written, 8 blocks are 
 in number and kind like 8 blocks, then inform him that a 
 sign is used to express the same thing, and put on the board 
 8 blocks = 8 blocks, and ask the pupil to write what the 
 sign = means. When he is able to write, = means that 8 
 blocks are in kind and number like 8 blocks, he has made an 
 important step. Repetition of the whole process must follow 
 until he writes, = means alike in number and kind. Then 
 take any two objects of the same kind, as two chairs, and 
 enter into details of resemblances. Weigh one chair, or esti- 
 mate its wei;j:ht, and ask for the weight of the other. Take 
 two books of the same edition, open at any page, and ask 
 pupil to read what is in the other book at same place, hand- 
 ing him the open book. Do not be surprised if he wants the 
 other book ! Time sufficient should be given to secure a per- 
 fect assimilation of this principle. 
 
 -The pupil must be required to do this throughout the course. 
 
' PRACTICAL LESSONS. 27 
 
 (2) Let the pupil make two wholes, the same in number 
 and kind as before. Ask him to separate one pile into two 
 parts, diffisrent in size. Ask him in what respects the one 
 pile is like the two piles. When he states, " S.ime in num- 
 ber and kind," ask for differences. When he states, '' One is 
 in two parts, and in the other all are in one pile," then ask 
 him to write down the piles, one after the other. Let him 
 count every pile. Then give him two piles with different 
 numbers in them, and ask him to make one i)ile as large as 
 both without counting. When he has done this, ask ques- 
 tions as before, and let him write down the names of piles as 
 before. On the board write results thus : 
 
 5 blocks 3 blocks 8 blocks. 
 
 Ask the pupil to put in signs to give relations. If he 
 can not use the signs, then so conduct the exercises as to in- 
 duce him to write, " 5 blocks put into one pile with. 3 blocks 
 are the same in number and kind as 8 blocks," or something 
 equivalent, and then give the signs, thus: 
 
 5 blocks + 3 blocks = 8 blocks. 
 
 Repeat, by giving the pupil three unequal piles, and ask 
 him to make one pile as large as the three without counting, 
 and go through all the steps to 
 
 7 blocks + 3 blocks + 2 blocks = 12 blocks. 
 
 Continue in repetition, increasing the number of parts. 
 
 (3) Give the pupil three unequal piles, and ask him to 
 make one pile as large as the three without counting. Then 
 form three other piles, each as large as the former, and with 
 a whole for them, all without counting. Repeat until he has 
 as many sets of piles as there are piles in one set. Then let 
 the pupil form three equal piles without counting. Now ask 
 him to put one of these latter piles with the first pile of the 
 first set. Ask him if the large pile is a whole for the three 
 piles. He will answer, "No." Ask him to make it a whole 
 for them, and he will immediately put one of the equal piles 
 
28 PEDAGOGICS. 
 
 with the whole. Repeat this process with second and third 
 sets, the only change being to put one of the extra equal piles 
 with the second of the three piles ; do likewise with third 
 set. Repeat until the pupil is familiar with the process, and 
 can write it up. Then, as the steps are made with objects, let 
 each be written up with figures on pads or slates, and then 
 follow on the board, thus : 
 
 5 blocks + 3 blocks -f 4 blocks = 12 blocks. . 
 
 6 blocks ' = 6 blocks. 
 
 11 blocks + 3 blocks + 4 blocks = 18 blocks. 
 
 5 blocks + 3 blocks + 4 blocks =12 blocks. 
 6 ])l()cks = 6 blocks. 
 
 5 blocks + 9 blocks + 4 blocks = 18 blocks. 
 
 5 blocks + 3 blocks + 4 blocks = 12 blocks. 
 6 blocks = 6 blocks. 
 
 5 blocks + 3 blocks -f 10 blocks = 18 blocks. 
 
 Ask for and secure resemblances and differences of the 
 three processes as they appear on the board. 
 
 (4) Is to be taught in a precisely similar manner to the 3d 
 principle. 
 
 (5) Give the pupil two unequal piles, and ask him to 
 make one pile as large as both. Then ask him to make new 
 piles, putting two straws in the now i)iles for every one straw in 
 thenar's; then to make a whole for his new parts. Then let 
 him compare the number in the new whole to the number in 
 the old whole. He will answer, "Two for one." Ask him 
 how he knows that the new whole has two straws for every 
 one straw in the old whole, when he did not make the new 
 whole in that way. If he can not answer, repeat until he 
 can see the reason for the fact. Then, in repeating, let him 
 make two piles the same size as each part of old whole, and 
 put these equal piles together — another way to put two for 
 •one. Gradually introduce the expressions, "two piles for 
 
PRACTICAL LESSONS. 29 
 
 one pile/' and '* two times one pile," so that the pupil under- 
 stands that " two straws for one straw," gives same results as 
 *' two piles for one pile," and understands the force of the ex- 
 pression '^two times." When pupils are prepared for it, let 
 figures be used, thus: 
 
 4 sts. + 3 sts. = 7 sts. Two for one gives 
 8 sts. -f 6 sts. = 14 sts., all of which is to be writ- 
 ten from actual work with things. Then put, thus : 
 
 4 sts. + 3 sts. = 7 sts. 
 2 = 2 
 
 8 sts. -f 6 sts. = 14 sts. 
 
 In repetition vary the number of parts, and the number /or 
 one, until the pupil is perfectly familiar with the steps. Like the 
 (1) principle, this principle requires much time and patience. 
 
 (6) To be taught precisely as principle (5), except to take 
 one straw in the new parts for every two straws in the old 
 parts, etc. 
 
 (7) Give the pupil, say, twelve straws, and ask him to 
 give each of three pupils an equal share without counting. 
 Give the pupil any number of straws, and a>k him to separate 
 them into a given number of equal parts. When the pupil can 
 do this readily, then let him form equal wholes, and ask him 
 to separate one of the wholes into, say, three equal parts. 
 Ask questions ivhaty how, and ichy, as before. Ask him to- 
 write up in figures. He writes, 4 sts. -f 4 sts. + 4 sts. = 12 
 sts. Give him three books, and ask him to write that up. 
 He will write, 3 books. Ask him to write up same number 
 of any objects. He writes, 3 pencils, 3 slates, etc. Now ask 
 him to do the same with the piles of straw, and porhnps he 
 will write, 3 piles of straw. Ask for name of pile. He an- 
 swers, 4 sts. Now he will probably write, 3 4 sts. Direct 
 him to use the comma, thus : 3, 4 sts. Repeat until the pupil 
 is famijitir with the naming. 
 
 Review principles (3), (4), (5), and (G) at this point,, 
 usincj two or more straws in lieu of one as a counter. 
 
30 PEDAGOGICS. 
 
 (8) Is taught precisely as the 5th principle, with perfectly- 
 apparent changes. 
 
 (9) To be taught as (8) or as (6). 
 
 (10) Give the pupil 12 straws, and ask him to make, with- 
 out counting, another whole of the same size. Then ask him to 
 separate one of the wholes into three equal parts. Then ask 
 him to form new parts, by taking one straw from each of the 
 three parts until all are gone. Then ask him to make a new 
 whole for the new four equal parts. Ask for relation of this 
 new whole to the old whole. When he answers that they 
 are the same in number and kind, ask how he knows that 
 fact. Kepeat this process with different numbers of equal 
 piles until the pupil assimilates this principle, which is so 
 very important to much that follows. 
 
 How (8)\ (9)\ (8)}, (9)1, etc., grow out of the other prin- 
 ciples from which they derive their name, must be apparent, 
 on reflection, and to teach them is but a repetition of the 
 original principle with slight changes. 
 
 (11) Make three equal piles of straws before the whole 
 class without counting them. Call them respectively A, B, 
 and C. Add two straws to pile A and five straws to pile C, 
 and ask the class to compare the number in A to the number 
 in C. Make all possible variations with the same numbers 
 in A and C, but let B remain the same. Let the pupils write 
 up as follows : 
 
 A has 3 straws more than B. 
 
 C has 5 straws more than B. 
 
 .-. A has 2 straws less than C. 
 
 A has 3 straws less than B. 
 
 C has 5 straws less than B. 
 
 .-. A has 2 straws more than C, etc., etc. 
 It is well here to show, at this point, the algebraic signs 
 applicable : 
 
 -f 3 — (+ 5) = —2, first example above. 
 — 3 — (— 5) = +2, second example above.* 
 
 * Note— This illustration gives eight cases. 
 
PRACTICAL LESSONS. 31 
 
 The average pupil does this work without much trouble. 
 
 (12) Is taught by taking any two piles of straws with 
 different numbers and going through the process indicated. 
 
 (13) By the use of numbers the following generic state- 
 ment is easily taught. Let A be the variable product and B 
 the variable factor and C the constant factor; then multiply- 
 
 A = BC 
 Ai= B^C 
 
 ing or dividing B multipb'es or divides A, 
 whence A -^ A^ = B -f- B^ whence A : A^ 
 = B : B\ the direct proportion. 
 (14) By the use of numbers the following is likewise 
 easily taught. Let A be the constant product and B and C 
 
 A= BC 
 A = Bi- C 
 
 the variable factors ; then, multiplying B 
 divides C, whence B -h B^ = C^ ~- C, or 
 B : B^ = C^ : C, the indirect proportion. 
 (15) (16) Are so easily taught by the use of straws and 
 blocks that illustration is not needed. 
 
 HOW TO USE EXAMPLES FROM TEXT-BOOKS. 
 
 Alternating with and supplementing the work already 
 given, much practice by the pupil must be had in working 
 problems. These may be originated by the teacher, or taken 
 from books. In every case they should be made to serve as 
 additional *' wholes" to secure assimilation of principles. 
 
 It is thought to be necessary here, before leaving the sub- 
 ject, to enter into details somewhat as to how to use the ex- 
 amples so as to secure the end desired, i. e., to make them 
 repetitions. It is to be noted that examples from books have 
 not been recommended till after the principle has been assim- 
 ilated through objective teaching. This recommendation, 
 therefore, presumes the existence of the principle in the mind 
 of the pupil, although in an inchoate state. The first ques- 
 tion when an example is presented should be, " What princi- 
 ple is contained here?" A failure to get the proper answer 
 need not discourage the teacher, as it is for some time the rule 
 and not the exception. 
 
32 PEDAGOGICS. 
 
 Questioning in the domain of *' what," " how," and " why," 
 will lead to its discovery and to the proper solution. With 
 large classes it is well to have all do simultaneously on pads 
 or slates what the teacher does on the board in response to 
 answers to his questions. 
 
 In general, a number of problems can be treated in a les- 
 son. After tliis study of a lesson, the whole work should be 
 erased, and the pupils required to make an exact reproduction 
 of it for the next time. This reproduction lesson is a valu- 
 able one, as it leads the way to independent work by steps 
 possible of accomplishment by all. 
 
 More difficult practice is secured by leaving all numbers 
 blank in the example under consideration, proceeding by 
 questions as before. Examples treated in this way may 
 be left on pads, the requirement for the reproduction lesson 
 being to fill the blanks, and bring solutions according to usual 
 forms of written answers. 
 
 When the details of operations (addition, multiplication, 
 etc.,) have become automatic through practice, and mistakes 
 are ho longer made, it is advisable to have solutions formu- 
 lated by signs, to express the operations necessary. 
 
 Note— If a teacher instructs after this method throughout the whole course 
 in numbers, the tables will be learned incidentally, just as the letters are 
 learned through the application of the word method in teaching reading. 
 
 LANGUAGE. 
 
 The illustrations in language-work to follow will be em- 
 braced under the following headings : Word Teaching, Reading, 
 and Grammar. 
 
 Introductory remarks are inserted here to elucidate the 
 relations of the postulates to such work. 
 
 The necessity for language is felt by an individual who 
 wishes to impart his thoughts to others or to liimself; its con- 
 venience is felt by one who wishes to recall a principle in 
 order to apply it, or a thought-object in order to compare it 
 
PKACTICAL LESSONS. 33 
 
 with others. It is pertinent to remark here that memorized 
 definitions fail to serve the convenience of the learner. His 
 own formulations only are availahle to him for progress in in- 
 tellectual work. Constant opportunities ought, therefore, to 
 be given him to write his own definitions, rules, or other prin- 
 ciples assimilated. 
 
 What was said in regard to the necessity of language is of 
 such importance to progress in its use that it is almost worthy 
 of being formulated as a separate postulate. Its bearing upon 
 teaching will be apparent when one reflects that unless the 
 pupil has the motive to impart his knowledge at the time he 
 gets it, then no necessity can, exist for its use, and he will lapse 
 into inattention during the lesson, or forget the fact after- 
 ward. 
 
 If the pupil is made conscious of what he learns [see page 
 10] the desired end will be reached, for he has the giving mo- 
 tive as an inheritance. 
 
 Thought-objects record themselves in language as words, 
 phrases, clauses, and sentences; thought-unities take form as 
 generic words and sentences, and thought-verities as sentences, 
 either elliptical or complete. 
 
 When a tangible object has been perceived, and its asso- 
 ciations with the individual perceiving are intimate, a necessity 
 exists for a name for it. Proper names, as Fido and William, 
 are the only formulations from intellect-perceiving. 
 
 When the second step, comparing, has been made by the 
 intellect, class names, as, horse, running, swiftly, black, etc., are 
 learned. Phrases expressive of relations, as, with a stick, on 
 a fence, in a field, are also conceived. Complex relations, as, 
 The black horse 7'uns in afield, The tree is bending before the wind, 
 are likewise apprehended at this stage. 
 
 When the intellect has completely acted in any case, a 
 general truth or a universal truth has been assimilated. It 
 exists as a content of certain relations of certain thought- 
 objects that have been brought together as a ** whole." Ex- 
 amples of such mind-action formulated are. The vnnd has force. 
 Sustenance is necessary to life. 3 
 
34 PEDAGOGICS. 
 
 This analysis of the fuuctions of language is thought to be 
 necessary for the teacher to enable him to intelligently direct 
 those under his charge. The following principles are recom- 
 mended to teachers, to be used in the manner outlined below, 
 in connection with both reading and grammar lessons. They 
 will serve the purpose of " waking up" the pupil to a com- 
 prehension of what he does in talking, writing, reading, and 
 hearing. Frequent repetitions are necessary to insure assim- 
 ilation. 
 
 I. Sentences are identical when all their words 
 
 are identical. 
 
 II. Sentences vary in meaning as their words 
 
 vary. 
 
 III. A sentence has essential parts which, put 
 together, make up the meaning. 
 
 IV. Each modifier of the predicate decreases its 
 horizon of meaning. [The subject is regarded as 
 a modifier.] 
 
 The following method of presenting the data for these 
 principles, it is believed, will recommend itself for its sim- 
 plicity and directness. 
 
 PKINCIPLE I. 
 
 Write two or three sentence^ exactly identical as far as the 
 words that compose them are concerned, as : 
 Mary loves her doll. 
 Mary loves her doll. 
 Alary loves her doll. 
 
 Ask the following questions :* 
 
 Are these expressions alike in meaning? 
 
 There are very few who will not unreservedly answer, 
 *'Yes," to this question. If ''yes" is the general answer, 
 continue questioning in "what" after this manner, "How 
 many parts (words) in each?" "What does Mary mean?" 
 
 '■'It is better to have answers written, as sueli a course secures effort on the 
 part of each pupil. 
 
PRACTICAL LESSONS. 35 
 
 "loves?" "her?" "doll?" Does Mary mean the same in 
 each sentence? Division in opinion inevitably resnlts at this 
 point if the teacher has held the attention Avell. 
 
 Continue by questioning with " haw." For example: 
 How do you know the Mary is the same in each sentence? 
 Is there only one Mary in the world ? All will agree that if 
 different Marys are meant different meanings attach to the 
 sentences. 
 
 Question further : " If the Marys are different, can the 
 dolls be the same?" Agreement will again result in saying 
 that the dolls are different. The class that is thus led to agree 
 will also agree in saying that " Sentences are identical when 
 their words or parts are the same in meaning," if the question 
 is asked. A complete assimilation can be secured by an- 
 nouncing that the sentences are indentical in meaning, and 
 then asking " why?" 
 
 PRINCIPLE II. 
 
 Make changes as follows : 
 
 1. Mary loves her doll. 
 
 2. Mary loves her cat. 
 
 3. Mary loves her mother. 
 
 4. 3Iary loves her hreakjast. 
 
 Call for resemblances and differences in the separate units 
 (sentences). Question in the domain of " what" until all the 
 meanings in "loves" are brought to view according to its 
 modifiers, doll, cat, mother, breakfast. There are also different 
 meanings to " her" in the separate sentences which might be 
 brought to view by questioning, but it will not be necessary 
 to be exhaustive in analyzing the units into their parts. Com- 
 pare (1) and (2) by questioning as to how the separate mean- 
 ings result. If necessary, change " cat" to " doll " in (2), in 
 order to make them identical. Compare others in the same 
 way, keeping the intellect busy in observing "how" differ- 
 ences result. 
 
36 PEDAGOGICS. 
 
 Add other sentences to the group, such as : 
 
 5. 3fary loves my doll. 
 
 6. 3Tary loves everybody. 
 
 7. 3Iary loves a hot breakfast. 
 
 Make the comparison of the new sentence with another in 
 the group from which it differs in only one word, and the an- 
 swer to " how" will take the form : By changing the " her" 
 in (1) to " my" in (5). By changing " her mother " in (3) 
 to " everybody" in (6), etc., etc. When the class have _per- 
 ceived and compared consciously in answer to "what" and 
 *' how," they will readily assimilate the principle in answer to 
 the question, " Why do sentences vary in meaning?" 
 
 PRINCIPLE III. 
 
 Arrange the words of a short story in columns, thus : 
 
 air the Henry 
 
 John threw a 
 
 large other in 
 
 it caught ball 
 
 persons into William 
 
 every and his 
 
 hands play saw 
 
 enjoyed them ' several 
 
 their one at 
 
 much very it 
 
 Tell the class that these are the words of a story. Ask 
 them to look over the list and tell what things happened. 
 The result will no doubt be, seeing, throwing, catching, lAayiiig, 
 enjoying. 
 
 Ask who did these things, and get, William, John, Henry^ 
 persons. 
 
 Ask when these things happened ; the past form of the 
 verbs will give a cue in this case. 
 
 Ask in what order the happenings took place. This will 
 
PRACTICAL LESSONS. 37 
 
 result in getting throwing, catching, seeing, and enjoying, as the 
 natural order of events. 
 
 After arranging who did the throwing, etc., the class are 
 prepared to write the story, as follows : 
 
 *' William threw a large ball into the air. Henry caught 
 it in his hands. John and several other persons saw them at 
 play. Every one enjoyed it very much." 
 
 On the first trial many of the minor modifiers will be 
 overlooked. They can be supplied by asking questions like 
 the following: What is large used for? Into what, do you 
 suppose? At what? Enjoyed vilvAi'l etc., etc. 
 
 When the complete story has been constructed, question 
 upon the office of the several words used. This is but going 
 over tlie same ground again, and it will be found that the 
 pupils will answer promptly, as follows: 
 
 To tdl what happened, to tell who did something, to tell where 
 it ivas thrown, etc. 
 
 Lead them tlien to observe that each sentence has (1) a 
 word to tell what is said, (2) a word to tell what it is said of, 
 and (3) phrases or words to tell kind, time, manner, -place, etc. 
 
 Call these predicate, subject, and viodifiers, and have them 
 point them out in other sentences. Several repetitions of this 
 work, or something similar, will be necessary to secure com- 
 plete assimilation of the principle. 
 
 PRINCIPLE IV. 
 
 Commence with part of a phrase, thus : 
 
 Into tJie, 
 
 and have the members of the class to suggest endings, as 
 follows : 
 
 fair 
 
 I water 
 1. Into the -{ room 
 
 I house 
 
 t etc. 
 
38 
 
 PEDAGOGICS. 
 
 Combine into the generic phrase, into something or some- 
 ivhere. Selecting one of the species, continue thus: 
 
 ( arrow 
 1 ball 
 2. Into the air the^ bird 
 I stone 
 tetc. 
 
 Proceeding as before, construct : 
 
 f sped 
 
 I flew 
 
 3. Into the air the arrow •{ shot 
 
 I went 
 l^ etc. 
 
 Selecting again, complete the sentence : 
 
 4. Into the air the arrow sped. 
 
 Compare (1), (2), (3), and (4), with a view of making 
 the assimilation that sped fixes the meaning of the whole. 
 
 Taking sped as the basis, construct the equivalent general- 
 ization : 
 
 Something somewhere sped. 
 
 Construct a horizon to represent this meaning, and smaller 
 ones within it to represent the restricted meaning as modifiers 
 are added, thus: 
 
PRACTICAL LESSONS. 39 
 
 Numbering the horizons as in the diagram, and setting up 
 a comparison among them, the pupil may be led to make the 
 assimilation formulated by the principle. 
 
 Many repetitions, however, will be necessary in order to 
 secure thorough mastery of it. 
 
 Note.— A complete generic idea involving every element may be expressed 
 by the following formula: 
 
 Something, somewhere, sometime, somehoiv, somewhy, -1 ^^1'^ 
 
 The predicate or verb in assuming tense form expresses always existence, or 
 its alternative action, and generic time, and holds elliptically the other elements 
 of the idea. All modifiers of the predicate are but expressions of the character 
 of certain elements in the idea seeking expression. If any particular element 
 only demands a generic expression it does not assume form ; if it exists in a 
 specific degree some adjunct or word as a modifier of the elliptical form ex- 
 presses it. 
 
 The modality of the idea is expressed by the particular form its language 
 representative takes, viz., as a statement, as an interrogatory, or as a command. 
 
 The quantity of the idea is expressed by the modifiers as a group or whole. 
 
 Illustrations are given below. 
 
 I. 1. Something: A night of storm. 
 
 2. Somewhere: (held generically.) 
 
 3. Sometime: (expressed in /o?/oi<;gd.) 
 
 4. Somehow: (expressed ii\ followed.) 
 
 5. Somewhij : (held generically.) 
 
 6. { f 2.f-"* " } ^o^lowed a day of sunshine. 
 
 7. Its modality is apparent in the fact that it is a statement. 
 
 8. Compare : 
 
 A night of storm follows a day of sunshine, 
 
 ^Mghts of storm (jj'jfj^} followed by {jJalj^^} o^ f^unshine, or other ex- 
 pressions of similar ideas to that under analysis, and the qnantity becomes 
 apparent. 
 
 II. 1. Something: my father. 
 6. Exists; sometime: lived. 
 
 2. Somewhere: beside the Tyne. 
 
 The other constructive elements are held generically in "lived," and are 
 therefore elliptical. The modality and quantity will be apparent through com- 
 parison. 
 
 "^' timetime:} dawn and lend (thine aid). 
 
 A <inmi>hr,n, ■ i o" our darkucss (modifies generic idea in " dawn ")• 
 4. i>omeiiow. -^ U5 _ (^^ ^g) (modifies generic idea in " lend "). 
 
 " Thine aid " is a modifier of the elliptical object inhering in " lend." The 
 other constructive elements are h<4d generically in the predicate, and modality 
 and quantity are apparent iu the form. 
 
 Other examples are not necessary to make apparent the fact that every Eng- 
 lish sentence, whatever its mode, may be analyzed as the examples are by com- 
 "paring with the generic sentence. 
 
 Reflection will show that if sentences are studied as "wholes" in this way, 
 and comparisons made in the manner indicated, that the assimilations made by 
 the pupils will be of the highest value to them in understanding what they 
 read, and in expressing their thoughts with clearness and force. 
 
40 PEDAGOGICS. 
 
 WORD TEACHING 
 
 When a child first enters school he has a large stock of 
 words in his speaking vocabulary. The aim of the teacher 
 should be, at this stage of his education, to make him ac- 
 quainted with iJiPse in their written and printed forms. 
 
 This is the primary course of study in reading. By neces- 
 sity some new words will be added to his vocabulary during 
 the two or three years necessary to bring him up with what 
 he already knows. 
 
 If this is well done, his after work in reading is easy. 
 But at every stage of his education his teacher ought to 
 present thoroughly all the new word material he encounters 
 in his text-books. 
 
 An illustration is given below of how^ this should be done, 
 both witli w^ords already in the vocabulary and with words it 
 is desired to put there. 
 
 In this work the teacher should have Postulates III and 
 IV in mind. The illustrations are taken from actual practice, 
 the first with a class during their second month in school, 
 the second with children entering upon their third year. 
 
 Teacher (writing the word "run" on a card): Who can 
 tell me what that says ? 
 
 Pupil (selected from a number who volunteered) : It says 
 run. 
 
 T. : Can you run ? 
 
 The pupil assented, and after a little persuasion ran to his 
 seat. The teacher then, to test their knowledge of the word, 
 asked questions and got the following statements : 
 
 A boy can run. 
 
 A horse can run. 
 
 Inquiring as to the difference in the running, he found 
 they associated it with the legs. This indicated that the 
 meaning was not generic to them. The next question was, 
 **Can a box run?" This produced a general laugh, and 
 many emphatic "noes." ''Why not?" asked the teacher of 
 
PRACTICAI. LESSONS. 41 
 
 one pupil, who evidently had a reason in his mind. " Because 
 it has no legs," was the prompt reply. 
 
 " Can a wao^on run ? " asked the teacher. There was some 
 hesitation, but many answered, " Yes." " But it has no legs; 
 how is that ?" There was quiet for some time. At length a 
 hand went up, and the very wise reply, ''Its wheels are its 
 legs," was mo'lestly given. The teacher then illustrated the 
 meaning of the word by calling attention to the clock which 
 was ruanwg and to water on a sheet of paper, anr] left the 
 word for another. 
 
 The perceivinri powers of the children had been exercised 
 in recognizing the different actions ; their compirinrj powers 
 had been exercised in observing the differences and resem- 
 blances in the actions. Their asiimilatlng powers were prob- 
 ably exercised in getting a more generic meaning for the 
 word. This latter was the aim of the teacher; how well he 
 succeeded could only be known by testing the class at some 
 subsequent les-on. 
 
 Tiie next illustration is of a new word. A girl had asked 
 to have the word "fiitigued" from the reading lesson ex- 
 plained. The teacher persuaded her to run to and fro in the 
 room a number of times. After she had done this she was 
 asked how she felt. "I feel tired," Wi\^ the reply. ''Some 
 people would say fatigued " remarked the teacher. 
 
 Both words were then written on the board and copied by 
 the children. A comparison was set up by suppositions as 
 follows: How are you apt to feel if you sit awhile after you 
 are tired or fatigued ? Does your teacher feel fdgued or 
 tired after her day's work ? Have you ever had a tired feel- 
 ing after school or after studying a long while? Did you 
 ever hear any one say she was exhausted^ [This word was 
 added to the group on the board and copied when a child 
 answered affirmatively.] What had she done to exhaust 
 her? Was Mary exhausted awhile ago? When would you 
 use exhausted^ When would you use tired f When use 
 fatigued f 
 
42 PEDAGOGICS. 
 
 The answers of the children are not given, nor the whole 
 conversation. The children were led to observe that fatigued 
 is a species of tired, and that exhausted is tired carried so far 
 that a person has to stop. This was illustrated by the prim- 
 itive meaning of the word. 
 
 It was not possible nor desirable at that lesson to make 
 the meaning fatigued generic. The aim of the teacher was 
 simply to have the class perceive, compare, and classify it. 
 That this was probably done will be apparent to one who 
 scrutinizes the work. 
 
 No formal statement was attempted of the truths taught 
 in either lesson, nor was a definition essayed for any word. 
 All proper word teaching contemplates a trial at the it.se of 
 the word at some later period. This serves both as a review 
 and a test of the work done. 
 
 READING. 
 
 In the primary course the pupil deals, as a rule, with words 
 he already knows the mt-aning of. 
 
 At the time he learns to know the written or printed form 
 his teacher ought to make the effort to have him assimilate a 
 more generic meaning for each word. In addition to his les- 
 sons in learning words, which is the foundation for pn^gress, 
 he should also have lessons in learning phrases, such as, on a 
 box, into a house, to the wall. 
 
 There are many prepositions and other such words whose 
 meanings are not susceptible of objective illustration or of 
 clear definition. If phrases are taught in the same way as 
 words are, these meanings are assimilated. 
 
 The main difficulty in teaching reading has always been to 
 get the children to comprehend the meaning of the sentences 
 before them. This difficulty will always exist to the teacher 
 who requiies a child to learn to read by reading another per- 
 son's thoughts. If the hist year's work in reading were to 
 be entirely of sentences of his own composition, it is believed 
 that the load would be lifted in a great measure. Observa- 
 
FKACTICAL LESSONS. 43 
 
 tion will convince anyone that the more nearly a teacher con- 
 forms to this rule, the more easily do his pupils learn to rea«l. 
 
 To express this principle in practical form would be to say: 
 A child will learn to read more readily if he makes the first 
 series of lessons for himself. 
 
 In reality he does this, if he learns at all, for it is mani- 
 festly impossible for one to get the author's exact thought in 
 any case. 
 
 The product from reading a sentence to any mind is not 
 the thought of the author, but the thought of the reader 
 coming into the mind as an assimilation, from the relation of 
 certain thought-objects, suggested by the words of the sen- 
 tence, standing before him as " whole." 
 
 Unless a child has had practice in expressing relations ob- 
 served, he is not prepared to analyze such relations when ex- 
 pressed by another. The oral expression of relations does not 
 resemble the equivalent written or printed relation to a great 
 enough degree for the pupil to recognize their idenity until 
 he has made the intermediate step of formulating some of the 
 relations he has observed. 
 
 To illustrate all this : Suppose the mind holds as a complex 
 picture the following thought-objects : A dog — aboy — chasing — 
 a road — across (something) —and past time. It is easy for that 
 mind to compose the whole into one complex relation, and 
 say : " The dog chased the boy across the road." 
 
 After doing this, and recognizing the written words, " the 
 dog chased," etc., as being identical with the same words 
 spoken, he can easily, on hearing or seeing something written 
 in the same idiom, get a thought from it. The fact that 
 children are unwittingly put to work in strange idioms, when 
 set to practice in first readers and primers prepared by dis- 
 tinguished (?) authors, accounts for much of the labor ex- 
 pended by primary teachers. 
 
 Nothing is easier than to get children themselves to make 
 the first lessons they are to read. 
 
 A description of the teacher's desk and the objects upon 
 
44 PEDAGOGICS. 
 
 or near it, with their relations to each other and to the desk ; a 
 narrative of the adventures they had when it rained, and they 
 could not go out to recess; a description of a doll party in 
 progress before them; a description of see-sawing, or some 
 other game ; in fact, all the events and scenes of home or 
 school life are open to the teacher for selection. 
 
 But care must be taken to have the lessons as recorded for 
 practice expressed in their own idioms. They must be led by 
 degrees to express themselves in the forms used by older peo- 
 ple. As a rule they can not get thought from sentences pre- 
 pared by mature minds until they have adopted to some 
 extent, in conversation, the habitual forms of expression be- 
 longing to maturity. 
 
 The principles thus far illustrated as applicable to primary 
 work in teaching reading apply, with modifications, through- 
 out the course. 
 
 1. New word-material must be introduced objectively, and 
 at subsequent lessons the specific meanings assimilated must 
 be made generic. 
 
 2. Lessons upon phrases and clauses and sentences must 
 be given, alternating with the practice lessons. Repetitions 
 of such work as has been recommended under Language 
 serves the purpose indicated. 
 
 3. Reproduction of lessons read, or abstracts prepared in 
 advance of lessons that are very difficult, are valuable as read- 
 ings for classes. 
 
 An outline of the work contemplated by (3) is given below. 
 The lesson selected for outline is taken from Butler's Fourth 
 Reader. Have the children dictate the following, from in- 
 spection of the lesson if new, from memory if they have al- 
 ready recited it : 
 
 CHARACTERS, 
 
 a Brahmin, a third rogue, 
 
 a rogue, a dog, 
 
 a second rogue, the gods. 
 
PRACTICAL LESSONS. 45 
 
 HAPPENINGS. TIMES. 
 
 vowing, a certain day, 
 
 going to buy, at same time, 
 
 inventing, before, 
 
 questioning, just then, 
 
 replying, soon after, 
 
 exclaiming, later, 
 protesting, 
 
 paying, places. 
 
 sacrificing, the market place, 
 
 smiling. home of Brahmin. 
 
 Other groups, as motives, to cheat, to sacrifice, etc.; or re- 
 lated THINGS, as bag, pot of ghee, etc., etc., may be added 
 if necessary to comprehension of the " whole." 
 
 Enough questioning must be done in what and how to enable 
 the children to get a firm mental grasp of the story. 
 
 Let them write it in character, that is, let one tell it from 
 the standpoint of the author, another as the Brahmin, another 
 as one of the rogues, and still another as the dog, or one of 
 the gods. 
 
 Select meritorious efforts as matter for reading lessons. 
 These ought to be copied on separate sheets for preservation. 
 
 GRAMMAR. 
 
 To present this subject successfully, the teacher must lead 
 the pupil to assimilate the principles underlying constructions 
 through his own experiences. In other words, the pupil's 
 own sentences, or sentences made b^'' the teacher using only 
 words that are in the pupil's vocabulary, must be the basis for 
 comparison. 
 
 In general, any principle of grammar may be taught by 
 composing a group of sentences or phrases having the prin- 
 ciple desired to be taught prominent, either as a resemblance 
 or as a difference. 
 
46 PEDAGOGICS. 
 
 For example, suppose it is desired to prepare the pupil 
 to understand the definition, "A noun is in the nominative 
 case when it is the subject of a verb." Compose a group 
 similar to the following : 
 
 1. A boy walks. 
 
 2. A horse walks. 
 
 3. A man walks. 
 
 4. A cow walks. 
 
 Question upon the details of meaning in these sentences 
 and in the particular words until the pupil loses sight of the 
 words that compose them. He will do this when you enable 
 him to picture in his mind the different acts. His percep- 
 tion must be made clear. Proceed by comparing to discover 
 that boy, horse, man, and cow have a common use, viz., to tell 
 which animal walks. 
 
 Add others to the group, varying as below : 
 
 5. A toad hops. 
 
 6. A squirrel leaps. 
 
 7. A bird flies. 
 
 By comparing these with the others, the resemblance, 
 which still holds throughout, will assume a more generic 
 form, thus : To tell which animal moves. 
 
 In the same way "which animal" may be made to assume 
 the form, "which thing," and "moves" to take the more 
 generic meaning, " acts." 
 
 This case or use of a noun needs a name, and after giving 
 it, the pupil's crude answer to the question, " When is a noun 
 used in the nominative case?" compared Avith the definition 
 given in the text-book, will enable him to comprehend the 
 latter. 
 
 The same word, used in different ways in a group of sen- 
 tences, may be used to develop any scheme of cases one may 
 wish to employ. For illustration, take the following group: 
 
PRACTICAL LESSONS. 47 
 
 1. A man drank water. 
 
 2. A horse threw the man. 
 
 3. A man's liat is hirge. 
 
 4. A boy spoke to the man. 
 
 5. Joseph is a 7nan. 
 
 1. Question upon the meaning (in the domain of "what") 
 until the details are distinct and the words are lost sight of. 
 
 2. Que.stion by comparing till the cases or several uses of 
 man are distinct. 
 
 3. Parallel each case with a group, as follows: 
 
 1. A man drank water. 
 
 2. A Jiorse drank water. 
 
 3. A coiv drank water. 
 
 1. A horse threw the man. 
 
 2. A horse threw the boy. 
 
 3. A horse threw the lady. 
 
 1. A man's hat is large. 
 
 2. A lady's hat is large. 
 
 3. A giant's hat is large. 
 
 1. A boy spoke to the man. 
 
 2. A boy spoke to tiie horse. 
 2. A boy spoke to the driver. 
 
 1. Joseph is a man. 
 
 2. Henry is a boy. 
 
 3. Carlo is a dog. 
 
 And from these groups lead the pupils to assimilate what con- 
 stitutes each case. 
 
 It is not deemed necessary to add further illustrations in 
 this subject, as those given are a 'fair type of all grammar 
 work. 
 
48 PEDAGOGICS, 
 
 GEOGRAPHY. 
 
 In this subject intellect is occupied more in perceiving than 
 in any other process, as the number of data necessary to 
 arrive at a truth are so much more numerous in most cases 
 than in other subjects. 
 
 In general the principles that affect the life or character 
 of a pupil are not assimilated until after the period of school 
 life has expired. For illustration: A man is a<ked to leave 
 his home and become a citizen of another country or province 
 of his own. Now the data he has in reference to that country 
 or province constitute the " whole" that contains the princi- 
 ple or truth which is to determine a course of so much inter- 
 est to himself and family. Upon his decision rests the future 
 happiness and prosperity of himself and those dependent on 
 him. In like manner principles that govern investments of 
 money, ventures in commerce, etc., etc., are all assimilated 
 through geographical data which have been accumulating in 
 the mind since early childhood. 
 
 Every human being is so related to geographical data 
 that any great success in life is impossible of attainment 
 without a comprehensive knowledge of the subject. 
 
 Its importance being paramount, then it folhnvs that the 
 teacher who introduces the topic to a child should adapt his 
 work so as to prepare the pupil for assimilations that will 
 serve him well when he needs them. 
 
 The method employed in geography should be the same 
 as has been illustrated in Arithmetic and in Language. It 
 should vary in detail to suit the peculiarities of the subject, 
 these requiring more work in perceiving and comparwg than in 
 asswillatlng. Tiiere are many assimilations a pupil needs to 
 make as he proceeds, and the teacher should cause him to 
 make them in proper order. 
 
 " The world is my home," should be among the first assim- 
 ilations made by one properly instructed in geography. This 
 
PRACTICAL LESSONS. 49 
 
 assimilation, though it may be made imperfectly at first, con- 
 nects the pupil by new ties to the eartli, gives him an inter- 
 est in its study that will never flag through life, keeps alive 
 his attention, energizes his memory for the Herculean task of 
 storing away the countless data of this science, and rouses his 
 imagination to enter upon the pleasing task of constructing 
 that grand concept of the world that is to be the chief means 
 of solacing his leisure hours spent in reading, that is to be 
 the vehicle by whicii he may visit distant lands while quietly 
 resting at home, and that is to bring success to his ventures 
 in business. 
 
 The younger the chihlren are the less apt will they be to 
 take an interest in the study of geography from books and 
 maps, for the reason tliat they have no cares upon ihem and 
 do not understand the relations in which they stand to the 
 world. As soon as thev are led to comprehend that all they 
 have, and all they will ever need to use for food, clothing, 
 and shelter are won by hard toil Irom nature's stores, and 
 that if they wish to have periods of rest and enjoyment dur- 
 ing life they must learn nature's secrets, and be able to gain 
 a living by a minimum of toil, they will be inspired to equip 
 thenfselves for the task before them by storing up geograph- 
 ical knowledge. 
 
 By keeping this in mind, and by grouping the facts of the 
 lesson so as to suggest it, even young children may be im- 
 pressed by this thought. 
 
 Many assimilations requiring special lessons and extra time 
 devoted to them aside from the regular text lessons are nec- 
 essary to make the general work profitable in the highest 
 degree. Such are : 
 
 (a) "A map is a representation of a part or the whole of 
 the earth's surface." 
 
 (6) *'The ocean is the great source of all life." 
 (c) ''Life thrives where climate permits and where sus- 
 tenance abounds." 
 
 4 
 
50 PEDAGOGICS. 
 
 (d) " Climate depends upon latitude, elevation, prevailing 
 winds, and contiguous ocean currents." 
 
 (e) "Population follows natural highways." 
 (/) ''Cities are built upon rivers or coasts." 
 (^) "Mines are found in mountainous sections." 
 
 Qi) " Manufactories and mills are located upon streams 
 having natural waterfalls." 
 
 (i) "An indented coast line is favorable to commerce." 
 
 A correct method in geography requires that the whole of 
 the instruction should be founded upon, and the detached 
 facts be learned by the light shed upon them by a series of 
 general truths such as are given above. These are not given 
 as a complete series, but as illustrative of the utility of such 
 work. Thousands of facts in geography will be learned with 
 great facility if the general truth of which each is a species 
 is known beforehand, and these same facts will be remem- 
 bered with much greater ease. 
 
 Suppose, for illustration, the following texts are encoun- 
 tered:* 
 
 " Arabia is chiefly a hot, desert plateau with oases of different 
 sizes, in which dates, grapes, tamarinds," and other fruits grow. It 
 has no general government, the inhabitants being ruled by sheiks 
 or chiefs." 
 
 "The Empire of Japan consists of islands which contain 
 mountains, streams, forests, and a well-cultivated soil. The prin- 
 cipal occupations of the Japanese are agriculture, manufactur- 
 ing, and mining. Its exports comprise tea, rice, silks, porcelain, 
 fans, and lacquered ware." 
 
 -:i:- * *• * -;K- *■ *- * -:•:■ -:;:• -:•:- * 
 
 " Kentucky is about half the size of Kansas. Its surface is 
 mostly hilly, and slopes' toward the northwest. The southeastern 
 part is mountainous. In production of tobacco, hemp, and flax 
 Kentucky surpasses every other State in the Union, The "blue- 
 grass" region, in the basins of the Licking and Kentucky rivers, 
 is celebrated for fine horses. Louisville, at the Falls of the Ohio 
 River, is the most important tobacco market in the country." 
 
 * These extracts are copied from Barnes' Complete Geograph5\ 
 
PRACTICAL LESSONS. 51 
 
 A great many facts are embraced in these three extr.icts. 
 The text-book from which they are taken contains nearly one 
 hundred pages of similar matter. Is it too much to know? 
 Can one be said to be educated in geography unless he knows 
 much more than is given here of each of one hundred coun- 
 tries and important provinces? Can we expect to teach it 
 all as detached matter ? 
 
 The answers to these questions are obvious, and suggest a 
 method founded upon ammilations for general principles, and 
 patient filling in by adding to the original "wholes" from 
 which assimilations were made the new^ facts as they are per- 
 ceived after comjMring them with the original data. 
 
 To illustrate the method suggested : 
 
 Suppose a class to have already assimilated the truths 
 marked above as (a), (b), (c), etc., etc., would they not be 
 much more apt to remember what is said about Louisville, 
 about the government of Arabia, and about the occupations of 
 the Japanese and their exports f 
 
 Is there any fact in either of the extracts that is not a 
 species of one of the general truths given., or of some other 
 important one in a full series? Would not a pupil so in- 
 structed, after reading what is here given, even if his text- 
 book omitted the facts, be able to say confidently : " There 
 are large cities in Japan, but not in Arabia?" Would he 
 not also be able to say that Louisville is a manufacturing 
 city, and that the people of the "bluegrass region" are 
 wealthy, cultured, and inclined to field sports? 
 
 Are there not other facts of the countries mentioned which 
 are indissolubly linked with those given in the extracts, and 
 which would be readily appropriated by a mind prepared for 
 the task ? 
 
 Directions are given below as to how to prepare '* wholes" 
 for the assimilation of general truths as a basis for after- 
 study. 
 
 1. A proper *' whole" for making the assimilation, "A map 
 is a representation of a part of the earth's surface," is the con- 
 
52 PEDAGOGICS. 
 
 struction by the pupil of one or more maps of yome region or 
 district with which he is familiar. Wiien he has done this 
 with the teacher's aid, and has used the same conventional 
 signs on his map that are used in his text book to mark rivers, 
 lakes, mountains, etc., he is ready to get ideas from the maps 
 in his book.* 
 
 2. •' The ocean is the great source of all life." 
 
 Take for a " whole" the elements that contribute to sup- 
 port life in animals and plants. Appeal to the pupils' ex- 
 periences as to what terminates and prolongs life. The steps 
 are easy to the assimilation mentioned. 
 
 3. *' Life thrives where climate permits and sustenance 
 abounds." 
 
 Take for a " whole " the cities (abodes of men) in United 
 States, Mexico, Central America, Dominion of Canada, and 
 (?) Greenland. 
 
 Compare as to population, etc., etc. 
 
 Ask ivhy the facts are so, and the assimilation is made. 
 
 Plants and animals of different regions in North America 
 can be compared to make the same assimilation. 
 
 4. " Cities are built upon rivers or sea-coasts." 
 
 Make a " whole" of the locations of large cities on the map 
 of North America, and from it, by questioning, get the assimi- 
 lation. 
 
 Enough examples have been given to illustrate how readily 
 this work may be done. 
 
 The continents ought to be studied one at a time, and the 
 principles referred to ought to be taught from the details of 
 the first continent, as thoroughly as possible. 
 
 Such "wholes" as are given below should be used for 
 reviews, the details to be supplied from memory by the 
 pupils: 
 
 * However perfect may be the maps of a text-book, they will not suffice to 
 illustrate fully such texts as have been quoted above. Relief maps of conti- 
 nents are a necessity for the best instruction. These can be made by a teacher, 
 using paper pulp or putty, or some other plastic material for the elevations. 
 Fine maps of this character are now made for sale. 
 
PRACTICAL LESSONS. 53 
 
 CUBA. 
 
 Gulf of Mexico — Florida — Spain — Havana — Matanzas — 
 oranges — lemons — tobacco — sugar — mahogany — rosewood — 
 Columbus — 1492 — hurricanes — Spaniards — Negroes, etc., etc. 
 
 After these details are arrived at, the general direction be- 
 ing, " Put down what Cuba makes you think of" — as a class 
 exercise — and arranged logically, have the class write up the 
 geography of the island. 
 
 These "wholes" may be made of many topics, as Amazon, 
 Andes, cotton, rice, coal, Caucasian race, etc. They serve 
 admirably to put knowledge in a classified form into the 
 memory. 
 
 Many new words are brought into the vocabulary by the 
 study of geography. The requirements of Postulate IV, as 
 well as illustrations under Reading in this Monograph, make 
 it certain that a teacher should have the geography read by 
 the pupils, and not recited from memory, as was the universal 
 method not many years ago. In other words, there ought to 
 be no reciting of answers with books closed, and maps hid, 
 except in review lessons, illustrated above. 
 
 ETHICS. 
 
 At the foundation of right doing lies right thinking. 
 Every member of society stands in certain relations to his 
 fellows, and certain duties are incumbent on him. These 
 duties are two-fold, viz., To individuals and to the whole. 
 
 To fulfill any duty marks a man as possessing the virtue 
 that is its fulfillment. Honesty is a virtue that will inhere in 
 any individual who respects the property-rights of others. 
 And so for all virtues. Now is it important to instruct 
 young persons in ethics? And can it be done without teach- 
 ing the tenets of any church ? 
 
 No one who has observed the growth of the money-getting 
 
54 PEDAGOGICS. 
 
 feeling in this country, who has observed its ruthless hand 
 corrupting legislation, defiling religion, and grinding poverty, 
 can for a moment deny that something ought to be done to 
 rescue us from that state into which we are drifting, a state 
 in which the only tie that shall bind us is that weak one 
 known as " honor among thieves." 
 
 The church, or rather churches, of the land ought to see to 
 it, while they have the power over public opinion, that ethics 
 is introduced and taught in the common schools. This is 
 the only means by which all classes can be reached. No 
 other influence extends to every home in the land. 
 
 The necessity for teaching ethics being apparent, and the 
 medium through which enlightenment is to come provided, 
 it only remains to agree upon the curriculum and the 
 method. 
 
 No church prejudices can be offended if the teachers make 
 the dictionary the basis of their work. By this simple 
 means all contentions can be quieted, and the good work of 
 training the youth of our land morally, be consummated. 
 
 Man, "created in God's image," is a progressive being, 
 and inherits a tendency to admire the beautiful, to recognize 
 the true, and to retain the good. If noble ideals are ])laced 
 before him, and connected with his daily walk, he will strive 
 to reach them and gradually realize them. 
 
 The experiences of a race in conduct record themselves in 
 the vocabulary of that race in the names for virtues and vices. 
 Now, if the teacher will but give lessons upon these ab- 
 stract terms, he will be laying the foundation for correct con- 
 duct. If the same pains were taken in school to acquaint the 
 children with the meanings of honesty and fortitude as are 
 taken to teach exponent and predicate nominative, the results 
 in ethics would be similar to the results in science. 
 
 Postulate IV assumes that words must be made generic in 
 meaning to the child to be in any high degree useful to him. 
 Now, to make any word generic in mind, its full range of 
 meaning must be brought to consciousness, and comparison 
 
PRACTICAL LESSONS. 
 
 55 
 
 o"2«^:3 2. ^ ^ 
 
 
 lat approach it in meaning, 
 tosite in meaning, 
 aching the virtue expressed 
 below. 
 
 i-&.'^£^lg^ > ORTITUDE. 
 
 :?^i §^o|g. g and 
 
 jfio ^p'^^^i"^ 2 nder financial reverses. 
 
 a-^ t^ oq B ^ H- ^ W 3h, 
 
 giS^^s Q id 
 
 S.£: S^i... 3Qg.^ o . ,3f a limb. 
 
 ^^ ^^^l"i ^ 's. Garfield, Joan d' Arc, 
 
 ^1 §^§12^'-^ E imozin, Jesus Christ, Casabi- 
 
 EE s ^ ?-2 ^.'/5 p read to the class. Compare 
 
 »g: Si^'^^^a^E S* courage, bravery, endurance, 
 
 q J? ^ g.M§ ^-^ S rs possessing like qualities. 
 
 11 o^^^ii R ualities 
 o 
 
 •midity, hesitation, fear, treach- 
 
 early every case a pupil will 
 
 r^ ^ «>^.®.^ ^^ » «e a man or woman of forti- 
 
 ^ ^ £ c ^^.c ^ o • almost certainly, to assimi- 
 
 §|^S-g^*3-3| f the teacher will but take 
 
 ^^ I §^ ll S^ ? imples oi' fortitude that have 
 
 &^§ S^'S tf §^J3 i ^ f he can bring these to the 
 
 ^Ig' S-Bi-^o-s i, ibited in their own conduct, 
 
 ^^ o^^Sis^^S changing the current of their 
 
 2° =?o ^ § ^ i- a"y ^^"^^^ a^^ necessary, and 
 
 p- =f P 7 ^ ?r.^ I lasting impression. 
 
 pies observed by them, and if 
 on the subject of any lesson, 
 1 that they have learned the 
 begin to exhibit in their con- 
 
54 PEDAGOGICS. 
 
 feeling in this country, wh 
 corrupting legislation, defilii 
 can for a moment deny thai 
 rescue us from that state ir 
 in which the only tie that 
 known as " honor among th 
 
 The church, or rather chi 
 it, while they have the pow' 
 is introduced and taught i 
 the only means by which i 
 other influence extends to e 
 
 The necessity for teach ir 
 medium through which enl 
 it only remains to agree 
 method. 
 
 No church prejudices car 
 the dictionary the basis o 
 means all contentions can b 
 training the youth of our la 
 
 Man, " created in God's 
 and inherits a tendency to i 
 the true, and to retain the ^ 
 before him, and connected ^ 
 to reach them and gradually 
 
 The experiences of a race 
 the vocabulary of that race i 
 Now, if the teacher will I 
 stract terms, he will be layir 
 duct. If the same pains we. 
 children with the meanings 
 taken to teach exponent and 
 in ethics would be similar to 
 
 Postulate IV assumes tha 
 meaning to the child to be u 
 Now, to make any word ge 
 meaning must be brought • 
 
PRA.CTICAL LESSONS. 55 
 
 of it must be made with others that approach it in meaning, 
 and with others still that are opposite in meaning. 
 
 An outline of a *' whole" for teaching the virtue expressed 
 by the word Fortitude is presented below. 
 
 EXAMPLES OF FORTITUDE. 
 
 (a) A woman burying her child, 
 
 (6) Sending her son to battle, and 
 
 (c) Comforting her husband under financial reverses. 
 
 (c?) A soldier on a forced march, 
 
 (e) Confronting the enemy, and 
 
 (/) Suffering the amputation of a limb, 
 
 (g) Historical examples: Mrs. Garfield, Joan d' Arc, 
 Washington, Marshal Ney, Guatimozin, Jesus Christ, Casabi- 
 anca, etc.. etc. 
 
 Let these examples be told or read to the class. Compare 
 them with examples of strength, courage, bravery, endurance, 
 resolufeness, persistence, and others possessing like qualities. 
 Compnre also with examples of timidity, liesiiation.Jear, treach- 
 ery, and others having opposite qualities. 
 
 If this work is well done, in nearly every case a pupil will 
 be inspired with a desire to become a man or woman of forti- 
 tude. Moreover, he may be led, almost certainly, to assimi- 
 late a principle for guiilance, if the teacher will but take 
 pains to add to the " whole " examples offortitude that have 
 been exhibited by children. If he can bring these to the 
 memory of the children, as exhibited in their own conduct, 
 he is almost sure to succeed in changing the current of their 
 lives. 
 
 Repetitions of the work with any word are necessary, and 
 also tests in order to be sure of a lasting impression. 
 
 If pupils can point out examples observed by them, and if 
 they can construct an essay upon the subject of any lesson, 
 no better evidence can be given that they have learned the 
 meaning of the term. If they begin to exhibit in their con- 
 
56 PEDAGOGICS. 
 
 duct an example of a virtue taught tliem, it is proof positive 
 that they have assimilated a rule for action. 
 
 Note.— The manner of giving such lessons ;is has been outlined here, is 
 more elaborately treated under Character Education. The nature and value of 
 the "Hypothetical Discourse" in teaching right conduct is there illustrated 
 fully. 
 
 ALGEBRA. 
 
 The authors understand that what is written here concern- 
 ing algebra is but part of arithmetic. Hence it ought to be 
 taught as such and at tlie same time with arithmetic. The 
 use of a letter to represent any number seems as simple as 
 the use of any class name, and is as easily learned by the 
 average pupil. 
 
 In the review of Principle (2) of Arithmetic (see page 24), 
 the use of any number of things as a unit should be made 
 very familiar to the pupil. There he learns that 
 
 3, 4sts. -f 5, 4 sts. -f 6, 4 sts. = 14, 4 sts. 
 
 Such examples as: 
 
 5, 3 sts. 4 6, 5 sts. + 5, 8 sts. + 5, 9 sts. =? 
 should be given the pupil, expecting him to apply Principle' 
 10 (see page 24), and write: 
 
 3, 5 sts. -f- 6, 5 sts.+ 8, 5 sts. + 9, 5 sts. = 26, 5 sts 
 The units and coefficients should finally reach up into the 
 thousands. The transition to 
 
 3, a sts-. + 6, a sts. -f- 8, a sts. + 9, a sts. = 26 a sts.. 
 is simple and is easily made. To this end vary the number of 
 things in the unit while the coefficients remain the same; 
 thus by resemblances disclosing the same demand for a class 
 name for the number of things in the unit as for any object, 
 as chair. 
 
 The use of this method in subtraction, as in Principle 11 
 (see page 25), will familiaiize the pupil with the use of let- 
 ters as names for any number. 
 
 In arriving at Principle 10^ (see page 24), the following 
 steps are safe. By Principle 10; 6, 12 sts. == 12, 6 sts., omit 
 
PRACTICAL LESSONS. 57 
 
 ting the things 6 ■ 12 = 12 • 6 (1). So, also, 3, 2 sts. = 2, 3 
 sts., omitting the things 3 2 = 23. So, also, 3, 4 sts. = 4, 
 3 sts., 3-4=43. Substitute in (1) and we have : 
 
 3 2 3 4 = 4 3 2 3 = 4 • 2 3 • 3, etc. Doing likewise 
 with 4 and we have : 3-2-3-2-2 = 2-22-33 = 72. 
 Having, by repetitions, establi.-^hed Principle 10', then exer- 
 cise the class thoroughly thus: What and how many prime 
 factors are in 12? in 8? in 17? in 54? etc. Speak of 8 as 
 having three 2's as factors; of 12 as having two 2's and one 
 3 as factors, etc. Ask at the same time for the number of 2's 
 as units in 8, in 12, etc. Wiite on tlie board 2 + 2+ 2 + 2=4, 
 2's =8, and 2 • 2 • 2 = 8. Do the same with 12^ 16, 24,' etc. 
 If the attention of the pupil is called to use of 4 in 4, 2's, and 
 the question asked, why not^ise a figure to express the number 
 of 2's as factors in 8, 16, 32, etc., pupils find no difficulty in 
 appreciating the need, and are prepared for 2 2 • 2 = 2'^ = 8, 
 etc. Now ask for the /actors of the product of 12. and 24 
 without knowing the product, and pu])ils easily write 12 • 24 = 
 2 • 2 • 3 X 2 • 2 • 2 • 3, and applying Principle 10', we have 
 12 • 24 = 2 2 2 2 3 3 = 2* • 3^ ; with which result parallel 
 12 + 24 = 6, 2's -f 12, 2's = 18, 2's, and 12 • 24 = 2^ • 3 x 
 2"' • 3 = 2" • 3"^ and the average pupil has discovered for him- 
 self the principle that exponents of like factors are added in 
 multiplication. Place on the board such examples as: 
 
 24 X 36 X 72 X 96 X 48 X 144 = ? 
 
 and ask for the factors of the product without finding it. On 
 the board, after pupils find it, write: 
 
 24 X 36 X 72 X 96 X 48 x 144 = 2^' 3». 
 2» 3 X 2^ 3^^ X 23 32 X 2^ 3 X 2* 3 X 2* 3^. 
 
 Then : 
 
 a'b' c'd' X aH'd' x a'c'd' x cM*= ? 
 
 and others. Then : 
 
 a«* 6^« X a^ 6'" = ? 
 ^864 ^565 X ^m 5796 ^ V. 
 
58 PEDAGOGICS. 
 
 and others of like kind, ending the group with a*" 6" x a^ 6' = ? 
 and after a little repetition nearly all will readily do such ex- 
 amples as : 
 
 Then give such a group as follows : 
 
 a'H''^ X ab= ? '» 
 
 ^569^999 X ab = ? 
 
 and others, ending with a*" 6" X ab =? and a majority will be 
 able to work the last example. The greatest care must be 
 exercised throughout the whole of such work to let the })upil 
 discover for himself the results, and how as well as w^hy it is 
 so. It is not necessary to call the attention of the reader to 
 the application of the various postulates in the work given 
 here. 
 
 In order to lead the pupil to discover for himself the mul- 
 tiplication of polynomials the following "whole" is sug- 
 gested: Let the pupil multiply 46 by 68, and then put on 
 the board as he answers the various questions: "What are 
 the parts of 46?" " \Yhat are the parts of 68?" etc. 
 
 46= 40-f 6= 22-10-f2 -8, 
 
 68= 60-f 8= 2-3 -10+ 2« 
 
 "^)8= 320 + 48= +2»-10-f2*-3 
 
 276 =2400-f 360 =2^ • 3 • 10^-f 2^ • 3^ • 10 
 
 ' 3128=24^0-f 680+48=2^ • 3 • 102+2^ • 3^ ■ 10 + 2^ • 10-f2* • 3 
 
 A few repetitions of this " whole" will enable the pupil to 
 work with ease such examples as: 
 
 (^ar b"" -f a'' ¥) x (a^ b^ + a ¥) = ? 
 
 It will be observed that the use of the " 10," as above in- 
 dicated, will gain two ends, viz: (1) Make the pupil familiar 
 with the scale of tens, and (2) make the teaching of division 
 of polynomials easy. 
 
 In order to enable the pupil to arrive at the meaning of 
 
 m 
 
 a« proceed thus : Ask what does §, 12 mean ? Pupil answers, 
 
PRACTICAL LESSONS. 59 
 
 Separate " 12" into three equal parts, and take two of these 
 parts as units. 12 = 4 + 4 -f 4 .-. §, 12 = 4 + 4 = 2, 4's 
 — 8. Then ask: " What does 8^ mean?" A few pupils an- 
 swer immediately without any repetition, Separate 8 into three 
 equal factors, and take two of them as factors. Repetition 
 will enable nearly all pupils to arrive at same result. Place 
 on board after pupils have solved them : 
 
 S^=2^ : 16^ = 2» : etc. 
 
 8 =2- 2 -2 :16 =2-2-2-2: etc. 
 
 and ask what a" means. To assure results write a = 6" and 
 6"* = c, and ask pupils what «« equals. Use such examples as : 
 
 3 3 .3 
 
 2'^? (2^) = ? (2^0=? freely. 
 
 Teaching division of monomials is an easy matter. Space 
 forbids details ; the results arrived at below will indicate pro- 
 cesses. Remember, pupils must arrive at results for them- 
 selves. Ask pupils to find all the exact divisors of 12 by the 
 vse of factors, and when they have done the work place on the 
 board as follows, calling attention to the names of the parts : 
 
 
 Divisor. Quotient. 
 
 Multiplicand 
 
 . Multipl: 
 
 
 
 2 =2 3 
 
 r 
 
 2 
 
 X2 3 
 
 Dividend. 
 
 2-2 = 3 
 
 Product. 
 
 2-2 
 
 X 3 
 
 12- 
 
 - i 
 
 2 3 = 2 
 
 12= ^ 
 
 2 3 
 
 X 2 
 
 2 2 3 
 
 
 3 =2-2 
 
 3 
 
 X2 2 
 
 
 ^ 2 
 
 •2-3 = 1 
 
 .2 
 
 2-3 
 
 X 1 
 
 Then ask pupils to do likewise with 24, 36, etc. Then 
 place on the board such examples as : 
 
 r 2' • 3 • 5^ = ? f 2^ • 3 • 5» X ? 
 
 I 23- 3^ -53 = ? I 23- 32 -53 X? 
 
 23.H*.5^_^^ 3^-5^ = ? 23-3*-5^=<; 3»-5^x? 
 
 I 2^ ■ 3* • 5^ = ? I 2' • 3* ■ 5' X ? 
 
 t 5' =? 15^ X? 
 
 After repetition with figures use letters freely both as 
 factors and exponents. 
 
 To teach division of polynomials, reverse process of teach- 
 ing multiplication. 
 
60 PEDAGOGICS. 
 
 In subtraction, after pupils have read up their notes on the 
 subject, give them two numbers, such as 57 and 96, and let 
 the pupils compare them as found in their notes. After repe- 
 tition, if necessary, put on the board as follows: 
 
 (+ 96) - (+ 57) = 4- 39 (+ a) - (+ 6) =? 
 
 (+ 96) - (- 57) = -f 153 (+ a) - (- b) =? 
 
 (_ 96) - (+ 57) = - 153 (- a) - (-1- b) =? 
 
 . (_ 96) - (- 57) = - 39 (-a) - (- b) =? 
 
 (+ 57) - (+ 96) = - 39 (+ 6) - (+ a) =? 
 
 (+ 57) - (- 96) = + 153 (-f b) - (- a) =? 
 
 (_ 57) _ (4- 96) = - 153 (- b) - (+ a) =? 
 
 (_ 57) _ (_ 96) = -f 39 (- b) - (- a.) =? 
 
 and require pupils to write answers in parentheses thus: 
 -f (a — 6), + (a -f 6), — (a -\- b), etc., having informed 
 them that the number "a" is greater than the number "6." 
 Some pupils will do the work without difficulty. Repetition 
 with large numbers will call the attention of the pupils to 
 what they do and how they do it. If, then, a few pupils 
 remain who have not succeeded, by questioning in the whq^, 
 how, and why, the teacher will enable all, or nearly all, to do 
 the work by themselves. 
 
 Announcing the proposition that John has five debts less 
 of six dollars each than James, and requesting the pupil to 
 compare John to James, will enable him to discover that the 
 product of — 5 and — 6 is + 30. 
 
 Let the pupil be led to make the following "whole," and 
 he learns when trinomials can be separated into two binomial 
 factors, and how to do it: 
 
 42 X 43 =(4 • 10 -f 2) (4 • 10 + 3)= 4^ • 10^ -f 5 • 4 • 10+ 6 
 54 X 56 ==(5 • 10 + 4) (5- 10 -h 6)= 5^10^+ 10- 5 10 + 24 
 78 X 79 =(7 10 + 8) (7-10 + 9)= 7^102+ 17- 7- 10 + 72 
 
 When three or four of these are done, ask pupils to use 
 letters, and if they fail, ask them to observe closely what 
 they do and how they do it, and continue : 
 
PRACTICAL LESSONS. 
 
 61 X 67 =(6 10+ 1) (6 10 + 7)= 62-102+ 8- 6 10+ 7 
 39 X 33 =(3 10 + 9) (3 10 + 3)= 32- 10^ +12 • 3- 10 +27 
 
 Then many pupils will generalize thus: 
 
 (a -10 + 6) (a -10 + c)= a^ 10» +(6 + c) a • 10 + 6c. 
 
 Those who fail can generally be brought by questioning in 
 detail as to what, how, and why to reach the desired result. 
 Then put x for 10 and get : 
 
 {ax + 6) {ax -{- c)= a^ x^ -\- (b -\- c) ax + be. 
 
 In applying this result proceed as follows : place on the board 
 
 r 
 
 a'x'' + 10aa; + 
 
 l 
 
 and request the class tofin-i third terms, and factor resulting 
 polynomials. Some will do this work without any more 
 teaching. With others, for relation of 10 and the third term, 
 call attention to 6 + c and be in the general expression, and 
 lead them to do as follows : 
 
 10: 
 
 Then after the same manner place on the board : 
 
 f 9 + 1 
 
 9x1= 9^ 
 
 
 8+2 
 
 8 X 2 = 16 
 
 
 7+3 , 
 6 + 4 ^"^ 
 
 7 X 3 = 21 
 
 ^ The third terms 
 
 6 X 4 = 24 
 
 desired. 
 
 5+5 
 
 5l X 5 = 25 
 
 
 l¥ + l 
 
 ¥ xf = ^J 
 
 ■ 
 
 a'x' -i- 
 
 ► ax + 36 
 
 and ask pupils to supply coefficients of second term, and fac- 
 tor the results. A few repetitions serve to familiarize the 
 pupil with the work. 
 
62 
 
 PEDAGOGICS. 
 
 Put on a table two piles of 40 straws each, and let the 
 class write up on their pads, verifying the result by inspection 
 of the straws : 
 
 2, 40 sts. = 80 sts. 
 
 Then opposite each pile place two piles of 19 each, with 2 
 straws to the left of each pair of 19's. Then lead the pupils 
 to write up the result as follows, verifying as before : 
 
 2 (2 sts. + 2, 19 sts.) = 80 sts. 
 
 Then with other straws, for each 19 arrange three piles of 5 
 straws each with a pile of 4 to the left of each group of three 
 5's. As before lead the pupil in verifying and writing up, as 
 
 follows : 
 
 2 [2 sts. + 2 (4 sts. + 3, 5 sts.)] = 80 sts. 
 
 With another 80 straws make an arrangement based on 
 the last result by separating the 5's into piles of 3 and 2, and 
 arrive at the following arrangement of straws : 
 
 I I 
 
 I I I I 
 
 I I I I 
 
 I 
 
 I i 
 
 I I 
 I I 
 
 I I 
 
 I I 
 
 n I I I 
 
 I I I I 
 
 I I 
 I I 
 I I 
 I I 
 I i 
 I I 
 
 Pupils when asked will generally succeed in wri 
 the result, which is as follows : 
 
 ing up 
 
 80 sts. 
 
 2 I 2 sts. + 2 [4 sts. 4- 3 (3 sts. + 2 sts.)] 1 = 
 
 If any fail to do so repetitions will assure success. 
 Continue in repetitions by making arrangements of straws 
 that will give such results as follows : 
 
 3 j 2 sts. + 2 [3 sts. 4- 5 (4 sts. + 1 st.)] l = 174 sts. 
 
PRACTICAL LESSONS. 63 
 
 Reverse the process by giving a parenthetical expression, 
 thus : 
 
 2^3sts. + 2 I 4 sts. + 2 [5 sts. + 3 (2 sts. + 3 sts.)] j ) = 182 sts. 
 
 And require the pupils to arrange the straws to correspond. 
 
 GEOMETRY. 
 
 The intention in these remarks on teaching geometry is 
 only to introduce the subject and indicate the manner of ap- 
 plication of the postulates. 
 
 Prepare a number of similar rectangles cut out of paste- 
 board. Give each pupil three or four of these rectangles, and 
 one not similar to them. The three or four similar rectangles 
 constitute a "whole." The pupil is expected (1) to discover 
 in what respects they resemble each other ; (2) to discover 
 the principle, a content of these resemblances, that " Rect- 
 angles whose sides are equimultiples, when placed on each 
 other properly, will have their free corners in the same 
 straight line." It would be well to have a five-sided figure 
 in full view of the class. Pupils will generally write, in ef- 
 fect, as follows: *' These four pieces of pasteboard resemble 
 in having four sides, four square corners, and in being longer 
 than they are wide. They differ in the lengths of their sides." 
 A few questions in the what will develop in their minds that 
 they resemble in having opposite sides the same length, and 
 equally distant apart at the ends. Ask the pupils to place 
 the rectangles cornering together on each other, and the fact 
 that the free corner of the dissimilar one is out by itself will 
 call their attention to the fact that the three similar rectangles 
 have tJieir free corners in the same line, which they will verify 
 with their rulers, and announce that the three rectangles re- 
 semi)le in '' pointing in the same direction." 
 
 Take the odd rectangle from them and ask them to reduce 
 the three, by scales given, to the same size on their pads, when 
 they will discover the idea that their sides are equimultiples. 
 
64 PEDAGOGICS. 
 
 Then ask the pupils to make a number of rectangles 
 on their pads with sides equimultiples. Some will do this 
 by drawing the diagonal of the large rectangle and make the 
 others corner on it. Others will take two numbers, find the 
 equimultiples, and construct the rectangles. 
 
 Now ask them to discover how many times a smaller rect- 
 angle is contained in a larger, and they will generally do the 
 work with ease. Then, by comparing results in numbers with 
 the corresponding common multiplier, they discover that the 
 former is the square of the latter. Ask them to explain why 
 this is so, and they will answer, that the multiplier tells how 
 many of the smaller rectangles can be constructed in the 
 larger each way, the product of which numbers gives the 
 whole number of the smaller contained in the larger, because 
 the number in a row multiplied by the number of rows will 
 give the whole number. Now call their attention to the fact 
 that the square of any number is contained in the square of 
 any multiple of that number, a number of times represented 
 by the square of the multiplier; or, referring to figures pre- 
 pared on the board, show the same thing between the base of 
 the smaller rectangle and its multiple, the base of the larger 
 rectangle, and they arrive at the principle that "The ratio 
 of similar rectangles is the ratio of the squares on correspond- 
 ing sides." 
 
 Ask them for the number of square inches in a rectangle, 
 and few pupils fail to answer: "Multiply the number of 
 inches in length by the number of inches in width." Then 
 they can readily be led to disvover the principle that "The 
 ratio of similar rectangles is the ratio of the squares," from the 
 fact that areas are products of bases and altitudes, the com- 
 mon multiplier entering as a factor in both length and width. 
 
 Give each pupil a rectangle and a parallelogram of equal 
 bases and altitudes (a "whole"), and ask for resemblances 
 and differences, and the average pupil will readily discover 
 the equality of areas among other resemblances. A few 
 questions will enable all to discover that fact. 
 
PRACTICAL LESSONS. 65 
 
 Give each pupil three similar parallelograms cut out of 
 pasteboard, and they will readily discover the resemblances 
 and differences as they did with the rectangles, etc. 
 
 Give the pupils similar right triangles cut out of paste- 
 board, and by use of rectangles they readily discover relations 
 and areas, etc. 
 
 Give the pupils similar obtuse angled triangles, and they 
 readily discover the fiicts as above. 
 
 The serious difficulties of the pupils begin with the at- 
 tempt to discover the three bases and their altitudes of one 
 obtuse angled triangle.-^ By standing the triangle on any 
 base they find the corresponding altitude, but are confused 
 by the figure. A little patience with three separate triangles 
 will enable them to apply the principle so as to find the area 
 of one obtuse angled triangle in the three modes. 
 
 THE ANGLE. 
 
 It is hardly necessary to premise that a pupil must know 
 what "direction" is in order to understand the "difference 
 of two directions," which is an angle. 
 
 Ask all the pupils to point at some object in the room, and 
 then to write up what they were doing. Then ask every 
 pupil to point in the direction that object is from where he 
 sits, and let them *' write up" that act also. Then, pointing 
 in some direction, ask all to point in the same direction that 
 you are pointing, and write up that also. 
 
 Mark two points on the board, and ask one pupil to make 
 an arrow pointing from one to the other point, and another 
 pupil at the same time to make an arrow from the second 
 point to the first, and ask all to write up. 
 
 Secure a number of long pointers ; call up a number of 
 boys and let them point now at this object and now at that, 
 and then in any indicated direction. Place two boys wide 
 
 *Soine pupils overcome this diflftculty by constructing the three parallelo- 
 grams, of which the triangle is half, and finding the three bases and altitudes 
 through the three parallelograms. 
 
 5 
 
66 PEDAGOGICS. 
 
 apart with pointers; ask them to point in the same direction. 
 Call -up a third and fourth to point in the same direction. 
 Ask : ''Are these all the same direction, or are they only 
 pointing in the same direction ? " 
 
 Make a number of points on the board, and let one pupil 
 elect a direction for his arrow ; then let pupil after pupil 
 make arrows from other points in the same direction ; then 
 ask a number of pupils in different parts of the room to give 
 the same direction with pointers. Ask, again, if these rep- 
 resent the same direction or are only pointing in the same 
 direction. 
 
 Starting with a clean board, make an arrow diagonally up 
 on the board, and ask each pupil to do the same on his pad. 
 Name the arrow A, with letter at the point. Then draw an- 
 other arrow as distant as practicable in the same direction ; 
 ask pupils to do likewise, and ask pupils to name this direc- 
 tion. Certainly all who put A at its point understand the 
 matter. Then put A at its point on the board. Some inches 
 away from the first arrow draw a second, making an angle 
 with A, and when pupils have done likewise, ask for a name. 
 Put B at its point and draw another arrow in the same direc- 
 tion some feet away, and name as before. So continue until 
 you have on the board and the pupils have on their pads a 
 number of arrows in each of a number of directions. Ask 
 pupils which direction, B or C, differs more from A. After 
 a little exercise in this matter, ask pupils how to make it evi- 
 dent that C differs more from A in direction than B does. 
 Some pupil will suggest taking a point and drawing three ar- 
 rows in directions of A, B, and C. Continue this exercise 
 until pupils are familiar with the idea of difference of two 
 directions and begin to call it "angle." 
 
 Ask all your pupils to point at you, and then ask them to 
 think that you are pointing at every one of them, and write 
 up facts as to resemblances and differences of directions. 
 Some will use the word " opposite." Some will say : " You are 
 pointing just the other way from that in which I am point- 
 
PRACTICAL LESSONS. 67 
 
 ing." Use the words " opposite directions," and apply them 
 to the case in hand. 
 
 Place four boys, A, B, C, and D, in different parts of the 
 room ; ask A and B to point at each other, and ask C to 
 point in a direction opposite to the direction in which A is 
 pointing, and D to point in direction opposite to the one in 
 which B is pointing. Then ask some pupil to use a pointer 
 and point in a direction midway between these opposite 
 directions. He will probably try to get midway between the 
 four boys, but if you have the four boys properly located he 
 will find that impossible. Then write on the board the two 
 propositions, viz: "Place your person midway between the 
 pupils," and " point in a direction midway between the oppo- 
 site directions." Ask for resemblances and differences. When 
 satisfactory answers are received, ask the pupils at their seats, 
 without leaving their seats, to point in a direction midway 
 between the opposite directions. A number will do this 
 for you without delay, and if you give out six pointers, you 
 will have six different directions which are midway between 
 the given opposite directions. Then take four points on the 
 blackboard at considerable distances from each other, name 
 them A, B, C, and D. Ask some pupil to put an arrow with its 
 point at A ; a second pupil to put an arrow with its point at 
 B, pointing in opposite directions from that at A; a third 
 pupil to place an arrow with its point at C, pointing in oppo- 
 site direction from the arrow at A; and likewise place an 
 arrow at D in the opposite direction from that at B. Let 
 pupils write up ivhat and how, and then give out pointers to 
 different pupils to give direction midway between these oppo- 
 sites, and then let a number of pupils draw arrows at differ- 
 ent points, E, F, G, etc., pointing in directions midway be- 
 tween the opposites that are on the board. Then the pupils 
 are prepared for the name, 7ight angle. 
 
 With this unit, they should be required to actually meas- 
 ure a number of acute and obtuse angles. This measurement 
 of angles with a. right angle for a unit is readily taught by 
 the methods of this Monograph. 
 
68 PEDAGOGICS. 
 
 Ask the pupils to draw a triangle like one on the board, 
 which the teacher makes obtuse angled. Ask the pupils to 
 separate it into its parts. The average pupil will readily find 
 the six parts. Ask him to construct another triangle with 
 any three of the six parts. He will probably not select the 
 three angles ; if he does, resemblances and differences will 
 disclose the facts in the case, as it does whatever three parts 
 he may select. Then let him select three other parts, and 
 construct another triangle, and so continue ; the teacher 
 always asking for resemblance and difference between the 
 resulting triangle and the one he started with, until he is per- 
 fectly familiar with the evident principle in the case. Of 
 course, when he happens to select two sides and an angle 
 opposite one of the sides, he may have a result, well known 
 to the reader, which must be treated as correct principles in 
 teaching demand. 
 
 With older pupils it requires some four weeks, an hour 
 each day, to do this work well ; with younger pupils, some 
 ten weeks. Older pupils at this stage ought to have now and 
 then a proposition to study, as found in the average geometry 
 of the day. The teacher ought to write on the board such a 
 demonstration for the younger pupils to copy on their pads 
 and study under the teacher's directions, with the what, how, 
 and why while writing the propositions. 
 
 It seems sure that all of geometry can be taught after the 
 same plan, but it has been found that pupils use books in a 
 satisfactory manner after this period. 
 
 Note.— The observant teacher will perceive that all the principles of arith- 
 metic (pages 24 and 25) apply to geometry. 
 
 Principles (13) and (14) in geometry take the following 
 
 forms, viz : 
 
 AocB).-.A--A' = B--B'.-. 
 A'oc B' f A : A' = B : B'. 
 
 and 
 
 Boc:^I..B^B' = C'--C. 
 
 B'oc ^1 B : B' = C : C. 
 
PRACTICAL LESSONS. 
 
 69 
 
 Also an additional 2>riiiciple appears in this connection, 
 which may be generically stated thus : 
 
 r B 1 
 
 C 
 
 Aoc^ J, } 
 
 etc. 
 
 __L 
 D 
 
 E 
 
 ^etc. > 
 
 * B Cetc. ^ 
 
 A = -— — X (some constant^). 
 
 D E etc. 
 
 'This constant must be used in the generic expression. 
 
 1 
 
EDUCATION OF CHARACTER, 
 
 What a man does once under given circumstances does not 
 proclaim his character ; but if he does any one thing repeat- 
 edly under like circumstances, that one act may be regarded 
 as a phenomenon of his character. If a boy habitually comes 
 into the school-room when the bell rings, we credit him with 
 promptness as one element of his character. And so, every 
 habit of the individual is a mark of his character. 
 
 If a man gives habitually, as calls are matle upon him, he 
 must be credited with liberality. His failing to give at any 
 one time does not invalidate the previous estimate. More- 
 over, a man does not sit in judgment upon his own acts ; the 
 standard of right action is fixed by public opinion ; it changes 
 from age to age. Just now, for us, it has its foundation in 
 the precepts of Christ, and he who does his duty faithfully 
 must conform his teaching to that standard. Now, do not 
 these facts lead inevitably to the conclusion that he who suc- 
 ceeds in molding character aright must fix habits of action 
 that to the world indicate excellence in character? 
 
 A man's whole life is spent in accomplishing ends through 
 means. If all the ends he seeks are good, and all the means 
 employed by him are right, then his character is perfect. 
 
 Now, certain ends, as food, clothing, etc., demand a large 
 share of every one's energies and time for their accomplish- 
 ment. Satisfying them becomes in fact the business of his 
 life. For gaining these constant ends, by comparing the 
 means that he has from time to time employed, he assimilates 
 certain principles. These laws as constant means control to 
 a great extent his habits and develop his character. 
 
 The ends one shall seek are suggested by his feelings ; these 
 command his Will and it obeys ; he seeks the suggested ends; 
 
EDUCATION OF CHARACTEK. "Tl 
 
 his experunces commence. Certain ends acconipii.^hed''0»* 
 means employed bring him into conflict with his^environment, 
 and he experiences pain where he anticipated pleasure. Now 
 his Intellect begins its benign work ; he makes a rule for him- 
 self in each case of experienced pain ; his Intellect gives a 
 lesson to his emotional nature. 
 
 But Emotion again prompts him, and again his Will obeys. 
 Again his environment inflicts pain, and as his promptings must 
 have been stronger than at first to overcome his determina- 
 tion, so his pen-istence is greater. His Intellect, this time 
 starting from principle, can make its lesson more forcible. 
 
 As often as this conflict may be waged, just so often is the 
 end the same. The determination dictated by the intellect 
 will become getieric, and a habit be born. 
 
 Passion, in some cases, may temporarily or permanently 
 control the Will, but the individual ever remembers the les- 
 sons of his Intellect, and despises himself when disobeying its 
 mandates. 
 
 Those habits which are acquired through a triumph of 
 the intellect over the emotional nature are good, because they 
 are founded on truth, the assimilation of which is the work 
 proper of the intellect. Bad habits are acquired by obeying 
 the emotional nature. Such are observed to prevail with 
 peoples and individuals whose intellects are naturally weak, 
 or who have been so unfortun ite as to have had meager intel- 
 lectual training. 
 
 The problem to be solved by the teacher or the parent 
 who undertakes to educate the character of a young person 
 is : To prepare him to so act as to be in harmony with an ever- 
 varying environment. 
 
 The pupil's character will be educated aright if he acquires 
 good habits and drops such bad habits as he may have fallen 
 into. Good habits are at war with bad habits, and, if the 
 teacher will but re-enforce the good in the struggle, their vic- 
 tory will be more certain. 
 
 Fault-finding, lecturing, and scolding are among the worst 
 
< J PEDAGOGICS. 
 
 ti.eans a teacher can employ to cure bad habits, for the very 
 apparent reason that the pupil does not realize that the fault- 
 finding is directed, not at his person but at his habit ; he infers 
 that his teacher does not love hirn, and this impression puts 
 the teacher outside of the pupil's environment for good, and 
 makes his influence a nullity or an actual evil. 
 
 Good habits must be cultivated systematically, and herein 
 lies the solution of the problem. What are the elements of 
 that solution, what are the laws that should govern the 
 teacher? The objective point for the teacher is to lead the 
 pupil to form generic determinations.* As has already been 
 indicated, the making of these generic determinations are the 
 turning-points in life. Victor Hugo said : "A tuft of sod 
 against which a soldier rests his heel in the conflict may de- 
 cide the fate of a nation." 
 
 So, a little thing may often mar or make a character. A 
 '' word in season " by his teacher may turn a boy from the 
 downward path, or by a single mistake in judgment that teach- 
 er may start him on the road to ruin. Every person of mature 
 years can recall many such turning-points in his life. They 
 abide in memory with peculiar force, because each of them 
 marks a triumph of temptation, or a victory for truth, the 
 very sap upon which the intellect feeds. 
 
 Now, can these determinations and their resulting good 
 habits be made to come to pass with any certainty, or must 
 we regard them as providential entirely? 
 
 As a teacher's wisdom may decide in answering this ques- 
 tion, so will his practice be shaped. If he believes that Provi- 
 dence alone determines, he will leave the issue in His hands ; 
 if the teacher believes that he is one instrument of Providence 
 for the well-being of his pupil, he will feel called on to work 
 as well as pray. 
 
 '^ By a generic determination is meant a resolntion fo act at all times and in 
 all places according to the dictates of the law conceived to be proper. There is 
 a difference between determining to quit wine and determining to quit all in- 
 toxicating liquors; between resolving to be prompt to-morrow and to be 
 prompt ev'3ry day: the one is particular, the other generic. 
 
EDUCATION OF CHARACTER. 73 
 
 There are certain conditions in this problem df •(^duxjalkig 
 character which are constant. Success can in no case be cer- 
 tain unless these are satisfied, viz: 
 
 1. Every pupil has an environment which 
 differs more or less from that of every other 
 pupil. 
 
 2. The pupil's intellect is a part of his own 
 environment. 
 
 3. The teacher must know the environment of 
 each pupil. 
 
 4. The teacher must know himself as he is. * 
 
 The teacher must know the particular environment of 
 eacli pupil in order to put into it good influences that are lack- 
 ing, and to take out bad influences that are present. 
 
 What will produce good results with one will often pro- 
 duce the contrary results with another; what is needed to 
 influence one is already in another's environment, or if put 
 there would do no good. A boy who loves music can be 
 benefited by it ; one who loves it not fails to be influenced 
 by it. The '* I do not like that" of a person that he respects 
 causes a child to pause ; where respect is wanting he does not 
 often heed it. A teacher once had occasion to lecture a lad 
 about something he had done. " I wish you would ask your 
 Uncle Will what he thinks about such an offense," he ven- 
 tured as a feeler. The boy responded, with a blush, "I will, 
 but don't you tell him first. Let me tell him." That teacher 
 had found a new element to put in that boy's environment; 
 his desire to retain his Uncle Will's love became a disciplinary 
 force with the boy from that day. 
 
 Tom Brown needed the gentle influence of the pastor's 
 son upon his rugged nature; he needed care as a burden in 
 his life to discipline him ; the little timid boy needed a manly 
 
 * This condition can be understood by reading carefully Christ's qualifica- 
 tions as a teacher as outlined in Hebrews ii. 17-18; iv, 15, and those of Paul in 
 1st Corinthians, ix, 19 to 22. 
 
74 PEDAGOGICS. 
 
 protector; the wise Arnold brought them together. It was 
 a simple thing to do, but it produced a great change in the 
 life of each. This story of Tom Brown at Rugby, however 
 much a fiction, tells some wonderful facts in character educa- 
 tion. 
 
 That every pupil's intellect is a part of his environment 
 for good is apparent from what has been said above in refer- 
 ence to good habits and the conflict antecedent to their form- 
 ation. 
 
 That every pupil has a different environment or total of 
 influences is sure. One has a father, another has not; one 
 has an Uncle Will, another has an Uncle Ben; one reads 
 good books, another nothing ; one is a prey to certain vices, 
 another is free from them ; one comes from a home where 
 religion has sway, another knows nothing of it. 
 
 No two individuals are alike, because no two have the same 
 environment. 
 
 Stupendous is the task upon the teacher of undertaking to 
 train the characters of forty children, each having a different 
 environment; great is his responsibility, but he should not 
 shrink from the one or be appalled at the other. Much can 
 be done by him in improving the environments of the several 
 children in his charge ; much can be done by him in educating 
 their characters if he will but systematize his work. 
 
 The same postulates apply in educating the character, as 
 are given in a former section to govern the teacher in train- 
 ing the intellect.* 
 
 In arranging his " wholes" for lessons in character a little 
 reflection will show the teacher that they must be compre- 
 hensive enough to cover all grades of character-development 
 in the class. That this is possible with any class will be appar- 
 ent when one reflects that there is rarely very great dissimi- 
 
 * Postulate II will not be satisfied in a character-lesson unless the pupil's 
 intellect, dominating his will, is one factor of his environment. He theu be- 
 comes in truth "self-active;" i. e., he completes the "whole" through which 
 he makes a generic determination. 
 
EDUCATION OF CHARACTER. 75 
 
 larity in their individual environments. These "wholes" must 
 always be made up in part of material in the actual environ- 
 ment of the pupil, and the matter of them must be so pre- 
 sented as to cause each one to make a personal application of 
 the matter presented to his own conduct; this is best done by 
 a hypothetical talk, as will be illustrated later. 
 
 From what has been said above, the following principles 
 for the guidance of the teacher may be inferred : 
 
 I. *' Wholes " are identical only so far as their 
 
 parts are the same. 
 
 II. A " whole " is made up of parts related. 
 
 III. Varying the parts varies the "whole."* 
 
 * 
 
 But a grave responsibility rests upon the teacher who con- 
 structs "wholes" to influence tlie life of a child. Wisdom 
 has been defined to be, "The use of the best means for the 
 attainment of the best ends." Whewell says, " We conceive 
 prudence to be the virtue by which we select right means for 
 given ends, while wisdom implies the selection of right ends 
 as well as right means." 
 
 This being true, to guide his pupil to the highest ultimate 
 ends the teacher must make his "wholes" serve as right 
 means. A fourth principle then may be stated, as follows : 
 
 IV. The best interests of an individual are se- 
 cured in the attainment of the best "wholes" 
 possible. 
 
 An evident corollary of this principle is : 
 
 * One will not appreciate at a casual reading that these principles lie at the 
 very foundation in character training. The lapse of time, ihe influence of the 
 weather, the incidental influence of what has happened the same day, a thou- 
 sand little influences that are potent in every " whole " presented by a teacher 
 make it necessary to regard the truths asserted above at all times and in every 
 lesson. One may attempt to do to-morrow or next year what he has success- 
 fully done to-day; but if he copies himself he will fail. The day, the hour, 
 the pupils, and he himself are all changed elements in the " whole." 
 
76 PEDAGOGICS. 
 
 V. The best interests of his associates are the 
 
 ]best interests of an individual. 
 
 The mind of man has three distinguishable yet not separ- 
 able elements, viz., latellect, Emotion (sensibility), and Will. 
 These three in their functions are similar to the three Depart- 
 ments of our Government. Will is Executive, Emotion is Leg- 
 islative, and Intellect Judicial. 
 
 The mind, through Emotion, by means of conscious resem- 
 blances and differences, discovers the concrete relations of sense- 
 objects, and determines the Will. 
 
 The mind, through Intellect, by means of conscious re- 
 semblances and differences, discovers the abstract relations of 
 sense-objects. It either approves or declares null and void 
 the work of Emotion. 
 
 The Will, if it be a strong Executive, obeys the mandates 
 of the Intellect ; if it be weak or corrupt, it may fail in its duty. 
 
 This analysis of the functions of mind suggests two prin- 
 ciples which are to the teacher alternatives : 
 
 VI. The teacher must provide a "whole" (envi- 
 ronment subject to change) for his pupil, 
 such that the concrete and abstract relations 
 of the objects composing it 'will both act har- 
 moniously in directing the will of the pupil. 
 
 Or, this being impracticable : 
 
 VII.* The teacher must try by hypothetical dis- 
 course to secure in the mind of the pupil a 
 corresponding generic determination. 
 
 It must be evident to the reader that no one is able, in any 
 
 * It will hardly be possible, in any case, to so arrange a school as to keep 
 evil influences out of a child's environment entirely, yet what can be done in 
 this direction ought not to be neglected. Just so far as is practicable Principle 
 VI should guide the teacher, but generally it will be found that Principle VII 
 has also to be applied. 
 
EDUCATION OF CHARACTER. 77 
 
 case calling for action in the now, to make a law for himself 
 except from his past experiences. 
 
 The education of character consists largely in giving occa- 
 sion for the most varied possible experiences on the part 
 of the pupil. Hence the teacher must give to his pupil the 
 most varied environments possible, or, as Postulate I requires, 
 bring the pupil into as many and varied " wholes " as possi- 
 ble, and by repetition of such "wholes" secure assimilation 
 of desired principles and consequent good habits. 
 
 These considerations are of sufficient importance to sug- 
 gest another principle : 
 
 VIII. The teacher must familiarize himself with 
 the actual of his pupils, so that, as occasion 
 offers, he may extend and vary their experi- 
 ences. 
 
 Now, as every good habit results from a triumph of the 
 intellect over the emotional nature, and as every intellect will 
 decide all cases according to what it thinks best for itself, and 
 as the real best interests of an individual are generally found 
 in sacrificing some of present pleasures, it becomes a difficult 
 matter for the teacher to secure the formation of habits that 
 are verily good. He must, therefore, take as his guide the 
 truth expressed below, and by repetitions of " wholes," based 
 upon their experiences, cause his pupils to assimilate and 
 apply it by practicing self-sacrifice : 
 
 IX. The future best interests of an individual 
 require, in general, a present sacrifice of 
 
 some pleasure. 
 
 * 
 * * 
 
 The teacher is one of the most important elements in the 
 changing environments of his pupil. While all minds are alike 
 in kind, probably no two are the same in degree. These dif- 
 ferences in degree in minds tend to produce differences in kind 
 
78 PEDAGOGICS. 
 
 in character. For these reasons another principle of the 
 gravest importance presents itself: 
 
 X. The teacher must treat every pupil in ac- 
 cord with that pupil's character. 
 
 Rules should be as few as possible, and should be of that 
 kind alone which are essential to secure unity and harmony 
 in the conduct of the school. Also pupils should be taught 
 practically to understand that no law applies to them as indi- 
 viduals until they have violated its requirements. 
 
 The tenth principle, indeed, calls for the very highest 
 order of tact on the part of the teacher. If a pupil hears 
 the bell which rings him to the class-room as a tyrannical 
 command which is to be obeyed reluctantly, then that pupil 
 is not entering into his " whole " freely ; his is not a self-act; 
 while he may enter the, class-room and learn ever so much 
 intellectually, he has not completed his "whole," and his 
 character is not being educated; the teacher is failing with 
 that pupil, and must continue to fail until in some way he can 
 bring the pupil into a " better mind." ^ 
 
 If, however, the pupil hears that bell as a clock ringing 
 out the time of day when duty calls him to work, and goes 
 gladly to his class, then he has entered into his " whole;" his 
 character is being educated ; the teacher is succeeding with 
 him. 
 
 However much importance may be properly attached 
 to the education of the mind, yet none the less importance 
 must be attached to the healthful education of the body. It 
 does not seem that a sound mind can coexist with an unsound 
 body. A differentiation of functions for individuals or for 
 classes in society which extends to the destruction of a health- 
 ful equilibrium of the physical structure or mental structure 
 of the individual can not be conceived to be the best in- 
 terests of society. Hence the principle : 
 
EDUCATION OF CHARACTER. 79 
 
 XI. The teacher must ever attend to the health- 
 ful development of the body of the pupil. 
 
 * 
 
 An education which fails to give the body of the individ- 
 ual as an instrument into the possession of the mind is sadly 
 out of joint with a healthful natural economy. A truly edu- 
 cated mind is ever using its body as an instrument in a strug- 
 gle with the environment of the now. The present is the 
 womb of the future. The dreamer of a future which is not 
 founded on the present is the slave of his body. For such 
 a being the final wreck of hope is certain. To destroy is not 
 to establish. It is the pupil's mind, not the teacher's, which 
 must control freely the bo<^ly of the pupil. The tom-cat-like 
 teacher of mice-like pupils can never educate the young cor- 
 rectly. Happy the pupil wiiose teacher can steer him clear 
 of both the Scylla of license and the Charybdis of slavery in 
 his education. Hence: 
 
 XII. The true teacher must ever have regard for 
 the establishment of such an environment as 
 .will demand every day the exercise of the 
 body as an instrument of the mind.* 
 
 * * * 
 
 It will be observed, on reflection, that in all correct teach- 
 ing, in mathematics, language, and the like, the pupil is him- 
 self ever entering as a part of every "whole," and that 
 hence in all proper education the character of the pupil is 
 being educated. In an important sense assimilation means 
 appropriation of the objective whole in a subjective state. 
 The pupil who is so taught as to form the habit of obedience 
 to assimilated principles in sciences is thus forming the habit 
 of obedience to every principle of every kind. 
 
 Therefore: 
 
 *The truth announced in this principle is Nature's demand for the intro- 
 duction of manual training into schools. 
 
80 PEDAGOGICS. 
 
 XIII. The end of all true teaching is the educa- 
 tion of character. 
 
 DIFFERENTIATION IN CHARACTER. 
 
 Between boys and girls there are differences in character 
 which become more marked when they become men and 
 women. These are brought about by the promptings of 
 desires seeking ends, thus giving birth to habit*, good or bad. 
 
 As the ends apt to become constant, which are sought by 
 the two sexes, are necessarily different, a difference in char- 
 acter is to be expected. But the difference is not so great as 
 to make it inexpedient to educate the sexes together, as was 
 once the rule. 
 
 However desirable it may be (and it would be better) to 
 have separate schools for boys and girls, it has been fbuiid 
 impracticable, and will probably remain so for some time, to 
 have other than mixed schools for primary and secondary 
 grades. 
 
 The general problem, then, of educating character must 
 be complicated necessarily by the primal differentiation, male 
 and female. What is said further, therefore, should be under- 
 stood as drawn from resemblances and differences in conduct 
 without reference to sex. 
 
 Character manifests itself in habits; and, as persons are 
 observed to have many or few habits, so they need to be clas- 
 sified as to character according to these resemblances. 
 
 Active and passive are suggestive terms by which to character- 
 ize these two types of character, and will be used in this discus- 
 sion to refer respectively to persons of many and of few habits. 
 
 Of persons who have developed or are developing active 
 characters, some incline to contract good habits, while others 
 heedlessly drift into bad habits. 
 
 Positive and negative are terms that will be used in this discus- 
 sion to name characters as they may be differentiated by this ob- 
 servation. 
 
EDUCATION OF CHARACTER. 
 
 81 
 
 Of persons who have few habits — passive in character — 
 some are observed to tend toward the positive, others toward 
 the negative, \yhile a few can not be said to exhibit any ten- 
 dency whatever. 
 
 These three classes of characters will be spoken of as passive- 
 positive, passive-negative, and typical-passive. 
 
 For the convenience of the reader the full classification is 
 here shown : 
 
 f Positive, 
 I (good habits). 
 
 I Negative, 
 1^ (bad habits). 
 
 Character. 
 
 (^ Passive. 
 
 Passive-positive, 
 (tends to good habits). 
 
 Passive-negative, 
 (tends to bad habits). 
 
 Typical -passive, 
 (no tendency observed). 
 
 Somewhere in one of the classes named every boy or girl 
 entering school finds his or her place. Each type of charac- 
 ter demands an appropriate general manner of treatment. 
 "To treat all alike" is a principle that defeats the end of 
 educating character, whatever it may accomplish in securing 
 good order and no complaints. 
 
 It follows, then, that a teacher, to succeed, must know his 
 children, i. e., knoiv their habits, and apply the proper treat- 
 ment to have habits continued if good, to change them if bad, 
 and to induce habits if they are lacking. 
 
 If the child is positive in character, it is because he has had 
 kind and wise treatment. Such g0v>d habits as he has ac- 
 quired were l)Drn of his trying to make others happy, and 
 have thus far been fostered by having his efforts appreciated, 
 
 6 
 
82 PEDAGOGICS. 
 
 As a rule, such children must be treated in school exactly as 
 they have been treated at home. 
 
 This class of children bring apples to the teacher, or offer 
 parts of their lunch to him, or volunteer to help him ; if their 
 little courtesies are not appreciated and recognized, they will 
 graduUy discontinue them, and be injured in character by the 
 heedless behavior of the teacher. 
 
 If a child is negative in character, he has been treated 
 unwisely at home. Too much has been done for him by his 
 parents or elders ; not cares enough have been put upon him ; 
 his selfish desires have been too much gratified ; he has heard 
 too much of the evil and too little of the good that he and 
 others do ; he has been lectured too much ; or his efforts to 
 do right (every child makes them) have not been observed 
 and commended. This class of children are at " outs" with 
 every thing that offers to restrain them in their desires ; they 
 enter school with feelings toward the teacher similar to those 
 of a criminal toward his jailer. 
 
 The proper line of treatment for one of this class is to 
 find out, first, how he expects you to do when he tries you, and 
 then disappoint him by doing some other way. He m.ust be 
 made to experience pain for his misdeeds. Now, it he expects 
 a whipping, he will take it and exult in his victory, because 
 he has steeled himself to bear it ; but if some other punish- 
 ment is given it breaks him up. 
 
 Punishments ought to be in the nature of effects from 
 causes. This makes them a part of the environment of a 
 child, and hence they contribute to his education in right 
 doing. But setting traps and watching them for victims is not 
 the province of the teacher who wishes to educate character. 
 
 Negative characters need to be kept busy; cares must be 
 put upon them ; they must be brought into environments that 
 will cause them in a natural way to desire to do right. They 
 expect the teacher to watch them ; hence he must not watch 
 them. They have not been trusted by others ; he must trust 
 them. 
 
EDUCATION OF CHARACTER. 88 
 
 Children who are passive in character are usually made so 
 by actual cruelty ; by repression of their activities, which 
 amounts to cruelty ; by being overtasked physically ; by being 
 allowed to indulge their appetites to excess, or by being 
 allowed to contract unhealthy habits. 
 
 Such children are listless at play and inattentive at les- 
 sons ; are slow and awkward in movement, and imitators of 
 others in every thing ; they are easily persuaded and easily 
 influenced; negatives make cat's-paws of them. 
 
 The proper treatment of them consists (1) in making 
 them active, and (2) in pursuing the line of treatment appro- 
 priate to the tendencies they may manifest. 
 
 "Making them active" can be accomplished, generally, 
 through some study or play that will interest them. Try the 
 whole range of things done at school till the pupil's natural 
 bent is found. Give him free run in this pursuit until he has 
 acquired independent action. By degrees he can be led to 
 take interest, and become active in other studies or plays. 
 
 Drawing, modeling, and making things, if introduced into 
 the regular curriculum, would save m:iny a passive child that 
 schools, as now organized, fail to interest and educate. 
 
 The foregoing analysis and remarks have been intended to 
 assist the teacher as far as possible in systematizing his inter- 
 course with those under his charge. If he will observe the 
 habits of his pupils he can, in a few days, or weeks at most, 
 classify them as: Positive, negative, passive-positive, passive- 
 negative, and typical-passive. 
 
 This classification made, when a pupil tells you something, 
 or asks a favor, or is observed to do a willful act, it assists in 
 determining promptly what to do for his good. 
 
 A little boy, for illustration, tells you that Johnny has 
 taken his ball. If both are negatives, you know at once that 
 it was an act of reprisal. If Johnny is a positive, you know 
 he has a claim on the ball that he thinks is good. If the 
 boy who complains is a positive and Johnny is a negative, you 
 know it is either a robbery or a case of plaguing. If Johnny 
 
84 ( PEDAGOGICS. 
 
 is a passive, you should investigate the case fully in order to 
 reclassify him. If the complainant is a, passive, you know he 
 needs protection. 
 
 No child is positive in every habit, neither is any one nega- 
 tive entirely. Care must be taken, therefore, to discriminate 
 in every case that arises as to whether the parties concerned 
 are positive or negative as to the habit involved in the case. 
 
 These suggestions have been made to guide the teacher in 
 his every-day intercourse with his pupils. Much may be 
 done in this way by a wise teacher, watchful of their w^elfare, 
 to educate the characters of his pupils, but no one ought to be 
 satisfied with this alone. Evil should be attacked and dis- 
 lodged by regular approaches. 
 
 Children can be influenced by nature and law in the same 
 way as their elders are. They are more susceptible, in fact, 
 to good influences, because they have not become hardened in 
 wrong-doing; because their passions have not become impe- 
 rious by long indulgence, and because their intercourse with 
 the world has not yet made them lose faith in promises not 
 backed up by bonds, and does not yet incline them to regard 
 every one who approaches them " bearing gifts" as a perfidious 
 "Greek." The trustfulness and faith of children is great! 
 Verily, he who is given charge of them has " talents of gold 
 entrusted to his care," and it behooves him not to bury them 
 in the earth as did the foolish servant, but to so use them as 
 to return them, increased in value, to those who lent them. 
 
 When new words are met in the daily lessons whose mean- 
 ings relate to ethical conduct, especial pains should be taken, 
 as has been illustrated on page 53, that the learning of the 
 new word be accompanied with the formation of a determina- 
 tion to act in accordance with the meaning assimilated. 
 
 HYPOTHETICAL DISCOUESE. 
 
 Moreover, at stated times, regular lessons should be given 
 in the form of "talks" or conversations with the children 
 about right behavior. At each of these lessons the teacher 
 
EDUCATION OF CHARACTER. 85 
 
 should make it the objective point to cause the children to 
 assimilate some moral principle of wide application. 
 
 To insure assimilation of the principle and the consequent 
 application of it by the children (see Postulate VIII, page 
 20,) in their conduct, it is absolutely necessary that there 
 should have been violations of it in deed or thought in their own 
 experiences, and that these violations should be brought to 
 their memory by the "talk." 
 
 The bringing together of these facts of their experience, 
 along with other facts brought into the discourse by the 
 teacher, constitutes constructing a "whole" from which, 
 through comparison, the principle desired may be assimilated. 
 
 This discourse, in its subject-matter, is apt to be largely 
 hypothetical. It is never advisable to allude to the facts of 
 their experiences, except as a supposition, or as things the 
 teacher once knew to happen. 
 
 Any one may become expert in constructing a proper 
 address to inculcate a lesson in conduct if he will but take the 
 pains to collect the facts necessary, and remember that the 
 law. No one can learn a truth by reading it or hearing it unless he 
 knows it already in its elements, is never broken in the sphere 
 of moral any more than in that of intellectual training. 
 
 A practical illustration is given below of a lesson from 
 actual practice. The circumstances from which the data were 
 derived, which served as the "elements known already" by 
 the pupils, were as follows : 
 
 One Saturday in November the boys of a school organized 
 a rabbit hunt. About twenty were engaged, and four rabbits 
 were caught. Those who had caught the rabbits evidenced 
 by their after-conduct an intention not to share the prey 
 equitably. Certain directions were given to the cook by them 
 as to how the rabbits were to be dressed, and to the table-boy 
 as to where to set the dishes the next morning. The teacher 
 had gathered all this in the course of the evening after the 
 hunt. He said nothing to the boys at the time, and only 
 interfered so far as to disturb the table arrangement the next 
 
86 PEDAGOGICS. 
 
 morning. The rabbits were served from the head of the 
 table along with the steak and other common dishes. Some 
 surprise was apparent in the faces of a few, but no protests 
 were made. The rabbit hunt and feast, in a few days, were 
 no longer talked about. 
 
 Soon thereafter, at chapel exercises one morning, the fol- 
 lowing diagram was placed on the board by the teacher : 
 
 C men ~) C 
 
 < y co-operate < 
 
 ( not men \ (^ 
 
 men ) ( associate 
 
 Animals , , ^ , 
 
 herd. 
 
 The habits of wolves and other animals were discussed by 
 the teacher. The fact of their co-operation was brought out. 
 Its general object, viz., to secure prey for eating, was dwelt 
 upon. Their after-conduct, seizing and devouring each for him- 
 self, was exhibited. The fact that no sharing was a principle 
 with wolves and other animals was made prominent. The end 
 of their co-operation was shown to be in the securing of prey. 
 
 The conduct of men in co-operating was then taken up 
 and compared with that of animals. A hunt of wolves had 
 been elaborated, a supposed hunt of men was narrated in 
 detail. Their conduct when prey was secured was contrasted 
 with that of the wolves. Their motives in co-operating were 
 examined, and the fact that their co-operating becomes per- 
 manent was emphasized, as also the fact that sharing is a prin- 
 ciple with men. 
 
 Just enough was said in the discourse to insure the recall of 
 the rabbit episode in the minds of the boys. No one was per- 
 sonally mentioned ; no one was criticised ; no one reproved. 
 
 The discourse accomplished the end intended, i. e., it caused 
 the assimilation of a principle by the boys, as was evidenced 
 in a few days by remarks made in criticism of certain actions 
 questioned about. 
 
 The lesson also incidentally served to classify properly 
 the meanings of "associate" and "herd," as applied to 
 actions of animals, the one being permanent and the other 
 temporary co-operation. 
 
YB 34908 
 
 L'ZfOZC 
 
 ^7 544:^90 
 
 UNIVERSITY OF CALIFORNIA LIBRARY