Charles De Garmo

SECTION I
REMARKS ON THE TEACHINGS OF PARTICULAR BRANCHES OF STUDY

CHAPTER I
Religion

232. The content of religious instruction is for theologians to determine, while philosophy bears witness that no knowledge is able to surpass the trust of religious faith. But both the beginning and the end of religious instruction call for remarks from the point of view of pedagogy.

Religious instruction culminates, if it does not end, in the rite of confirmation, and the subsequent admission to the Holy Communion. The former is characteristic of a particular Christian denomination; the latter, on the contrary, of the whole brotherhood of Christians. Now the profound emotion which marks the first Communion service should imply a conquest over the feeling of separation from other denominations, especially since the mere admission to Communion is conditioned on the general requirement of earnest ethical aspiration. It is thus assumed that members of other confessions, provided they are communicants at all, have fulfilled the same condition. Preparatory instruction must work toward this end all the more, since with many persons Christian love for those who differ from them in important articles of faith belongs to the more difficult duties. Moreover, the fact that this same instruction necessarily had to set forth clearly fundamental denominational differences, lends additional weight to the necessity of inculcating the virtue of Christian charity.

233. In academic schools, if Greek is begun early enough, it is possible to deepen the impressions of Christian teaching by the dialogues of Plato that bear on the death of Socrates, particularly the “Crito” and the “Apology.” Being the weaker, however, impressions of this sort should precede the time when the solemn initiation into Christian fellowship produces its whole powerful effect.

234. Going back in thought, we find that the portion of religious instruction which deals with characteristic denominational distinctions, presupposes that which deals with tenets common to all Christians, and we find that this in turn has been preceded by Bible stories, including those of the Old Testament. But the question arises, “Must we not go back to something more fundamental still?”

235. Religion cannot possibly be adequately presented by treating of it merely as a perpetuation of something historical and past. The teacher must needs make use also of the present testimony furnished by the adjustment of means to end, in nature. But even this, for which some knowledge of nature is prerequisite, and which leads up to the ideas of wisdom and power, is not the first step.

236. True family feeling is elevated easily and directly to the idea of the Father, of the father and mother. Only where such feeling is wanting does it become necessary to make churches and Sunday observance the starting-point as indications of humility and gratitude. An all-pervading love, providence, and watchful care constitute the first concept of the Highest Being,—a concept limited by the mental horizon of the child, and expanding and becoming more elevated only by degrees.

237. The process of elevating religious concepts and purifying them of unworthy admixtures must, however, have taken place, and the true concepts must have been deeply impressed, before the mythological conceptions of antiquity become known; in which case the latter will produce the right effect by the contrast between the manifestly fabulous and crude, and the worthy and sublime. If managed properly, this subject presents no difficulties.

238. But there are other difficulties,—difficulties growing out of individual peculiarities. While some would be harmed by much talk about sin, because they would thus either become acquainted with it, or else be filled with fantastic terror, there are others whom only the strongest language can move, and still others who themselves preach against the sins of the world, and, at the same time, front the world in proud security. Then there are those who brood over ethical problems, and who, without having heard of Spinoza, argue that what the Highest Judge has permitted to happen he has approved of, whence might is the practical proof of right. There are contemners of mere morality, who think that prayers will consecrate their evil actions. Isolated traces of such perversions may indeed be met with even in children, especially if their glib reproduction of the sermon, or worse yet, their praying aloud, has happened to receive praise.

Hence it is necessary to observe the effect of religious instruction on each individual. Another task for home training.

CHAPTER II
History

239. The most common blunder that younger teachers of history are apt to make is that, without intending it, they become increasingly prolix in presentation. It is not that interest deepens, but that the network of events lures them, now one way, now another. This of itself evinces preparation; but mental preparation alone does not suffice; preliminary practice, too, is necessary.

Young teachers of history, like young teachers in other subjects, are prone to error. What the prevailing error in a given study will be, is likely to depend upon conventional methods of presenting it. In Germany it is customary for the teacher himself to be the historian through whose mind all historical knowledge passes on its way to the children. But just as good writers of history are rare, so good teachers of history are likely to be few, since in an important sense they are at once teachers and oral historians. Where the text-book is depended upon for the narrative, as in the United States, a different difficulty presents itself to the teacher. What shall he do with the text, all the pupils having read it? Perhaps the commonest method is to call upon them one by one to reproduce it in class. But this is a deadening process, since it compels nineteen pupils to sit passive while the twentieth recites the words that the nineteen could repeat equally well. If, therefore, the besetting fault of the teacher of history in German is prolixity, that of the American teacher is tediousness. The German method is that of primitive man, where the legends of the tribe are handed down from father to son by word of mouth; the American presentation of history is modern, where all the resources of scholarship and the advantages of the printing press are utilized. Each method has peculiar advantages, the former having the possible charm of first-hand narrative, the latter that of accuracy and comprehensiveness. The narrative method is greatly superior to that of the text-book with children whose powers of reading are not well developed; the text-book, together with its available accessories, is greatly to be preferred with older pupils capable of large amounts of reading. The following sections give a vivid description of the narrative method at its best; the commentary will attempt to show how the printed page may be made equally attractive, and, at the same time, much more useful.

240. If, to begin with, a purely chronological, but accurate, outline-view of history is to be imparted, the teacher must be able to traverse mentally the whole historical field, going with equal readiness back, forward, or across (synchronistically). The notable names must form definite groups and series; and the teacher must possess facility in making the most notable names stand out clearly from the groups, and in condensing the most salient points of a long series into a short series.

If this mastery of subject-matter is important for the narrator, it is equally important for the teacher who depends upon print for the narration. Observation of current history teaching betrays the fact that the teacher rarely becomes master of his material to such an extent that he can throw it into new forms. As it stands in the book, he probably knows it; but to take liberties with the facts, to expand parts, or throw masses into brief outline, to make new groupings, or to change a long series into a short one, usually lies beyond his ability. This lesson the American teacher must learn through a better mastery of his materials.

241. Again, the teacher must make himself perfectly familiar with general notions that relate to classes of society—constitutions, institutions, religious customs, stages of culture—and that serve to explain events. But not only this; he must study likewise the conditions under which he can develop them and keep them present in the minds of his pupils. This consideration alone shuts out most generalizations from the first lessons in history. And, accordingly, ancient history, whose moving causes are simpler than the more modern political factors, maintains its place in presentations of historical material to younger pupils.

American history is better than ancient history in respect to its richness of picturesque variety. It is, moreover, easier for children to comprehend, since our present conditions have emerged directly from our pioneer state. Not only are constitutions, institutions, and religious customs to be studied, but the economic conditions of those early times are particularly worthy of study, since they are both important and interesting. Methods of farming, of conducting household affairs, such as cooking, making fires, producing clothing, securing shelter, means of transportation on land and water, methods of communication, and many other similar topics are of interest to the young.

242. Furthermore, due attention must be given to the difficulty of narrating well a complex event. The very first condition is continuity of the thought-current, in order that the thread of the story may remain unbroken, except where there are intentional rests. This, in turn, presupposes fluency of speech, careful cultivation of which is indispensable to a good presentation of historical events. But mere fluency does not suffice. There must also be resting-places, because otherwise alternate absorption and reflection cannot be secured; and because, without such pauses, even the formation of the series fails, since what has preceded arrests what follows. It is therefore not immaterial where a historical lesson begins and ends, and where the reviews are inserted.

While the narrator can utter words in succession only, the event has, in his mind, a very different form, which it is his business to convey to his hearers. Nor does the form of the event resemble a level plane; on the contrary, a manifold interest lifts some things into prominence and lets others sink. It is essential, accordingly, to distinguish how far, in a given instance, the narration should follow in a straight line the succession of events, and where, on the other hand, it should deviate to include accessory circumstances. The very language used must possess the power to induce side-glances and retrospective views, even without leaving the main road. The narrator must have skill to introduce descriptions here and to linger over pictures there, but must be able also, while moving his hearers, to retain his own self-control and to keep his bearings.

243. There remains one other requisite of prime importance, namely, the utmost simplicity of expression. The condensed and abstract language of more recent historians is hardly suited even to the highest class of a secondary school; a sentimental or witty treatment, such as that found in modern novelists, must be avoided entirely. The only safe models are the ancient classics.

The most serious fault with the text-book method is the barrenness arising from condensation. To teach history solely from a single book, even if this be among the best, is to produce an atrophy of the historical interest. It is on this account that successful teachers introduce large amounts of collateral reading, not of similarly condensed books, which would be like remedying the drouth with more dry weather, but of sections from fuller works on the same subject. In American history the pupil is directed to read selected portions of standard works like those of Fiske, Parkman, McMaster, Turner, Tyler, or earlier historians. In English history he is sent directly to such men as Gardiner, Green, Freeman, Traill, Ransome, Cunningham and McArthur, Harrison and Macaulay. The method of copious readings has, in turn, its disadvantages, the most conspicuous of which is diffusiveness. It is easy for the student to become so absorbed in a mass of details that he lose the proper sense of proportion, or overlook the relative importance of events, or fail to fix firmly in mind the causal series that binds all together. In the case of either of the methods described, it is the teacher who is responsible for order and for clearness of detail. In the one case his narrative must have the artistic unity of the finished historian; in the other he must so manage a wealth of given material that the golden chain of cause and effect shall be seen binding diversity into unity. The ability to do the first is of a much rarer order than that of the second, for the art of teaching is not so difficult as the art of historical composition. The remedy for the specific difficulty which modern text-book teaching of history encounters will be discussed under paragraph247.

The stories of Herodotus should serve the teacher as the basis for practice. In fact, they should actually be memorized in an accurate but fluent translation. The effect on children is surprising. At a later stage use may be made of Arrian and Livy. The method of the ancients of letting the principal characters utter their views and set forth their motives with their own lips, the narrator abstaining from reflections of his own, should be scrupulously imitated, and should be departed from only in the case of manifestly artificial rhetorical devices.

244. The course of preparation outlined above(240–243) having gone hand-in-hand with a thorough, pragmatic study of history, it is further necessary, in the exercise of the art acquired, to learn to expand or contract, according to circumstances and the specific aims of each occasion. Concerning this point no generally applicable rules can be given, on account of the great variety of possible cases; but the following suggestions should be noted:—

In general, all helps whereby historical objects may be represented to sense—portraits, pictures of buildings, of ruins, etc.—are desirable; maps for the more ancient times must be regarded as particularly indispensable. They should always be at hand, and their study should not be neglected. Among these helps must be included charts, substantially like that by Strass entitled “The Stream of Time,” which places before the eye not only synchronistic events, but at the same time shows also the alternate union and division of countries. The lack of such aids causes the loss of much time and temper over mere memory work.

Again, attention is due to the following four aspects of the teaching of history:—

245. (1) In the first place, even the earliest lessons in geography give rise to the question, whenever the description of a country is finished, “How did things look in this country formerly?” For it is a part of correct apprehension that cities and other works of man should not be regarded as of equal age with mountains, rivers, and oceans. Now, although the teacher cannot stop, during the time set apart for geography dealing with the present, to show and explain maps illustrative of the past, it will be useful, nevertheless, to add a few remarks about the early history of the country under discussion. The art of narration, however, is out of place here, inasmuch as the question, although reaching back in time, is suggested by the country. Mention of former activity, such as migrations and wars, is made simply for the purpose of adding life to the conception of a stationary surface. At the beginning, the notes on by-gone periods in connection with the geography of Germany will accordingly be as brief as possible; gradually, however, as France, England, Spain, Italy, are being studied in succession, these historical notes become knit together, and history is thus, so to speak, made to loom up in the distance. How far to go in this direction can be determined more definitely by distinguishing between the requirements of the first, and of the second course in geography. In the first course the most general statements may suffice, e.g., that not so very long ago Germany was split up more than now; that there were older times, when cities and neighboring princes often made war upon each other; that the barons used to live on more or less inaccessible heights; but that, in the interest of better order and stricter surveillance, Germany was divided into ten districts, etc.

The second course will admit of more historical facts than the first, although still only very few pertaining to an older epoch. Only the more recent events can be conveniently connected with geography, except in the case of still extant historical monuments,—such, for instance, as the ruins in Italy, the composite language of England, the peculiar political organization of Switzerland with its many subdivisions, visible on the map, and its diversities of language.

If, as is sometimes recommended, the plan is adopted of preparing the way for the study of mediÆval and modern history by a separate introductory course in short biographies, such a plan, though at best only fragmentary in its results, becomes at least more feasible where historical notes of the kind just mentioned are incorporated with the lessons in geography. But in this case it is all the more essential to have a chronological chart upon the wall, to some dates of which the teacher must take every opportunity to refer, in order that the pupils may obtain at least some fixed points. Otherwise scattered biographies are liable to occasion great confusion.

246. (2) The chief basis for the earlier stages of historical teaching will always be Greek and Roman history. It will not be inappropriate to commence with a few charming stories from Homeric mythology, since there is a close connection between the history of a people and their religion. Two wrong ways, however, are to be avoided: one, that of giving a detailed theogony or of including objectionable myths, for the sake of completeness, which would here be devoid of a rational purpose; the other, that of having the mythological elements memorized. Only true history should be memorized by children. Mythology is a study for youths or men.

Persian history must be told approximately in the sequence and setting given by Herodotus; to it the history of Assyria and of Egypt may be joined in the form of episodes, Greece being kept well in the foreground. The stories from the Old Testament, on the other hand, form a chain of lessons by themselves. The history of Rome must at first retain its mythical beginnings.

Whatever German opinion may be regarding the beginnings of historical instruction for their own children, American history possesses strong claims for precedence when we come to children of the United States. If we regard the chief intellectual purpose of history for the student to be the understanding of the present status through a knowledge of the historical progress that has led to it, then the primitive and pioneer history of this country is infinitely more valuable than any other to an American child, for in it lie enfolded the forces that have developed our people; whereas Greece and Rome are as distant in influence as they are in time. It is the mythology of Greece and Rome that most attracts children; but this belongs to literature rather than to history. Accounts of battles are about the same the world over, but it takes more maturity of mind to understand the Greek rage for individuality after the rise of philosophy, than it does to understand a corresponding feeling among the American pioneers, to say nothing of the desirability of teaching the latter as a phase of our own development. For reasons of simplicity, therefore, as well as for psychological nearness and national importance, American history must take precedence over that of Greece and Rome for American children.

247. Suppose, now, that detailed stories after the models furnished by the ancients have won the attention of the pupils; the mere pleasure of listening to stories can nevertheless not be allowed to determine continuously the impression to be produced. Condensed surveys must follow, and a few of the main facts be memorized in chronological order.

The following suggestions will be in place here. The chief events are to attach themselves in the memory to the memorized dates in such a way that no confusion can arise. Now, a single date may suffice for the group of connected incidents constituting one main event; if it seems necessary to add another, or a third, well and good, but to keep on multiplying dates defeats the very end aimed at. The more dates the weaker their effect, on account of the growing difficulty of remembering them all. In the history of one country dates should rather remain apart as far as possible, in order that the intervening numbers may be all the more available for purposes of synchronistic tabulation, by which the histories of different countries are to be brought together and connected. The same sparing use should be made of the facts of ancient geography, but those that are introduced must be learned accurately.

Granted that the primitive method of historical narration by the teacher is the most effective in its appeal to the beginner, it must be maintained that the combined knowledge and literary skill of modern historians infinitely surpass the powers of the ordinary teacher. The modern problem is, not how to compose history, but how to utilize that which has been composed. It is, in short, to guard against the confusion that comes from diffuseness. Wide historical reading may be as bad for the student as wide reading of novels. The mind may surrender itself to the passing panorama as completely in the one field as in the other, until the impressions made are like those of a ship upon a sea. The remedy is the thorough organization in the mind of the student of the knowledge gained in diverse fields. This is secured by teacher or author, or both. Some authors secure clearness of outline by topics, references, and research questions. Larned’s “History of England” concludes every chapter in this way. As an illustration we may quote from Chapter XVI, which narrates the quarrel between King Charles and his people:—

202. Charles I.

Topic.

1. Charles’s character and views.

References.—Bright, II, 608, 609; Green, 495; Montague, 118; Ransome, 138, 139.

203. Bad Faith in the Beginning of the Reign.

Topic.

1. Charles’s marriage and broken pledges.

Reference.—Bright, II, 608, 614.

204. The First Parliament of King Charles.

Topics.

1. Charles’s designs and his treatment of Parliament.
2. Attitude of Commons and their dissolution.
3. The King’s levies.

Reference.—Gardiner, II, 502, 503.

Research Questions.—(1)What were the legal and illegal sources of the King’s revenues? (Ransome, 151, 155). (2)What might be said to constitute the private property of the crown? (3)What contributed to make Charles’s court expensive? (Traill, IV, 76). (4)How would this need for money make for parliamentary greatness?[25]

In a similar way the remaining topics of this section of English history are recorded, guiding the pupil in his outlines and his readings. With suitable care on the part of the teacher to see that the student fixes the outline firmly in mind, there is no danger of becoming lost in a wilderness of words. At the same time the pupil’s mind is enriched from many noble sources, instead of being limited by the presumably meagre resources of a single teacher. By this method the child may enjoy the benefits of modern erudition, without at the same time being harmed by dissipation of mental energy.

Other authors reach the same ends by different means. Fiske’s “History of the United States,” for example, concludes each chapter with a topical outline in which cause and effect are emphasized. At the close of Chapter X, on the “Causes and Beginning of the Revolution,” we find the following:—

Topics and Questions

76. Causes of Ill Feeling between England and her Colonies.

1. What was the European idea of a colony, and of its object?
2. What erroneous notions about trade existed?
3. What was the main object of the laws regulating trade, etc.?

77. The Need of a Federal Union.

1. One difficulty in carrying on the French wars.
2. An account of Franklin.
3. Franklin’s plan of union, etc.

78. The Stamp Act Passed and Repealed.

1. The kind of government needed by the colonies.
2. How Parliament sought to establish such a government.
3. The nature of a stamp act, etc.

79. Taxation in England.

1. How Pitt’s friendship for America offended GeorgeIII.
2. The representation of the English people in Parliament.
3. How the representation of the people is kept fair in the United States.
4. How it became unfair in England.
5. Corrupt practices favored by this unfairness.
6. The party of Old Whigs.
7. The Tories, or the party of GeorgeIII.
8. The party of New Whigs and its aims.
9. Why George III was so bitter against Pitt.
10. The attitude of the King toward taxation in America.
11. The people of England not our enemies, etc.

At the close of these topics there follows a list of fifteen “Suggestive Questions and Directions,” with page references to Fiske’s “The American Revolution,” Vol.I, the whole being concluded by eighteen topics for collateral reading from “The American Revolution,” and from Cooke’s “Virginia.”[26]

It is a significant fact that modern text-books for children are being prepared by masters in the various departments of knowledge, not a little thought being bestowed upon the highest utilization of all modern instruments for arousing the intelligent interest of the pupils. This being the case, it is idle to rely upon primitive methods, however potent they may have been in the past, with pupils who have learned to read fluently.

[25] Larned, “History of England,” Houghton, Mifflin & Co., p.396.[26] Fiske, John, “A History of the United States for Schools,” Houghton, Mifflin & Co., Boston, pp.211–215.

248. The general surveys that follow the detailed narratives have this advantage for the pupil: he infers of his own accord, that in periods of which not much is told, a great deal took place, nevertheless, which the history or the teacher passes over in silence. In this way the false impressions are prevented that would be produced by purely compendious instruction, which indeed, at a later stage, becomes in a measure unavoidable.

249. (3) MediÆval history derives no assistance from the study of the ancient languages, nor is it closely related to present conditions; there is difficulty in imparting to the presentation of it more than the clearness obtainable through geography and chronology. But more than this is requisite: the burden of mere memory work without interest would become too great. The fundamental factors, Islamism, Papacy, the Holy Roman Empire, Feudalism, must be explained and given due prominence. Most of the facts down to Charlemagne may be made to contribute additional touches to the panorama of the Great Migration. With Charlemagne the chain of German history begins, and it will usually be considered advisable to extend this chain to the end of the Middle Ages, in order to have something to which synchronous events may be linked later on. Yet some doubt arises as to the value of such a plan. To be sure, the reigns of the Ottos, the Henrys, the Hohenstaufen, together with intervening occurrences, form a tolerably well-connected whole; but as early as the interregnum there is a sad break, and although the historical narrative recovers, as it were, with the stories of Rudolph Albrecht and Ludwig the Bavarian, there is nothing in the names of succeeding leaders, from CarlIV to FrederickIII, that would make them proper starting-points and connecting centres for the synchronism of the whole period in question. It might be better, therefore, to stop with the excommunication of Ludwig the Bavarian, with the assembly of the electors at Rhense, and with the account of how the popes came to reside in Avignon. Then—going back to Charlemagne—France, Italy, even England, may be taken up, and greater completeness given to the history of the crusades. Farther on, special attention might be called, in a synchronistic way, to Burgundy and Switzerland, and to the changing fortunes of the wars between England and France. French history may then leave off with the reign of CharlesVIII, and English history with that of HenryVII, while German history, from Maximilian on, is placed again in the foreground. The Hussite wars will be treated as forerunners of the Reformation. Other events must be skilfully inserted. Many modifications of grouping will have to be reserved for subsequent repetitions.

250. (4) In presenting modern history, the teacher will do well to avail himself of the fact that modern history does not cover so long reaches of time as mediÆval history does, and that it falls into three sharply defined periods, the first of which ends with the treaty of Westphalia, the second extends from this date to the French Revolution, and the third, to the present. These periods should be carefully distinguished, the leading events of each should be narrated synchronistically, and a recital of the most essential historical facts about each country should follow. Only after each has been handled in this way, and the subject-matter presented has been thoroughly impressed upon the memory by reviews, will it be well to pass on to a somewhat fuller ethnographical account reaching back into the mediÆval history of each country and extending forward to our own times. No harm is done by going over the same ground again for the purpose of amplifying that which before appeared in outline only.

The chief point is, that no course of instruction which claims at all to give completeness of culture can be regarded as concluded before it has introduced the pupil to the pragmatic study of history, and has taught him to look for causes and effects. This applies preËminently to modern history, on account of its direct connection with the present; but mediÆval and ancient history, too, have to be worked over once more from this point of view. History should be the teacher of mankind; if it does not become so, the blame rests largely with those who teach history in schools.

251. A well-compiled and well-proportioned brief history of inventions, arts, and sciences should conclude the teaching of history, not only in gymnasia, but also and especially in higher burgher schools, because their courses of study are not supplemented by the university.

Moreover, the whole course in history is properly accompanied by illustrative poetical selections, which, although perhaps not produced during the different epochs, yet stand in some relation to them; and which in some measure, even if only by illustrating ages very far apart, exhibit the vast differences in the freest activities of the human mind.

Note.—National history is not the same for each land, nor everywhere of equal interest, and, owing to its connection with larger events, often unintelligible to young minds when torn out of its place and presented by itself. If its early introduction is desired in order to kindle the heart, special pains must be taken to select that which is intelligible and which appeals to boyhood.

CHAPTER III
Mathematics and Nature Study

252. Aptitude for mathematics is not rarer than aptitude for other studies. That the contrary seems true, is owing to a belated and slighted beginning. But that mathematicians are seldom inclined to give as much time to children as they ought is only natural. The elementary lessons in combination and geometry are neglected in favor of arithmetic, and demonstration is attempted where no mathematical imagination has been awakened.

The first essential is attention to magnitudes, and their changes, where they occur. Hence, counting, measuring, weighing, where possible; where impossible, at least the estimating of magnitudes to determine, however vaguely at first, the more and the less, the larger and the smaller, the nearer and the farther.

Special consideration should be given, on the one hand, to the number of permutations, variations, and combinations; and, on the other hand, to the quadratic and cubic relations, where similar planes and bodies are determined by analogous lines.

Note.—This is not the place for saying much that might be said concerning that which renders early instruction in mathematics unnecessarily difficult. But it may be remarked in brief that some of these difficulties arise from the terminology, some from the teacher’s accustomed point of view, and some from the multiplication of varying requirements.

(1) The phraseology used forms an obstacle, even to the easiest steps in fractions. The fraction ?, for example, is read two-thirds, and, accordingly, ?×?, two-thirds times four-fifths, instead of, multiplication by two and by four, and division by three and by five. The fact is overlooked that the third part of a whole includes the concept of this whole, which cannot be a multiplier, but only a multiplicand. This difficulty the pupils stumble over. The same applies to the mysterious word square root, employed instead of the expression: one of the two equal factors of a product. Matters grow even worse later on when they hear of roots of equations.

(2) Still more might be said in criticism of the erroneous view according to which numbers are recorded as sums of units. This is true as little as that sums are products; two does not mean two things, but doubling, no matter whether that which is doubled is one or many. The concept of a dozen chairs is not made up of 12 percepts of single chairs; it comprises only two mental products,—the general concept chair and the undivided multiplication by 12. The concept one hundred men likewise contains only two concepts,—the general concept man and the undivided number 100. So, also, in such expression as six foot, seven pound, in which language assists correct apprehension by the use of the singular. Number concepts remain imperfect so long as they are identified with series of numbers and recourse is had to successive counting.

(3) In arithmetical problems the difficulty attaching to the apprehension of the things dealt with is confounded with that of the solution itself. Principal and interest and time, velocity and distance and time, etc., are matters which must be familiar to the pupils, and hence must have been previously explained, long before use can be made of them for practice. The pupil to whom arithmetical concepts still give trouble should be given concrete examples so familiar to him that out of them he can create over again the mathematical notion and not be compelled to apply it to them.

253. The measuring of lines, angles, and arcs (for which many children’s games, constructive in tendency, may present the first occasion) leads over to observation exercises dealing with both planes and spheres. Skill in this direction having been attained, frequent application must be made of it, or else, like every other acquirement, it will be lost again. Every plan of a building, every map every astronomical chart, may afford opportunities for practice.

These observation exercises are to be organized in such a manner that upon the completion of mensuration the way is fully prepared for trigonometry, provided that besides the work in plain geometry, algebra has been carried as far as equations of the second degree.

Extended discussions as to the place and value of the ratio idea in elementary arithmetic are found in “The Psychology of Number,” by McLellan & Dewey,[27] and in “The New Arithmetic,” by W.W.Speer.[28] The former work advocates early practice in measuring with changeable units, claiming that the child should early acquire the idea of number as the expression of the relation that a measured somewhat bears to a chosen measurer, and making counting a special case of measuring. Mr.Speer makes the ratio idea still more prominent by furnishing the school with numerous sets of blocks of various sizes and shapes with which to drill the pupils into instantaneous recognition of number as the ratio between two quantities. For an extended examination of these principles the reader may well consult Dr.DavidEugene Smith’s able treatise on the teaching of elementary mathematics.[29]

Note.—It is now nearly forty years since the author wrote a little book on the plan of Pestalozzi’s A, B, C, of observation, and he has often had it used by teachers since. Numerous suggestions have been given by others under the title, “Study of Forms.” The main thing is training the eye in gauging distances and angles, and combining such exercises with very simple computations. The aim is not merely to secure keenness of observation for objects of sense, but, preËminently, to awaken geometrical imagination and to connect arithmetical thinking with it. Indeed, exercises of this sort constitute the necessary, although commonly neglected, preparation for mathematics. The helps made use of must be concrete objects. Various things have been tried and cast aside again; most convenient for the first steps are triangles made from thin hard-wood boards. Of these only seventeen pairs are needed, all of them right-angled triangles with one side equal. To find these triangles, draw a circle with a radius of four inches, and trace the tangents and secants at 5°, 10°, 15°, 20°, etc., to 85°. The numerous combinations that can be made will easily suggest themselves. The tangents and secants must be actually measured by the pupils; from 45° on, the corresponding figures, at first not carried out beyond tenths, should be noted, and, after some repetition, learned by heart. On this basis very easy arithmetical examples may be devised for the immediate purpose of gaining the lasting attention of the pupils to matters so simple. Observations relating to the sphere require a more complicated apparatus, namely, three movable great circles of a globe. It would be well to have such means at hand in teaching spherical trigonometry. Needless to say, of course, observation exercises do not take the place of geometry, still less of trigonometry, but prepare the ground for these sciences. When the pupil reaches plain geometry, the wooden triangles are put aside, and observation is subordinated to geometrical construction. Meanwhile arithmetic is passing beyond exercises that deal merely with proportions, to powers, roots, and logarithms. In fact, without the concept of the square root, not even the Pythagorean Theorem can be fully grasped.

“Herbart’s A, B, C, of Sense Perception,” together with a number of minor educational works, has been translated into English.[30] It abounds in shrewd observations and ingenious devices, yet as a whole it represents one of those side excursions, which, though delightful to genius, is not especially useful to the world. To drill children into the habit of resolving a landscape into a series of triangles, may indeed be possible, but like any other schematization of the universe, is too artificial to be desirable. Nevertheless, a limited use of the devices mentioned in this section might tend to quicken an otherwise torpid mind.

[27] McLellan & Dewey, “The Psychology of Number,” International Education Series, D.Appleton & Co., New York, 1895.[28] Speer, W. W., “The New Arithmetic,” Ginn & Co., Boston, 1896.[29] Smith, David Eugene, “The Teaching of Elementary Mathematics,” Ch.V, The Macmillan Co., New York, 1900.[30] Eckoff, William J., “Herbart’s A, B, C, of Sense Perception,” International Education Series, D.Appleton & Co., New York, 1896.

254. But now a subject comes up that, on account of the difficulties it causes, calls for special consideration, namely, that of logarithms. It is easy enough to explain their use, and to render the underlying concept intelligible as far as necessary in practice—arithmetical corresponding to geometrical series, the natural numbers being conceived of as a geometrical series. But scientifically considered, logarithms involve fractional and negative exponents, as also the application of the Binomial Theorem. The latter, to be sure, is merely an easy combinatory formula so far as integral positive exponents are concerned, but, limited to these, is here of comparatively little use.

Now, since trigonometry in its main theorems is independent of logarithms, but is little applied without their aid, the question arises whether beginners should necessarily be given a complete and vigorously scientific course in logarithms, the highly beneficial instruction in trigonometry being postponed until after the successful completion of such a course, or whether the practical use of logarithms is to be permitted before accurate insight into underlying principles has been gained.

Note.—The difficulty encountered in this subject—undoubtedly one of those difficulties most keenly felt in teaching mathematics—is after all only an illustration of the injurious consequences of former sins of omission. If the geometrical imagination were not neglected, there would be ample opportunity, not only for impressing far more deeply the concept of proportion, demanded even by elementary arithmetic, but also for developing early the idea of function. The object lessons mentioned above have already illustrated the dependence of tangents and secants on angles. When these relations of dependence have become as familiar as may be expected after a half year’s instruction, sines and cosines also are taken up. But it is not sufficient to leave the matter here. Somewhat later, about the time when mensuration is introduced, the squares and cubes of natural numbers must be emphasized, and very soon committed to memory. Next it should be pointed out how by finding the differences of squares and cubes respectively, and then adding these differences, the original numbers may be obtained again. A similar treatment should be accorded to figurate numbers.

Small wooden disks, like checker-pawns, commend themselves for the purpose. By means of them various figures are found. The pupils are asked to indicate how many disks they need to construct one or the other kind of figures. A further step will be to show the increase of squares and cubes corresponding to the increase of the root, and to make this information serve as the preparation for the elementary parts of differential calculus. Now the time has come for passing on to the consideration of consecutive values of the roots, which are found to differ by quantities of continuously decreasing smallness as one progresses continuously through the number system. And so, after the logarithms of 1, 10, 100, 1000, etc., also of 1/10, 1/100, etc., have been gone over many times, forward and backward, the conception is finally reached of the interpolation of logarithms.

255. In schools where practical aims predominate, logarithms should be explained by a comparison of the arithmetical with the geometrical series, and the practical application will immediately follow. But even where recourse is had to Taylor’s Theorem and the Binomial Theorem, the gain to the beginner will not usually be very much greater. Not as though these theorems, together with the elements of differential calculus, could not be made clear; the real trouble lies in the fact that much of what is comprehended is not likely to be retained in the memory. The beginner, when he comes to the application, still has the recollection of the proof and of his having understood it. Indeed, with some assistance he would be able, perhaps, to again retrace step by step the course of the demonstration. But he lacks perspective; and in his application of logarithms it is of no consequence to him by what method they have been calculated.

What has been said here of logarithms may be applied more generally. The value of rigid demonstrations is fully seen only when one has made himself at home in the field of concepts to which they belong.

It is customary in American schools to take up elementary algebra and elementary geometry upon the completion of arithmetic, both algebra and geometry being anticipated to some extent in the later stages of arithmetic. The following paragraphs from the pen of DavidEugene Smith[31] indicate some of the advance in algebra since Herbart’s time:—

“The great revival of learning known as the Renaissance, in the sixteenth century, saw algebra take a fresh start after several centuries of complete stagnation. Tartaglia solved the cubic equation, and a little later Ferrari solved the biquadratic. By the close of the sixteenth century Vieta had put the keystone in the arch of elementary algebra, the only material improvements for some time to come being in the way of symbolism. For the next two hundred years the struggle of algebraists was for a solution of the quintic equation, or, more generally, for a general solution of an equation of any degree.

“The opening of the nineteenth century saw a few great additions to the theory of algebra. The first was the positive proof that the general equation of the fifth degree is insoluble by elementary algebra, a proof due to Abel. The second was the mastery of the number systems of algebra,—the complete understanding of the negative, the imaginary, the incommensurable, the transcendent. Other additions were in the line of the convergency of series, the approximation of the real roots of numerical equations, the study of determinants—all finding their way into the elements, together with the theories of forms and groups, which must soon begin to influence the earlier chapters of the subject.

“This hasty glance at the development of the subject is sufficient to show how it has been revolutionized in modern times. To-day it is progressing as never before. The higher culture is beginning to affect the lower; determinants have found place in the beginner’s course; graphic methods, objected to as innovations by some who are ignorant of their prominence in the childhood of science, are reasserting their rights; the ‘imaginary’ has become very real; the inheritances of the algebra-teachers’ guild are being examined with critical eyes, and many an old problem and rule must soon go by the board. It is valuable to a teacher to see what changes have been wrought so that he may join in the movement to weed out the bad, to cling to the good, and to reach up into the realm of modern mathematics to see if, perchance, he cannot find that which is good and usable and light-shedding for the elementary work.”

The true order of elementary mathematics, according to Dr.Smith, is substantially as follows:—

1. Elementary operations of arithmetic.
2. Simple mensuration, correlation with drawing, the models in hand:— Inductive geometry—the primitive form of the science.
3. Arithmetic of business and of science, using the simple equation with one unknown quantity wherever it throws light upon the subject.
4. Simple theory of numbers, the roots, series, logarithms.
5. Elementary algebra, including quadratic and radical equations.
6. Demonstrative plane geometry begun before the algebra is completed and correlated with it.
7. Plane trigonometry and its elementary applications.
8. Solid geometry. Trigonometry. Advanced algebra, with the elements of differentiation and integration.

“The student should then take a rapid review of his elementary mathematics, including a course in elementary analytic geometry and the calculus. He would then be prepared to enter upon the study of higher mathematics.”

[31] Compare Smith, David Eugene, “History of Modern Mathematics,” in Merriman & Woodworth’s “Higher Mathematics,” Wiley, New York, 1896.

256. Demonstrations taking a roundabout way through remote auxiliary concepts are a grave evil in instruction, be they ever so elegant.

Such modes of presentation are rather to be selected as start from simple elementary notions. For with these conviction does not depend on the unfortunate condition requiring a comprehensive view of a long series of preliminary propositions. Thus Taylor’s Theorem can be deduced from an interpolation formula, and this, in turn, from the consideration of differences, for which nothing is needed beyond addition, subtraction, and knowledge of the permutation of numbers.

The following account of imaginary and complex numbers by Dr.DavidEugene Smith is so lucid that it is given at length:—

“The illustrations of the negative number are so numerous, so simple, and so generally known from the common text-books that it is unnecessary to dwell upon them.[32] Debt and credit, the scale on the thermometer, longitude, latitude, the upward pull of a balloon compared with the force of gravity, and the graphic illustration of these upon horizontal and vertical lines—all these are familiar.

“But the imaginary and complex numbers have been left enshrouded in mystery in most text-books. The books say, inter lineas, ‘Here is v-1; it means nothing; you can’t imagine it; the writer knows nothing about it; let us have done with it, and go on.’ Such is the way in which the negative was treated in the early days of printed algebras, but now such treatment would be condemned as inexcusable. But there is really no more reason to-day for treating the imaginary so unintelligently than for presenting the negative as was the custom four hundred years ago. The graphic treatment of the complex number is not to-day so difficult for the student about to take up quadratics as is the presentation of the negative to one just beginning algebra.

“Briefly, the following outline will suffice to illustrate the procedure for the complex number:—

Number line from -5 to +5

“1. Negative numbers may be represented in a direction opposite to that of positive numbers, starting from an arbitrary point called zero. Hence, when we leave the domain of positive numbers, direction enters. But there are infinitely many directions in a plane besides those of the positive and negative numbers, and hence there may be other numbers than these.

“2. When we add positive and negative numbers we find some results which seem strange to a beginner. For example, if we add +4 and -3 we say the sum is 1, although the length1 is less than the length4 or the length-3; yet this does not trouble us because we have considered something besides length, namely, direction; it is true, however, that the sum of 4 and -3 is less than the absolute value of either. This is seen to be so reasonable, however, from numerous illustrations (as the combined weight of a balloon pulling up 3lbs., tied to a 4-lb. weight), that we come not to notice the strangeness of it; graphically, we think of the sum as obtained by starting from 0, going 4 in a positive direction, then 3 in a negative direction, the sum being the distance from 0 to the stopping-place.

Graph of 1 multiplied by v-1 twice

“3. If we multiply 1 by -1, or by v-1·v-1, or by v-1 twice, we swing it counter-clockwise through 180°, and obtain -1; hence, if we multiply it by v-1 once, we should swing it through 90°. Hence we may graphically represent v-1 as the unit on the perpendicular axis YY', and this gives illustration to v-1, 2v-1, 3v-1, ··· -v-1, -2v-1, -3v-1, or, more briefly, ±i, ±2i, ±3i, ··· where i stands for v-1. We therefore see that i is a symbol of quality (graphically of direction), just as is + or -, and that -3 · 5i, iv5, etc., are just as real as -3 · 5, v5, etc. It is impossible to look out of a window -3 · 5 times as it is to look out -3 · 5i times; strictly, one number is as ‘imaginary’ as the other, although the term has come by custom to apply to one and not to the other.

Representation of 3+2i as the hypotenuse of a right-angled triangle with sides of 3 and 2i units

“4. The complex number 3 + 2i is now readily understood. Just as 3 + (-2) is graphically represented by starting from an arbitrary zero, passing 3units in a positive direction (say to the right), then 2units in the opposite direction, calling the sum the distance from 0 to the stopping-point, so 3 + 2i may be represented graphically. Starting from 0, pass in the positive direction (to the right in the figure) 3units, then in the i direction 2units, calling the sum the distance from 0 to the stopping-place.

“Of course the question will arise as to the hypotenuse being the sum of the two sides of the right-angled triangle. But the case is parallel to that mentioned in paragraph2; it is not the sum of the absolute values, any more than is 1 the sum of the absolute values of 4 and -3; it is the sum when we define addition for numbers involving direction as well as length.

“A simple illustration from the parallelogram of forces is often used to advantage.

Parallelogram of two forces +3 and +2i with resultant OP

“Suppose a force pulling 3lbs. to the right (+3lbs.) and another pulling 2lbs. upwards (+2ilbs.); required the resultant of the two. It is evident that this is OP, i.e., OP = 3 + 2i.

“This elementary introduction to the subject of complex numbers shows that the ‘imaginary’ element is easily removed, and that students about to begin quadratics are able to get at least an intimation of the subject. This is not the place for any adequate treatment of these numbers: such treatment is easily accessible. It is hoped that enough has been presented to render it impossible for any reader to be content with the absolutely meaningless and unjustifiable treatment found in many text-books.”[33]

[32] See Beman & Smith’s “Elements of Algebra,” p.17.[33] For an elementary presentation of the subject, see Beman and Smith’s “Elements of Algebra,” Boston, 1900. For a history of the subject, see Beman and Smith’s translation of Fink’s “History of Mathematics,” Chicago, 1900, or Professor Beman’s Vice-Presidential Address before the American Association for the Advancement of Science, 1898, or the author’s “History of Modern Mathematics,” already mentioned.

257. The pedagogical value of mathematical instruction, as a whole, depends chiefly on the extent to which it enters into and acts on the pupil’s whole field of thought and knowledge. From this truth it follows, to begin with, that mere presentation does not suffice; the aim must be rather to enlist the self-activity of the pupil. Mathematical exercises are essential. Pupils must realize how much they can do by means of mathematics. From time to time written work in mathematics should be assigned; only the tasks set must be sufficiently easy. More should not be demanded and insisted on than pupils can comfortably accomplish. Some are attracted early by pure mathematics, especially where geometry and arithmetic are properly combined. But a surer road to good results is applied mathematics, provided only the application is made to an object in which interest has already been aroused in other ways.

But the pupils ought not to be detained too long over a narrow round of mathematical problems; there must also be progress in the presentation of the theory. Were the only requisite to stimulate self-activity, the elementary principles might very easily suffice for countless examples affording the pupil the pleasure of increasing facility, and even the delight arising from inventions of his own, without giving him any conception of the greatness of the science. Many problems may be compared to witty conceits, which may be welcome enough in the right place, but which should not encroach on the time for work. There ought to be no lingering over things that with advancing study solve themselves, merely for the sake of performing feats of ingenuity. Incomparably more important than mere practice examples is familiarity with the facts of nature, and such familiarity renders all the better service to mathematics if combined with technical knowledge.

258. Even young children may very well busy themselves with picture books illustrating zoÖlogy, and later with analyses of plants which they have gathered. If early accustomed to this, they will, with some guidance, readily go on by themselves. At a later time they are taught to observe the external characteristics of minerals. The continuation of the study of zoÖlogy is beset with some difficulties on account of the element of sex.

Though industriously debated, there is no field of education more undecided both as to matter and method than nature work in the grades. Some scientists would teach large amounts of well-classified knowledge; others are content when they have secured a hospitable frame of mind toward nature. If a love for flowers and birds can be cultivated in children, the latter class are satisfied that the best result has been attained. Thus a discussion arises as to which is the more valuable, attitude or knowledge.

It is feared by some that any attempt to teach real science, even of an elementary kind, will result in a paralysis of permanent scientific interest. To this it is replied that a sentimental regard for Æsthetic aspects of nature insures little or no true scientific interest.

Both sides are, in large measure, wrong; for, though apparently antagonistic in their aims, they make merely a different application of a common principle, which, if not wholly erroneous, is at least inadequate. Both parties assume that the end to be attained in nature study is something only remotely related to the pupil’s practical life. One would present nature for its own sake as scientific knowledge; the other would offer it for its own sake as a source of Æsthetic or other feeling. The scientist often assumes that to a pupil a scientific fact or law is its own excuse for being. He thinks there must be a natural, spontaneous response to such a fact or law in the breast of every properly constituted child, so that, to imbue the mind with the scientific spirit, it is only necessary to expose it to scientific fact.

Perhaps, unfortunately for the normal child, this view is somewhat encouraged by the biographies of scientific geniuses. On the other hand, those who hold the poetic view of nature assume that there must be a native response to natural beauties in every child; so that the true method is to expose him to nature’s beauty, when rapture is sure to follow. Unfortunately again for the pupil, this view is also encouraged by the influence of the nature poets. The result is that natural science is presented as an end in itself—in the one case as scientific knowledge, in the other as the lovable in nature.

While it may be admitted that a few children will respond now to the one stimulus, now to the other, the great mass are not thrilled with rapture at nature’s beauty, nor are they fettered by scientific interest in her laws. To become an object of growing interest to children, nature must have a better basis than natural childish delight in the novel, or reverence for scientific law. The first of these is evanescent, the second feeble.

We may agree with the scientist as with the poet, that both science and poetic appreciation are desirable ends, but they cannot be imparted to the childish mind by didactic fiat.

If there is one service greater than another that Herbart has rendered to education, it is in bringing clearly to our consciousness the supreme importance of the principle of apperception, or mental assimilation, as a working basis for educative processes. So long as a fact or a principle or system of knowledge stands as an end in itself, just so long is it a thing apart from the real mental life of the child. Even a formally correct method of presentation, should it even appeal at once to all ‘six’ classes of interest, will fail to create more than a factitious mental enthusiasm. It is like conversation that is ‘made’ interesting; it may suffice to lighten a tedious hour, but it awakens no vital response. When, however, the natural love of novelty or inborn response to the true is reinforced by a sense of warm personal relationship, when the facts of forest, or plain, or mine, or animal life flood the mind with unexpected and significant revelations concerning either the present or the past in close personal touch with the learner, then instruction rests upon an apperceptive basis. Abstractions that before were pale, beauties that were cold, now receive color and warmth because they get a new subjective valuation that before was impossible.

A sedate sheep nibbling grass or resting in the shade, a skipping lamb gambolling on the green, are suitable objects of nature study. Their pelts, their hoofs, their horns, their wool, are worthy of note as scientific facts. A diluted interest may even be added by recitation of the nursery rhymes about “Little Bo-Peep” and “Mary had a Little Lamb.” But these are devices for the feeble-minded.

If the teacher can reveal to the pupil the function of wool in making garments for the race, and can lead him to repeat the processes by which, from time immemorial, the wool has been spun into yarn and woven into cloth; if, at the same time, the influence of this industry upon the home life, both of men and women, can be shown, the study of the sheep becomes worthy the attention even of a boy who can play foot-ball or of a girl who can cook. The literature of the sheep is no longer infantile or fatuous. We have a gamut reaching from Penelope to Priscilla. In the words of Professor Dewey: “The child who is interested in the way in which men lived, the tools they had to do with, the transformation of life that arose from the power and leisure thus gained, is eager to repeat like processes in his own action; to make utensils, to reproduce processes, to rehandle materials. Since he understands their problems and their successes only by seeing what obstacles and what resources they had from nature, the child is interested in field and forest, ocean and mountain, plant and animal.... The interest in history gives a more human coloring, a wider significance, to his own study of nature.”[34]

The conclusion arising from this argument is that nature study as an end in itself, or a thing apart from the real or imagined experiences of the pupil, is but a faint reflection of what it may become under a more rational treatment. In order of time, nature study in the earliest grades may indeed rest upon the mere delight of the childish mind in the new, the strange, the beautiful, and especially in the motion of live creatures, and may be reinforced by childish literature. When boyhood and girlhood begin, however, then the industrial motive, first in the home environment, then of primitive times, becomes the chief reliance for an abiding interest. In the reproduction of primitive processes, there is of necessity a historical element. When nature has attained a firm apperceptive basis through imitation of primitive industrial processes, and has obtained a historical background, then it may properly be further reinforced by literary reference. The poetic value of nature will now appeal to the mind with a potency that springs from inner life and experience; scientific law will now have some chance of appealing to the mind with something of the same reverence that Kant besought for the moral law. The true order of appeal in nature study is therefore as follows: For infancy, natural curiosity and delight in the movements of living creatures; for the age of boyhood and girlhood, imitation, real or imaginary, of processes depending upon natural objects and forces, together with historical and literary reference; secondarily, nature work may also appeal to youthful interest in natural law or beauty.

[34] Dewey, John, “The Aim of History in Elementary Education,” Elementary School Record, November, 1900, University of Chicago Press.

259. With the foregoing should be conjoined much attention to external nature, to the changes corresponding to the seasons, and to means of intercommunication.

Under this head belongs, on the one hand, observation of the heavenly bodies,—where sun and moon rise, how the latter waxes and wanes, where the north star is found, and what arcs are described by the brighter stars and the most conspicuous constellations.

Here belongs, on the other hand, technological knowledge, acquired partly through direct observation, partly through lessons in descriptive physical science. Technology ought not to be considered merely from the side of the so-called material interests. It furnishes very important connecting links between the apprehension of the facts of nature and human purposes. Every growing boy and youth should learn to handle the ordinary tools of the carpenter as well as rule and compasses. Mechanical skill would often prove far more useful than gymnastic exercises. The former benefits the mind, the latter benefit the body. With burgher schools should go manual training-schools, which does not mean that the latter must necessarily be trade schools. Finally, every human being ought to learn how to use his hands. The hand has a place of honor beside language in elevating mankind above the brute.

The foregoing store of information also enters into the study of geography; how, will appear in the next chapter.

The soundness of the foregoing remarks is witnessed by the rapid development of manual training-schools in the last decade, and the almost universal desire, if not practice, of providing considerable amounts of manual training for the pupils of the grammar grades. The girls usually have some form of sewing and cooking, while the boys have sloyd or other similar tool work in wood. The rationale of requiring girls to do carpenter work instead of the forms of manual exercise that especially pertain to their sex is not yet satisfactorily established.

260. On the observation of the heavenly bodies is based popular astronomy, which provides a test as to whether the mathematical imagination has been properly cultivated.

261. Elementary statics and mechanics will serve as an early introduction to physics, which combines with the easiest portions of chemistry. Long before physics is formally presented, it must be foreshadowed by many things stimulating the attention. Notice is directed to clocks, mills, the most familiar phenomena of atmospheric pressure, to electrical and magnetic toys, etc. In burgher schools, at least, so much must be said about buildings and machines as is necessary to incite to further study in the future. The same holds for the fundamental facts of physiology.

262. As often as a new topic for study is introduced, it is important to give prominence to some of the salient facts, and these must be accurately memorized. Moreover, pupils need to have practice in exact description. Where practicable, these descriptions are corrected by actually looking at the objects themselves.

Hasty and superficial observation of objects presented for inspection always calls for severe criticism; else collections and experiments become valueless. Nor should objects be shown too lavishly; pupils must often be told beforehand what they will have to look for. Frequently it may serve the purpose to employ successively good descriptions, pictures, and direct observation.

CHAPTER IV
Geography

263. As to geography, at least two courses may be distinguished. One of these is analytic and begins with the pupil’s immediate neighborhood, the topography of the place, while the other starts with the globe. Here only the former will be discussed, as the latter can be had directly from good text-books.

Note.—The usual method of taking the globe as the point of departure would be less open to criticism, if, in order to render the conception of the earth’s sphericity more intelligible, attention were directed to the shape of the moon, the observation being carried on occasionally with the aid of a telescope. But even if this is done, it still remains a blunder to substitute the faint and vague idea of a huge ball for direct perception. Equally injudicious is the plan of beginning with Portugal and Spain. That spot where pupils and teacher are at the moment is the point from which the pupils must take their bearings, and in thought extend their horizon. It will never do to pass over the natural starting-points provided by sense-perception.

Had the note to this section been properly heeded, we should not have had to wait for fifty years after Herbart’s death before witnessing the present rational methods of applying geographical science to elementary education. It is the proud boast of the modern elementary geography that it begins with a study of the pupil’s actual environment. The term home geography has now become a familiar one. It signifies that the pupil is taught to observe the geographical elements as they exist in his own neighborhood. He studies hills, watercourses, soil, woods, lakes, together with the industrial phenomena that come within the reach of his investigation. Upon this primary sense-basis he rears the structure of his geographical knowledge.

264. Geography is an associating science, and use must be made of the opportunities it offers for binding together a variety of facts, none of which should be allowed to remain isolated in the mind of the learner. It is not the mathematical portion, supplemented and made interesting by popular astronomy, that serves as the first connecting link between mathematics and history (second course); even the rudiments of geography may, on the basis of observation exercises, furnish practice in the determination of triangles which occur on the first maps used, although this step is not always necessary when once some skill has been acquired in singling out features worthy of note. (The determination of position by latitude and longitude is, for the first course, as irrational as the action of a traveller in Germany or France would be if he set about to put together the picture of the places where he expects to remain, with the aid of their relation to the equator and the first meridian.)

Physical geography presupposes some knowledge of nature, and furnishes the occasion for enriching that knowledge. Political geography designates the manner in which man inhabits and uses the earth’s surface. It is the pedagogical aim of instruction in geography to associate all this.

265. The teacher must cultivate the art of narration; his accounts must resemble those of a traveller. But the narrative should conflict with the determination of the relative position of places (by grouping them about one principal place, and in the case of more than one by the use of triangles) as little as, in teaching history, the story of events should conflict with the scheme of chronology. The two go together. The narrative is to present a clear picture, and to this end requires the support of a few fixed points in space. On the other hand, these points should not remain isolated; they are to be connected by the lines of the picture.

266. It is not a matter of indifference how many unfamiliar names are mentioned in one minute or hour. Nor is it immaterial whether they are uttered before or after perception of the picture which the map presents. The first requisite is that every map placed before the pupils be conceived of as a country; three, at most four, names of rivers, and the names of a few mountains are sufficient; completeness is out of place here. The few names given provide ample opportunity for fixing the position of notable points, both with reference to one another and to the boundary lines of the country.

Due prominence having been given to these geographical features, they should then be connected, say with the aid of a blackboard, on which they are roughly sketched one by one, and properly joined together afterward. In the case of the sources and outlets of rivers, this may be done by a line to indicate the course. If now the pupils have made good previous use of their eyes, especially if they have noticed the fall of brooks and rivers, and have observed the slope of the ground in a particular region,—if they have not, the deficiency must be made good first of all,—it will not be too early to pass on to a general description of the appearance which the country under consideration would present to a traveller. And now the time has come for a somewhat fuller mention of the names of rivers and mountains, but these names must at once be gone over several times by the pupils. Doing so will reveal whether the list of new names has been made too long; it is often largely due to carelessness in this respect, if the study of geography proves barren or onerous. Next in order follow detailed descriptions of particular wonders of nature, where there are such. Attention is then given to some of the principal cities, mention being made of the number of inhabitants. Here the determination of relative location comes in again, and for this the self-activity of the pupils is indispensable. Finally, human industry and art, so far as they relate to the products of the country, together with the little of political organization that pupils can grasp. The names of the provinces should ordinarily be omitted from the first course.

This section is suggestive of the old geography of the last half century,—location, names, maps, the barren details of the science. Geography is something richer than all this. The old geography was political in the foregoing sense. The first break was in making it physiographical, the last in making it social. Names as such are nothing, and physical facts little more, but both become of value as soon as they are brought into relation to man,—his life, his work, his recreation. Geography is not essentially the location of places, nor is it physiography, but it is a study of the essential facts concerning the surface of the earth as they are related to man himself; it is, in short, human in the fullest sense. It gives a concrete explanation of civilization; it explains the production, the exchange, and, to some extent, the consumption of goods. It contrasts countries, not so much by square miles, as by the number of miles of railroads they possess. (The most momentous fact of modern civilization is the railroad. Twelve billions of dollars are invested in it in the United States alone. In view of these facts, what shall be said of those recent geographies that keep the children poring over primitive maps for years—maps without a suggestion of a railroad in them? This is an illustration of how prone education is to lag behind the progress of society.)

267. The reviews, which should be frequent, must steadily work toward a growing firmness of association between names and places. Each name is to be referred to the place it designates; hence the sequence of names must often be reversed, and the map looked over in all directions and from all points of view. How far to go is determined in accordance with individual capacity. From some, only what is absolutely essential can be demanded; from others, much more, in order that they may exert themselves properly.

268. In the midst of other studies on which greater stress is laid, geography is as a rule slighted by pupils and sometimes even by teachers. This attitude merits severe criticism. Instruction in geography may be reduced to a minimum, the first course even requires this, but it should not be disparaged. With many pupils, geography is the first study which gives them the consciousness that they can learn as they are expected to learn. With all pupils, geography must connect the remaining studies and must keep them connected. Without it everything remains unstable. Historical events lack places and distances; products of nature are without the regions where they are found; popular astronomy, which is called upon so often to prevent and dispel erroneous notions, is deprived of its very basis, and the geometrical imagination of one of its most important incentives. If the facts of knowledge are allowed to fall asunder in this way, instruction endangers the whole of education.

CHAPTER V
The Mother-tongue

269. There would be less controversy about language teaching if existing differences in conditions were given proper attention.

The most general distinction to make is that between understanding and speaking. The distance between the two is a given factor at the time when regular instruction begins. It is very great in some cases, and, again, slight in others, according to individual aptitude and early surroundings.

270. First of all, one’s language was acquired by hearing it spoken, by receiving it from others, by imitation; it was refined or vulgar; it was perceived accurately or indistinctly; it was imitated by organs, good, bad, or indifferent. Little by little the imperfections of the earliest stage are outgrown, where cultured persons set a daily example and insist on correctness of speech. Sometimes, however, it takes years to bring about such a result.

271. Another factor, and one deeply rooted in individual temperament, is the stronger or weaker impulse toward expression through language. This fact elevates the language of each one above mere imitation; its improvement must start from the thoughts which it seeks to express. Striking progress of this kind often occurs during adolescence.

272. Now such facts might seem to point to the conclusion that no special periods of instruction are needed for the mother-tongue, or at least not for language lessons alone. On the one hand, it might be urged that cultured teachers will improve the language of their pupils by their mere example, and by the occasional corrections which will of course be necessary; while, on the other hand, the gradual progress of mental development will shape the means of expression from within, to the natural limits of individual capacity. But before accepting the view here given, we need to remind ourselves, in the first place, that for a long time the educated teacher is only imperfectly understood by the uneducated listener, and that instruction is very much impeded if each unusual turn of expression necessitates an inquiry as to whether its meaning is clear.

273. But this is not all. Language is also to be read and written. Hence, it becomes a standing object for consideration, and, to one whose knowledge of it is deficient, a source of embarrassment. Accordingly, the first thing for the teacher to do is to show analytically, on the basis of what has been read or written, how the meaning would be lost or altered if either single words were interchanged, or the inflectional endings (especially in German) were incorrectly chosen. That the synthesis of sentences should follow next, advancing step by step toward greater complexity, especially by means of various conjunctions, may be assumed to be well understood.

274. Now if all experienced equal difficulty in their reading and writing, the language lessons designed as a remedy would commend themselves in all cases, and might fittingly be carried to the same extent everywhere.

But here the widest divergence appears. Accordingly, where many are being taught together, the teacher will seek to connect language work with other subjects. Thus, in the course of the same recitation, analytic instruction may be directed to the language side for some pupils, while for others it may be given a far wider scope. Moreover, the accompanying written exercises may have a corresponding diversity.

275. The work of a recitation period will be further diversified by the introduction of exercises in reading aloud, and in oral reproduction. But never will it be possible to raise all pupils to the same plane of proficiency. Here, above all, the determining power of individuality must be acknowledged.

276. For older boys and young men, the work in the mother-tongue will consist partly in the study of excellent examples of the various kinds of poetry and oratory, partly in the writing of essays. Such study will prove the more profitable, the more perfect the models, the more suitably they are adapted to the stage of culture already attained by the student, and the more scrupulously the teacher refrains from forcing upon him a literary taste not congenial to his nature. The least promising of all written exercises are those in letter-writing. Confidential letters every one can write, each in his own way. Best of all are written exercises with a definite and rich store of thought to draw from and admitting of various forms of treatment. Several may then emulate each other in handling the same theme, and the process of correcting will awaken greater interest in consequence.

CHAPTER VI
Greek and Latin

277. As is well known, the exposition of grammatical distinctions and of the many turns of expression whereby language may become an adequate symbolization of thought, gains very materially in clearness by a comparison of the mother-tongue with Latin and Greek. Even with boys not more than eight years old the attempt may be made to utilize this advantage in the teaching of English, whether it has been finally decided, or not, that they are to take the regular classical course. Some boys learn, without much trouble, enough of Latin inflections to enable them soon to translate short sentences from the mother-tongue into Latin, and vice versa.

278. This experiment will not, however, be long continued; since, with the large majority of pupils, the difficulties accumulate so rapidly as to lead unavoidably to the admission that the burden cannot be assumed merely for the sake of incidental advantages. Moreover, the customary view, handed down from the time of the Reformation, of the relation of the classical languages to the sciences, and to the needs of the age, is undergoing a change more and more apparent from decade to decade. The labor implied in the study of the ancient languages now pays only where talent combines with the earnest purpose to achieve the most complete scholarship.

279. The manner of teaching the ancient languages, where they are regarded as a matter of necessity or conventionality, no account being taken of pedagogical considerations, need not be discussed here. It must rather be admitted at once that no pedagogical means whatever exist, whereby those who live with their interests strictly confined to the present could be brought to acquire, with genuine sympathy, the content of the works of antiquity.

280. Pedagogically considered, every difference in the degree of vivid realization of antiquity, in the degree of its correlation with other main departments of knowledge, and in the extent to which a disagreeable aftertaste of school-day drudgery is prevented, determines the greater or smaller value to be ascribed to the knowledge acquired. If the same realization could be secured without the ancient languages and without the potency of early impressions, then the studies mentioned in preceding chapters, which outline the work of burgher schools, would leave nothing further to be desired; and the study of the ancient languages in gymnasia would be a necessary evil, highly as their incidental advantages are usually extolled.

281. But languages alone give to a boy a picture neither of bygone ages nor of men of the past; to him they are solely troublesome tasks imposed by the teacher. Nor can golden maxims, fables, and short narratives change his attitude. For even if these are well suited to the youthful mind, they do not materially offset the aversion to the work on stems, which have to be memorized; inflections, which must be practised; and conjunctions, which are required for guidance in the study of periods.

Ancient history (243, 246) is the only possible groundwork for the pedagogical treatment of the ancient languages.

282. Now it is true that if Latin is begun first, Eutropius and Cornelius Nepos suggest themselves as suitable authors for study, as soon as the merest rudiments of Latin have been learned in connection with instruction in the mother-tongue(277). And their use is not to be entirely condemned, provided the teacher takes it upon himself to make the past present through narration. But, as is well known, these authors are after all very meagre, and, besides, where to look for a path beyond them still remains an open question.

283. The reasons which accord to Homer’s “Odyssey” the preference for early use are familiar.[41] They are patent to every one who attentively reads the “Odyssey” with constant reference to the various main classes of interest which teaching is to awaken(83–94). But the question involved is not merely one of immediate effect, but also of finding points of departure for the later stages of instruction. There can be no better preparation for ancient history than to establish an interest in ancient Greece by means of the Homeric story. At the same time, the soil is being made ready for the cultivation of taste, and for language study.

To reasons of this kind, derived directly from the chief aim of all teaching and opposed only by tradition (the conventional doing of the classics), the philologists will have to listen some time, if they are not willing that, with the growing importance of history and of the natural sciences, and with the increasing pressure of material interests, the study of Greek in schools should be pushed into a corner and suffer a reduction similar to that which has already taken place in the case of Hebrew. (A few decades ago Greek came very near being remitted for all but those intending to study theology.)

Of course, the “Odyssey” possesses no miraculous power to inspire those who have no talent whatever for language studies or do not take them seriously; nevertheless, as many years of experience have shown, it surpasses every other work of antiquity that might be selected in definite pedagogical effect. Moreover, its study does not preclude an early commencement of Latin (nor even of Greek, where that seems necessary); only Latin cannot be pushed with the customary rapidity at the same time; for the “Odyssey” requires an hour daily, and grammatical and lexicological work besides.

Experience has proved that the grammatical rudiments pertaining to declension and conjugation must be worked over very carefully first, although reduced to what is absolutely essential. Besides, the first lessons in the “Odyssey” ought not to exceed a few lines each time; and, during the first months, no accurate memorizing of words is to be demanded. But farther on the acquisition of a vocabulary must be vigorously insisted on; in fact, it becomes the pupil’s most necessary collateral work. By continued effort in this direction a considerable portion of the whole stock of words is gradually acquired; the language forms are supplied with the content to which they refer, and through which they become significant. The teacher must know exactly, not only when to hasten on, but also when to delay; for every perceptible gain in facility is likely to betray pupils into some carelessness which needs to be corrected at once. With good pupils it is not infeasible to read the whole of the “Odyssey,” since facility increases very rapidly toward the end. Nevertheless, such work should not extend much beyond two years; otherwise weariness sets in, or time is taken from other things. In schools it will be well to assign the first four books to one class, perhaps the class composed of pupils nine or ten years old, the next class to begin with BookV. To determine exactly how many books each class can work up thoroughly is unnecessary, as good translations can be used to fill in the gaps that occur. The reason for the division just made will be manifest at once upon a closer inspection of the “Odyssey.” Some books more advanced pupils may later on read by themselves, but they should be expected to render an account of what they are doing. It is not necessary at this stage to explain in detail the rarer peculiarities of the Homeric dialect. Such things may well be deferred until, later in the course, the study of Homer (of the “Iliad”) is resumed. The teacher who is afraid of the difficulties connected with the plan presented should remind himself of the fact that progress by any other path is equally beset with difficulties. While at work on Homer, care should be taken to keep pupils from being influenced simultaneously by such tales as those from the Arabian Nights, because they blunt the sense of the wonderful.

284. Only two poets, two historians, and two philosophers need to be mentioned to indicate the continuation of the course. Homer and Virgil; Herodotus and CÆsar; Plato and Cicero. What authors should precede these, or should intervene, or follow, may be left for circumstances to determine. Xenophon, Livy, Euripides, Sophocles, and Horace will probably always retain a place by the side of those mentioned; Horace especially offers brief maxims, the after-effect of which the educator should by no means underestimate. It is obvious that Virgil and Herodotus are rendered much easier by taking up Homer first; on the other hand, the return to Homer (to the “Iliad”) during adolescence, is as little to be omitted, if only on account of mythology, as the return to ancient history for purposes of pragmatic study(250). Again, the syntactical scheme of the ancient languages, which involves far greater difficulties than do even inflections and vocabulary, is more easily mastered by placing the poets before the prose-writers, because then the pupils are not compelled to struggle with all the difficulties of sentence structure at once. At any rate, it is desirable that, just as the student’s Greek vocabulary is built up from the “Odyssey,” his hoard of Latin words should be drawn from the “Æneid.” The latter, however, will hardly be read entirely, because it cannot be gone over with nearly the same rapidity as the latter books of the “Odyssey,” when facility in reading has been attained. CÆsar’s “Bellum Gallicum” must be studied with exceptional carefulness, since its style comes nearer to being a desirable first model for the student of Latin than the style of the other authors in use. After this has been accomplished, the strictly systematic teaching and memorizing of Latin syntax, together with selected brief examples, is in order as one of the main lines of work. In Plato several books of the “Republic,” especially the first, second, fourth, and eighth, constitute a desirable goal. That Cicero should be revealed to young minds on his brilliant side first, namely, as orator, need scarcely be mentioned. Later on his philosophical writings become important; but many passages require a fuller development of the subject-matter than is given by him.

Cicero should frequently be read aloud, or rather declaimed, by the teacher. An orator demands the living voice; the usual monotonous reading by the pupils fails to do justice to him. As regards Tacitus for school use, there is a difference of opinion. Generally speaking, authors that say much in few words are particularly welcome, not merely to the explaining teacher, but also to the responsive pupil. The opposite is true of Cicero; he must be read rapidly in order to be appreciated.

285. Experience has long since shown how much or how little can be done with students in Greek and Latin composition; and no method will ever be devised which would induce earlier than at present that degree of mental maturity which reveals itself in a good Latin style. So long as gymnasium pupils are no more select than they now are, the majority, so far as writing Latin is concerned, will begin something that will never lead to successful performance. It would be better, instead, to practise diligently that which can be achieved, namely, composition during the recitation hour, with the assistance of the teacher, and, afterward coÖperative consideration of the appointed task, by the pupils. This plan secures the advantage of set essays without the disadvantage of innumerable mistakes, the correction of which the pupil rarely remembers. Joint labor is interesting, and can be adapted to every age. As a substitute for essays, abstracts in Latin of texts previously interpreted are to be recommended, these abstracts to be made at first with the help and afterward without the help of the book in question. To abstract does not mean to imitate, and ought not to mean that. To imitate Cicero requires Cicero’s talent, and unless this exists, the attempt to imitate, it is to be feared, will result in cold artificiality. Even CÆsar is not so simple that his style could be taught and learned. But many passages of CÆsar may be memorized; at first short sentences, then longer periods, finally whole chapters. The usefulness of this practice is attested by experience.

CHAPTER VII
Further Specification of Didactics

286. The more precise determination of the theory of instruction depends on the nature of particular subjects of instruction, on the individuality of the pupil, and on the external conditions of ethical life.

287. Where the goal to be reached is technical knowledge and multiformity of scholarship, each branch of study asserts its claims to thoroughness without regard to the rest. Such is the attitude of the state, which requires many men with special training, together constituting an efficient whole. Hence it disseminates knowledge and establishes institutions of learning, without inquiring, save with reference to future official appointments, who the individuals are that avail themselves of the offered opportunities.

288. The family, on the other hand, interested as it is in the individual, must take the pedagogical point of view, according to which every human being is to realize the best he is capable of. It is essential that families should grasp this distinction, and accordingly concern themselves, not with greatness of particular achievements, but with the totality of culture possible for the individual.

289. Closely connected with the foregoing is the difference between interest and skill. Skill of various sorts can be obtained by force; but it is of no value to general culture when the corresponding interest is lacking.

Insistence on this distinction is a sufficient answer to much uncalled-for criticism and much unwarrantable assumption of superior knowledge concerning the results of early stages of instruction. These results, it is charged, are inadequate; if this or that had been converted earlier into ability to do, greater progress would have been made. But when interest has not been aroused, and cannot be aroused, compulsory acquisition of skill is not only worthless, leading as it does to soulless mechanical activity, but positively injurious, because it vitiates the pupil’s mental attitude and disposition.

290. Whether the pupil’s individuality will endure without injury the pressure which drill in skilful performance would necessitate, is a question which at times cannot be decided except by trial. Reading, arithmetic, grammar, are familiar instances.

291. The more perfect the instruction, the greater the opportunity it affords for comparing the excellences and faults of the individuals receiving it simultaneously. This point is of importance both to the continuation of instruction and to training; to the latter, because the teacher’s insight into the causes of the faults which training has to combat is deepened.

292. The ethical life may attach itself to views embracing the universe; it may, on the contrary, move within a very narrow range of thought. Now while it is true that external circumstances will usually set limits to instruction, its scope should nevertheless not be narrower, but in every way wider than the realm of necessary, everyday prudence. Otherwise the individual will always be in danger of exaggerating his own importance and that of persons closely related to him.

293. It is more difficult, as a rule, to extend the mental horizon in the direction of the past, than within the present. In teaching girls, therefore, and children from the lower classes, greater prominence is given to geography and whatever can be grouped about it than to historical studies. Again, in cases where a shortening of the course of study becomes necessary, it becomes well-nigh necessary to take account of the difference in question. But, conversely, where the scope of instruction is to be wide, the historical side, because more difficult, must receive increased attention.

294. Some faults are inherent; they are a part of the pupil’s individuality. Others have sprung up in the course of time; and of these, again, some have been influenced by the factor of individuality more than others. Faults that the pupil commits are left out of account for the present. With increasing years some of the inherent faults grow, others diminish. For there is a continual change of relation between that which man derives from experience,—between those ideas which rise spontaneously, and those masses of ideas which approach stability. There is, besides, an ever varying succession of diverse reproductions. All this change is pervaded throughout by the consciousness of one’s own body (the original base of support for self-consciousness) with respect not merely to its needs, but also to its powers of motion and fitness for use. Again, the apprehension of the similar is being multiplied; the ideas of things approximate to general concepts. In addition, the process of judging is shaping more and more the material presented; accordingly the manner in which the individual analyzes and puts in order his knowledge becomes gradually determined. On the one hand there is a growing confidence of affirmation; on the other, questions remain, the answer to which is given over to the future. In part they become transformed into longing expectation.

Upon all that has been enumerated, the physical organization of the individual exerts retarding and furthering influences. The effect of the body is seen in a certain physiological resistance to psychical processes, and in strong physical impulses far more complex, no doubt, than ordinary experience shows.

295. Very frequently the fact forces itself upon us, that persons who have passed through many vicissitudes of fortune can nevertheless be recognized by individual traits that were already noticeable in youth. Here a certain uniformity reveals itself in the characteristic way and manner in which such persons involuntarily seize upon and work up various impressions. In order to arrive at a just estimate of his pupils, the teacher should observe this permanent element as early as possible.

Some always know the right moment and whither it calls them; they always perform the nearest duty, and have their stock of knowledge uniformly well in hand. Others bury themselves in thought, and give themselves up to hopes and fears, to plans and projects: they live in the past or in the future, resent being disturbed by the present, and require time and effort to bring themselves back to it. Between the former and the latter are found others, who do indeed note the given and the present, not, however, to take it as it appears, but rather to look beyond, for the purpose of spying what lies concealed behind, or in order to move, displace, interfere, perhaps to distort, ridicule, and caricature. With many the tendency described is merely superficial. They play and tease—a common manifestation of youthful animal spirits. Now the question arises: how much seriousness lies back of the playfulness. How much depth beneath the animated surface? Here temperament enters as a factor. The play of one with a sanguine temperament comes to an end; but where sourness of temper is habitual, there danger threatens, if, as commonly happens, sport turns to earnest. Self-assertion plays a part also, manifesting itself in various ways. It assumes one form in him who has confidence in his strength, physical or mental, and another form in those who know their weakness—with or without the mental reservation as to the future employment of artifice or cunning, and so also with more or less acknowledgment of the superior power or authority. Passionate playing, on the whole, implies little seriousness; but may well indicate sensitiveness and a propensity to freedom from restraint. Prudence in sport is a sign of ability to take the opponent’s point of view, and to foresee his plans. Love of play is far more welcome to the teacher than indolence, or languid curiosity, or gloomy seriousness; it is one of the minor faults, if now and then work is forgotten over a game and time wasted; the situation is more grave, sometimes very grave indeed, where extravagance, or greed of gain, or secretiveness, or bad company is involved. In such cases decided interference on the part of the teacher is necessary.

296. Since courage and rationality grow with increasing years, the faults of mere weakness leave room for hope of improvement, although there is need of an invigorating mode of life, invigorating physically and mentally, and of counsel and reproof in particular instances. Under continued watchful care weak natures improve much more than at first thought would seem to be likely.

297. Unsteadiness, continual restlessness, where they accompany good health without being the result of external stimulation, are doubtful indications. Here it will be well to look to the sequence of thoughts. Where, in spite of variableness in general, thoughts are sound and well connected, this restlessness is not a serious matter. The case is worse when the opposite is true, especially when the vascular system appears very irritable, and dreamlike reveries occur. Here the danger of insanity is seen lurking in the distance.

The appropriate treatment for such pupils consists in holding them strictly to definite tasks, especially to those occupations that compel a close observation of the external world, and in exacting the performance of the work assigned, without failing to encourage whatever is undertaken from choice.

298. Sensual impulses and violence of temper are apt to go from bad to worse as pupils grow older. Against these, careful supervision, earnest censure, and the whole rigor of moral principles must be brought to bear. Momentary ebullitions of passion, however, unless persistently obstinate attempts are made to justify them, need to be handled gently, that is, as evils calling for precaution and vigilance.

299. The faults hitherto noted lie for the most part on the surface. Others have to be studied as occasion offers in instruction.

There are minds so dull that even the attempt merely to secure connection with definite portions of such thoughts as they have does not succeed. Easy questions intended to raise their ideas into consciousness only increase the resistance to be overcome. They are seized with embarrassment from which they seek to escape, sometimes by a simple, “I don’t know,” sometimes by the first wrong answer that comes to hand. Mental activity has to be enforced, yet remains feeble at best, and it is only in after years, under pressure of necessity, that they acquire some facility for a limited sphere. Others, whom one would be inclined to call contracted rather than generally limited, because by them reproduction is performed successfully but within a narrow compass, exhibit a lively endeavor to learn, but they learn mechanically, and what cannot be learned in that way they apprehend incorrectly. These undertake, nevertheless, to form and express judgments, but their judgments turn out to be erroneous; hence they become first discouraged and then obstinate. Again, there are those whose ideas cannot be dislodged, and still others whose ideas cannot be brought to a halt. These two classes call for a more detailed consideration.

300. Among the various masses of ideas(29) some necessarily acquire permanent predominance, others come and go. But if this relation reaches full development and becomes fixed too early, the controlling ideas no longer admit of being arrested to the extent necessary for the reception of the new material offered by instruction. This fact explains the experience that clever boys, notwithstanding the best intentions to receive instruction, yet frequently appear very unreceptive, and that a certain rigidity of mind, which in later manhood would not occasion surprise, seems to have strayed, as it were, into boyhood. No one should allow himself to be betrayed into encouraging such narrowness by commendatory terms such as pertain to strength and energy; just as little, however, should clumsy teaching and its sequel, listless learning, be left out of account, as having no bearing on this state of affairs.

For, rather may it be assumed that the fault mentioned might have been largely forestalled by very early instruction of all kinds, provided such instruction had been combined with a variety of attractive rather than of too difficult tasks. Where, on the other hand, mental nervousness has once taken root, it cannot be eradicated by all the art and painstaking effort of a multitude of teachers. When the questions of a child, six years old let us say, give rise to the apprehension that they proceed from a too contracted mental horizon, there should be no delay about resorting to manifold forms of stimulation, especially in the way of widening the pupil’s experience to the greatest practicable extent.

301. On the other hand, it is not rare to find boys, and even young men, in whose minds no one thought-mass attains to any very prominent activity. Such boys are always open to every impression and ready for any change of thought. They are wont to chat pleasantly, and to form hasty attachments. Here belong those who learn easily and forget as quickly.

This defect, too, when once confirmed, resists all skill and good intentions; strength of purpose, from the very nature of the case, is out of the question. The situation varies in gravity, however, according to the influences of the earliest environment. If these proved distracting, the fault mentioned assumes alarming proportions even in minds otherwise well endowed. But where some form or other of necessary respect has been steadily at work, the youth will raise himself to a higher plane than the boy gave promise of doing. Least of all, however, can the teacher allow himself to be betrayed into hoping for a future development of talent by superficial alertness, combined, it may be, with droll fancies, bold pranks, and the like. Talent reveals itself through persistent endeavor, sustained even under circumstances little favorable to it, and not until such endeavor clearly manifests itself is the thought of giving it support to be entertained.

The two faults under discussion may indeed come to light only in the course of time; nevertheless, they are inherent faults, and can be mitigated, to be sure, but not completely cured.

302. Far easier to deal with are the erratic movements of energetic characters capable of ardent enthusiasm. The mere thoroughness and many-sidedness of good instruction, which emphasizes and aims to effect rational connection and balance of mind, obviously supply the corrective.

303. Originally it would have been easier to have prevented those faults which are due to the mismanagement or to the omission of early government, instruction, or training. But with time, the difficulties of a cure grow in a very rapid ratio. In general, it is well to note that the teacher has every reason to congratulate himself, if, after early neglect, there appear under improved treatment some belated traces of those questions which belong to the sixth or seventh year of childhood(213).

CHAPTER II
The Sources of Moral Weakness

304. Under this head five main points come up for consideration:—

• (1) Tendencies of the child’s will impulses.
• (2) Ethical judgments and their absence.
• (3) Formation of maxims.
• (4) Organization of maxims.
• (5) Application of organized maxims.

305. (1) Where training has not provided for occupation and for the distribution of time, we must always expect to encounter an activity which has no aim, and which forgets its own purposes. From such a state of affairs arise a craving for liberty averse to all control, and, where several pupils are grouped together, contention, either for the possession of something or for the sake of showing off. Each wants to be first; recognition of the just equality of all is deliberately refused. Mutual ill-will intrenches itself and stealthily waits for an opportunity to break forth. Here is the fountain head of many passions; even those which spring from excessive sensuousness must be classed under this first head, in so far as they are promoted by lack of regulated activity. The havoc caused by passions is a pervading element in the discussion of all of the remaining topics.

306. (2) It is true that education usually counteracts the tendency to indolence and to unruliness, not only by the use of the spur and the bridle, but also through guidance in the direction of the proprieties; giving rise to the thought “what will others say,” it shows existing conditions as mirrored in the minds of others. But when these others are compelled to remain silent, or when the pupil is sure of their partiality, or is exposed to their errors of judgment, the effect is to vitiate rather than to arouse the ethical judgment.

Nevertheless, calling attention to the judgment of others, and not merely of particular individuals, is very much better than waiting for the spontaneous awakening of ethical judgment. In most cases the waiting would be in vain. Matters of ethical import are either too close to the ordinary human being, and so, of course, to the boy left entirely to himself, or they are too remote, i.e., either they have not as yet passed outside the pale of affection or aversion, or else they are already fading from the field of vision. In neither case can an ethical judgment be formed with success. At any rate, it will vanish before it can produce an effect.

In order to reach those ethical judgments on which morality rests, the child must see will images, see them without the stirring of his own will impulse.

These will images, moreover, must embrace relations, the single members of which are themselves wills, and the beholder is to keep such members equally in sight, until the estimate of value rises spontaneously within him. But such contemplation implies a keenness and calmness of apprehension not to be looked for in unruly children. Hence it may be inferred how necessary training is—serious, not to say severe, training. Unruliness must have been tamed and regular attention secured. The preliminary condition fulfilled, it is further essential that there shall be no lack of sufficiently distinct presentations of the foregoing will images. And even then the ethical judgment often matures so tardily that it has to be pronounced in the name of other persons—persons higher in authority.

307. In this connection the instances of one-sidedness of ethical judgment must not be overlooked, such as occur when one of the practical ideas stands out more prominently than another, or when that which is outwardly proper rises above them all.

308. (3) All desires persistently operative and productive of fluctuating states of emotional excitement, therefore rightly called passions, lead to experiential knowledge of the beneficial and the injurious. The beneficial suggests frequent repetition in the future, the injurious continued avoidance. Accordingly rules of life take shape, and the resolution always to observe them is made. In other words, maxims result.

From simple resolution to actual observance is still, to be sure, a far cry. But the claim for the universal validity of the rule, so that the individual may regard it as applicable to others as well as to himself, enters the mind far more directly by way of desires which point forward to similar cases in the future, than it does under the guidance of ethical judgments whose universal element is abstracted from given single instances with difficulty. In fact, this difficulty is often so great that the ethical judgment itself may be missed in the search for the universal.

309. Now, the promptness and loyalty of obedience to the sum total of duties, once recognized as such and fixed through the maxims adopted, are passed upon by the moral judgment. Correct moral judgment, therefore, presupposes true insight into the value of will, which insight again can be obtained only through the ethical estimate as a whole. But in view of the circumstances pointed out a moment ago, we must expect to come upon maxims that are false or at least inaccurate. Under the latter head fall points of honor, social obligations, fear of ridicule.

310. (4) Maxims ought to form a unit, but in youth they are not fully determined even singly, much less are they closely united into a definite whole. The proviso of exceptions still clings to them, so also that of future tests through experience.

The maxims arising out of the desires and pleasures can never be brought into perfect union with those springing from ethical judgments. Accordingly the wrong subordination takes place, or, at all events, a contamination of the latter by the former.

311. (5) In the application of maxims more or less unified, the volition of the moment is apt to prove stronger than the previous resolves. Hence, man becomes only too prone to condone and fall in with discriminations between theory and practice. The consequence is a certain moral empiricism, which, if nothing else will do to justify its disregard of moral law, falls back upon pious feelings. Plans of action are formed without regard to maxims, but with the apparent compensation of another kind of morally regular life.

Such contempt of moral judgment gains ground and spreads ruin all the more, the farther the ethical judgments on which morality must rest fall short of the clearness that ought to mark them, and the cruder the pupil’s knowledge is of the antithesis between them and maxims of utility or pleasure.

312. The natural aid to the formation and union of maxims is the system of practical philosophy itself. But the teaching of it involves difficulties. One of them is that such marked differences occur among young men in the relation of systematic exposition to the grade of culture which they have attained. For observations of this nature, religious instruction prior to confirmation provides an early opportunity. How such instruction is to be given, is, of course, by no means immaterial, but, after all, the moral sentiments, which it gathers together and strengthens, must, in substance, already exist.

Again, if the end sought were more strictly scientific form for the moral sentiments, there would have to be ground for presuming that the student is able to appreciate that form and has acquired skill in the use of logical methods. The study of logic, together with appropriate exercises, would obviously be a necessary preliminary step. Prerequisites like these need to be borne in mind, especially in the case of lower schools and all other institutions that do not, as a rule, lead to the university.

313. Erroneous systems of ethics, moreover, might occasion the adoption of very absurd measures, concerning which, on account of the importance of the subject, at least something has to be said. Everything would be turned upside down, if, instead of bringing together and uniting maxims under the concept virtue, the attempt were made to deduce from some one formula of the categorical imperative a multiplicity of maxims and from these, rather than from the original ethical judgments, the estimates of will values, the final undertaking being, perhaps, to divert the will itself by such operations.

On the contrary, the will must early have been given such direction by government and training, that its lines of tendency will of themselves coincide as nearly as possible with the paths disclosed later, when the pupil is being shown the way through ethical judgments. Those beginnings of evil noted above(305) must not be permitted to appear at all, for their consequences usually prove ineradicable. But even so, it is not certain that a way can be hewn through the errors of others to truer judgments. When, however, both ends have been gained, experience and history and literature must next be called in, in order to show clearly the confusion into which the maxims based upon pleasure and passion plunge human beings. Not until now has the time come for more or less systematic lectures, or for the study of suitable classical writers. Lastly, there will still be need of frequent appeals to moral obedience, and it will be found necessary to reinforce these appeals by reflections of a religious character.

CHAPTER III
The Effects of Training

314.

1. Training prevents passions in that it:—
   • (1) satisfies needs,
   • (2) avoids opportunities for violent desires,
   • (3) provides employment,
   • (4) accustoms to order,
   • (5) demands reflection and responsibility.
2. Training influences the emotions in that it:—
   • (1) checks violent outbreaks,
   • (2) creates other emotions,
   • (3) and supplements self-control.
3. Training impresses the courtesies of life (counteracts bad manners), consequently:—
   • (1) the deportment of individuals is made approximately uniform;
   • (2) the number of possible points of social contact becomes much greater than where strife and contention rule;
   • (3) while the development of one or the other individual is checked, the more important energies are not stifled, provided excess of severity be avoided.
4. Training makes cautions, for:—
   • (1) It restricts foolhardiness,
   • (2) It warns against dangers,
   • (3) It punishes in order to make wiser,
   • (4) It observes and accustoms the human being to the thought of being observed.

315. Looked at as a whole, these obvious and familiar effects of training show at once that, generally speaking, its power to lessen evil is very great, and that it is capable of effectively acting upon the interrelations of various masses of ideas. But they suggest also the presence of danger. Training, by driving evil from the surface, may give rise to clandestine deeds.

316. When this happens, the relations between teacher and pupils grow increasingly abnormal, since secret practices become general and concerted, and the pupils assume a studied behavior in the presence of the teacher.

The consequences are well known:—Inexorable severity in dealing with concealed offences when discovered; great leniency in the case of open transgressions; recourse to the machinery of supervision, often even to secret watching, in order that the system of concealment may not get the better of education.

317. It lowers the dignity of the teacher to take part habitually in a competition between spy and concealers. He must not demand to know everything, although he ought not to allow his confidence to be victimized by clumsy or long-continued deception.

Such difficulties, however, only make it more intensely necessary that the foundation of education be laid during the earliest years, when supervision is still easy, and the heart is reached by formative influences with greater certainty than ever afterward, and that, if possible, families should not for any length of time lose sight of their own members.

Ethical and moral judgments can be simulated; the finest maxims and principles may be learned by rote; piety may be put on as a cloak. Unmask the hypocrite, however, and turn him out, and, forthwith, he plays his game over again elsewhere. Nothing remains but recourse to severity which deters, and constant occupation under close supervision in another quarter, in order that he may get away from the hiding places of his misdeeds. Sometimes banishment is capable of bringing about improvement.

318. The will is most directly tractable in social relations, where it appears as common will. In infancy, the child, wholly devoted to his mother, is manageable through her; at a later period training is surest of success when it promotes attachments among the young and carefully fosters the seeds of goodness. The social ideas, purified by teaching, must gradually be added.

319. But as far back as boyhood, factions spring up and exclusive sets are formed, facts which the teacher cannot permit to elude his vigilance.

When a kind of authority is granted to some older and tried pupils over those younger and less mature in judgment, the former become responsible; but the latter are not on that account relieved of all reflection on their own part, nor are they obliged to submit to every, though plainly unreasonable, demand of the former.

CHAPTER IV
Special Faults

320. First of all it is necessary to distinguish between those faults which the pupil commits and those which he has. Not all faults one commits are direct manifestations of those he possesses; but those which are committed repeatedly may grow permanent. This truth must be made clear, and must be impressed upon the mind of the pupil to the full extent of his powers of comprehension.

321. In the case of false steps caused from without by unnoticed pitfalls, or made in spite of a firm resolve to the contrary, the pupil is himself usually frightened by what he has done. If so, all depends on the gravity of his offence as compared with the degree of his horror.

There is a host of minor faults, blunders, and even acts resulting in damage, which tax the patience of the teacher severely; but it would imply a mistaken conception of the difficulty of moral education, if he should repel the frankness of his pupils by harsh treatment of such offence. Frankness is too essential a factor to be sacrificed; once gone it will hardly ever wholly return.

322. But the first lie uttered with evil intent, the first act of theft, and similar actions positively detrimental to morality or health, have to be dealt with severely, and always in such a way that the pupil who thought he was permitting himself a slight fault, is made to experience most thoroughly both fear and censure.

323. Serious treatment of a first offence is demanded also where pupils try to see how far they may safely disregard authority and command. It is important, however, not to overestimate the intention of these attempts; important also to exhibit strength, but not anger. Yet there are cases where the teacher must seem to act with some warmth, because the necessary treatment, if combined with coldness, would only intensify bitterness and cause pain an inordinate length of time. But very likely as much feeling as is expedient will show itself upon simply laying aside the assumed coldness.

324. On the restoration of perfect order after a period during which government and training were lacking, a large number of faults will disappear of themselves, and accordingly do not require to be combated one by one. Respect for order, and incentives sufficiently strong to regular activity, are the main things.

325. Faults which the pupil seems to possess are often only the borrowed maxims of the society which he hopes to enter. Here it becomes the business of education to set him right, if possible, and to elevate his view of human relations, in order that he may disdain the false appearances he before held in esteem.

326. Faults which an older pupil actually possesses rarely occur singly. Moreover, they are seldom fully disclosed; their appearance is determined by a prudent regard for circumstances. During the period of education such faults can, indeed, be largely prevented from growing worse, but the radical improvement of those who are secretive from prudence is rarely to be thought of before they have become more prudent still, too proud for concealment, and more susceptible to the true estimate of moral values.

Where older boys and young men are found to possess unused talents, and where instruction can be so arranged as to develop them, there is some prospect of supplying a counterbalance to those habits which have been contracted. But, in general, efforts looking toward a lasting reform are successful only when made at an early age. At all events, where there is much to amend, the feeling of dependence on strict training must be kept alive for a long time.

327. More success is likely to attend the endeavor to correct those faults which are not tolerated within the social class of which the pupil regards himself a member. Two factors determine the proper mode of procedure: the importance of making the pupil acquainted with the worthiest side of his social group, and, on the other hand, the unavoidable necessity of causing him to see its less noble features in case he discovers in it free scope for his inherent faults.

328. Here the pupil’s capacity for education, as well as the limits of that capacity, are brought home to the teacher. As boys approach manhood, they let birth and external circumstances designate for them that class of society to which they will belong. The class defined, they seek to acquire its form of life, and to get into its main current. On the way thither they accept and take along so much of higher motives, of knowledge and insight, as, on the one hand, instruction offers and training favors, and as, on the other hand, the individuality of each one, which the earliest impressions have further determined, is ready to assimilate. Those are rare exceptions who, through the development of an absorbing interest of some kind, in religion, or science, or art, have become less susceptible to the attractive force of their social class. Their course has been marked out by the instruction which induced the absorption; henceforth they are self-actively engaged in the pursuit of whatever accords with the end in view, and accept only a small part of what is presented to them.

329. Specific forms of a pupil’s attitude toward society, especially the relative prominence in his mind of state or family relations, will have to receive due consideration in marshalling motives to counteract particular faults. Indeed, the same is true of the appeal to those motives through which it is sought to establish a preponderance of worthier endeavor over moral imperfection in general.

330. On discovering that his own efforts encounter impediments, the individual teacher might easily come to think that society could do everything, if it only would, and if it possessed the necessary insight. Further reflection, however, reveals the existence of difficulties peculiar both to state and family.

331. The state needs soldiers, farmers, mechanics, officials, etc., and is concerned with their efficiency. Its attitude toward a large number of persons, whose existence as individuals has significance only in a narrow sphere, is, in general, far more that of supervision designed to prevent the harm they might do, than one of direct helpfulness. He who is able to render competent service receives preferment; the weaker has to give way to the stronger; the shortcomings of one are made good by another.

332. The state applies its tests to what can be tested, to the outward side of conduct and of knowledge. It does not penetrate to the inner life. Teachers in public schools cannot penetrate much farther; they, too, are more concerned with the sum total of knowledge imparted by them, than with the individual and the way in which he relates his knowledge to himself.

333. To the family, however, no stranger can make up for what one of its members lacks; to the family the inner condition becomes so manifest, and is often felt so keenly, that the merely external does not satisfy. It is obvious, therefore, that moral education will always remain essentially a home task, and that the institutions of the state are to be resorted to for educative purposes only with a view to supplementing the home.

But on closer inspection it is found that family life is very often too busy, too full of care, or too noisy, for that rigor which is undeniably required both for instruction and for morality. Luxury and want alike harbor dangers for youth. Consequently families lean on the state for support more than they ought.

334. Private institutions as such do not possess the same motive power as either state or family, and are seldom able to make themselves independent of the comparisons to which they are exposed, because of the fact that they are expected in one case to take the place of the state schools, and in another that of the family.

Nevertheless, sturdy minds which do not require the emulation obtaining in schools can be advanced more rapidly, and instruction adapted more easily to individual needs, than in public institutions. As for training, moreover, the evils that may spring from environment can be prevented more successfully than is possible in many families.

If the institutions in question could choose from among many teachers and many pupils, they might, under otherwise favorable circumstances, be able to achieve great results. But the fact of a picked set of pupils alone shows how little the whole need of education would be met. Besides, even those that were chosen would bring with them their earliest impressions; they would incline toward the social conditions for which they believe themselves to be destined; the faults of individuality(294 et seq.) would cling to them, unless such faults were recognized before the selection, and were avoided by exclusion.

335. As much as possible, then, education must return to the family. In many cases private tutors will be found to be indispensable. And of instructors excellently equipped as to scholarship, there will be the less lack, the better the work done by the gymnasia.

It must be noted, also, that instead of being the most difficult, the most advanced instruction is the easiest of all, because imparted with the least departure from the way in which it was received. People are therefore mistaken when they assume that private tutors are capable of furnishing an equivalent only for the lowest classes in gymnasia. A far greater difficulty lies in the fact that even the most skilful and active tutor cannot give as many lessons as a school provides, and that accordingly more has to be left to the pupil’s own efforts. To be sure, this is exactly the mode of instruction which suits the bright student better than one that must accommodate itself to the many, and which on that account must progress but slowly.

336. But home education presupposes that sound pedagogical views have been arrived at in the home, and that their place is not occupied by absurd whims or half knowledge. (Niemeyer’s famous work, “The Principles of Education and of Instruction,” is intelligible to every educated person, and has been widely known for many years.)

337. The necessity of sound pedagogical knowledge in the home becomes all the more urgent where teachers, private or public, change frequently—whereby inequalities of instruction and treatment are introduced which need to be corrected.

CHAPTER II
Concerning Schools

338. The school system and its relations to local authorities, on the one hand, and to the general government, on the other, form a vast and difficult subject involving not merely pedagogical principles, but also such aims as the maintenance of higher learning, the dissemination of useful information, and the practice of indispensable arts. In university lectures a few words on such topics suffice, since young men who accept a school position assume, at the same time, obligations which for a long time to come prescribe for them the path they must follow.

339. They must, in the first place, consider the character of the school in which they are to instruct. The school programme provides them with information concerning the scope of the curriculum, the established relations of the branches of instruction to one another, and the various stages in each subject. The teachers’ conference affords them an insight into multiplex relations to authorities, parents, and guardians, and to the pupils, also relations leading to coÖperation, more or less perfect, on the part of the teachers. The whole of the educational effort directed upon younger, intermediate, and older pupils is presented in one view; it is known also where the pupils come from, with what kind of preparation, and where as a rule they go upon leaving the school.

340. It must obviously make a vast difference whether pupils look forward to the university, or whether the gymnasium is filled with boys who do not intend to pursue higher studies; whether a burgher school sets a final examination to mark the stage of general culture to which the school is expected to advance the pupils, or whether the pupils enter and leave without well-defined reasons according to what seems best to their respective families; whether an elementary school is conducted merely as an institution preparing for gymnasia or burgher schools, or whether its course provides for the suitable education, during his whole boyhood, of the future artisan, etc.

The American school system possesses this great advantage over that of Germany,—it has an educational ladder planted in every elementary school upon which any child from any social class may mount as high as his ambition incites, or his means and ability permit. It is the only suitable system in a democracy, where opportunity should be open to all. Even to obtain greater perfection than the German school system has ever attained, a democratic nation cannot afford to impair its present organization, in so far as it makes advancement possible to every aspiring soul.

341. In each case the official activity entered upon must adjust itself properly to the whole, the outlines of which are given. These determine the proportion and the subdivision of the store of learning to be kept ready for use, the degree of confidence to be shown to pupils as to knowledge already acquired, and the manner in which they are to be addressed. It is important that the teacher should appear before his class adequately prepared and with confident self-possession, that he should look about attentively at every one and make each pupil feel at once that it would not be easy for him to undertake anything without being noticed.

342. The questions to be put to the pupils need to be formulated clearly and concisely, and they must follow each other in easy sequence. The answers must be corrected and, when necessary, repeated, in order that all may hear them. No pause should be unduly prolonged; no explanation to the weaker pupil should be allowed to become oppressively tedious to the more advanced. Those who are at work at the moment must be assisted, but ought not to be disturbed by much interrupting talk. The current of thought is to be invited and accelerated in all, but not hurried, etc.

Such requirements instruction will meet with greater or less difficulty, according as classes are small or large and the inequality of pupils great or slight.

343. In the assigning of work the capacity of each pupil must be taken into account as much as possible, in order that no one may surrender to ill-humor and discouragement on account of excessive demands, nor any one permit himself carelessly to abuse a task too easy for him.

344. Inequalities of division resulting from rearrangements of classes, or other changes, must be pointed out to the authorities as clearly as possible, for the purpose of urging a more even distribution and a reduction of excessive numbers.

345. In the course of the gradual extension of such efforts many a defect will come to light. It may be found, for instance, that the school is not a whole, because of the lack of a competent teacher for an important subject, or because of marked inequalities of knowledge and culture due to the preparatory schools, or because the school (such as those in small towns) follows the curriculum of a gymnasium while its real aim is supposed to be that of a burgher school, etc.

346. Reports of such single defects will as a rule lead only to correspondingly partial improvements in the system and to relief from the most onerous perplexities, since it is seldom found possible to organize the system of a whole province at once in such a way as to make one harmonious whole.

347. But in case comprehensive reforms of the school system were undertaken, it would be necessary not merely to tolerate great multiformity, but even to create it purposely. For division of labor is in all human performance the right path to better things; and the preceding discussion must have shown with sufficient clearness how much depends on a more discriminating segregation of pupils.