Problem, a Motive.—The foregoing description and examples of the educative process have shown that new knowledge necessarily results whenever the mind faces a difficulty, or need, and adjusts itself thereto. In other words, knowledge is found to possess a practical value and to arise as man faces the difficulties, or problems, with which he is confronted. The basis of conscious activity in any direction is, therefore, a feeling ofneed. If one analyses any of his conscious acts, he will find that the motive is the satisfaction of some desire which he more or less consciously feels. The workman exerts himself at his labour because he feels the need of satisfying his artistic sense or of supplying the necessities of those who are dependent upon him; the teacher prepares the lessons he has to present and puts forth effort to teach them successfully, because he feels the need of educating the pupils committed to his care; the physician observes symptoms closely and consults authorities carefully, because he feels the need of curing his patients; the lawyer masters every detail of the case he is pleading, because he feels the need of protecting the interests of his client. What is true of adults is equally true of children in school. The pupil puts forth effort in school work because he feels that this work is meeting some of his needs.
Nature of Problem.—It is not to be assumed, however, that the only problem which will prompt the individual to put forth conscious effort must be a purely physical need, such as hunger, thirst, or a distinct desire for the attainment of a definite object, as to avoid danger or to secure financial gain or personal pleasure. Nor is it to be understood that the learner always clearly formulates the problem in his own mind. Indeed, as will be seen more fully later, one very important motive for mastering a presented problem is the instinct of curiosity. As an example of such may be noted a case which came under the observation of the writer, where the curiosity of a small child was aroused through the sight of a mud-turtle crawling along a walk. After a few moments of intense investigation, he cried to those standing by, "Come and see the bug in the basket." Here, evidently, the child's curiosity gave the strange appearance sufficient value to cause him to make it an object of study. Impelled by this feeling, he must have selected ideas from his former experience (bug—crawling thing; basket—incasing thing), which seemed of value in interpreting the unknown presentation. Finally by focusing these upon this strange object, he formed an idea, or mental picture, which gave him a reasonable control over the new vague presentation. Such a motive as curiosity may not imply to the same degree as some others a personal need, nor does it mean that the child consciously says to himself that this new material or activity is satisfying a specific need, but in some vague way he knows that it appeals to him because of its attractiveness in itself or because of its relation to some other attractive object. In brief, it interests him, and thus creates a tendency on the part of an individual to give it his attention. In such situations, therefore, the learner evidently feels to a greater or less degree a necessity, or a practical need, for solving the problem before him.
Knowledge Gained Accidentally.—It is evident, however, that at times knowledge might be gained in the absence of any set problem upon which the learner reacts. For example, a certain person while walking along a road intent upon his own personal matters observed a boy standing near a high fence. On passing further along the street, he glanced through an opening and observed a vineyard within the inclosure. On returning along the street a few minutes later, he saw the same boy standing at a near by corner eating grapes. Hereupon these three ideas at once co-ordinated themselves into a new form of knowledge, signifying stealing-of-fruit. In such a case, the experience has evidently been gained without the presence of a problem to guide the selecting and relating of the ideas entering into the new knowledge. In like manner, a child whose only motive is to fill paper with various coloured crayon may accidentally discover, while engaged on this problem, that red and yellow will combine to make orange, or that yellow and blue will combine to make green. Here also the child gains valuable experience quite spontaneously, that is, without its constituting a motive, or problem, calling for adjustment.
Learning without Motive.—In the light of the above, a question suggests itself in relation to the lesson problem, or motive. Granting that a regular school recitation must contain some valuable problem for which the learning process is to furnish a solution, and granting that the teacher must be fully conscious both of the problem and of its mode of solution, the question might yet be asked whether a problem is to be realized by the child as a felt need at the beginning of the lesson. For example, if the teacher wishes his pupils to learn how to compose the secondary colour purple, might he have them blend in a purely arbitrary way, red and blue, and finally ask them to note the result? Or again, if he wishes the pupils to learn the construction of a paper-box or fire-place, would he not be justified in directing them to make certain folds, to do certain cutting, and to join together the various sections in a certain way, and then asking them to note the result? If such a course is permissible, it would seem that, so far at least as the learner is concerned, he may gain control of valuable experience, or knowledge, without the presence of a problem, or motive, to give the learning process value and direction.
Problem Aids Control.—It is true that in cases like the above, the child may gain the required knowledge. The cause for this is, no doubt, that the physical activity demanded of the pupil constitutes indirectly a motive for attending sufficiently to gain the knowledge. But in many cases no such conditions might exist. It is important, therefore, to have the pupil as far as possible realize at the outset a definite motive for each lesson. The advantage consists in the fact that the motive gives a value to the ideas which enter into the new knowledge, even before they are fully incorporated into a new experience. For example, if in a lesson in geometrical drawing, the teacher, instead of having the child set out with the problem of drawing a pair of parallel lines, merely orders him to follow certain directions, and then requests him to measure the shortest distance between the lines at different points, the child is not likely to grasp the connections of the various steps involved in the construction of the whole problem. This means, however, that the learner has not secured an equal control over the new experience.
Pupils Feel Its Lack.—A further objection to conducting a lesson in such a way that the child may find no motive for the process until the close of the lesson, is the fact that he is himself aware of its lack. In school the child soon discovers that in a lesson he selects and gives attention to various ideas solely in order to gain control over some problem which he may more or less definitely conceive in advance. For this reason, if the teacher attempts, as in the above examples, to fix the child's attention on certain facts without any conception of purpose, the pupil nevertheless usually asks himself the question: "What does the teacher intend me to do with these facts?" Indeed, without at least that motive to hold such disconnected ideas in his mind, it is doubtful whether the pupil would attend to them sufficiently to organize them into a new item of knowledge. When, therefore, the teacher proposes at the outset an attractive problem to solve, he has gone a long way toward stimulating the intellectual activity of the pupil. The setting of problems, the supplying of motives, the giving of aims, the awakening of needs—this constitutes a large part of the business of the teacher.
Pupil's Problem versus Teacher's.—But it is important that the problem before the pupil at the beginning of the lesson should really be the pupil's and not the teacher's merely. The teacher should be careful not to impose the problem on the pupils in an arbitrary way, but should try to connect the lesson with an interest that is already active. The teacher's motive in teaching the lesson and the pupil's motive in attending to it are usually quite different. The teacher's problem should, of course, beidentical with the real problem of the lesson. Thus in a literature lesson on "Hide and Seek" (Ontario Third Reader), the teacher's motive would be to lead the pupil to appreciate the music of the lines, the beauty of the images, and the pathos of the ideas; and in general, to increase the pupil's capacities of constructive imagination and artistic appreciation. The pupil's motive might be to find out how the poet had described a familiar game. In a nature study lesson on "The Rabbit," the teacher's motive would be to lead the pupil to make certain observations and draw certain inferences and thus add something to his facility in observation and inference. The pupil's motive in the same lesson would be to discover something new about a very interesting animal. In general, the teacher's motive will be (1) to give the pupil a certain kind of useful knowledge; (2) to develop and strengthen certain organs; or (3) to add something to his mechanical skill by the forming of habitual reactions. In general, the pupil's motive will be to learn some fact, to satisfy some instinct, or perform some activity that is interesting either in itself or because of its relation to some desired end. That is, the pupil's motive is the satisfaction of an interest or the promotion of a purpose.
Pupil's Motive May Be Indirect.—It is evident from the foregoing that the pupil's motive for applying himself to any lesson may differ from the real lesson problem, or motive. For instance, in mastering the reading of a certain selection, the pupil's chief motive in applying himself to this particular task may be to please and win the approbation of the teacher. The true lesson problem, however, is to enable the learner to give expression to the thoughts and feelings of the author. When the aim, or motive, is thus somewhat disconnected from the lessonproblem itself, it becomes anindirectmotive. While such indirect motives are undoubtedly valuable and must often be used with young children, it is evident that when the pupil's motive is more or less directly associated with the real problem of the lesson, it will form a better centre for the selecting and organizing of the ideas entering into the new experience.
Relation to Pupil's Feeling.—A chief essential in connection with the pupil's motive, or attitude, toward the lesson problem, is that the child shouldfeela value in the problem. That is, his apprehension of the problem should carry with it a desire to secure a complete mastery of the problem from a sense of its intrinsic value. The difference in feeling which a pupil may have toward the worth of a problem would be noticed by comparing the attitude of a class in the study of a military biography or a pioneer adventure taken from Canadian or United States sources respectively. In the case of the former, the feeling of patriotism associated with the lesson problem will give it a value for the pupils entirely absent from the other topic. The extent to which the pupil feels such a value in the lesson topic will in most cases also measure the degree of control he obtains over the new experience.
As will be seen inChapter XXIX, where our feeling states will be considered more fully, feeling is essentially a personal attitude of mind, and there can be little guarantee that a group of pupils will feel an equal value in the same problem. At times, in fact, even where the pupil understands fairly well the significance of a presented lesson problem, he may feel little personal interest in it.One of the most important questions of method is, therefore, how to awaken in a class the necessary interest in the lesson problem with which they are being presented.
1.Through Physical Activity.—It is a characteristic of the young child to enjoy physical activity for the sake of the activity itself. This is true even of his earliest acts, such as stretching, smiling, etc. Although these are merely impulsive movements without conscious purpose, the child soon forms ideas of different acts, and readily associates these with other ideas. Thus he takes a delight in the mere functioning of muscles, hands, voice, etc., in expressive movements. As he develops, however, on account of the close association, during his early years, between thought and movement, the child is much interested in any knowledge which may be presented to him in direct association with motor activity. This fact is especially noticeable in that the efforts of a child to learn a strange object consist largely in endeavouring to discover what he can do with it. He throws, rolls, strikes, strivestoopen it, and in various other ways makes it a means of physical expression. Whenever, especially, he can discover the use of an object, as to cut with knife or scissors, to pound with a hammer, to dip with a ladle, or to sweep with a broom, this social significance of the object gives him full satisfaction, and little attention is paid to other qualities. For these reasons the teacher will find it advantageous, whenever possible, to associate a lesson problem directly with some form of physical action. In primary number work, for example, instead of presenting the child with mere numbers and symbols, the teacher may provide him with objects, in handling which he may associate the number facts with certain acts of grouping objects. It is in this way that a child should approach such problems as:
How many fours are there in twelve?How many feet in a yard?How many quarts in a peck? etc.
How many fours are there in twelve?How many feet in a yard?How many quarts in a peck? etc.
The teaching of fractions by means of scissors and cardboard; the teaching of board measure by having boards actually measured; the teaching of primary geography by means of the sand-table; the teaching of nature study by excursions to fields and woods; these are all easy because we are working in harmony with the child's natural tendency to be physically active. The more closely the lesson problem adjusts itself to these tendencies, the greater will be the pupil's activity and hence the more rapid his progress.
2. Through Constructive Instinct.—The child's delight in motor expression is closely associated with his instinctive tendency to construct. When, therefore, new knowledge can be presented to the child in and through constructive exercises, he is more likely to feel its value. Thus it is possible, by means of such occupations as paper folding or stick-laying, to provide interesting problems for teaching number and geometric forms. In folding the check-board, for example, the child will master necessary problems relating to the numbers, 2, 4, 8, and 16. In learning colour, it is more interesting for the child to study different colours through painting leaves, flowers, and fruits, than to learn them through mere sense impressions, or even through comparing coloured objects, as in the Montessori chromatic exercises. A study of the various kindergarten games and occupations would give an abundance of examples illustrative of the possibility of presenting knowledge in direct association with various types of constructive work.
A. Activity must be Directly Connected with Problem.—It may be noted, however, that certain dangers associate themselves with these methods. One danger consists in the fact that, if care is not taken, the physical activity may not really involve the knowledge to be conveyed, but may be only very indirectly associated with it. Such a danger might occur in the use of the Montessori colour tablets for teaching tints and shades. In handling those, kindergarten children show a strong inclination to build flat forms with the tablets. Now unless these building exercises involve the distinguishing of the various tints and shades, the constructive activity will be likely to divert the attention of the pupil away from the colour problem which the tablets are supposed to set for the pupils.
B. Not too much Emphasis on Manual Skill.—Again, in expressive exercises intended merely to impart new knowledge, it may happen that the teacher will lay too much stress on perfect form of expression. In these exercises, however, the purpose should be rather to enable the child to realize the ideas in his expressive actions. When, for example, a child, in learning such geographical forms as island, gulf, mountain, etc., uses sand, clay, or plasticine as a medium of expression, too much striving after accuracy of form in minor details may tend to draw the pupil's attention from the broader elements of knowledge to be mastered. In other words, it is the gaining of certain ideas, or knowledge, and not technical perfection, that is being aimed at in such expressive movements.
figure
3. Instinct of Curiosity as Motive.—The value of the instinct of curiosity in setting a problem for the young child has been already referred to. From what was there seen, it is evident that to the extent to which the teacherawakens wonder and curiosity in his presentation of a lesson problem, the child will be ready to enter upon the further steps of the learning process. For example, by inserting two forks and a large needle into a cork, as illustrated in the accompanying Figure, and then apparently balancing the whole on a small hard surface, we may awaken a deep interest in the problem of gravity. In the same manner, by calling the pupils' attention to the drops on the outside of a glass pitcher filled with water, we may have their curiosity aroused for the study of condensation. So also the presentation of a picture may arouse curiosity in places or people.
4. Ownership as Motive.—The natural pleasure which children take in collection and ownership may often be associated with presented problems in a way to cause them to take a deeper interest in the knowledge to be acquired. For example, in presenting a lesson on the countries of Europe, the collection of coins or stamps representative of the different countries will add greatly to the interest, compared with a mere outline study of the political divisions from a map. A more detailed examination of the instincts and tendencies of the child and theirrelation to the educative process will, however, be found inChapter XXI.
5. Acquired Interest as Motive.—Finally, in the case of individual pupils, a knowledge of their particular, or special, interests is often a means of awakening in them a feeling of value for various types of school work. As an example, there might be cited the experience of a teacher who had in his school a pupil whom it seemed impossible to interest in reading. Thereupon the teacher made it his object to learn what were this pupil's chief interests outside the school. Using these as a basis for the selecting of simple reading matter for the boy, he was soon able to create in him an interest in reading for its own sake. The result was that in a short time this pupil was rendered reasonably efficient in what had previously seemed to him an uninteresting and impossible task.
6. Use of Knowledge as Motive.—In the preceding cases, interest in the problem is made to rest primarily upon some native instinct, or tendency. It is to be noted, however, that as the child advances in the acquisition of knowledge, or experience, there develops in him also a desire for mental activity. In other words, the normal child takes a delight in the use of any knowledge over which he possesses adequate control. It is to be noted further, that the child masters the new problem by bringing to bear upon it suitable ideas selected out of his previously acquired experiences. It is evident, therefore, that, when a lesson problem is presented to the child in such a way that he sees a connection between it and his present knowledge and feels, further, that the problem may be mastered by a use of knowledge over which he has complete mastery, he will take a deeper interest in the learning process. When, on the other hand, he has imperfect control over the old knowledge from which the interpreting ideas are selected, his interest in the problem itself will be greatly reduced. Owing to this fact, the teacher may adapt his lesson problems, or motives, to the stage of development of the pupils. In the case of young children, since they have little knowledge, but possess a number of instinctive tendencies, the lesson problem should be such as may be associated with their instinctive tendencies. Since, however, the expressing of these tendencies necessarily brings to the child ideas, or increases his knowledge, the pupil will in time desire to use his growing knowledge for its own sake. Here the child becomes able to grasp a problem consciously, or in idea, and, so far as it appeals to his past experience, will desire to work for its solution. Thus any problem which is recognized as having a vital connection with his own experience constitutes for the child a strong motive. For older pupils, therefore, the lesson problem which constitutes the strongest motive is the one that is consciously recognized and felt to have some direct connection with their present knowledge.
Relation to Pupil's Knowledge.—Since the conscious apprehension of the problem by the pupil in its relation to his present knowledge constitutes the best motive for the learning process, a question arises how this problem is to be grasped by the pupil. First, it is evident that the problem is not a state of knowledge, or a complete experience. If such were the case, there would be nothing for him to learn. It is this partial ignorance that causes a problem to exist for the learner as a felt need, or motive. On the other hand it is not a state of complete ignorance,otherwise the learner could not call up any related ideas for its solution. When, for example, the child, after learning the various physical features, the climate, and people of Ontario, is presented with the problem of learning the chief industries, he is able by his former knowledge to realize the existence of these industries sufficiently to feel the need of a fuller realization. In the same way the student who has traced the events of Canadian History up to the year 1791, is able to know the Constitutional Act as a problem for study, that is, he is able to experience the existence of such a problem and to that extent is able to know it. His mental state is equally a state of ignorance, in that he has not realized in his own consciousness all the facts relative to the Act. In the orderly study of any school subject, therefore, the mastery of the previous lesson or lessons will in turn suggest problems for further lessons. It is this further development of new problems out of present knowledge that demands an orderly sequence of topics in the different school subjects, a fact that should be fully realized by the teacher.
Recognition of Problem: A. Prevents Digressions.—An adequate recognition of the lesson problem by the pupil in the light of his own experience is useful in preventing the introduction of irrelevant material into the lesson. Young children are particularly prone (and, under certain circumstances, older students also) to drag into the lessons interesting side issues that have been suggested by some phase of the work. As a rule, it is advisable to follow closely the straight and narrow road that leads to the goal of the lesson and not to permit digressions into attractive by-paths. If a pupil attempts to introduce irrelevant matter, he should be asked what the problem of the lesson is and whether what he is speaking of willbe of any value in attaining that end. The necessity of this will, however, be seen more fully in our consideration of the next division of the learning process.
B. Organizes the Lesson Facts.—The adequate recognition of the lesson problem is valuable in helping the pupil to organize his knowledge. If you take a friend for a walk along the streets of a strange city engaging him in interesting conversation by the way, and if, when you have reached a distant point, you tell him that he must find his way back alone, he will probably be unable to do so without assistance. But if you tell him at the outset what you are going to do, he will note carefully the streets traversed, the corners turned, the directions taken, and will likely find his way back easily. This is because he had a clearly defined problem before him. The conditions are much the same in a lesson. When the pupil starts out with no definite problem and is led along blindly to some unknown goal, he will be unable to retrace his route; that is, he will be unable to reproduce the matter over which he has been taken. But with a clearly defined problem he will be able to note the order of the steps of the lesson, their relation to one another and to the problem, and when the lesson is over he will be able to go over the same course again. The facts of the lesson will have become organized in his mind.
Precautions.—If the teacher expects his pupils to become interested in a problem by immediately recognizing a connection between it and their previous knowledge, he must avoid placing the problem before them in a form in which they cannot readily apprehend this connection.The teacher who announced at the beginning of the grammar lesson, "To-day we are going to learn about Mood in verbs" started the problem in a form that was meaningless to the class. The simplest method in such a lesson would be to draw attention to examples in sentences of verbs showing this change and then say to the class, "Let us discover why these verbs are changed." Similarly, to propose as the problem of the history lesson "the development of parliamentary government during the Stuart period" would be to use terms too difficult for the class to interpret. It would be better to say: "We are going to find out how the Stuart kings were forced by Parliament to give up control of certain things." Instead of saying, "We shall study in this lesson the municipal government of Ontario," it would be much better to proceed in some such way as the following: "A few days ago your father paid his taxes for the year. Now we are going to learn by whom, and for what purposes, these taxes are spent." Similarly, "Let us find out all we can about the cat," would be inferior to, "Of what use to the cat are his sharp claws, padded feet, and rough tongue?"
On the other hand, it is evident that, in attempting to present the problem in a form in which the pupils may recognize its connection with their previous experiences, care must be taken not to tell outright the whole point of the lesson. In a lesson on the adverb, for instance, it would not do to say: "You have learned how adjectives modify, or change the meaning of, nouns. To-day we shall study words that modify verbs." A more satisfactory way of proceeding in such a lesson would be to have on the black-board two sets of sentences exactly alike except that the second would contain adverbs and the first would not. Then ask: "What words are in the second group of sentences that are not in the first? Let us examine the use of these words." In the same way, to state the problem of an arithmetic lesson as the discovery of "how to add fractions by changing them to equivalent fractions having the same denominator" is open to the objection of telling too much. In this case a better method would be to present a definite problem requiring the use of addition of fractions. The pupil will see that he has not the necessary arithmetical knowledge to solve the problem and will then be in the proper mental attitude for the lesson.
A few additional examples, drawn from different school subjects, are here added to illustrate further what is meant by setting a problem as a need, or motive.
A. History.—The members of a Form IV class were about to take up the study of the influence of John Wilkes upon parliamentary affairs during the reign of George III. As most of the pupils had visited the Canadian Parliament Buildings and had watched from the galleries the proceedings of the House of Commons, the teacher took this as the point of departure for the lesson. First, he obtained from the class the facts that the members of the Commons are elected by the different constituencies of the Dominion and that nobody has any power to interfere with the people's right to elect whomsoever they wish to represent them. The same conditions exist to-day in England, but this has not always been the case there. There was a time when the people's choice of a representative was sometimes set aside. The teacher then inquired regarding the men who sit in the gallery just above the Speaker's chair. These are the parliamentary reporters for the important dailynewspapers throughout the Dominion. They send telegraphic despatches regarding the debates in the House to their respective newspapers. These despatches are published the following day, and the people of the country are thus enabled to know what is going on in Parliament. Nobody has any right to prevent these newspapers from publishing what they wish regarding the proceedings, provided, of course, the reports are not untruthful. These conditions prevail also in England now, but have not always done so.
The work of the lesson was to see how these two conditions, freedom of elections and liberty of the press, have been brought about. The pupils were thus placed in a receptive attitude to hear the story of John Wilkes.
B. Arithmetic.—A Form IV class had been studying decimals and knew how to read and write, add and subtract them. The teacher suggested a situation requiring the use of multiplication, and the pupils found themselves without the necessary means to meet the situation. For instance, "Mary's mother sent her to buy 2.25 lb. tea which cost $.375 per lb. What would she have to pay for it?" Or, "Mr. Brown has a field containing 8.72 acres. Last year it yielded 21.375 bushels of wheat to the acre. Wheat was worth 97.5 cents per bushel. What was the crop from the field worth?" The pupils saw that, in order to solve these questions, they must know how to multiply decimals. Multiplication of decimals became the problem of the lesson, the goal to be attained.
C. Grammar.—The teacher wished to show the meaning ofcaseas an inflection of nouns and pronouns. He had written on the black-board such sentences as:
I dropped my book when John pushed me.When the man passed, he had his dog with him.
I dropped my book when John pushed me.When the man passed, he had his dog with him.
He asked the pupils what words in these sentences refer to the same person, and obtained the answer thatI,my, andmeall refer to one person, andhe,his, andhimto another. Then, he proposed the problem, "Let us find out why we have three different forms of a word all meaning the same person." The problem was adapted to animate the curiosity of the pupils and call into activity their capacity for perceiving relationships.
D. Literature.—The teacher was about to present the poem, "Hide and Seek," to a Form III class. He said, "You have all played 'hide and seek.' How do you play it? You will find on page 50 of yourOntario Third Readera beautiful poem describing a game of 'hide and seek' that is rather a sad one. Let us see how the poet has described this game." The pupils were at once interested in what the poet had to say about what was to them a very familiar diversion, and, while the lesson was in progress, their capacity for sympathy and for artistic appreciation was appealed to.
E. Geography.—A Form III class was to study some of the more important commercial centres of Canada. Speaking of Montreal, the teacher proposed the problem, "Do you think we can find out why a city of half a million people has grown up at this particular point?" The pupils' instinct of curiosity was here appealed to and their capacity for perceiving relationships was challenged.
F. Composition.—The teacher wished to take up the writing of letters of application with a class of Form IV pupils. He wrote on the black-board an advertisement copied from a recent newspaper, for example, "Wanted—A boy about fifteen to assist in office; must be a good writer and accurate in figures; apply by letter to Martin & Kelly, 8 Central Chambers, City." Then he said, "Some day in the near future many of you will be called upon to answer such an advertisement as this. Now what should a letter of application in reply to this contain?" The class at once proceeded, with the teacher's assistance, to work out a satisfactory letter. Here, a purpose for the future was the principal need promoted.
G. Nature Study.—The pupils of a Form II class had been making observations regarding a pet rabbit that one of their number had brought to school. After reporting these observations, the pupils were asked, "What good do you think these long ears, large eyes, strong hind legs, split upper lip, etc., are to the rabbit?" Here the problem set was related to the children's instinctive interest in a living animal, appealed to the instinct of curiosity, and challenged their capacity to draw inferences.
Knowledge Obtained Through Use of Ideas.—As already noted, the presented problem of a lesson is neither a state of complete knowledge nor a state of complete ignorance. On the other hand, its function is to provide a starting-point and guide for the calling up of a number of suitable ideas which the pupil may later relate into a single experience, constituting the new knowledge. Take, for example, a person without a knowledge of fractions, who approaches for the first time the problem of sharing as found in such a question as:
Divide $15 between John and William, giving John $3 as often as William gets $2.
In gaining control of this situation, the pupil must select the ideas $3 and $2, the knowledge that $3 and $2 = $5, and the further knowledge that $15 contains $5 three times. These various ideas will constitute data for organizing the new experience of $9 for John and $6 for William. In the same manner, when the student in grammar is first presented with the problem of interpreting the grammatical value of the worddrivingin the sentence, "The boydrivingthe horse is very noisy," he is compelled to apply to its interpretation the ideas noun, adjectival relation, and adjective, and also the ideas object, objective relation, and verb. In this way the child secures the mental elements which he may organize into the new experience,or knowledge (participle), and thus gain control of the presented word.
Interpreting Ideas Already Known.—It is to be noticed at the outset that all ideas selected to aid in the solution of the lesson problem have their origin in certain past experiences which have a bearing on the subject in hand. When presented with a strange object (guava), a person fixes his attention upon it, and thereupon is able, through his former sensation experiences, to interpret it as an unknown thing. He then begins to select, out of his experiences of former objects, ideas that bear upon the thing before him. By focusing thereon certain ideas with which he is perfectly familiar, as rind, flesh, seed, etc., he interprets the strange thing as a kind of fruit. In the same way, when the student is first presented in school with an example of the infinitive, he brings to bear upon the vague presentation various ideas already contained within his experience through his previous study of the noun and the verb. To the extent also to which he possesses and is able to recall these necessary old ideas, will he be able to adjust himself to the new and unfamiliar presented example (infinitive). It is evident, therefore, that a new presentation can have a meaning for us only as it is related to something in our past experience.
Further Examples.—The mind invariably tries to interpret new presentations in terms of old ideas. A newspaper account of a railway wreck will be intelligible to us only through the revival and reconstruction of those past experiences that are similar to the elements described in the account. The grief, disappointment, or excitement of another will be appreciated only as we have experienced similar feelings in the past. New ideas are interpreted by means of related old ideas; new feelings and actsare dependent upon and made possible by related old feelings and acts. Moreover, the meaning assigned to common objects varies with different persons and even with the same person under different circumstances. A forest would be regarded by the savage as a place to hide from the attacks of his enemies; by the hunter as a place to secure game; by the woodcutter as affording firewood; by the lumberman as yielding logs for lumber; by the naturalist as offering opportunity for observing insects and animals; by the artist as a place presenting beautiful combinations of colours. This ability of the mind to retain and use its former knowledge in meeting and interpreting new experiences is known in psychology asapperception. A more detailed study of apperception as a mental process will be made inChapter XXVI.
Learner's Mind Active.—A further principle of method to be deduced from the foregoing is, that the process of bringing ideas out of former experiences to bear upon a presented problem must take place within the mind of the learner himself. The new knowledge being an experience organized from elements selected out of former experiences, it follows that the learner will possess the new knowledge only in so far as he has himself gone through the process of selecting the necessary interpreting ideas out of his own former knowledge and finally organizing them into new knowledge. This need for the pupil to direct mental effort, or attention, upon the problem in order to bring upon it, out of his former knowledge, the ideas relative to the solution of the question before him, is one of the most important laws of method. From the standpoint of the teacher, this law demands that he sodirect the process of learning that the pupil will clearly call up in consciousness the selected interpreting ideas as portions of his old knowledge, and further feel a connection between these and the new problem before him.
Learner's Experience Analysed.—The second stage of the learning process is found to involve also a breaking up of former experience. This appears in the fact that the various ideas which are necessary to interpret the new problem are to be selected out of larger complexes of past experience. For example, in a lesson whose problem is to account for the lack of rainfall in the Sahara desert, the pupil may have a complex of experiences regarding the position of the desert. Out of this mass of experience he must, however, select the one feature—its position in relation to the equator. In the same way, he may have a whole body of experience regarding the winds of Africa. This body must, however, be analysed, and the attention fixed upon the North-east trade-wind. Again, he may know many things about these winds, but here he selects out the single item of their coming from a land source. Again, from the complex of old knowledge which he possesses regarding the land area from which the wind blows, he must analyse out its temperature, and compare it with that of the areas toward which the wind is blowing. Thus it will be seen that, step by step, the special items of old knowledge to be used in the apperceptive process are selected out of larger masses of experience. For this reason this phase of the learning process is frequently designated as a process of analysis.
Problem as Object of Analysis.—Although the second step of the learning process has been described as a selecting of elements from past experience, it might be supposed that the various elements which the mind hasbeen said to select from its former experiences to interpret the new problem, come in a sense from the presentation itself. Thus it is often said, in describing the present step in the learning process, that the presentation embodies a certain aggregate of experience, which the learner can master by analysing it into its component parts and recombining the analysed parts into a better known whole.
Analysis Depends upon Selection.—It is not in the above sense, however, that the term analysis is to be applied in the learning process. It is not true, for instance, when a person is presented with a strange object, say anornithorhynchus, and realizes it in only a vague way, that any mere analysis of the object will discover for him the various characteristics which are to synthesize into a knowledge of the animal. This would imply that in analysis the mind merely breaks up a vaguely known whole in order to make of it a definitely known whole. But the learner could not discover the characteristics of such an object unless the mind attended to it with certain elements of its former experiences. Unless, for instance, the person already knew certain characteristics of both birds and animals, he could not interpret the ornithorhynchus as a bird-beaked animal. In the case of the child and the mud-turtle, also, there could have been no analysis of the problem in the way referred to, had the child not had the ideas, bug and basket, as elements of former experience. These characteristics, therefore, which enter into a definite knowledge of the object, do not come out of the object by a mere mechanical process of analysis, but are rather read into the object by the apperceptive process. That is, the learner does not get his new experience directly out of the presented materials, but builds up his new experience out of elements of his former knowledge. In other words, thelearner sees in the new object, or problem, only such characteristics as his former knowledge and interest enable him to see. Thus while the learner may be said from one standpoint to analyse the new problem, this is possible only because he is able to break up, or analyse, his former experience and read certain of its elements into the new presentation. To say that the mind analyses the unknown object, or topic, in any other sense, would be to confound mental interpretation with physical analysis.
A Further Example.—The following example will further show that the learner can analyse a presented problem only to the extent that he is able to put characteristics into it by this process of analysing or selecting from his past experience. Consider how a young child gains his knowledge of a triangle. At first his control of certain sensations enables him to read into it two ideas, three-sidedness and three-angledness, and only these factors, therefore, organize themselves into his experience triangle. Nor would any amount of mere attention enable him at this stage to discover another important quality in the thing triangle. Later, however, through the growth of his geometric experience, he may be able to read another quality into a triangle, namely two-right-angledness. This new quality will then, and only then, be organized with his former knowledge into a more complete knowledge of a triangle. Here again it is seen that analysis as a learning process is really reading into a new presentation something which the mind already possesses as an element of former experience, and not gaining something at first hand out of the presented problem.
Problem Directs Selection.—It will be well to note here also that the selecting of the interpreting ideas is usually controlled by the problem with which the mind isengaged. This is indicated from the various ways in which the same object may be interpreted as the mind is confronted with different problems. The round stone, for instance, when one wishes to crack the filbert, is viewed as a hammer; when he wishes to place his paper on the ground, it becomes a weight; when he is threatened by the strange dog, it becomes a weapon of defence. In like manner the signxsuggests an unknown quantity in relation to the algebraic problem; in relation to phonics it is a double sound; in relation to numeration, the number ten. It is evident that in all these cases, what determines the meaning given to the presented object is theneed, orproblem, that is at the moment predominant. In the same way, any lesson problem, in so far as it is felt to be of value, forms a starting-point for calling up other ideas, and therefore starts in the learner's mind a flow of ideas which is likely to furnish the solution. Moreover, the mind has the power to measure the suitability of various ideas and select or reject them as they are felt to stand related to the problem in hand. For example, when a pupil is engaged in a study of the grammatical value of the worddrivingin the sentence, "The boy driving the horse is very noisy," it is quite possible that he may think of the horse at his own home, or the shouting of his father's hired man, or even perhaps the form of the worddriving, if he has just been viewing it in a writing lesson. The mind is able, however, to reject these irrelevant ideas, and select only those that seem to adjust themselves to the problem in hand. The cause of this lies in the fact that the problem is at the outset at least partly understood by the learner, which fact enables him to determine whether the ideas coming forward in consciousness are related in any way to this partially known topic. Thus in the example cited, thelearner knows the problem sufficiently to realize that it is a question of grammatical function, and is able, therefore, to feel the value, or suitability, of any knowledge which may be applied to it, even before he is fully aware of its ultimate relation thereto.
Control of Old Knowledge Necessary.—But notwithstanding the direction given the apperceptive process through the aim, or problem, it is evident that if the pupil is to select from his former experiences the particular elements which bear upon the problem in hand, he must have a ready and intelligent control over such former knowledge. It is too evident, however, that pupils frequently do not possess sufficient control over the old knowledge which will bear upon a presented problem. In endeavouring, for example, to grasp the relation of the exterior angle to the two interior and opposite angles, the pupil may fail because he has not a clear knowledge of the equality of angles in connection with parallel lines. For this reason teachers will often find it necessary (before bringing old knowledge to bear upon a new problem) to review the old knowledge, or experience, to be used during the apperceptive process. Thus a lesson on the participle may begin with a review of the pupils' knowledge of verbs and adjectives, a lesson on the making of the colours orange and green for painting a pumpkin with its green stem may begin with a recognition of the standard colours, red, yellow, and blue, and the writing of a capital letter with a review of certain movements.
Preparation Recalls Interpreting Ideas.—It must be noted that this review of former knowledge always implies, either that the pupil is likely to have forgotten atleast partially this former knowledge, or that without such review he is not likely to recall and apply it readily when the new problem is placed before him. For this reason the teacher is usually warned that his lesson should always begin with a review of such of the pupil's old knowledge as is to be used in mastering the new experiences.
A. Aids the Understanding.—The main advantage of this preparatory work is that it brings into clear consciousness that group of ideas and feelings best suited to give meaning to the new presentation. Without it, the pupil may not understand, or only partially understand, or entirely misunderstand the lesson. (1) He may not understand the new matter at all because he does not bring any related facts from his past experience to bear upon it. Multiplication of decimals would in all probability be a merely mechanical process if the significance of decimals and the operation of multiplying fractions were not brought to bear upon it, the pupil not understanding it at all as a rational process. (2) He may only partially understand the new matter because he does not see clearly the relation between his old ideas and the new facts, or because he does not bring to the new facts a sufficient equipment of old ideas to make them meaningful. The adverbial objective would be imperfectly understood if it were not shown that its functions are exactly parallel with those of the adverb. The pupil would have only a partial understanding of it. (3) He may entirely misunderstand the new facts because he uses wrong old experiences to give them meaning. Such was evidently the difficulty in the case of the young pupil who, after a lesson on the equator, described it as a menagerie lion running around the earth.Many of the absurd answers that a pupil gives are due to his failure to use the correct old ideas to interpret the new facts. He has misunderstood because his mind was not prepared by making the proper apperceiving ideas explicit.
B. Saves Time.—There is the further advantage of economy of time, when an adequate preparation of the mind has been made. When the appropriate ideas are definitely in the forefront of consciousness, they seize upon kindred impressions as soon as these are presented and give them meaning. On the other hand, when sufficient preparation has not been made, time must be taken during the presentation of the new problem to go back in search of those experiences necessary to make it meaningful. Frequent interruptions and consequent waste of time will be inevitable. Time will be saved by having the apperceiving ideas ready and active.
C. Provides for Review.—One of the most important values of the preparatory step is the opportunity given for the review of old ideas. These have to be revived, worked over, and reconstructed, and in consequence they become the permanent possessions of the mind. The pupil's knowledge of the functions of the adverb is reviewed when he learns the adverb phrase and adverb clause, and is still further illuminated when he comes to study the adverbial objective. Further, the apperceiving ideas become more interesting to the pupil, when he finds that he can use them in the conquest of new fields. He has a consciousness of power, which in itself is a source of satisfaction and pleasure.
Must not be too Long.—Two precautions seem advisable in the preparatory step. The first is that too long atime should not be spent over it. There is sometimes a tendency to go back too far and drag forward ideas that are only remotely connected with the new ideas to be presented. Under such conditions much irrelevant material is likely to be introduced, and often a train of associations out of harmony with the meaning and spirit of the lesson is started. This is especially dangerous in lessons in literature and history. Only those experiences should be revived which are necessary to a clear apprehension of the ideas or a full appreciation of the emotions to be presented in the new lesson.
Must Recall Vital Ideas.—The most active, vivid, and powerful ideas in the pupil's mind are those which are closely connected with his life. This suggests the second precaution, namely, the use wherever possible of the ideas associated with his surroundings, his games, his occupations. When this is done, not only will the new knowledge have a much greater interest attached to it but it will also be much more vividly apprehended. This will be referred to further in connection with the use of illustrations in teaching.
Teachers, however, are not always agreed as to the amount of time or emphasis to be given to this preparatory step. If the teacher can assure himself that a lesson is following in easy sequence upon something with which the children are undoubtedly familiar, he may, many argue, safely omit such preparatory work. Indeed it is evident that after leaving school the child will have no personal monitor to call up beforehand the ideas that he must apply in solving the problems continually presenting themselves in practical life. On the other hand, however,it is to be remembered that the young child is, at the best, feeling his way in the process of adjusting himself to new experiences. For this reason, the first work for the teacher in any lesson is to ascertain whether the pupils are in a proper attitude for the new knowledge, and, so far as is necessary, prepare their minds through the recall of such knowledge as is related to the new experiences to be presented. Although, therefore, the step of preparation is not an essential part of the learning process, since it constitutes for the pupil merely a review of knowledge acquired through previous learning processes, it may be accepted as a step in the teacher's method of controlling the learning process.
The following additional examples as to the mode and form of the step of preparation may be considered by the student-teacher:
In a lesson in phonic reading in a primary class, the preparation should consist of a review of those sounds and those words which the pupil already knows that are to be used in the new lesson. In a nature study lesson on "The Rabbit," in a Form II class, the preparation should include a recall of any observations the pupils may have made regarding the wild rabbit. They may have observed its timidity, its manner of running, what it feeds upon, where it makes its home, its colour during the winter and during the summer, the kind of tracks it makes in the snow, etc. All these facts will be useful in interpreting the new observations and in assisting the pupils to make new inferences. In a lesson in a Form III class on "Ottawa as a Commercial Centre," the preparation consists of a recall of the pupil's knowledge regarding the position of the city; the adjacent rivers, the Ottawa,Gatineau, Rideau, Lièvre, Madawaska; the waterfalls of the Rideau and Chaudière; the forests to the north and west, with their immense supplies of pine, spruce, and hemlock; and the fact that it is the Dominion capital. All these facts are necessary in inferring the causes of the importance of Ottawa. In a literature lesson in a Form III class onThe Charge of the Light Brigade, the preparation would involve a recall of some deed of personal heroism with which the pupils are familiar, such as that of John Maynard, Grace Darling, or any similar one nearer home. Recall how such a deed is admired and praised, and the memory of the doer is cherished and revered. Then the teacher should tell the story of Balaklava with all the dramatic intensity he is master of, in order that the pupils may be in a proper mood to approach the study of the poem. In a grammar lesson on "The Adverbial Objective" the preparation should consist of a review of the functions of the adverb as modifying a verb, an adjective, and sometimes another adverb. Upon this knowledge alone can a rational idea of the adverbial objective be built. In an arithmetic lesson on "Multiplication of Decimals," in a Form IV class, the preparation should involve a review of the meaning of decimals, of the interconversion of decimals and fractions (for example, .05 = 5 hundredths; 27 ten-thousandths = .0027, etc.); and of the multiplication of fractions. Unless the pupil can do these operations, it is obviously impossible to make his knowledge of multiplication of decimals anything more than a merely mechanical process.
Before closing our consideration of preparation as a stage of method, it will be well again to call attention tothe fact that this is not one of the four recognized stages of the learning process, but rather a subsidiary feature of the second, or apperceptive stage. In other words, actual advance is made by the pupil toward the control of a new experience, not through a review of former experience, but by an active relating of elements selected from past experience to the interpretation of the new problem.
Learning a Unifying Process.—It has been seen that the learner, in gaining control of new knowledge, must organize into the new experience elements selected from former experiences. For instance, when a person gains a knowledge of a new fruit (guava), he not only brings forward in consciousness from his former knowledge the ideas—rind, flesh, seed, etc.,—to interpret the strange object, but also associates these into a single experience, a new fruit. So long also as the person referred to in an earlier chapter retained in his consciousness as distinct factors three experiences—seeing a boy at the fence, seeing the vineyard, and finally, seeing the boy eating grapes—these would not, as three such distinct experiences, constitute a knowledge of grape-stealing. On the other hand, as soon as these are combined, or associated by a relating act of thought, the different factors are organized into a new idea symbolized by the expression,grape-stealing.
Examples From School-room Procedure.—A similar relating process is involved when the learner faces a definite school problem. When, for instance, the pupil gains a knowledge of the sign ÷, he must not only bring forward in consciousness from his former knowledge distinct ideas of a line, of two dots, and of a certain mathematical process, but must also associate these into a new idea, division-sign. So also a person may know that airtakes up more moisture as it becomes warmer, that the north-east trade-winds blow over the Sahara from land areas, and that the Sahara is situated just north of the equator. But the mind must unify these into a single experience in order to gain a knowledge of the condition of the rainfall in that quarter.
Deals with Former Experiences.—This mental organizing, or unifying, of the elements of past experiences to secure control of the new experience, is usually spoken of as a process of synthesis. The term synthesis, however, must be used with the same care as was noted in regard to the term analysis. Synthesis does not mean that totallynewelements are being unified, but merely that whatever selected elements of old knowledge the mind is able to read into a presented problem, are built, or organized, into a new system; and constitute, for the time being, one's knowledge and control of that problem. This is well exemplified by noting the growth of a person's knowledge of any object or topic. Thus, so long as the child is able to apperceive only the three sides and three angles of a triangle, his idea of triangle includes a synthesis of these. When later, through the building up of his geometric knowledge, he is able to apperceive that the interior angles equal two right angles, his knowledge of a triangle expands through the synthesis of this with the former knowledge.
All Knowledge a Synthesis.—The fact that all knowledge is an organization from earlier experiences becomes evident by looking at the process from the other direction. The adult who has complete knowledge of an orange has it as a single experience. This experience is found, however, to represent a co-ordination of otherexperiences, as touch, taste, colour, etc. Moreover, each of these separate characteristics is an association of simpler experiences. Experiencing the touch of the orange, for instance, is itself a complex made up of certain muscular, touch, and temperature sensations. From this it is evident that the knowledge of an orange, although a unity of experience in adult life, is really a complex, or synthesis, made up of a large number of different elements.
What is true of our idea of an orange is true of every other idea. Whether it be the understanding of a plant, an animal, a city, a picture, a poem, an historical event, an arithmetical problem, or a scientific experiment, the process is always the same. The apperceptive process of interpreting the new by selecting and relating elements of former experience, or the process of analysis-synthesis, is universal in learning. Expressed in another form, what is at first indistinct and indefinite becomes clear and defined through attention selecting, for the interpretation of the new presentation, suitable old ideas and setting up relationships among them. Analysis, or selection, is incomplete without an accompanying unification, or synthesis; synthesis, or organization, is impossible without analysis, or selection. It is on account of the mind's ability to unify a number of mental factors into a single experience, that the process of unification, or synthesis, is said to imply economy within our experiences. This fact will become even more evident, however, when later we study such mental processes as sense perception and conception.
It is to be noted, however, that the selecting and the relating of the different interpreting ideas during the learning process are not necessarily separate and distinctparts of the lesson. In other words, the mind does not first select out of its former knowledge a whole mass of disconnected elements, and then later build them up into a new organic experience. There is, rather, in almost every case, a continual interplay between the selecting and relating activity, or between analysis and synthesis, throughout the whole learning process. As soon, for instance, as a certain feature, or characteristic, is noted, this naturally relates itself to the central problem. When later, another characteristic is noted, this may relate itself at once both with the topic and with the formerly observed characteristic into a more complete knowledge of the object. Thus during a lesson we find a gradual growth of knowledge similar to that illustrated in the case of the scholar's knowledge of the triangle, involving a continual interplay of analysis and synthesis, or of selecting and relating different groups of ideas relative to the topic. This would he illustrated by noting a pupil's study of the cat. The child may first note that the cat catches and eats rats and mice, and picks meat from bones. These facts will at once relate themselves into a certain measure of knowledge regarding the food of the animal. Later he may note that the cat has sharp claws, padded feet, long pointed canines, and a rough tongue; these facts being also related as knowledge concerning the mouth and feet of the animal. In addition to this, however, the latter facts will further relate themselves to the former as cases of adaptation, when the child notes that the teeth and tongue are suited to tearing food and cleaning it from the bones, and that its claws and padded feet are suited to surprising and seizing its living prey.
Example from Study of Conjunctive Pronoun.—This continuous selecting and relating throughout a process of learning is also well illustrated in the pupil's process of learning theconjunctive pronoun. By bringing his old knowledge to bear on such a sentence as "The menwhobrought it returned at once"; the pupil may be asked first to apperceive the subordinate clause,who brought it. This will not likely be connected by the pupil at first with the problem of the value ofwho. From this, however, he passes to a consideration of the value of the clause and its relation. Hereupon, these various ideas at once co-ordinate themselves into the larger idea thatwhois conjunctive. Next, he may be called upon to analyse the subordinate clause. This, at first, also may seem to the child a disconnected experience. From this, however, he passes to the idea ofwhoas subject, and thence to the fact that it signifies man. Thereupon these ideas unify themselves with the wordwhounder the ideapronoun. Thereupon a still higher synthesis combines these two co-ordinated systems into the more complex system, or idea—conjunctive pronoun.
figure
This progressive interaction of analysis and synthesis is illustrated by the accompanying figure, in which the wordwhorepresents the presented unknown problem;a,b, andc, the selecting and relating process which results in the knowledge,conjunction;a',b', andc', the building up of thepronounnotion; and the circle, the final organization of these two smaller systems into a single notion,conjunctive pronoun.
The learning of any fact in history, the mastery of a poem, the study of a plant or animal, will furnish excellent examples of these subordinate stages of analysis and synthesis within a lesson. It is to be noted further that this feature of the learning process causes many lessons to fall into certain well marked sub-divisions. Each of these minor co-ordinations clustering around a sub-topic of the larger problem, the whole lesson separates itself into a number of more or less distinct parts. Moreover, the child's knowledge of the whole lesson will largely depend upon the extent to which he realizes these parts both as separate co-ordinations and also as related parts of the whole lesson problem.
Nor does this relating activity of mind confine itself within the single lesson. As each lesson is organized, it will, if fully apprehended, be more or less directly related with former lessons in the same subject. In this way the student should discover a unity within the lessons of a single subject, such as arithmetic or grammar. In like manner, various groups of lessons organize themselves into larger divisions within the subject, in accordance with important relations which the pupil may read into their data. Thus, in grammar, one sequence of lessons is organized into a complete knowledge of sentences; another group, into a complete knowledge of inflection; a smaller group within the latter, into a complete knowledge of tense or mood. It is thus that the mind is able to construct its mass of knowledge into organized groups known as sciences, and the various smaller divisions into topics.