UNIVERSITY OF CALIFORNIA AT LOS ANGELES THE ESSENTIALS OF METHOD. A DISCUSSION OF THE ESSENTIAL FORM OF RIGHT METHODS IN TEACHING. 6 2_ (Pbsrrtoation, - served. (Compare Drbal, "Empirische Psychologic," p. 161.) This notion of the perception of individual objects in space through the senses has been extended very generally by German authors, to an inner perception (innere Anschauung) of individual notions not given by the senses. For instance, in grammar, the relation of one word to another may be perceived even though the outward form gives no hint of the relation ; as, a noun in the nominative or objective case. As can readily be seen, this extension is very convenient for pedagogy, since it helps to emphasize the fact that we reach general laws only through individual facts. 16 THE ESSENTIALS OF METHOD. Pfisterer ("Padagogische Psychologies' p. 229) remarks: "We distinguish commonly, and not without reason, a double observation (Anschauung), an outer and an inner. The outer observation is that mediated through the senses; the inner is quite as much an observation by means of the inner senses as it is an observation of what goes on within. An observation by means of the inner senses is neces- sary, because not only all processes of the inner world, but also many phenomena and activities of the outer world, especially all that pertain to historical and social life, cannot at all or but partially and with great effort be brought under the observation of the senses. What re- mains but to bring them under inner, spiritual observa- tion, or to lead them before the inner senses (powers of presentation and imagination) by vivid description or narration ? By means of these, the child's mind can and should get a more or less clear image of a thing or activity, and mentally < see ' and enjoy it. without ever having per- ceived it in this form by the senses." If I take two pieces of paper of the same shape and size, fold each of them into eight equal parts, and tear off five parts from each paper, I shall find by counting that I have six parts left. By means of this concrete illustration, T have received an individual 'notion of the fact, that X 2 = f . In this case, my notion is not of an object, but of certain numerical relations ; yet it is a notion of an individual case of these relations, and is, hence, just as truly a concrete or individual notion as that gained from seeing, touching, smelling, and tasting the apple. If I take a vessel with a spout, fill it full of water, place a floating body upon the surface of the water, and then compare the weight of the displaced water with the weight of the floating body, I shall get an individual TOE INDIVIDUAL NOTION. 17 notion, or what is the same thing, a concrete illustration of the fact that a floating body displaces its own weight of water. What is true of the physical world and its relations is equally true of the spiritual world and its relations. In the pages of history we get concrete or individual notions, of bravery, of vigilance, of celerity, of the nobility of patriotism, of the vanity and wickedness of ambition, of the contemptibleness of cowardice, indecision, or. treason. A moral truth, though it cannot be presented to the senses, may be individualized, or made concrete, by concrete illus- tration; as, through the story of George Washington and his hatchet. Every fable is the concrete illustration of some moral or intellectual truth, and thus gives an individual notion of this truth. In the same way moral lessons are individualized throughout our history and in most of our imaginative stories. The main point in this whole matter is that our knowledge starts with the indii-idual notion, whether it is of the things of sense, of their relations, or of the concrete embodiment of any purely intellectual or moral truth. In any case, and in all cases, real knowledge must start with and be based upon the concrete, individual notion. 1 1 Pestalozzi. Instruction must not only be based upon sense percc;>- tion, but also upon inner or intellectual perception. It is also very important for us to emphasize for instruction that power of silent receptivity, which allows the matter of instruction to penetrate the depths of the soul, to grow and ripen, even without the illumination of reflection. Herbart (vol. i. p. 120, edition by O. Willnian). The marrow of educa- tion is itself destroyed, if the first fresh presentations become old without being perceived ; if lifeless repetitions are tediously extended, where in- terest should eagerly seize ; if the forms of speech, in which wealth of conviction even best loves to express itself, are bereft of their spirit, and laid away as corpses in the caverns of memory. 18 THE ESSENTIALS OF METHOD. . THE GENERAL NOTION. 3. Language reflects thought Tis the mirror reflects the image of him who stands before it. For this reason, a study of language is often the most direct road to an under- standing of the various elements of thought. We will, therefore, approach the next stage of our topic by calling to mind some of the implications of language. We say that a noun is the name of an object, but this object must primarily be an object of thought, for names do not inhere in things ; they are only means by which one mind is able to "convey" its own ideas to another mind. But actual things of sense correspond to ideas gained through a normal use of the senses, hence, secondarily and mediately the noun is the name of the object itself, and no confusion need arise from thinking of the noun as a symbol of an actual physical thing in space or of an idea of the mind. 1 A noun may be considered in two ways : (1) As to the quantity or number of that to which it applies, called the extent of the noun (or notion, which the noun represents) ; and (2) As to the qualities or attributes which belong to that to which the noun applies, called the content of the noun (or notion, which the noun represents). The extent may evidently include one, or some, or all. In the sentence, Socrates identifies virtue with wisdom, only one person is meant by the word, Socrates ; hence this word represents an individual notion. But in the sentence, Man is mortal, it is clear that the extent of the noun is not individual but general, that all men are included by the word man. The same thing is true of the words virtue and wisdom in the preceding sentence, for these are general * Compare Everett, The Science of Thouyht, p. 67. THE GENERAL NOTION. 19 terras. They do not refer to particular virtues or wisdoms. With regard to extent, they differ from man and similar words in not being numerically considered. General names, like man, virtue, ^visdom, are called common nouns. They can apply to individual objects, or to limited numbers or quantities, only through limitation by adjectives. Thus, this man, tall oaks, much wisdom. Common nouns, therefore, being general names, always express general notions. When unlimited by adjectives, the common nonn (hence the general notion which it represents) always embraces the whole extent of that to which the noun refers. 4. But, as we have seen, the noun (hence the notion) has also content, which will vary as the extent is expanded or contracted. One might think of a rose as the synthesis of its various attributes of form, color, odor, etc. In any individual rose these attributes would be numerous and perfectly definite. The color, for instance, would be white or red ; but in the general notion rose, particular attributes can no longer be assigned, for only those attributes could belong to rose in general which are common to all roses. Nouns may then be limited by reference to their content. Adjectives which modify in this way are called qualifying adjectives, be- cause they apply to the attributes or qualities belonging to that which the noun represents ; for instance, Black sheep are rare. Here the general class sheep is restricted or limited in extent by the qualifying adjective black. In the sentence, The v-oolhj sheep is a timid animal, the word woolly does not limit the extent of the notion, for this attribute .is common to all sheep, unless, perchance, the professor of the university of Lagado was successful, who spent many years in trying to raise sheep without wool. 20 THE ESSENTIALS OF METHOD. From what has been said, it may be seen that when the extent of a notion is smallest (one), its content is greatest ; and that when its extent is greatest (all of its class or kind), the content is least ; in general, the greater the extent, the smaller the content, and vice versa. Thus, the term animal embraces a far greater number of individuals than the term quadruped, but at the same time there are fewer character- istics which are common to all animals than are common to all quadrupeds. The term cat is less than quadruped in extent, but it is richer in content. The same can be seen in the general terms tree, forest-tree, oak, white-oak. Here the extent constantly narrows, but the content, i.e., the number of common characteristics, constantly increases. But, though when logically considered, extent and content of notions are related as indicated, it does not follow that knowledge of content grows meager as knowledge of extent enlarges. Were this true, we should have to say that the more the zoologist extends his classes, the less he would know about them. All effective learning is occupied quite as much with enriching content as with widening extent. It is evident, therefore, that knowledge should never be divorced from the individual thing, however broad its generalization may become. Not only is the idea of the general notion familiar in grammar, but it manifests itself in a rudimentary stage in early childhood. How a child forms such an idea may be seen from an illustration. Suppose he has observed a number of dogs of various breeds, but has seen no one of them more than once. If there were, say, ten of them in all, the external common characteristics of all have been observable ten times, whereas the individual characteristics of each dog have appeared but once. Thus, the fact that THE GENERAL NOTION. 21 all dogs have ears has been manifested ten times, though the characteristic of cropped ears, or of silky ears, may have occurred but once. So of the muzzle, the tail, the legs, etc. Savages, as Herbert Spencer shows, form general notions, but naturally of a much more elementary character than is the case with civilized races. Indeed, the history of the language seems to show that vague general terms preceded specific individual ones. As soon as the child can say cat, doy, horse, intelligently, he has passed beyond the individual object ; his knowledge has attained to a certain degree of universality. As we shall see hereafter, he can truly know an individual object only when he can subsume it under a general notion. 5. A general notion is unlike the individual, also, in that it cannot be imaged or pictured to the mind. Every image in the mind must be individual, and in being indi- vidual it ceases to be general. I can imagine or picture any individual tree, even one which I have never seen, but it remains individual. It is this tree; viz., the one I am picturing to myself. It has definite form, color, size ; its leaves are of a certain pattern, its bark has a peculiar forma- tion. The general notion, or conception, tree, however, cannot possess these individual peculiarities, since it must include all trees. My general notion tree is rather a general rule or scheme for the formation of any individual image of a tree. If one thinks of such notions as are expressed by the abstract noun, such as redness, heat, goodness, it is plain that any individual notion of one of these qualities would imply a definite degree, but the general notion would include all degrees. For example, it would be impossible to find a point registered on a thermometer, which alone indicates heat. The same is true to a greater extent with 22 THE ESSENTIALS OF METHOD. the more abstract terms force, matter, quality, being. These must in truth always be thcmght ; they cannot be perceived individually. (Compare Dr. W. T. Harris, " Illinois School Journal," July, 1888.) The general notion is therefore a general scheme, or rule, for the formation of individual notions, and is usually expressed in a definition. It is a product of thought, and has no external, objective existence apart from individual objects. It is vain to seek the univer- sal horse, except so far as it is embodied in every horse. But the general notion has a truth and reality in these objects, for it finds a concrete embodiment of its character- istics in them. The general notion, in its various stages of extent and content, is the necessary result of perception and reflection. It is that characteristic of mind that separates human in- telligence from the intelligence of the brute, if we may judge from the fact that animals do not use language, and hence do not appear to have any symbols for generalization. A dog, for instance, has the individual notions, cow, rabbit; nor does he ever mistake the one for the other, though these notions, like the first conceptions of the child, are vague and indistinct. But his intelligence appears to stop at this stage. Not so with man. Man's intelligence sees the general in the particular; it discerns the common character- istics necessary to the notion of each individual, and by reflection forms a general conception. This fact, as we shall see, has great significance in education, and must never be forgotten. ^ 6. Just as we found it expedient to enlarge our idea of the individual notion beyond the ordinary notions gained through the senses, so, likewise, shall we find it advanta- geous to extend our idea of general notions beyond those gained from the comparison of similar objects of sense. THE GENERAL NOTION. 23 Thus, in the multiplication of a fraction by an integer, we may pass by reflection or insight from the concrete individ- ual notion of the numerical relations of objects to the general truth that a fraction is multiplied by multiplying its numerator, because the mind perceives the universality of a mathematical process whenever it clearly understands the conditions. From the individual example of the amount of displacement by a floating body, we may easily pass to the general notion that any floating body displaces its own weight of the liquid in which it floats. From the individual case of the merit of telling the truth, in the case of George Washington, we may pass by reflection to the general fact that truthfulness is right, and that lying is wrong. Noti- cing the characteristics of several individual circles, we soon find those which are common ; viz., plane surface, curved boundary, and equidistance of all points on the circumfer- ence from a "point within the circle. From these we con- struct our general notion of the circle, which in this case takes the form of a definition. The general notion, therefore, thus extended and un- derstood, embraces not only notions of material objects, their qualities and relations, but definitions, as in mathe- matics and natural science ; laws, as the laws of gravitation, cohesion, repulsion, etc.; principles, as of economic or politi- cal life, or of warfare, etc. ; moral maxims, as, e.g., the cate- gorical imperative, So act that through your oivn will the rules of your conduct might become universal laws. CH'APTER II. APPERCEPTION, OR THE ASSIMILATION OF KNOWLEDGE. 7. WE have seen that all knowledge begins with the individual notion ; but, unless that which is perceived is understood, unless it is apprehended by being brought into vital relation to what is already known, it can do little or nothing to widen real knowledge; for, only that is truly known which is assimilated, or properly related to other elements of knowledge. The whole mental life is manifested through these ideas, or notions, or concept*, both individual and general, of which we have been speaking. Perception gives us the individual notion ; conception, or reflection, the general. But to receive a new perception, or individual notion, is not necessarily to understand it. This new perception must enter into certain relations to knowledge already in the possession of the mind, before it can be assimilated or understood. 8. Before entering upon an extended explanation of apperception, a general view of the subject may be obtained by attention to what others say of its meaning and impor- tance. Lange, in his excellent monograph upon apperception, says: "The apperception is that reciprocal action of t\vo similar notrons or masses of notions by which the weaker, the more isolated, the individual notion or group of notions, is intimately united with those which are richer, stronger, 24 APPERCEPTION. 25 and more systematically ordered." He continues : " One has no eye, no receptivity, no understanding for that for which one has no related thought, no connecting points, no rich store of related concepts." Again, referring to the importance of apperception in the facility and certainty with which the mind acts, he says : " Without apperception, the mind, with vastly greater effort, would accomplish far smaller results. There are few, indeed, who suspect how much our apperception supports our perception, how it relieves the senses of the greater part of their labor, so that we hear with a half-attentive ear, and perceive with a half-divided attention. The secret of this extraordinary result is to be sought in the fact that the apperception refers the new to the old, the strange to the familiar, the unknown to the known, the uncomprehended to that which, as comprehended, forms our spiritual possession." Lotze (" Mediz. Psych.," p. 504) says : " Language rightly distinguishes between simple perception, and that appercep- tion through which we receive certain impressions into the rational unity of our empirical self, and feel their relation to our earlier experiences and their worth for the further development of our personality." Lazarus (" Leben der Seele," II. p. 20) says : " By percep- tion we understand the reception of an image given to the soul through the senses ; by apperception we are to under- stand the reception of an externally given perception into the series of similar conceptions already in the mind." Kern ("Grundriss der Paedagogik," 9) says: "The fusion of two masses of concepts, or notions, after a pre- ceding transformation of one through the other, we call apperception." Wundt ("Grundzflge der physiologischen Psychologie," 2 Aufl. II. p. 20() says: "Perception signifies the entrance 26 THE ESSENTIALS OF METHOD. of a notion into the field of view ; apperception, the entrance of a notion into the field of view of consciousness." Under the title Apperception, Dewey (" Psychology," p. 85) remarks : " If we inquire under what circumstances any object or event enters into our intellectual life as significant, we find that it is when it is connected in an orderly way with the rest of our experience. The mean- ingless is that which is out of harmony, which has no con- nection with other elements. The isolated, the separate, is never an object of knowledge." 9. The foregoing definitions presuppose considerable technical knowledge of the terminology and the general trend of thought in the psychological systems from which they are taken, so that the actual psychical processes involved in apperception are not very apparent to one not familiar with the peculiar terminology. To exhibit these processes somewhat more distinctly must now claim our attention. It is a fact well known to psychologists that the primary function of inteliigence is to formulate thought in the judg- ment. Whatever can be a matter of thought at all can be, and indeed in the last analysis, must be reduced to the form of the judgment. The nature of the judgment is seen in its symbol, or representation, the sentence. This is neces- sarily the junction of subject and predicate by the copula, expressed, or implied in the verb. There are three possible relations between subject and predicate, two of which in themselves add nothing to our knowledge : (1) The subject may be more general than the predicate ; as, An animal is a dog. (2) The subject and predicate may be identical ; as, A dog is a dog. (3) The subject may be less general than the predicate ; as, Carlo is a doy. APPERCEPTION. 27 The first of these forms has no value in extending our knowledge when the subject is understood, since the predi- cate is plainly seen to be only a/>art of the subject. When Hamlet wished to withhold information, he said, " There's ne'er a villain dwelling in all Denmark But he's an arrant knave." In this case the subject is a broader term than the predi- cate, and already contains it by implication. There is one case, however, when this form of the judgment is of value ; viz., when the subject of the judgment contains more than is clearly seen by the speaker. Thus in the judgment, This body has weight, only one thing is asset-ted, but exten- sion, impenetrability, origin, purpose, etc., are all involved in the subject body. The pedagogical si'gnificance of this fact will be dwelt upon later. The second, or identical, form of the judgment is useless, except when the form of the terms is different. Thus, 4 = 4, a = a, have no value ; but 2 X 2 = 4, or (a -|- b) 2 = a 2 -|- 2 ab -|- b 2 , and other mathematical equations furnish us with a valuable instrument for working out results. The only form of the judgment, therefore, which really widens o\ir knowledge is the third, or that in which the predicate is a broader term than the subject. Thus in the word earth there is not involved the idea of revolution, so that when I say to one who does not know the fact, The earth revolves, I have extended his knowledge through the synthetic judgment. So in the judgments, Carlo is a dog, Most coral is red, Newton discovered the law of gravitation. In every synthetic judgment, the predicate is a more general term than the subject, but we need, at this- point, to perceive clearly the relation of content and extent in these terms. Should we think only of extent and content 28 THE ESSENTIALS OF METHOD. in the strictly logical sense, the judgment, This object is an animal, it is plain to see would convey but very meager knowledge, for the single-celled amoeba is an animal, and has but few characteristics common to all animals. Should I say in answer to the query, What kind of ah animal? It is a vertebrate, I should greatly enrich the knowledge, for the content is much enlarged. Continuing, I say. It is a mammal ; it is carnivorous ; its family is Felidce ; its genus, Felis ; its species, Felis domesticus Linnams ; its variety, Angorensis. At each stage, I have narrowed the extent, and enriched the content of the notion of the object with which I started. But it must be remembered that with a mind which has had any considerable experience, the term, house-cat, for instance, though logically itself restricted to a compara- tively small extent, really presupposes the more extended terms, mammal, vertebrate, animal. 10. We may say, then, in general, that the amount of in- forriation conveyed by any given predication depends upon the wealth of content and the implied breadth of extent which the predicate-term has for the learner. If, then, per- ception gives me a new notion, I shall evidently understand or apprehend it when I can subsume it under some familiar predicate having greater extent and richer content than the new object of thought has presented to my mind. From the standpoint of the judgment, then, apperception may be denned as follows : Apperception is the siibsumption of a notion, usually newly given and more or less individual, under a predicate ic/tirh is more complete in content and extent, and which is usually older and more familiar. Apperception does not always follow perception immedi- ately, for years sometimes intervene between the learning APPERCEPTION. 29 of a fact and its comprehension. In general, a period of reflection commonly precedes the complete apperception of a new subject of knowledge; though, as Lazarus says, "The apperceiving conceptions usually stand, like armed soldiers, within the strongholds of consciousness, ready to pounce upon everything that shows itself within the portals of the senses, in order to overcome it, and make it serviceable to themselves." The new is not always apperceived by the old, for it often happens that old and apparently well-grounded ideas are revolutionized by some new-found truth, which compels a readjustment. This has often been the case in science. The Copernican theory of the solar system com- pelled a readjustment of the mediaeval religious conceptions which had grown up in accordance with the Ptolemaic idea that the heavens revolve about the earth. 11. ILLUSTRATIONS. In general, the older and broader predicates give the main significance to the new subject, but the new also gives added significance to what was formerly known. When, for example, a child goes to the menagerie for the first time, all his mental power is at first absorbed in taking in the multitude of new impressions which crowd upon his senses, and he stands in open-eyed wonder before the strange forms of animal life. But if he is to understand what he sees, he must begin to apply predicates. Old, or formerly conceived, notions begin to throw light on the new impressions ; while, on the other hand, the new notions supplement, fill out, extend, and illuminate the old. Thus, if the child comes to the tiger's cage, after having seen a house-cat, and then, perhaps, a wild-cat, a jaguar, or any other of the smaller members of the cat family, the wealth of old conceptions regarding the form, habits, and nature of these animals helps him to 30 THE ESSENTIALS OF METHOD. form a notion of the tiger much richer than he would have obtained were the tiger the first member of the cat tribe he had ever seen. On the other hand, the word cat now has a much wider significance to him than it had before he had learned to place the tiger in this category. When the child, seeing it snow for the first time, ex- claims, "Oh, mother, see how the butterflies are chasing one another," he is not consciously using a poetic figure, but is simply relating new notions to old ones through predication. "These objects which I see falling through the air are butterflies. They are chasing one another." Another child, noticing the picture of a serpent, said, "That is a tail." Another, seeing a team of mules, ex- claims, " Oh, see the horses ! No, not horses, rabbits ! " Another remarks, " Papa does not crawl through the fence, he unbuttons the bars." It is related of certain sailors that they induced a band of Esquimaux to sail with them on a visit to London. The sailors anticipated not a little enjoyment in observing the astonishment and admiration of the foreign visitors when they should behold the wonders of the great city. Great was the disappointment of the sailors, however, when the Esquimaux walked through the streets utterly indifferent to their surroundings. The explanation is simple. These inhabitants of the frozen North had no store of related predicates with which to interpret the wonders about them. We have no interest in that for which we have no under- standing, no related concepts. PART II. NECESSARY STAGES OF RATIONAL METHODS. CHAPTER III. APPERCEPTION OF INDIVIDUAL NOTIONS. 12. WE have seen how apperception, or the subsump- tion of new subjects under old predicates, is the condition of understanding. It must at the same time be the condi- tion of all interest, for the mind has no interest in that which it does not understand. Not all things understood are interesting, but nothing not understood, in some degree at least, can possibly awaken interest. There are, there- fore, two powerful incentives for the teacher to study the conditions of apperception, the desire to have his pupils comprehend, and the desire to have them interested. 13. It might, at first thought, seem that the native spontaneity of the mind would do all tha.t is necessary to bring up these related conceptions which are to serve as predicates for the new notions acquired through instruction, but reflection will show that this is true to a limited extent only. Who has not seen children completely baffled by some mathematical relation, which a skillful question or two would reveal ? Is it not a daily experience of the teacher to find pupils failing to comprehend statements in reading or grammar or number or natural science or geog- raphy, simply because their own spontaneity of mind is 31 32 THE ESSENTIALS OF METHOD. not sufficient to supply those interpreting ideas, which the teacher might easily cause to appear in consciousness ? It is, therefore, the first great function of the teacher to prepare the way for the rapid and efficient assimilation of that knowledge which the study hour or the recitation period is to furnish. 14. The teacher's activity in this first great depart- ment of education is naturally of two kinds : (1) The preparation of the child's mind for a rapid and effectire assimilation of new knowledge, and (2) The presentation of the matter of instruction in such order and manner as ivill best conduce to the most effective assimilation. PREPARATION. 15. From what has been said, it will be seen that this term means that preliminary effort of the teacher, which is designed to prepare the mind of the pupil for a ready apperception, or assimilation, of the new knowledge about to be presented. 16. To understand the real nature of this process, we must recur to the first form of the judgment, or that form in which the subject involves more than is seen in the predicate. The child when he enters school knows many things, has coupled many predicates to many subjects ; but neither at this stage nor at any subsequent stage of his education has he coupled to his subjects of knowledge all the predicates involved in them. According to the law of apperception no child can really learn and understand any new knowledge for which he has not a store of related con- ceptions which can be applied as predicates. It may be, and most probably will be, the case that these needed predi- cates are held in the child's knowledge only by implication, and that it will need a preparatory effort on the teacher's APPERCEPTION OF INDIVIDUAL NOTIONS. 33 part to bring the needed apperceiving conceptions to the full consciousness of the pupil. Preparation, therefore, seeks to recall former knowledge, and to bring to consciousness those needed and implied conceptions which through predi- cation should reach out like so many spiritual arms, to embrace and draw into living relations to themselves the new elements of knowledge which it is the business of the hour to cause to appear in the mind of the child. 17. Where, as with small children or in certain kinds of oral work, no lesson for study is assigned, this prepara- tion will take place, in general, at the beginning of each recitation, though it will often happen that a general prepa- ration covering a whole section of a subject may render much preparation on daily subdivisions unnecessary. This matter will be further discussed under the subject of inethod-irholes. In classes where lessons are regularly assigned in text-books, the main part of the preparation should be made when the lesson is assigned for study. A repetition of the same at the beginning of the recitation may be helpful. The nature and amount of preparation necessary will depend upon the mind of the pupil. In general, one year's work is a preparation for the next ; so of the work of each term or month or week or day, and it is on account of the laws of apperception that gaps in education are to be avoided. Hut this general preparation does not often suffice. Though facts enough to explain the new lesson may have been previously taught, the mind may, on account of forget fulness, or because it is busied with other things, remain unconscious of them at the time when they are needed to illuminate the new and make it instinct with meaning by supplying the appropriate predicates. Or, if the mind recalls the older and related conceptions, they 34 THE ESSENTIALS OF METHOD. may yet be dim and weak, or may fail to appear in the best order, or they may be mere feeble general impressions. Under such conditions, it is needful for the teacher to make special effort to put the minds of his pupils into proper relations to the lesson about to be imparted. These efforts may be considered in the following order: (1) A clear and attractive statement of the object of the lesson, or the end to be reached. Thus, for example, the teacher may say, "We have learned that the earth is a great ball or globe which is free in space. We will now consider whether it is at rest or in motion." Or, "We have seen that a fraction is multiplied by multiplying its numerator ; let us see if it can be multiplied in any other way." Or, "We have found that the nature of thought gives rise to the subject, the copula, and the predicate, or attribute, of the sentence ; let us see, if possible, what property of thought gives rise to the adjective." But little thought is needed to see that it would be very unpedagogi- cal not to have the pupil understand from the beginning what the aim of the lesson is. In the first place, an attrac- tive or forcible statement of the end to be reached, helps to dispel from the child's mind the distracting thoughts which may be sporting there, and to prepare the way for what the teacher wants to impart. Next, it helps to put the pupil into the frame of mind in which it is desired he should work. It excites expectation, stimulates interest, and allows instruction to begin under favorable conditions. It gives the pupil a favorable impulse towards right willing, and disposes him to self-activity in the solution of the appointed task. But when the end to be reached is not indicated, the danger is that not only the above-mentioned advantages will be sacrificed, but that the pupil, not know- ing where he is going, will become confused, especially if APPERCEPTION OF INDIVIDUAL NOTIONS. 85 he is kept long in the dark. He cannot go forward intelli- gently, nor can he retrace his steps. His mind is be- wildered by perceiving results for which he is no longer able to account. But if he advances with a clear conscious- ness of the end he is striving to reach, he will not become confused, unless the explanation itself is confusing. (2) With the purpose or aim of the lesson about to be pre- sented always in view, it is plain that the concepts result- ing from the analysis of the present store of knowledge should be derived or developed in unbroken and virtually connected chain from the beginning to the close ; for in this way the mind reaches its greatest capability of taking on and assimilating new knowledge. But if the time is spent in recalling past concepts without any regard to their co-ordination and logical connection, or in developing the non-essential, it is plain that the child's mind will not be so ready to apprehend the new lesson in its full signifi- cance. The teacher should, therefore, endeavor to discover which of those main concepts, already within the grasp of the child, need to be recalled or derived in order best to master the new lesson. He should then arrange these in their logical order, and proceed to bring them to the child's consciousness in this order. The ease with which this logical arrangement can be secured will depend largely upon the logical arrangement of the subject-matter of the daily lessons. If this is what it should be, but little effort at special arrangement is necessary in the preparation. The more remote the new lesson is from the recent study of the child, the more elaborate must be the preparation. Ordinarily a few sharply put questions will suffice to place the pupils in a frame of mind best adapted to understand the new lesson. (3) The preparation and the new lesson should not be 36 TIIE ESSENTIALS OF METHOD. mixed up together during the preparation, for this is likely to lead to confusion of thought, and may lead to a lack of interest. A foreshadowing of what is to come, however, may secure increased ' interest and mental activity. If, when a new truth is presented, a pupil discovers that he had dimly foreseen it, his pleasure in the acquisition may be greatly increased thereby. A skillful dramatist never fully reveals his plot ahead of its unfolding, nor does he, on the other hand, ever allow any great but entirely unex- pected culmination to occur. Every stage in his drama is a preparation for the next, but not a revelation of it. The revelation of the unknown but not altogether unexpected is a fine art with the dramatist and the novelist, and should be with the teacher. (4) The preparation should be so extended as to cover the entire matter of the new lesson, or such part of it as may be regarded as a method-whole, in order that time and interest may not be sacrificed by tiresome explanations after the presentation of the new matter has been begun. Wherever much of this appears necessary, it is certain that the preparation has been inadequate, or that the matter is not suited to the present mental acquirements or ability of the pupils. (5) As to the form of the preparation, it may be remarked that a free exchange of thought between teacher and pupils in the form of question and answer, or conversation, is the best. Anything that smacks of examination is out of place, since it is destructive of that free movement of thoiight which is here so desirable; furthermore, it effects no valuable result, besides being deadening to a direct interest in the subject. Pupils delight in an exercise which gives free play to their individuality, nor should this free play of thought be rudely checked, even though APPERCEPTION OF INDIVIDUAL NOTIONS. 37 matters important only in the eyes of the child should be developed. A skillful teacher can easily guide the free thought of the pupils to the main issue, without checking its spontaneity; besides, the announced purpose of the lesson makes it easy to keep out irrelevant matter. (6) Repetitions, and even drill upon the main points brought out, may be profitable, but an exhibition of deep earnestness of manner or tone is out of place in the prepa- ration. This should be reserved for a later stage, when it is desired to impress some new truth brought out by the lesson. When the teacher has done as much as he thinks profit- able in way of preparation, he will proceed, as a matter of course, to the presentation of the lesson. PRESENTATION. 18. It is not to be supposed that the child possesses so much knowledge when he enters school that there is in- volved in it all that he will subsequently need to know, so that a mere analysis of what he now has will reveal all that he should ever have. In this sense Jacotot's dictum, A/I is In all, is false. New knowledge must be imparted. Old predicates must be supplied with new subjects in which the predicates are not already involved. These new predi- cations enrich former ones, so that the subsuming of new subjects under old predicates widens and enriches old conceptions, which in turn extend the significance of sub- sequent elements of knowledge. Omitting the second, or identical, form of judgment, A is A, which as we have seen is valuable only as a mathematical instrument for ascertaining numerical relations, we come to the third form of the judgment, in which the predicate is a broader and deeper term than the subject. The first kind of judg- 38 THE ESSENTIALS OF METHOD. merit has been called analytical, because an analysis of the subject shows that the predicate was already involved in it. The third, or last, kind of judgment has been called synthetical, because the predicate is something united to the subject, something which is outside of the subject, not implied in it. In the word Carlo is not involved the idea dog, so that the sentence, Carlo is a dog, expresses a /true synthetic judgment. It is evident, then, that if the child is to learn anything new, the teaching must be of this synthetic, or additive, nature. Without the gaining and assimilating of new facts, or elements of knowledge, there can be but little advance in mental growth. At this stage of our investigation, it is entirely immaterial how these facts are obtained, so that they are neic, not already involved in what the pupil knows. Facts may, for example, be ob- tained by induction or by deduction, or they may be gained through a primary use of the senses; they may be learned from a book or from the lips of the teacher. In any case, / presentation sees that these facts are brought to the con- ' sciousness of the pupil in such a way that they may be readily assimilated, or, in other words, be properly under- stood. 19. An exhaustive treatise on presentation might con- sider the whole course of development for each branch of study, and also the relations of inter-dependence among the various subjects of the curriculum, because each of these departments of inquiry has a bearing on the reception and assimilation of knowledge. One large German pedagogical school advocate the presentation of most subjects according to what is called the historical stayes of culture ; this posi- tion being taken, on the theory that each child, in its development, passes through all the stages of thought through which the world has passed in its historical devel- APPERCEPTION OF INDIVIDUAL NOTIONS. 39 opment. We should, therefore, say they present to a child of any given age that stage in the development of the sub- ject in which the world was at the time now typically represented by the child. For example, Ziller and his followers recommend the following order of topics for religion and history : first year, " Grimm's Fairy Tales " (Marcheu) ; second year, " Robinson Crusoe ; " third year, Bible stories from the time of the patriarchs, " Legends of Thuringia" (Thiiringer Sagen) ; fourth year, Bible stories from the time of the Judges, then of the Kings, "Nibel- ungen Tales ; " fifth year, Bible stories from the time of Christ, History of Henry I., Otto I., Charlemagne ; sixth year, Bible stories from the time of Christ continued, Migra- tion of the Nations, Roman Empire and the Pope, The Crusades, The Middle Ages, Rudolph von Hapsburg; seventh year, The Original Congregations or Churches, The Apostle Paul, Discovery of America and its first settle- ment, History of the Reformation, The Thirty Years' War ; eighth year, Instruction in the Catechism, " Frederick the Great," The Napoleonic wars for independence, The Resto- ration of the German Empire. This school make religion and history the central sub- jects for the work of each year, and seek to relate all the other instruction to them. This is the idea of concentration, according to which no subject of study should be isolated from the others, but all school study should be related to some common center. Other eminent schoolmen claim that the arrangement and co-ordination of school studies should be quite otherwise. But, however interesting these topics may be in themselves, they lie beyond the range which has been set for this treatise on methods. 20. The questions of the selection, arrangement, and co-ordination of school studies being excluded from our 40 THE ESSENTIALS OF METHOD. present consideration, we have now to examine the guiding principles of a rational daily presentation of the matter of instruction. The Law of Successive Clearness. We have seen that any advance in knowledge comes by subsuming new subjects under old predicates, that this is the essence of apperception, or mental assimilation. But this mental movement is a movement in time. It requires a certain amount of time to gain a clear perception of the new ele- ments of knowledge, whether these elements originate through the senses or through the understanding. It also requires a certain amount of time for the predication.- Besides these two elements, there is an intellectual element of thought, which enables the mind to perceive relations between new and old elements of knowledge. As has been hinted before, there is a reciprocal action between new subject and old predicate. If the older and broader predi- cates enable the mind to understand the significance of the new elements of knowledge, so, on the other hand, do the new subjects broaden and complete the former concep- tions which serve as predicates. 1 1 Dr. W. T. Harris says (Rosenkranz, " Philosophy of Education," pp. 75, 7(5), " Perception is increased immensely in power by adding to it con- ception, which brings the aid of the general image in which are summed up all previous perceptions; thus perception re-enforced by conception is an individual activity re-enforced by the sum-total of the race activity, or at least by the sum-total of all previous activity of the same individual as well as by what he has learned from his fellows. Thus, too, percep- tion is still more increased by adding to it the thinking activity, which perceives necessary relations. Agassiz looks at a new tish from the Amazon River, and sees at once its type and its variations ; knows at once the great mass of its properties, functions, faculties, habits, and history, simply by its classification under already known genera, species, and sub- classes. This enables him to distinguish at once its variations from the general type, and to see the significance of its peculiarities. In the same APPERCEPTION OF INDIVIDUAL NOTIONS. 41 Upon the fact that certain easily distinguishable amounts of time are required for this reception and apprehension of individual notions, and the interaction between individual and general conceptions, is based THK LAW OF SUCCESSIVE CLEARNESS. 21. This law was first announced by Ratich, and was afterwards developed and applied by Herbart and Ziller. According to this idea, the matter of instruction must not be presented in the mass, but in small, logically connected sections, to each of which, in succession, the pupil should give his undivided attention. In this way, one by one, individual notions are clearly perceived. But, as already explained, individual notions are not assimilated until they are subsumed under predicates. It is thus evident that after the mind has given its concentrated attention to each of the successive sections of the lesson in turn, these sub- divisions must be brought into close relation and connec- tion ; i.e., must through predication be brought into a unity in consciousness. To neglect the division of the lesson into manner a botanist (Professor Gray, for example) glances at a tree as lie passes it rapidly, from the car window. He sees its resemblances and its differences, however, in that rapid glance, because he subsumes it under all that he knows; all that is known, in fact, as the aggregate result of all observations for thousands of years. By recognizing its series, class, sub-class, order, sub-order, tribe, genus, species, and variety, he is in- stantly in possession of information enough to make a library of books on the subject of that one tree. He saw enough, too, in the rapid glance to inform himself of its individual differences, its particular size, shape, and condition, in so far as these were peculiar. Contrast this with the infor- mation obtained by the sense-perception of an observer endowed with excellent sight but no knowledge of botany. Science, which is the product of conception and thinking, thus re-enforces sense-perception, which demands for its perfection those higher activities; and, vice versa, thinking and conception, which deal with the universal, or the possibility and the process which creates particular individuals, demand sense-per- ception to take cognizance of those individuals." 42 THE ESSENTIALS OF METHOD. minor unities, or sections, would be to sacrifice clearness of individual notions, and to get only crude general impres- sions of the whole. On the other hand, to fail to associate the parts of the lesson, and to bring them to consciousness as a logical unity, would be to leave the mind distracted by the apprehension of a confused mass of disconnected details. These two steps, the absorption of individual notions, and their apperception as connected, Herbart compares to the process of breathing, calling them the inspiration and expi- ration of the soul. Our maxim, step by step, has to do with this process, but it is incomplete, for it suggests only the subdivision, without hinting at its purpose, the clear per- ception of individuals and their proper synthesis in con- sciousness. 22. The matter of instruction must, therefore, be pre- sented in natural subdivisions, thus giving resting-places which allow the mind to recover from its absorption in the individual, and to fortify itself against distraction by bring- ing its knowledge into wholes. How minute the subdivi- sions of the lesson should be, must be determined by the age and mental strength of the pupils. Arithmetic and mathematics in general furnish the most perfect exemplifi- cation of the truth of the law of successive clearness, and of the necessity of obeying it. If the steps of reasoning in a problem are not separated and mastered one by one, there is instant danger of confusion, though the amount which a pupil can master at one impulse grows with advancing mental ability. The same law holds, also, in all other "branches. Take, for example, the first lesson in the Second Eeader. If the books are opened, and the pupils are di- rected to read at sight, the probability is that the result will be a failure. All the difficulties come at once upon, the pupil. Many of the old words will not be recognized APPERCEPTION OF INDIVIDUAL NOTIONS. 43 in their new surroundings, while the new words can of course not be grasped at once, nor can the new thought. In accordance with this law, the teacher must determine what the difficulties are likely to be, and then overcome them one by one. He should, for instance, refresh the minds of his pupils upon those words of the lesson which they have had before, but which they may not at once remember. He can do this by writing them upon the board in familiar sentences, or by pointing to them on the chart, or by spelling them out with detached letters. Then he must give instruction upon new words. He might, when the pupils know the subject of the lesson, easily draw from them the ideas likely to be found in such a lesson. He could then place upon the board the new words repre- senting these ideas, and by spelling, syllabicating, phonic analysis, etc., impress them upon the minds of his pupils. The reading may now proceed with some prospect of suc- cess, for the teacher has observed the law of successive clearness, has proceeded step by step. 23. The Series. Since all mental activity presup- poses time as its necessary condition, it follows that all our perceptions, and knowledge in general, so far as one ele- ment does not fuse or coincide completely with another, must be acquired and held in time series. Uponvthe intimacy of association depends very largely the power of reproducing, or remembering, all the numbers of a series when one of them is given. It follows from this, that it is a prime duty of the teacher to see that the elements of what is presented are arranged in natural series, so that intimate and lasting associations can be formed. As an illustration of how easily even bare words can be held if associated, let the reader note the following list of ten words, thinking as he reads of how each word suggests its successor ; Glad- 44 THE ESSENTIALS OF METHOD. stone, quarry, blasting, dynamite, Anarchists, Hayniarket, meadow, sheep, wool, protection. Having done this, lay aside the book, and repeat the list from memory. It is qiiite as easy to repeat it backward as forward, or to begin with any word of the series, and recite either way. Hun- dreds of words can be associated in this way, and easily re- cited forward and backward or from any intermediate word. But if we take ten unassociated words, we shall find much mental effort necessary to accomplish the same results, thus : quarry, Hayniarket, blasting, meadow, dynamite, wool, Gladstone^ sheep, protection, Anarchists. Few lessons can or should be arranged in this artificial way, but the laws of association as presented in our psy- chologies should be studied and constantly applied. This natural coherence of parts is one of the indications of a good text-book. Beware of the book which presents a mass of disconnected details. An observation of the laws of association in the formation of the series renders learning more easy and more permanent. This is especially recom- mended for those persons who have a poor verbal, or mechanical, memory. It is often necessary to form the series, even when direct association cannot be appealed to, as in the case of arith- metical tables. Time is an important element in fixing any series, and especially those of mathematics. Enough time should be given, so that any member, rising into consciousness, will instantly and surely recall the others. Thoughtful and constant repetition is essential to success in learning a series of disconnected facts. 24. Since knowledge is most easily gained and longest retained by an observation of the laws of association in the formation of the series, it is easy to see that it would be most unpedagogical to make a practice of destroying or APPERCEPTION OF INDIVIDUAL NOTIONS. 45 breaking up the series, by the insertion of new, or the sub- traction of old members. It is not difficult to see the loss which must occur in instruction, if, after a series has been laboriously fixed in the mind of a child, so that he is master of it, the teacher should proceed to undo his work by breaking up the series. Suppose, for example, a pupil learns a map-lesson in geog- raphy in a given grade. This lesson forms a series in which each member is related to others of the series, and serves to call them up. If now, upon going into the next grade, half a dozen new members be inserted into the former series, it is plain that the first series is destroyed, so that the injected members compel the learning of an entirely new series. This kind of procedure Avould, if sys- tematically continued, result in the constant formation and destruction of series, and thus cause great educational waste. If it be found necessary, however, to insert new matter into an old series, this should be understood by the pupil, and the amended whole be treated as a new series. It is possible, however, so to arrange instruction that each new fact taught shall be but an onward step in the development of the subject, causing only an extension, and not a destruction, of former series. This is illustrated in arithmetic, for example, in the successive mastery of tables; in history, in the continuation of topics taught in a more elementary form in the lower grades ; in grammar, in the more and more elaborate modification of the principal ele- ments of the sentence by means of words and inflections. In geography it would seem that names of places, rivers, etc., should be taught in a series but once, and that rather late in school life. The earlier grades should be learning series which will not need to be destroyed later through the introduction of new matter. 46 THE ESSENTIALS OF METHOD. 25. Fixing Series in the Mind. In order to impress it firmly on the mind, and to secure intimate fusion, or association of its parts, the series arising from each sub- division of the lesson must, without undue haste, be re- peated often enough and in enough different ways, so that the members will have sufficient time to become firmly united (Ziller). Next to the formation of the series in instruction comes the need of fixing it in the mind. This, as we have seen, needs time. It needs, also, a constant attention to the matter in hand. Repetition gives the time, and skill on the part of the teacher will secure the attention. Every teacher knows that repetition without attention accom- plishes little. One of the chief purposes of device in methods is to secure the requisite attention for the mastery of difficult series. Novelty of device is worthy of consid- eration, for what is new claims the attention of children. CHAPTER IV. TRANSITION FROM INDIVIDUAL TO GENEEAL NOTIONS. GENERAL VIEW. 26. It is a chief business of education to pass from dis- tinctly perceived individual notions to clear general notions (Pestalozzi). We have seen that without individual notions, knowledge, and consequently education, cannot begin ; and that without attaining to the general notion intelligence cannot be human. In these two facts is implied the truth of Pesta- lozzi's saying. It is this truth we try to express in the terms, education (educo), drawing-out process, mental power; depth of insight, genius, etc. Some have imagined the drawing-out process to mean getting from the children facts which have been taught to them, and in their original form ; i.e., drawing out at the faucet what has been poured in at the bung! If the drawing-out process means anything, it means the passing from the particular to the general, the transi- tion, through reflection, from individual to general notions. If pupils perform this transition but imperfectly, however, they become lost in the individual ; " they cannot," as one writer expresses it, " see the woods for the trees." Who does not know people who are able to take no more than a microscopic view of things ? Who does not know teachers that unceasingly cram their pupils with individual facts, hav- ing but little regard to their true meaning and their relation 47 48 THE ESSENTIALS OF METHOD. to the significant general truth which may be derived from these facts, in themselves entirely insignificant ? Twenty-five hundred years ago, Socrates taught men in the streets of Athens. He did not, however, spend his time in imparting new knowledge. It was not the indi- vidual horse, but the universal horse which claimed his attention. He said he was helping men to give birth to their ideas. Not ideas which they had, but could not express, but general truths implied in their knowledge, which they had not been able to derive alone. The Socratic method, therefore, is but one of the stages in any complete system of instruction. It seeks not to impart new facts, nor to assist in the assimilation or understanding of new knowledge through the mediation of former knowl- edge, but is concerned solely with the derivation or abstrac- tion of the rational content potentially contained in any given body of facts ; i.e., it tries to discover what is the general, or necessary, truth contained in any given body of individual notions. It is further evident that education must make it a special business to teach the child to pass easily and se- curely from the individual to the general, because the generalizations of children, savages, and uneducated or poorly educated persons are very elementary and incom- plete. They do not contain all the characteristics common to a given class, nor do they exclude all characteristics which inhere only in certain individuals. The untrained thinker is content with types chosen from among individu- als ; so that, even in the formation of general conceptions regarding things, the mind must be trained to distinguish the essential from the non-essential. But if this is true in things, how much more must it be true in regard to a per- ception of the necessary relation of things, and in respect FROM INDIVIDUAL TO GENERAL NOTIONS. 49 to what is essential and what is non-essential in character. Any general, for instance, knows enough to fight when he is surrounded and attacked, but not every one sees, as Grant did at Chattanooga, how the placing of a battery here, the arrangement of troops there, the forward movement in an- other place, will cause the frowning batteries to retreat, and the heavy lines of the enemy to roll back like clouds before the sun. Two men may have equal knowledge of the ele- mentary forces in physics ; the one sees the relation of these forces, and constructs a useful machine, the other allows his knowledge to lie inert and fruitless in his mind. Two lawyers may have the same knowledge of the facts in a law case ; the one sees the relation of things, that is, sees the general truth involved in the particulars, and wins his case. He sees the points ; the other sees all but the points. The one has learned to pass, by reflection, from the indi- vidual to the general ; the other has not. The necessity of proceeding from the individual, through reflection, to the general, as an educative process, has always been recognized by the great thinkers. "Percep- tions without conceptions are blind," says Kant, just as "conceptions without perceptions are empty." This means that intelligence cannot stop with the individual, but must through its own activity find the universal in the particular. Lessing, in his treatise on the fable, says, "Why is there in all sciences such a lack of discoverers and inde- pendent thinkers ? This question is best answered through another, Why are we not better educated ? God gives us the soul, but yen ins, talent, ability we must get through education. A boy whose whole mental powers are, so far as possible, constantly extended in every direction ; who is accustomed rapidly to compare all that is daily added to 50 THE ESSENTIALS OF METHOD. his store of knowledge with what he knew yesterday, in order to see if through this comparison he does not come upon things which were never told him ; who is constantly led out of one science into another ; who is taught to rise from the particular to the general as easily as to descend from the general to the particular again ; such a boy must become a genius, or one can become nothing in this world." It is our present duty to inquire into the nature of this process of passing from the individual to the general, in order to throw as much light as possible on methods of teaching. 27. Each general notion necessarily implies a number of individual notions to which it relates. It is plain that that which is common to two notions cannot be perceived as common unless the two notions are both in consciousness at the sapie time. Simultaneity is, therefore, a condition of all mental association. There is, also, a constant ten- dency to associate in some way things present to conscious- ness at the same time ; and, with untutored minds, even to associate simultaneous or successive events as causally con- nected when no such relation exists. Thus, if certain events are observed several times to be simultaneous with a given phase of the moon, superstitious people are likely to connect this phase of the moon and the events as cause and effect. It is evident, at once, that were there nothing but the original time connection of perceptions possible, our knowledge would be but a chaos of accidentally asso- ciated notions, and that any comprehensive general notions would be impossible. 28. The mind must, therefore, be trained to break up those accidental, historic associations, and to form new associations which shall accord icith the true nature of the notions asso- ciated. In other words, before any general notion can be FROM INDIVIDUAL TO GENERAL NOTIONS- 51 formed, memory must bring together in consciousness, a number of truly and logically related individual notions, which were, perhaps, historically separated in the order of their original perception. 29. We can, then, see likeness and difference in two or more notions, only when they are simultaneously in consciousness. It is equally evident that, in order to per- ceive these likenesses or differences, comparison of the various notions is also necessary. If, in this comparison of notions, we ?.*ssociate those things which naturally and of necessity belong together, we are cultivating thought, or insitjht ; if, however, we make arbitrary and fanciful con- nections, we are cultivating imagination. This discussion will be confined to those associations with which thought or insight is concerned. 30. Comparison of logically connected individual notions is, then, the first step in passing from the indi- vidual to the general. When several related notions present to consciousness are compared, it seems but a step of simple perception, perhaps through the judgment of identity (A = A), to see that an element of A is common also to H and C. Were there, frfr instance, but three indi- viduals embraced in the extent of any given general notion, and these three could all be present to consciousness at the same time, this simple perception of common characteristics and their synthesis would suffice to give rise to the general notion of these things. But it can easily be seen that any newly perceived object must at once be subsumed under a class, even though it be the class thing, or animate thing, or inanimate thing, or animal, or vegetable, or vertebrate, or invertebrate, etc.; so that the vital question is, How do new classes arise ? What is the process through which the mind passes in arriving at universals ? This is synony- 52 THE ESSENTIALS OF METHOD. mous with the question, What is the nature of induction ? The subject of induction has been treated at length by many learned men, but it has remained to Dr. William T. Harris to strip the subject of its mistiness, and to present it so clearly and simply that any ordinarily trained mind can comprehend it. 1 31. To his explanation we will now address ourselves. Intimately connected with the subject of induction is that of apperception, already discussed in a general way in these pages. We have found apperception to be, as" a general thing, the subsumption of new subjects under older, wider, and deeper predicates. We shall now find that Dr. Harris explains this process more exactly and from a different standpoint. His fundamental inquiry is, What is the rela- tion of the syllogism, as taught in logic, to apperception and to the formation of general notions ; or, in other words, What is the relation of the syllogism to apperception and to induction ? The syllogism consists of a major and a minor premise and a conclusion. The conclusion has a subject and a predicate, called terms. The subject and predicate of the conclusion appear also as terms in the two premises. The subject is symbolized by S, the predicate by P. There is also another term appearing in the premises, which serves to mediate between the subject and predicate of the conclu- sion, or to bring them together. It is symbolized by the letter M. We have now three symbols of terms which appear in the syllogisms. But these symbols may be differ- ently arranged, and according to the three chief arrange- ments possible, we have what are called the three figures of the syllogism. i Illinois School Journal, Nos. 88, 89, 90, 1888-89. FROM INDIVIDUAL TO GENERAL NOTIONS. 53 FIRST FIGURE. (1) M is P: Man is mortal. (2) R is Mr Socrafea w a man. (3) Hence, S is P : Hence, Socrates is mortal. Here the middle term (Jf) is the subject of the first premise^ and the predicate of the second, and unites the sub- ject and predicate of the conclusion, because it contains the subject (Socrates) and is itself included under the predicate (mortal). SECOND FIGURE. (1) S is M : This animal barks. (2) Pis M: Dogs bark. (3) Hence, S is P : Hence, this animal is (probably) a dog. Here the middle term (M) is the predicate in each pre- mise, and unites subject and predicate of the conclusion, because it contains both subject (this animal) and predicate (dog). This figure is valid, or invariably true, ouly in the negative. Thus : (1) S is M : This animal climbs trees. (2) No P is M : No dog climbs trees. (3) Hence, S is not 1': Hence, this animal is not a dog. As we shall see, however, apperception starts with the second figure, even though not valid, and fortifies itself by means of the first. THIRD FIGURE. (1) M is S : All men are animals. (2) M is P: All men are rational. (3) Hence (some) S is P: Hence, some animals are rational. Here the middle term (M) is the subject of the premises, and brings the subject and predicate of the conclusion together, because it is contained in them both. 54 THE ESSENTIALS OF METHOD. In the case of the apperception of objects perceived x through the senses, perception precedes apperception ; that is, the process begins with particulars, or attributes, and hence, if any figure of the syllogism is implied, it must be the second, for in this case the middle term (Jlf) is an attribute. To illustrate : Suppose I see a moving object in high grass. It looks like a tail curled over a back. The mind would act as follows : (1) That is a tail curled over a back. (2) Dogs curl their tails over their backs. (3) Hence, this object is (probably) a dog. or, according to the formula of the second figure, (1) S is M. (2) P is M. (8) Hence, S is P (probably). Accordingly, the first stage of apperception is taken by means of the second figure. But I wish to be sure, and I now proceed to test the correctness of my conclusion by the first figure of the syllogism, and I think (1) All dogs have ears of a general type, four legs, a certain general shape, etc. (2) This object has these characteristics. (3) Hence, this animal is a dog. or, according to the formula of the first figure, (1) M is P. (2) S is M. (3) Hence, S is P. Proceeding further with the identification, T think (1) My dog, Don, has one black ear, a white body, a slight limp in one hind leg, etc. (2) This dog has these characteristics. 3) Hence, it is Don. FROM INDIVIDUAL TO GENERAL NOTIONS. 55 When the process of apperception is analyzed, we find that it begins with a tentative identification of the new. object of perception with some well-known object, through the mediation of the second figure of the syllogism ; and that this first identification is verified or rejected by means of the first figure. Of course, it is not meant here, that children or even adults consciously use these syllogistic figures, but only that this is the natural movement of the mind in apperception. We come now to the question, How do general notions arise ? or, in other words, What is the process of mind in induction ? When the third figure is examined, it is apparent that it can be used only after the first two, for their action is pre- supposed in both major and minor premise. To say, all men are animals (M is S), is to recognize the subject (animals) in the middle term (all men). But this is the process of identifying, as explained through the second and the first figures. The same is true when we say, all men are rational (J/ is JP). Thus, in the third figure, there are two identifications, both involving the second and the first figures of the syllogism. The third figure, as we have seen, is (1) M is S. (2) M is P. (3) Hence, S is P. To see how this syllogism acts in giving us a new class, let us suppose that we are familiar with the common work- horse only. Now we see a very large dapple-gray animal, which by the other figures we find to be a horse. The following results : (1) M is S: This object is a horse. 56 THE ESSENTIALS OF METHOD. By a second identification, we have the second premise, (2) M is P : This object is very large, is dapple-gray, etc. (3) Hence, some horses are very large dapple-grays (or other colors) . We will call them Norman horses. We hare now from a single observation the basis of a neiv class. If no more obser- vations are made, this basis will remain only a potential class, it will not become actual. But should repeated observation give us new objects which can be identified as belonging with the object first observed, a well-defined class will arise. An important question now arises : What sort of charac- teristics shall be chosen for the formation of new classes ? Should a number of miscellaneous articles be placed before a child for classification, accidental and non-essential charac- teristics might be chosen as a basis, rather than more essen- tial ones. Scientific classification always seeks a vital or causal basis, while persons in immature stages of thought are content to classify according to characteristics which appeal most strongly to the senses. We may, therefore, distinguish two bases for new classes : (1) external, obtru- sive characteristics ; and (2) vital, or necessary (causal), characteristics. In the classification of animals, external marks of color, shape, size, presence or absence of append- ages, may be used as the basis ; but the naturalist looks deeper and classifies in accordance with characteristics which seem necessary to the existence of the animal ; as, e.g., the various organs for obtaining, masticating, and digesting food. For instance, a certain kind of animals, say, ruminants, might be loosely classified according to their horns or their hoofs, but a classification based upon the number and kind of teeth would be subject to far less varia- FROM INDIVIDUAL TO GENERAL NOTIONS. 57 tion ; for the teeth bear a much more intimate relation to the existence of the animal than do either horns or hoofs. The mind approaches scientific classification through many stages of convenient though loose classification, so that it becomes a great problem in education to know at any given stage of the child's mind just what degree of abstraction it is capable of attaining in each study. NOTE. The habit of generalizing upon insufficient data is a most common one, and is often indulged in, even by well-educated people, if they happen to make observations in an unfamiliar field. The fol- lowing incident will illustrate this point. An American professor was traveling in Germany, and being a little late, one summer day, had to run in order to catch his train. This, of course, started the perspira- tion, and, fearing he might take cold, the professor drew on his over- coat when he reached the car. A German had been an interested observer of the incident, and learning soon after that the professor was an American, he took out his notebook, and wrote as follows : " Americans put on their overcoats when they get warm." The pro- fessor, who had begun to chat with the German, noted the action, and suspecting something of its purport, asked the German what he had written. Upon being told, the professor laughed, but made no com- ment in remonstrance. Soon after, the conductor came along, and being an acquaintance of the German, stopped to chat with him, and finally offered him a cigar. The German replied that he did not smoke, but liked to have something in his mouth, and that conse- quently he usually held his lead-pencil there. Upon hearing this, the professor drew out his notebook hastily, and made this entry : "Ger- mans do not smoke cigars, they smoke lead-pencils." The German, of course, saw the action, and inquired its purport. Upon seeing the entry, he laughed, and proposed that both of them should revise their generalizations. 32. As we have seen, the general notion in the restricted sense is symbolized by the noun. Nouns are, therefore, in themselves abstract terms. It is easy to under- stand why the education which was based upon the word 58 THE ESSENTIALS OF METHOD. alone should become meaningless and formal, and we do not wonder that Pestalozzi revolted against it. He insisted that, instead of presupposing such an acquaintance with nature, and such an experience in general as would give a meaning to these abstract terms, the educator should proceed to give the child an experience of the individual, so far as he does not possess it, and then lead him by his own thinking to the general notion, which is symbolized by the noun, or expressed in definitions, rules, maxims, etc. In this way the word becomes a living force, instead of a dead form. Hence arose the motto, First the idea, then the word. This motto, if properly understood, is true and valuable, but may be easily misinterpreted. It is evident that, with little children, for instance, the motto cannot mean that the idea, or general notion as it really is, must be developed in its logical completeness so far as extent and characteristics are concerned. If this were so, the child should never have the word cat given to it until it had mastered a zoological system ; nor could it acquire the word line until able to master the metaphysical conception of extension in length, but without breadth or thickness, and until an ex- perience of lines of all sorts, straight, curved, and broken, had enabled it to arrive at a true logical conception of the line. At first, the word, though itself abstract, is to the child a sign of an individual object ; and, hence, at this stage, to give the idea before the word is to show the individual ob- ject. Later, the word becomes a symbol for some notion not definitely limited in extent and content, which serves as a type. This notion is often an indistinct image, only the main characteristics being emphasized ; it is Avell illus- trated in composite photography. In this stage, to give the idea before the word would be to develop a logically FROM INDIVIDUAL TO GENERAL NOTIONS. 59 imperfect general notion from the particulars which may be at hand. In the third stage, the word is a sign of a scientifically complete general notion, as the word tire, was to Professor Gray, or as the word line is to the mathema- tician. To give the idea before the word here would be to gain the ends of all knowledge before learning the common- est words of childhood. Long before this stage is reached, the word has been learned, and comes to the teacher as one of his greatest aids. Scientifically, to give the idea before the word, means nothing more than to proceed according to the law of apperception; i.e., to see that a predicate, greater in extent and content than the subject, can be applied by the child. If the predicate is only a little broader than the subject, there will be some appre- hension of the new idea. The more complete the predicates are, the more complete the apperception will be. 33. If the present view is correct, there must be con- stant progress from the individual to the general at all stages of school life. There must also be a constant progress in the character of the general, from those primary stages when types more or less individual in character represent the universal, and when accidental characteristics form the basis of classification, up to the complete, scientifically perfect general notion, which is the ripe final product of properly conducted education. To discover these various stages towards logical completeness in the general notion, for all ages of childhood and youth, and in all school studies, would lie, to sol re one of our most important pedagogical problems. So far as the child is concerned, this would imply a power on the teacher's part to discover at all stages the limit of the child's power to generalize ; or. in other words, to unify common characteristics in whatever realm of school study; to make valid generalizations. Too many 60 THE ESSENTIALS OF METHOD. of our authors talk as if there were a long period of the child's life in which he can do little but observe, when the perceptive powers absorb the whole energy of the mind ; and that, consequently, the sole duty of the teacher is to cram the mind with facts, making little or no effort, con- scious or unconscious, to enable the child to see the univer- sal which underlies the particular. This is certainly an erroneous and injurious view. That what has thus far been said is in full accord with the true spirit of the reform inaugurated by Pestalozzi, may be seen from the following quotation : " When I considered the whole of instruction, or, rather, instruction as a whole and in connection with the actual condition of the masses of children who are to be instructed, I could not conceal from myself that the school instruction, as I actually saw it, was wholly unfit for the great public and the lower classes. The feeling began, day by day, to develop in me that it was essentially impossible permanently to remove the great mass of school evils, unless teachers could arrive at the point when they could subordinate the mechanical form of all instruction to the eternal laws, whereby the human spirit rises from SENSE PERCEPTIONS TO CLEAR GENERAL CONCEPTIONS (general notions). In those laws I thought surely to find the thread out of which to weave a universal psychological method of instruction. " (1) Learn, therefore, to arrange thy perceptions, and to complete the simple before proceeding to the complex. " (2) Further, bring together in thy mind all those things which essentially belong together, in the same connection in which they are actually found in nature. " (3) Strengthen and intensify thy impressions of impor- tant objects, by bringing them nearer through art, and by making them act upon thee through the different senses. FROM INDIVIDUAL TO GENERAL NOTIONS. 61 " (4) Regard all the effects of physical nature as absolutely necessary, and recognize in this necessity the result of the power with which they unify their apparently hetero- geneous elements to the realization of their purpose ; and let the art with which thou, through instruction, workest upon thy race, as well as the results which it effects, be elevated to a like physical necessity, so that in all of thy doing, all means, however heterogeneous in appearance, work together for the accomplishment of their great pur- pose.'' This, then, is the great merit of Pestalozzi, that whereas the men of his time began instruction with the abstract, with irords whose content was unknown to the children, he began with the individual things, from which alone the abstractions could gain any significance in the minds of the pupils. Instead of presupposing an experience, he supplied one. Instruction is ever swinging between two extremes, under ived yenerals, and unyeneralized particulars. Undue conservatism tends to the former, and unthinking radicalism to the latter. Pestalozzi struck the golden mean, when he said, the mind must ever rise from clear individual to distinct general notions. SPECIFIC ( OXSTPERATIONS. 34. In our analysis of the nature of abstraction, or the passing from individual to general truth, we found that it arises, in general, through the comparison of related indi- vidual notions, and a positing, through induction, of the universality of the perceived common characteristics. It will now be helpful to distinguish between mathematical and non-mathematical generalizations, since the two are quite unlike. 35. Men never cease -to dispute about the significance 62 THE ESSENTIALS OF METHOD. of historical or social or economic facts, so that new gener- alizations are constantly formulated concerning them ; but when once the conditions of a mathematical problem are understood, there can be no further controversy. The generalizations of mathematics appeal to the mind as universally and necessarily true, as soon as they are per- ceived. In the idea straiyktness is not necessarily involved the idea shortness, but the mind lias only to think a straight line between two- points to perceive that this line measures the shortest distance between them. It' it be desired to deduce a rule for multiplying a fraction by an integer, a single problem will suffice as well as a thousand to bring the mind to a knowledge of the law and a belief in its universality. Suppose the illustrative problem to be, multi- ply f by 2. Let two pieces of paper having the same shape and size be taken and folded into fourths. Tear off ^ from each. What now remains of each is f . If, now, the nature of multiplication is already understood, which must be pre- supposed, the child will see that 2 times f, or 2 o's of 4ths, equals the value of the two remaining pieces of paper, or 6 fourths ; i.e., the number of parts has been doubled, their size remaining the same, and hence the value of the fraction has been doubled by multiplying the numerator by 2. In general, multiplying the numerator of a fraction multiplies the value of the fraction, because it multiplies the number of parts, leaving their size the same. Again, take the two pieces of paper, each containing f of the original paper, and arrange the 6 fourths into groups of two each. We find that there are three of them ; but two fourths equal one half, hence X 2=3, or this fraction is multi- plied by 2 by dividing its denominator by 2, for though the number of parts is the same, their size has been doubled. In general, dividing the denominator of a fraction FROM INDIVIDUAL TO GENERAL NOTIONS. 63 multiplies the value of the fraction, since it multiplies the size of the*parts, leaving their number the same. So of any mathematical truth, if it is once brought clearly to consciousness, its universality is at once felt. Is it not a sin that pupils should be taught arithmetic for years, without ever having been made conscious of the necessary validity of the rules and principles they constantly use ? Daily experience shows that pupils may finish arithmetic in the high school without having grasped the true mean- ing of even so simple a process as subtraction. Thus, if a pupil holds 8 sticks in one hand and 3 in the other, he will usually stand in confusion, if asked to show with the objects how many more there are in one hand than in the other. It is not necessary to wait until the pupil can per- form algebraic and geometric demonstrations of general mathematical truths before giving him any insight into them ; but this should be done through the presentation of one or more individual illustrations, when there is first need of using the generalization. 36. Next to mathematical general conceptions come those having to do with external nature. With mathemat- ics all is exact and limited ; with nature, on the contrary, inexactness and uncertain extension prevail. The notion trianyle may easily be defined with exactness ; not so the notion horse. But here as everywhere, we must begin with the known individual. In natural history, individual ob- jects must be carefully compared, their likenesses and differences noted, the accidental distinguished from the apparently essential, in order that the general notions may gain as much clearness and universality as the age and ability of the pupils permit. So in geography a. child's conception of a mountain, a river, a lake, an ocean, should be based upon what he has seen, first in nature about him. 64 THE ESSENTIALS OF METHOD. and then in pictorial representations. In physics, experi- ment should lead to the development of physical laws. Here we have, as in mathematics, an a priori element; i.e., the necessary belief of the mind in the uniformity of causa- tion. Like causes always produce like effects, provided the conditions do not vary. If, therefore, the principle of the siphon is grasped in an individual case, it will be understood in any other like case. 37. To develop true general notions concerning politi- cal or- social or ethical affairs is far more difficult than to do so in the realms of mathematics and the physical uni- verse ; first, because the senses cannot be appealed to, and, second, because of the infinitely more complex and entangling conditions. Compare such notions as state, na- tionality, society, justice, legal riyJit, moral good, with those of triangle, division of a fraction, mountain, lever. The com- plexity of the former is in sharp contrast to the relative simplicity of the latter. Instruction must, however, return as ever to the individual embodiments of these ideas ; for it is the universal law of all correct instruction that the general must be preceded by the particular, for there is no other way in which it can be understood. By this state- ment is not meant that pedagogical device is limited to one procedure. It may be that a mind can best be aroused by having some startling generalization hurled at it, which, however, can only be understood through much particulari- zation. Many good text-books introduce a topic by stating some broad general truth or law concerning it, but no good text-book assumes that the statement of a wide-reaching law is sufficient to explain and establish it. For example, Avery's " Elements of Natural Philosophy " begins al- most every topic with a definition, which is the expression of a general notion. Thus, at the head of the chapter on FROM INDIVIDUAL TO GENERAL NOTIONS. 65 machines is this: "WHAT is A MACHINE? A machine is a contrivance by means of which the power can be applied to the resistance more advantageously." Then follows a dis- cussion of what is contained in this definition. It matters not, therefore, whether one's general course is inductive or deductive ; this will depend largely upon the subject, and the mental maturity of those who are to pursue it. But one tiling is sure, there will never be any clear grasping of the significance of a general conception, until it has been tested at least, by individuals which are ranged under it. For the reason, then, that we first grasp the general through the particular, all ethical instruction should pro- ceed from individual cases of action involving a moral con- tent. Hence, it does not suffice to preach in school, except from the text of an actual event. Children can best get the first points of crystallization for moral truths from stories involving a moral content. Here the emotions are not unduly aroused, as they are likely to be where the action is one that touches them personally, so that the irrational nature of wrong action appeals to the under- standing as well as to feeling. History fulfills its noblest mission to the race on account of its ethical content and of the individual nature of the presentation. Every deed of heroism, of benevolence, of charity, of patriotism, is a con- crete embodiment of a precious virtue ; while every mean, cowardly, dastardly act is an individual protest against meanness, cowardice, or villainy. We can only continue the deposit about these starting points, until at last the soul is strong in itself to stand against temptation. $5 38. Most difficult of all is the formation of true general conceptions in the realm of (esthetic and religious truth. Here, again, we can but lay the beginnings of cor- 66 THE ESSENTIALS OF METHOD. rect ideas, and, as before, only by starting with individual illustrations. Call attention to the beauty in the flower, the tree, the bird, the landscape, the heavens. Awaken the first love of the beautiful in art by contrasting grace and beauty with ungainliness and ugliness. Teach rever- ence for age, for authority, for law, for the name of God. Awaken the feelings of love and thankfulness, in return for love and benefits. CHAPTER V. THE RETURN FROM GENERAL TO INDIVIDUAL NOTIONS. 39. WE have thus far considered two grand stages of rational methodology ; viz., the apperception, or assimilation of individual notions (preparation and presentation), and the transition from individual to general notions. One more equally important stage remains. This is the return from general to individual notions, or the application of derived universals to new particulars. Says Lange (Ueber Apperception, p. 129), "We have fallen from one extreme to the other : whereas, formerly a hard and lifeless instruc- tion laid the chief emphasis upon the memorizing of the text, it is the custom of our times largely to neglect the application of that which is learned; consequently, the ever-repeated complaint, that though our youth indeed know a great deal, they can do but little, that they possess indeed knowledge, but little capacity and readiness to act, and that upon leaving school, the knowledge largely dis- appears. Where drill and application are lacking, where a line of thought is developed, but in complete isolation from related thought, the capacity of applying this knowledge to its natural and appropriate field is soon lost, no matter how clear the original thought may have been." Pestalozzi goes even so far as to say (" How Gertrude," etc., XII.), "It is perhaps the most frightful gift which an evil genius makes to his age : knowledge without capacity to do." Why this stage of right method is so necessary and G7 68 THE ESSENTIALS OF METHOD. what are its essential features, will appear in the following sections. 40. Kant stated a profound and many-sided truth when he said -that notions without perceptions are blind, that they are mere empty forms. The man whose whole knowledge consists of abstractions has indeed a barren mind. He is able to deal in nothing but glittering gener- alities, so that his thinking pertains but slightly to the practical affairs of the world, in which alone man's destiny can be wrought out. Nor should we imagine that such thought marks more than an elementary stage of mind. Philology shows that language did not begin with the con- crete and gradually extend to the abstract, but that it began with the vague, the general, the indefinite ; as, with the verb, which represents no thing, but an action or a state, and with the pronoun as a verb-suffix, not indeed to repre- sent a noun, but to manifest a relation between the speaker and the object of thought. There must be a rich content of knowledge, as well as the generalizations derived from a few particulars. This can be obtained only by long and persistent application of abstractions a rule in arithmetic or grammar, for in- stance to appropriate fields of new particulars. It will not suffice to limit the study of differentiation to the indi- vidual notions from which the general was derived. Should a botanist know only the common characteristics of trees, the sight of a given tree could arouse no such wealth of conception as is supposed in the case quoted from Dr. Harris. Should he know only the individual characteris- tics of one tree, his experience of trees would still be meager and barren. If, then, knowledge is to have a full, rich content, as well as universality, the general truth gained must be perpetually enriched and re-euforced by application to new particulars. FROM GENERAL TO INDIVIDUAL NOTIONS. G9 41. There is need of a wide and persistent application of general truths, in order that they may become a perma- nent acquisition to the child. A principle in arithmetic, for example, even though fairly grasped by the pupil, will soon fade from his mind if extended application has not impressed it there. The need of doing this has usually been better recognized in arithmetic than in any other department of common school study. The fault of thought- less teaching in this branch has heretofore been, not so much a lack of application, as failure to teach the pupils to see the universality of the rules and principles ivhich they were using. The fact that the pupils are commonly drilled for a long time in the application of arithmetical rules, accounts in some measure for the lasting interest which teachers are able to awaken in this subject. That pupils remember these rules well is, therefore, not surprising, for in this branch they are better drilled in the application of principles than in any other. If this efficient drill upon new problems could be preceded by a derivation of general principles from particular cases, our instruction in this branch would be ideally correct. Furthermore, not only do pupils soon forget an unapplied generalization, but they can make it truly serviceable only by constant use. Practice makes perfect. 42. It is needful to practice a wide application of general truths, on account of the bearing of such practice upon all the affairs of life. The mind must be trained to distinguish the essential from the non-essential, the valid from the accidental or false, at all times and under all cir- cumstances. Man is constantly required to decide impor- tant questions which are complicated by details. The judge upon the bench must see the truth through a mass of conflicting testimony; the counsel before the bar must 70 THE ESSENTIALS OF METHOD. detect the weak points in his opponent's case, however covered by misleading evidence or argument ; the teacher must be able to see the most effective means of governing his school, or discover the straightest path to the pupil's understanding; the voter should be able to judge intelli- gently of the probable effect of any proposed political measure, however confusing and contradictory the argu- ments of politicians may be ; the merchant, the manufac- turer, and especially the speculator, needs the ability to weigh calmly the great factors, supply and demand, and com- petition, in the face of confusing but non-determining con- ditions. So in all departments of life, social, political, economical, the successful man, be he farmer or. warrior, merchant or teacher, is the one whose training enables him under all circumstances to recognize the important and enduring, however much they may be complicated with the accidental and non-essential. Such insight is not gained by the learning of individual facts, or by the memorizing of universal truths, but only by a constant, efficient applica- tion to a wide field of particulars, of general laws which have been consciously derived from individual cases. 43. Again, this perpetual return from the general to the particular is the most effective means for the co-ordina- tion of knowledge. It is too much the tendency of the schools to impart knowledge in parallel lines having little or no vital connection. For example, the studies whose common end is knowledge of the mother-tongue, such as reading, writing, spelling, composition, punctuation, gram- mar, rhetoric, are usually taught as separate and unrelated brandies of learning. When related studies are taught in this way, there must necessarily be great waste in the labor of learning, and great deficiency in the ready use of what is learned. To a greater or less degree, all knowledge FROM GENERAL TO INDIVIDUAL NOTIONS. 71 is related, all wisdom has a bearing upon every great enter- prise of life. To bring the mind to the consciousness of this unity of knowledge is one of the great functions of the school. The world is not so much surprised as grieved, however, when moral maxims appear to have little bearing on conduct, when the forms of religion lack the content of daily right living, when book-crammed brains cannot reduce their memorized theories to concrete practice. The most effective means for this desirable co-ordination of the knowl- edge at the pupil's command, aside from radical changes in the manner of presenting studies, is the thorough-going application of those generalizations at which the pupil has arrived, to all fields of particulars lying within his compass of thought. 44. With the foregoing exposition of the necessary stages of all right methods in mind, it is not difficult to discover where the prevailing treatment of various school studies has departed from correct pedagogical practice. The trinity of instruction embraces : (1) the apperception or assimilation of individual notions ; (2) the transition from the individual to the general (classes, rules, principles, maxims, etc.) ; (3) the return from the general notion to new fields of particulars. As we have seen, the fault in arithmetical instruction has been, not a lack of application, but a failure consciously to take the second step ; viz., to make the transition from given individual numerical rela- tions to a clear apprehension of the general principles involved. For example, though a general rule is given for division, pupils are rarely led even once to perceive clearly what is involved in such problems as the following : divide 10 apples equally among 5 boys ; and, having 10 apples, to how many boys can I give 2 apples each ? In grammar, .however, all of the vital points in instruction have been 72 THE ESSENTIALS OF METHOD. ignored to a greater or less degree. There has been, in our modern standard grammars, very little attempt to grasp vividly even individual facts of language, almost no attempt to develop general principles from individual illus- trations, and but meager and formal application of general laws to new particulars. Each subject is usually intro- duced by an underived definition, which is illustrated by a single sentence, and applied to a few disjointed, often meaningless, sentences. Thus, for illustration, we find such treatment as the following : " Verbs are divided, according to their use, into transitive and intransitive. A transitive verb receives or requires an object to complete its meaning. Example. The servant opened the door. What walls can guard me, or what shades can hide [mo] ? Pope. An intransitive verb neither receives nor requires an object to complete its meaning. Example. The sun rises. The horse runs." We have for application such sentences as the following : Anna loves her mother, The golden gates open, The moon silvers the distant hills, Mary has found her ring, Eleanor writes poetry, The snow melts, etc. What wonder that countless children have thought gram- mar " dry," when they have begun with abstractions whose full meaning they were never taught to see, and whose application, of the most formal kind, was to meager amounts of matter possessing often neither coherency nor inherent value ? We have been trying to discover what the essential ele- ments of a good method are. If one or more of these elements are ignored or slighted, the method is pedagogically unsound, and its results will be unsatisfactory, whether the fault be in the text-book, or in the teacher, or in both. But if the essentials of right methods are observed, there may be almost infinite variety of device in teaching and reciting FROM GENERAL TO INDIVIDUAL NOTIONS. 73 the lesson, without vitiating the results. This is the true scope for the individuality of the teacher and the text- book, but neither teacher nor book can ignore the essential forms of true methods without encountering partial or total failure. Until recently, formalism governed our teaching of gram- mar. The recitation of rules which had lost, or perhaps never had, content ; the endless repetition of forms value- less for thought ; and the ceaseless and formal iteration of the properties of the parts of speech in parsing, long after the last ripple of thought or interest had faded away, led finally to a revolt which is almost as irrational as that from which it would fly. In a vast number of schools, grammar proper has disappeared, and in its place has come the "language lesson." This consists chiefly in practice upon the art of composing, and is usually accompanied with some formal instruction upon such grammatical forms as appear in writing. This is well enough in the element- ary grades, but it is not grammar; it opens the mind to none of the great lines of thought to which grammar is the gateway, logic, rhetoric, psychology, philosophy. In geography and history the case is not greatly different. Text-books in geography often begin with abstract defini- tions, of which the child can have little or no apprehension. Thus, " The earth is the planet on which we live." Even with the simpler notions, such as mountain, river, plain, lake, island, cape, little effort is made to enable the child to arrive at proper conceptions, or even to obtain any conceptions at all. But perhaps the most serious fault of the current methods of teaching geography is, that the child is not taught to look within and beyond the individ- ual facts he learns. The subject remains in its individual- ized stage. There is no passing from individual to general 74 THE ESSENTIALS OF METHOD. notions, no application of geographical principles to new particulars. For this reason, no geographical fact appears to have more than a momentary and accidental relation to any other. Under such treatment, geography becomes a chaos of unrelated facts, having no progress, no develop- ment, no rational unification, no end. Facts are learned only to be forgotten, or to lie in the soul isolated and devoid of significance. Ritter and Guyot never subject geography to such irrational treatment, but then their books are not popular. They demand some thought on the part of the teacher, and thought is the last thing which the inexperienced or untrained teacher is able or willing to give. History, like geography, records a wilderness of facts. If our analysis of the essentials of right methods is correct, these facts should be grouped, not only so that they may be remembered, but so that the lessons they should teach may appear in the consciousness of the learner. This is true not alone of the ethical lessons with which history always abounds, but also of the immediate ends for which men struggle. When the objective point for which a war, a campaign, or a battle is conducted is once understood, it becomes a beacon-light by which the meaning of every movement may be examined. Historical facts are then vitally related and easily remembered. But to require an unthinking memorizing of facts, to impart a knowledge whose rational connection and significance depends upon accident, and whose application never appears, is to pursue a method as unpedagogical as it is easy. STATE NORMAL SiHOOL, LOS ANGELES, -:- CAL. CHAPTER VI. ADDITIONAL CONSIDERATIONS. METHOD-WHOLES. 45. A METHOD of teaching which deals solely or chiefly with individual facts, without regard to their logical inter- dependence and content, would naturally need to take no thought about the most efficient subdivision of the matter to be learned, since one halting-place would be as good as another. Thus, a certain number of words in spelling, a given number of places in a map-lesson in geography, a convenient number of pages in history would constitute the lesson. Only considerations of the time at disposal and the age of the pupils would determine these purely arbitrary subdivisions. With a rational view of the function of instruction and the necessary form of right methods, quite another principle of subdivision must be observed. In accordance with this idea, individual facts must be made to yield their rational content in the form of definitions, rules, principles, maxims, etc., which must in turn have a wide application to the whole field of new individual facts to which then are appropriate. It in evident, therefore, that there must be a subdivision of the matter of instruction for every impor- tant general notion which is to be derived and applied. Thus, each important definition or rule of mathematics or gram- mar should be treated by itself in derivation or develop- ment from individual facts, and in its appropriate applica- tion. Here the proper subdivision is almost a matter of 76 THE ESSENTIALS OF METHOD. course, but it is more difficult in the departments of history, geography, and natural history, where apparent progress is possible without any reflection whatever. In mathematics and grammar a separate division or method-whole can usually be treated every day ; but in the other departments named, a method-whole will frequently occupy the time of the class for several days. For example, Grant's Chatta- nooga Campaign may well be treated as a whole, as the working out of a single conception, yet it would ordinarily need more than a single recitation to complete the subject. In mathematical and physical geography, the subdivisions are as plainly marked as in mathematics and grammar ; but political geography is in special danger of aimless and use- less subdivision. Each group of political facts should be viewed as the manifestation of some idea, the result of some cause, social, physical, or economical ; for example, the rise of great cities, the development of manufacturing industries, the distribution of population, the prevalence of staple crops, the growth of facilities for transportation. If a section of country is to be studied, its rivers, moun- tains, towns, lines of communications, inhabitants, furnish topics for the individual facts ; a drawing of the whole brings the manifold into a unity ; while drawings from memory, the location of important points, imaginary jour- neys from place to place, descriptions of people, employ- ments, etc., furnish ample application. The younger the children are, the smaller must the subdivisions be. Only one caution needs to be given. Care must be taken not to atomize the instruction. The presupposition of brains on the part of the children must always be made, for they come to a thousand conclusions and take a thousand steps in thinking, which the teacher need not painfully point out. The teacher is needed for those steps which the children ADDITIONAL CONSIDERATIONS. 77 cannot take alone, the derivations and applications which they would not or could not make ; consequently, instruc- tion should deliberately plan for these greater matters of education, leaving the smaller ones to an awakened sponta- neity of the pupil, or to incidental instruction. With these general remarks on the subdivision of the matter of in- struction into method-wholes, the subject may be deferred until the practical illustrations are reached. RELATION OF SO-CALLED "METHODS 5 ' TO THE ESSENTIAL FORMS. 46. That the relation of the essential forms of instruc- tion, as exhibited in this volume, to what are usually known as "methods" of teaching may clearly appear, a brief analysis of the latter will now be given. Methods of imparting knowledge may be considered from three stand- points : (1) the learner, (2) the matter taught, and (3) the teacher. 1. Methods with regard to the learner. Nothing can be learned, except as it is apprehended under the forms of thought; of these, logic exhibits three: (1) the notion, (2) the judgment, (3) the syllogism. Knowledge can there- fore be imparted in the form of explication, predication, or demonstration. (a) The forms of explication. Notions, as the synthe- sized characteristics of things, form the elements of thought and, hence, of knowledge. The notion of a thing is con- veyed in two ways ; (1) by observation, and (2) by the words. The first gives the objective, or observation ; the second, the defining method. Observation evidently has to do with the first formal stage of instruction ; viz., the apprehension of the individual notion. Definition is the 78 THE ESSENTIALS OF METHOD. summary of the second stage ; viz., the transition to the general notion. (6) The form of predication. When two or more notions are brought into relation through the copula, we have the expression of the judgment, or a predication. When predi- cation is made without regard to progress in time, we have the descriptive method: this pertains to the first stage of instruction, in which new facts are learned. When the predication pertains to that which is becoming, or progress- ing in time, we have the genetic form of instruction : this may in turn be progressive or regressive, according as the predication takes the direction of the development or the reverse. History, for instance, may be regarded as a de- velopment in time, in which the events of one period appear as the cause of those of later periods. Like the descriptive predication, the genetic belongs to the first stage of instruc- tion, the imparting of information. (c) The form of demonstration. If two or more judg- ments are so related that a new judgment follows, the syllogism arises. A demonstration must proceed from a universal to a particular, or the reverse. The first gives the deductive proof; the second, the inductive. Induction answers especially to the second grand stage of instruction, for it is the business of induction to derive a universal truth from given particulars. Deduction corresponds most closely to the stage of application, or the return from universals to new particulars. 2. Methods with regard to the thing learned. An object of knowledge is analogous to the notion with its characteristics : it consists of a whole and its parts. One may begin with the whole and proceed to its parts, or one may begin with the parts and proceed to the whole. Thus, in geography, the earth itself, or the geographical facts in ADDITIONAL CONSIDERATIONS. 79 the neighborhood, may be the starting-point. The method which begins with the whole and proceeds to the parts is analytical ; that which begins with separate facts and works toward the total is synthetical. The essential forms of right methods may be observed with either of these pro- cesses ; e.g., it is indifferent, so far as observation of the essentials of right methods is concerned, whether grammar is begun with the sentence or with the word, whether gram- mar is taught analytically or synthetically. It goes without saying, that these two methods of treating a subject may be combined. 3. Methods with regard to the teacher. Aside from the first two considerations, the communication of knowledge is realized (1) through the monologue on the part of the teacher, or (2) through the dialogue, in which the question is an important factor. The monologue is important in imparting information, in the first stage ; and the dialogue (catechetical, Socratic, developing method), in preparation for apperception, in developing the universal from the particular, and in applying it to other particulars. 1 1 Compare Vogel, Encydopcdas der Pudagoyik, pp. (57-70. PART III. PRACTICAL ILLUSTRATIONS. CHAPTER VII. 47. THAT the young teacher may have a few illustra- tions of the practical workings of the ideas presented in this volume, the following working models are offered. All that is claimed for them is, conformity to the essential stages of a correct method; viz., a conscious effort to observe : (1) the apperception of new facts, in preparation and presentation; (2) the transition from individual to general notions, whether the latter appear as definitions, rules, principles, or moral maxims ; and (3) the application of these general truths to concrete facts, i.e., the return from universals to particulars. The illustrations cover all the studies of the common school curriculum, and often several grades of work in each. For many of the illustra- tions the author is more or less indebted to others, notably to Professor W. Kein, of the university of Jena, and to Dr. 0. Frick, director of the Frankeschen Stiftungen, in Halle. LANGUAGE. 48. Oral language-lesson for the first grade. SUBJECT-MATTER. THE WREN AND THE BEAR. I. (a) One summer's day, a bear and a wolf took a walk in the woods together. The wolf heard a beautiful song from a bird, and said, " Brother Bear, what kind of a bird is it that sings so 80 PRACTICAL ILLUSTRATIONS. 81 finely ? " " That is the king of birds," said the bear, " and before him we must bow." It was the wren, which is called the king of the hedge. Then said the bear, " If that is so, I should like to see his kingly palace; come, show me the way to it." "That won't do," said the wolf : " you must wait until the queen comes." (6) Soon the king and queen came, bringing food in their bills to feed their children, the little wrens. The bear wanted to follow them at once, but the wolf held him back by the sleeve, and said, " You must wait until the king and queen are gone." Then the bear and the wolf noticed the hole where the nest was, and went off. (c) But the bear could not rest until he had seen the palace, and after a short time went back to the nest and looked in. The king and the queen had flown away. He looked into the nest, but saw nothing except five or six young birds. "Is that the kingly palace ? " cried the bear. " That is a pretty palace ! You are no king's children, you are nothing but common children." But when the young birds heard this, they were very angry, and cried out, "No, we are not common children, our father is king, and our mother is queen. You shall be sorry for what you have said, Mr. Bear!" (rf) The bear and the wolf began to be afraid, and hurried back to their dens. The young birds screamed and scolded until their parents came again, bringing them more food. Then they said, " Even if we have to starve, we will not touch so much as a fly's leg until you have shown the bear that we are not common children. He has been here and has insulted us." (e) Then said the old king, " Don't worry, I will soon settle that matter." Then he and the queen flew to the bear's den, and shouted into the hole, "You old growling bear, why have you abused my children ? You shall be sorry for that, for I declare war against you." Then the war was declared, and the bear called together all four-footed animals to aid him, the ox, the donkey, the deer, the wolf, and all others to be found in the world. The king called together all the animals which fly in the air; not only all the birds, big and little, but all flies and gnats and bees and hornets. 82 THE ESSENTIALS OF METHOD. II. (a) When the war was about to begin, the king sent out his spies to find out who the general of the army Avas. The gnat, who was the slyest of all, flew into the woods where the bear and his friends were gathered, and lit on the under side of a leaf of the tree under which the matter was to be settled. The bear stood up, called out the fox, and said, " Fox, you are the most cunning of all animals, you shall be our general and lead us."- ' All right,'' said the fox, " but what sort of signs shall we agree upon?" Nobody knew. Finally the fox said, "I have a fine, long, bushy tail ; it looks like a fine red plume of feathers. When I hold it up, then everything is well, and you must march forward; but if I let it hang down, then run for your lives." When the gnat heard this, she fled at once to the king, and told him all about it. (b) At daybreak, when the battle was to begin, the four-footed animals rushed to the place with such fury that the earth trembled. The king came also with his army, through the air. They whizzed and screamed and buzzed until it was dreadful to hear them. But the king sent for the hornet and told him to fly down, settle on the under side of the fox's tail, and sting with all his might. When the fox got the first sting, he could not help jumping, but lie bore the pain, and kept his tail up. At the second sting he had to let his tail drop for an instant; at the third sting he could stand it no longer, but dropped his tail between his legs and screamed with pain. When the animals saw this, they thought everything was lost, and began to run, every one to his den. The birds had won the battle. in. Then the king and queen flew back to their children, and cried, " Children, be happy, eat and drink, for we have won the victory." But the young ones said, "We will not yet eat. The bear must first come before the nest and beg pardon, and say that we are kingly children." Then the king flew to the bear's den, and said, " You old, growling bear, you must go to my nest and ask pardon, and say that my children are kingly children, or you will have PRACTICAL ILLUSTRATIONS. 83 every rib in your body broken." The bear crept to the nest in fear, and begged for pardon. The young birds were now satis- fied. They came together, ate and drank, and had a jolly time till late into the night. TREATMENT. TJie entire story is considered a method- whole, but is subdivided for convenience of preparation and presentation, and of repetition by the children. (.4)1 STAGE OF APPERCEPTION. I. (1) Preparation for Section L We have leai'ned about the wolf and the seven kids, also about the wolf and the fox. Per- haps you have seen a bear? (Dancing bear, picture.) The wren, or the king of the hedge, is one of the smallest of birds. A king lives in a castle. (Pictures.) What is the castle of the hedge king? Who obeys him? (Animals.) Are they always peaceful ? What do they do sometimes ? Who has seen this ? (Fights between dogs, between cat and dog, etc.) Leaders, parties, war, victory. (2) Presentation. Teacher tells the story in sections to "bees and hornets," pausing at the end of each subdivision, a, b, c, d, and c, to have the story repeated by the children. ii. (1) Preparation for Section IL Now, there were two armies who were going to have a battle. What animals were on one side? What on the other? What kind of weapons did they have? Was each animal allowed to do whatever he wanted to? Who gave the orders for one side? For the other? General, scout, battle. Which side do you think will win? (2) Presentation. Story in sections a and b, to " the birds had won the battle." Children repeat as before. 1 To avoid needless repetition, let it be understood that the cnpital letter A stand- for the stage of apperception; B, for the transition from the. individual to the general notion ; and C, for the stage of application, or the return from general notions (definitions, rules, principles, maxims, etc.) to new individual notions. 84 THE ESSENTIALS OF METHOD. in. (1) Preparation for Section IIL The bear had lost the battle. Do you suppose the young birds were entirely satisfied ? Why not? What ought the bear to do yet? (2) Presentation. Story to the end, with repetition of the various sections until all the children can repeat the whole story in good language. This will require several recitations of twenty minutes each. (5)1 STAGE OF ELABORATION. Transition from particulars to generals. (3) Derivation of notional content. (In this case moral maxims.) The bear was very curious. He wanted to see what he sup- posed would be the castle of the king's children. But he judged according to appearances. Do appearances ever deceive ? (In- stances by the children.) Did he speak properly to the young birds, even if they had been what the bear supposed? lie insulted them. Was that right ? What did the fox call the wolf ? (See Grimm's story of "The Fox and the Wolf.") A glutton. Was this an insult ? Should children call names ? Did the young birds put up with everything ? What did they do ? FORMULATION OF MAXIMS. (1) Do not judge according to appearances. (2) Insult no one. (3) Guard your good name. (4) Do not be overcurious. (C)i STAGE OF APPLICATION. (4) Application Examples of children who are too curious. If any one is poorly clothed, what may one not say at once? Should he be insulted ? If any one insults you, how shall you act ? Examples. 1 See note at foot of page 83. PRACTICAL ILLUSTRATIONS. 85 49. Oral language-lesson for the second or third grade. THE SHIPWRECK. Adapted from " Robinson Crusoe." They had sailed several weeks, and Robinson had long since forgotten his intention to return home. Suddenly there arose a second storm, much more fearful than the first. The ship was tossed about on the sea like a nutshell, and the waves broke over the deck every minute. Then Robinson became dreadfully frightened, and thought every instant to find his death in the waves. The storm lasted for several hours. All at once Robinson felt a powerful shock. The ship had struck upon the rocks. At that instant the sailors cried out, " The ship has sprung a leak ! " The water rushed into the ship. Everybody cried for help. Each thought only of saving his own life. A boat was lowered into the sea at once, and all spiting in. They had not gone far from the ship, when a mighty wave upset the boat, and swallowed up all the men. Robinson was also thrown into the sea by the wave, but he succeeded in rising to the surface for an instant ; in the next he was again under water. Soon a wave lifted him up again, and he was able to keep his head and breast out of the water for a short time. He noticed that he was not far from land. Scarcely had he spied the shore when a wave dashed him so violently against a rock that he believed his last moment had arrived. But he had presence of mind enough to cling to the rock with his arms. This saved him; for, soon a returning wave dashed over him, and would have carried him away, had he not held f:ist. Now he clambered up the shore, but his strength was so far gone that he fainted. For a time he lay unconscious. As he opened his eyes, his first words were, " Where am I ?" He looked about for the men who had been with him in the boat, but nothing was to be seen of them. They were drowned in the sea, and he alone had re- mained alive. He fell upon his knees and thanked God for his rescue. 86 THE ESSENTIALS OF METHOD. TREATMENT. (Elaborate outline by a student of Illinois State Normal University.) Determine what subdivisions, if any, are needed. This section might be subdivided into two parts, the first being a description of the shipwreck as a whole (. . . " and swallowed up all the men"), the second relating the individual event concern- ing Robinson's wonderful rescue (. . . "thanked God for his rescue"). The idea to be developed out of the first part would be the tearfulness of a storm at sea; that of the second, the necessity of keeping his presence of mind in danger. But as it is a second storm, it may be supposed that something about such a calamity has been said in the first section ; moreover, the two ideas to be brought out are so nearly related that the entire section can be taken as one method-whole,. (A) (1) Preparation. Teacher: We have had many stories that tell us about life on the land or the continent; this time we may see, therefore, how things look on water, and what may happen when we are there. Who has ever seen a large river or a lake? Have you ever been in a ship there ? Yes; Mississippi, Lake Michigan, etc. How is a boat moved? Oars, sails, steam. Teacher mentions that the use of steam was not known in former times. Is a voyage on water pleasant, or not? O, yes. But rivers and lakes are not all the water we have. Who knows whither the Mississippi is flowing? The St. Lawrence? Any river ? Why does the sea not overflow ? Nobody. Teacher : This seems strange, and I myself studied about that when a boy; finally I found it out, and I'll tell you about it at some other time, if nobody anticipates me. Do you believe thei'e are any ships on the sea? How many? Pupils laughing. Do you think they are as large as those on rivers or lakes ? Who has ever seen one ? Teacher presents a picture of an ocean steamer and of a large sail vessel. Did you ever hear of Europe? O, yes; son of an immigrant. How do immigrants come from there, or how PRACTICAL ILLUSTRATIONS. 87 would you get there ? Why ? Do you know how the Chinamen come to this country ? The sea they have to cross is even much larger than that between America and Europe. Do you suppose you could see the shore at any time when at sea? Could the voyage be made in a shorter or longer time before the use of steam-power? What power only was then used to move these large vessels? You told me a while ago that traveling on water is very pleasant. Can you. think of a case where it would not be so? Wind, sweeping away whole towns. What effect will it have upon the water ? Upon the ship ? Tossing. How if the shore or some shallow place were near? What of the ship and the passengers ? Do you think such a case may be foreseen ? Can the storm be avoided ? Can any preparation be made to avoid danger? Did you ever see a small boat hung on the side of a largo vessel? What for? Ans. I thought it was for fishing or bathing. Not quite ; they are safety-boats ; a large sea vessel has several of them, perhaps a dozen. Would you now have courage enough to sail in such a vessel for a far country? A sailor's boy, who could not keep his seat quietly, "I should, I should!" You, boys? "O, yes." You. girls? (Doubts.) (2) Presentation. (a) Relate the story, being careful in the text. Stop at the point where the individual story begins. Let the pupils repeat thus far; correct false conceptions. Second part in the same way. (b) Do not interrupt the pupil at every moment ; let him have " his talk/' and see what his conception of the matter is. (c) Use correct and logical language, in repetition as well as the first time, or the pupils will correct you. () about something else. Must every sentence tell or assert something? Can you assert without asserting something? Can you assert anything without asserting it of something? How many elements, then, appear necessary to every sentence? FORMULATION. There are three essential elements in every sen- tence, SUBJECT, COPULA, and ATTRIBUTE; but the copula and attribute may be blended into one word when the attribute is verbal. (C.) (4) Select the essential elements in each of the sentences of your reading lesson (subject, copula, and attribute ; or, if the last two are blended, subject and verb). Remember that subject and attri- bute may have many modifying words. 52. A lesson in advanced grammar. NATURE AND USE OF THE ADJECTIVE. (A.) (1) Preparation. Review of the noun. What did we find the proper noun to be ? An individual name, or a name which if it/t- out limitation will apply to one object. Illustrate : John, Chicago. 96 THE ESSENTIALS OF METHOD. These names apply to their respective objects without any limita- tion or modification by adjectives. Is not the same thing true of common nouns ? No ; a common noun cannot apply to one object, or to a number of objects less than the whole class without being limited by an adjective. Illustrate : This apple, two boys, some trees, good children, a tall man. To what does a common noun refer when it is used without limitation ? To a whole class or to the totality of that to which it refers. Illustrate : Cats have sharp teeth and claws, i.e., all cats; water is good to drink; beauty is pleasant to look upon. Must every noun indicate some number or quantity of that which it names ? Of course. Classify objects according to number or quantity. One, some, all. What name have we given to that property of the noun by virtue of which it indicates a number or quantity ? Its extent. Show in a scheme what is possible with regard to the extent of the noun. ( (1.) One. , (Individual ) Extent of the Noun, i.e., ( 2 .) Some, f (i.) A limited No. the No. or quantity of that \ (Particular.) 1 (