=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 a.s.sistance. 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.

HOW TO SET LESSON PROBLEM

=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 cla.s.s. 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 cla.s.s, "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 cla.s.s 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 munic.i.p.al 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 att.i.tude for the lesson.

EXAMPLES OF MOTIVATION

A few additional examples, drawn from different school subjects, are here added to ill.u.s.trate further what is meant by setting a problem as a need, or motive.

=A. History.=--The members of a Form IV cla.s.s 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 cla.s.s the facts that the members of the Commons are elected by the different const.i.tuencies of the Dominion and that n.o.body 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 daily newspapers 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. n.o.body 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 att.i.tude to hear the story of John Wilkes.

=B. Arithmetic.=--A Form IV cla.s.s 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 of _case_ as an inflection of nouns and p.r.o.nouns. He had written on the black-board such sentences as:

I dropped my book when John pushed me.

When the man pa.s.sed, he had his dog with him.

He asked the pupils what words in these sentences refer to the same person, and obtained the answer that _I_, _my_, and _me_ all refer to one person, and _he_, _his_, and _him_ to 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 cla.s.s. He said, "You have all played "hide and seek." How do you play it? You will find on page 50 of your _Ontario Third Reader_ a 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 cla.s.s 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 cla.s.s of Form IV pupils. He wrote on the black-board an advertis.e.m.e.nt copied from a recent newspaper, for example, "Wanted--A boy about fifteen to a.s.sist 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 advertis.e.m.e.nt as this.

Now what should a letter of application in reply to this contain?" The cla.s.s at once proceeded, with the teacher"s a.s.sistance, to work out a satisfactory letter. Here, a purpose for the future was the princ.i.p.al need promoted.

=G. Nature Study.=--The pupils of a Form II cla.s.s 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.

CHAPTER X

LEARNING AS A SELECTING ACTIVITY

OR

PROCESS OF a.n.a.lYSIS

=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, const.i.tuting 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 const.i.tute 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 word _driving_ in the sentence, "The boy _driving_ the 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 acts are dependent upon and made possible by related old feelings and acts. Moreover, the meaning a.s.signed to common objects varies with different persons and even with the same person under different circ.u.mstances. 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 as _apperception_. A more detailed study of apperception as a mental process will be made in Chapter XXVI.

THE SELECTING PROCESS

=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 so direct 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 a.n.a.lysed.=--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 ma.s.s 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 a.n.a.lysed, 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 a.n.a.lyse 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 ma.s.ses of experience. For this reason this phase of the learning process is frequently designated as a process of a.n.a.lysis.

=Problem as Object of a.n.a.lysis.=--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 has been 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 a.n.a.lysing it into its component parts and recombining the a.n.a.lysed parts into a better known whole.

=a.n.a.lysis Depends upon Selection.=--It is not in the above sense, however, that the term a.n.a.lysis is to be applied in the learning process. It is not true, for instance, when a person is presented with a strange object, say an _ornithorhynchus_, and realizes it in only a vague way, that any mere a.n.a.lysis 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 a.n.a.lysis 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 a.n.a.lysis 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 a.n.a.lysis, 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, the learner 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 a.n.a.lyse the new problem, this is possible only because he is able to break up, or a.n.a.lyse, his former experience and read certain of its elements into the new presentation. To say that the mind a.n.a.lyses the unknown object, or topic, in any other sense, would be to confound mental interpretation with physical a.n.a.lysis.

=A Further Example.=--The following example will further show that the learner can a.n.a.lyse a presented problem only to the extent that he is able to put characteristics into it by this process of a.n.a.lysing 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 a.n.a.lysis 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 is engaged. 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 sign _x_ suggests an unknown quant.i.ty 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 the _need_, or _problem_, 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 word _driving_ in 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 word _driving_, 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, the learner 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.

LAW OF PREPARATION

=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 at least 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.

VALUE OF PREPARATION

=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.