A brief course in the teaching process

CHAPTER V
THE INDUCTIVE LESSON

We are skeptical to-day of that sort of teaching which aims mainly to equip children with a body of accepted knowledge in order that they may some time find use for this body of information in later life. We emphasize, rather, the control of mental activity which makes for the discovery of truth and the avoidance of error. Thinking of this sort is purposeful. We control or direct our ideas toward some end, toward the solution of some problem. One great purpose of teaching must be to provide the opportunity and the stimulus for this kind of thinking. We may not be able to lay down any fixed order of procedure, nor to devise any set of rules whereby children may be trained to be good reasoners; but we can consider what is involved in the process, point out the possibilities of interference, and suggest some of the means to be employed in encouraging this type of mental activity on the part of children. In this chapter we shall confine ourselves to that type of reasoning which we call inductive. This type of schoolroom exercise has usually been treated as composed of five steps; namely, preparation, presentation, comparison and abstraction, generalization, and application. We shall employ this classification to guide us in our discussion of the process.

Preparation: To prepare a child to reason in a given situation from the data in hand to the conclusions which must of necessity follow, it is first of all necessary that he should see that the situation presents a problem. We reason only when we have some aim or purpose which can be satisfied by the process. But if consciousness of aim or problem is at the foundation of this type of thinking, and if we are to deal with children in groups, it is essential that the situation which involves the problem be made the common possession of all. The step of preparation presents these two problems to the teacher: (1) to find a basis in experience already had, or to provide the experience which involves the problem to be considered; (2) to make the children feel the necessity for the solution, i.e. to make the problem vital to them.

In considering the necessity for common experience as a basis for discovering the problem to children, we are dealing with the principle of apperception. Briefly stated, it is this,—that any object or situation has meaning for us only as it connects itself with and is interpreted by our previous experience. Suppose, for example, that a group of first-grade children were asked to tell what made seeds grow. It is possible that some of them would not know, could not interpret from past experience, the meaning of seeds. If the class were at work in a large city, we could be sure that many had never been conscious that growing plants had any connection with seeds, and there would be few, if any, who had ever noticed the conditions under which such growth takes place. The first problem for the teacher in this case would be solved only when, through recall of past experiences, observations, or experiments, the experience “seeds growing” became the common possession of the group. This is an extreme case, one in which the experience which involves the problem is entirely wanting. At the other end of the series, we may have a problem for consideration, the basis for which is found in experiences common to all children. But even though this be the case, there will still be need for the recall of the experience and for making prominent some factor heretofore unnoticed before the children will be ready to reason. We may suppose that all children have had experience with streets or roads, but we shall want to recall many of these experiences in order to make significant the problem of transportation which we wish to consider in the class in home geography.

The step of preparation has only partially accomplished its purpose when the experience necessary to the realization of the problem has been recalled or provided. Still greater skill is required in making the child conscious of the problem. Indeed, it may well be argued that in the curriculum as it is at present organized, very many of the problems that we ask children to solve are problems for them only because we, as teachers, require that that certain piece of work be done. Often the child’s problem consists mainly in avoiding, as far as possible, the work which we require, which has little or no significance for him. Children would do much more thinking if we were only more careful to give them childish problems to solve. Too frequently the organization of knowledge which we impose is influenced exclusively by our adult logical conceptions. Not that children should be illogical, but rather that child logic and the child’s ability to reason depend upon his ability to appreciate problems, upon his experience, and upon his ability to interpret that experience. When we impose our adult point of view upon him, when we ask him to take our problem and with the data that we supply ask him to work out our solution, whatever else may be said of the exercise, it may not be called an exercise in reasoning by children.

If we do respect the child’s experience and point of view, the task still remains of making all of the group of children we teach conscious of the aim as their problem. There is no greater test of teaching skill than this. Can the teacher, after having brought to mind the experiences which are relevant to the work she wishes the children to do, make them conscious of a lack in this experience; can she awaken the need for further consideration of past experience and a desire to reconstruct and to amplify it? In proportion as she is able to accomplish this result, we may be sure that children are reasoning upon problems which are vital to them, and that the motive has been provided which will secure the maximum of controlled intellectual activity on their part. The best single test of the accomplishment of this ideal is to require that the statement of aim be made by the children themselves as a result of the guidance we have given. This conception of the meaning and significance of the aim suggests the solution of the difficulty which some people find in harmonizing the idea of instruction with the doctrine of self-activity.

Instruction, when properly conducted, does not impose the ideas, the problems, or the conclusions of adults upon children. Rather we are concerned in instruction with the child’s experience, his tendency to react, his need of adjustment; and our function as teachers is to guide him, to stimulate him to his own best efforts, to insure the maximum of self-activity while we guide this activity toward the accomplishment of ends which are desirable. The difficulty is, of course, that the problem for solution at any given time may not be equally vital to every member of the group. Here is where the element of control enters somewhat in opposition to the self-activity of the individual. But this condition of affairs is necessarily true both in school and out of it, for society sets up for us certain norms or standards of experience which must be realized by all, and we must for the sake of economy handle children in groups. If the problem is not beyond the child’s comprehension, if it deals with situations which are significant to him, if the solution derived has some bearing on his future action, if he has carefully scrutinized his experience in the light of the problem stated and has brought to bear those elements which are significant for its solution, we may be confident that the activity resulting is closely akin to that which is found in the controlled thinking of men the world over.

In order that it may be more easy for children to focus their attention upon the problem in hand, there is considerable advantage in a clear, concise, concrete, and preferably a brief statement of the aim.[7] A problem is half solved when one can state it clearly. So long as the problem is not sufficiently well defined to admit of accurate statement on the part of pupils, there is danger that there may be much wandering in its consideration. One of the great lessons to be taught in work of this sort is the need of examining the ideas as they suggest themselves to see whether or not they are relevant.

The argument as it has been stated above points to the statement of aim as the culmination of the step of preparation. This does not mean that a considerable period must always elapse in the conduct of an exercise of this type before the aim can be stated. There are occasions, and when the teaching has been good they should be frequent, when the lesson should begin with the statement of the problem discovered in a previous lesson and made clear in the assignment of work. In other cases the same aim may hold for several days; i.e. until the problem is solved. In general, as we advance through the grades, the ends for which children work should become relatively more remote, and the achievement of these ends should require a longer period of work. There is an advantage in setting up subsidiary aims which will make steps of progress in the realization of the larger purpose.

Another distinction that it is well to keep in mind concerns the development of intellectual interests on the part of children. The characteristic aim for a first-grade child may make its appeal chiefly to his desire for satisfaction, which has little intellectual significance; but education fails if it does not make for an increase of interest in intellectual activity. For example, a first-grade boy may be led to count because he wants to be able to tell how many marbles he has, or how to measure the materials he uses in constructive work; while the mathematician may work night and day upon a problem of mathematics because of a purely speculative interest in the result. We may not hope to produce the great mathematician in the elementary school, but we may hope after a certain point has been reached in our study of arithmetic that a boy will recognize the necessity for drill in addition simply because he realizes that in the ordinary affairs of life this knowledge is required.

Presentation: The full realization of the problem to be solved involves a consideration of data already at hand in experience. When we have the problem clearly in mind, we examine this experience more carefully to see what bearing it may have upon the solution, or we gather further data, observe more critically or more extensively, or experiment in such a manner as to involve the solution of our problem. What is the function of the teacher during this part of the process? There is no single answer to this question. Sometimes the work of the teacher will consist almost wholly in helping children to recall their past experience and to apply it to the question at hand. At another time, when experience is lacking, the teacher must direct children to the sources of data, guide them in their observations or experiments, or even give them outright all of the data that she can bring to bear on the situation. It will not always be economical to wait for children to gather the data for themselves, just as it is not always feasible to require them to reach conclusions for themselves. There are times when the best teaching consists in demonstration, and occasions arise when the only feasible course for the teacher is to literally flood the children with data from which they may draw their conclusions.

Again the problem of gathering data becomes the problem of memory. We want children to think, and we should insist that they gather facts with reference to the solution of some problem; but the solution may not always be immediate. We may suspend judgment while we gather further facts and organize them. The facts gathered for one purpose, when rearranged with reference to a new problem, take on a new meaning. If this be true, we may not in our zeal for clear thinking neglect the tools with which we work. There may be some people who have a great many facts and who reason little, but no one can reason without data. Our ability to think logically upon any topic is conditioned by our ability to see facts in new relations, to reorganize our data with reference to new problems; but facts we must have, and a memory stored with facts is one of the greatest aids to thinking.

One of the means mentioned above for the gathering of data was observation. It is necessary that we appreciate the fact that observation involves something more than having the thing present to the senses. Our observations are significant for our thinking when we have clearly in view the problem which the observations are to help solve. Teachers sometimes make the mistake of supposing that when children have objects with which to work they have a problem. It is not unusual to hear teachers speak of objective work as concrete work. Now the concreteness of a situation is not at all dependent upon the presence of objects. Logically a situation may be concrete, and yet present no objects to the senses. On the other hand, objects may be present, children may be directed to use them, and yet in the absence of any real problem the work done may be of the most abstract sort. Objects help to make a situation concrete when the problem under consideration demands their presence, or when they help to make clear the situation under consideration. For example, children may have peas or beans in solving problems in addition; they serve to present objectively the reality which is symbolized by the teacher or pupils in their written work, but this does not make the work in addition concrete. The concreteness of these exercises will depend upon the need which children feel of the ability to find the sum of two or more numbers. The beans will be significant, beyond their use as objects, to illustrate the one-to-one correspondence between symbolic representation and reality, only if the problem of summation which at that time engages their attention concerns the sum of certain numbers of beans. Indeed, it may be claimed that the use of one set of objects continuously to illustrate a process in arithmetic hinders rather than helps the child in his ability to reason in this situation, since he may come to consider this chance relationship of beans and addition as essential. He may think that he ought always to add when he is given beans.

A good illustration of the necessity for a well defined problem for guidance when observations are to be made is found in the futility of much work that is done, or rather left undone, when children are taken on excursions. The directions which follow for the conduct of excursions are those which should be followed whenever work in observation is required, those which have reference to the handling of a large group of children in the field being added.

1. The teacher must have clearly defined in her own mind the purpose of the observation. If the teacher has not definitely formulated the problem, the observation of the children will surely be purposeless.

2. It is not enough that the teacher know just what data she expects the children to gather toward the solution of a particular problem; she must know exactly what data are available under the conditions governing the observation.

3. The preliminary work must have prepared children for their observations by giving them very definite problems to solve. Often it will be advantageous to have these problems written in notebooks.

4. Children not only need to want to see, but also need to be directed while they are observing. Nothing is easier than to look and not see that which is essential.

5. It is always advisable to test the success of the observations while they are being made. There is nothing more difficult than to correct a misconception growing out of careless or inadequate observations.

6. It is well to remember that not merely number of observations counts in the solution of a problem. It is rather observations under varying conditions which give weight to our conclusions. One intensive observation may be worth a thousand careless ones.

7. When children are taken on excursions, great care must be exercised to keep them under proper guidance and control. The organization of children into smaller groups with leaders who are made responsible for their proper observance of directions will help. These leaders should have been over the ground with the teacher before the excursion. The assistance of parents, teachers, or of older pupils will at times be necessary.

8. There should be definite work periods during the excursion, just as in the schoolroom or laboratory.

9. A whistle, as a signal for assembling at one point, will help in out-of-door work, provided it is clearly understood that this signal must be obeyed immediately, and under all circumstances.

Comparison and abstraction: With the problem clearly defined and the data provided, the next step consists of comparison and the resulting abstraction of the element present in all of the cases which makes for the solution of the problem. In the ordinary course of our thinking the sequence is as follows: We find ourselves in a situation which presents a problem which demands an adjustment; we make a guess or formulate an hypothesis which furnishes the basis for our work in attempting to solve the problem; we gather data in the light of the hypothesis assumed, which, through comparison and abstraction, leads us to believe our hypothesis correct or false; if the hypothesis seems justified by the data gathered, it is further tested or verified by an appeal to experience; i.e. we endeavor to see whether our conclusion holds in all cases; if this test proves satisfactory, we generalize or define; and lastly this generalization or definition is used as a point of reference or truth to guide in later thinking or activity.

There is danger that we may overlook the very great importance of inference in this process. We cannot say just when this step in the process will be possible, but it is possibly the most significant of all. A situation presents a problem. Our success in solving the problem depends upon our ability to infer from the facts at our command. Often many inferences will be necessary before we succeed in finding the one that will stand the test. Again with the problem in mind we may be conscious of a great lack of data and may postpone our inference while we collect the needed information. There is one fallacy that must be carefully guarded against in dealing with children, as also with adults; namely, the tendency once the inference has been made to admit only such data as are found to support this particular hypothesis.

It is this ability to infer, to formulate a workable hypothesis, which distinguishes the genius from the man of mediocre ability. It is the ability to see facts in new relations, the giving of new meaning to facts which may be the common possession of all, that characterizes the great thinker. Other people knew many of the facts; but it took the mind of a Newton to discover the relationship existing among these data which he formulated in the law that all bodies attract each other directly in proportion to their weight and inversely in proportion to the square of the distance separating them. As we teach children we should encourage the intelligent guess. We would not, of course, encourage mere random guessing, which may be engaged in by children to have something to say or to blind the teacher. A child who offers a guess or hypothesis should be asked to give his ground for the inference, should show that his guess has grown out of his consideration of the data in hand. It is fallacious to suppose that this kind of thinking is beyond the power of children. They have been forming their inferences and testing them in action from the time that they began to act independently.

There is one element in the consideration of the step of comparison which cannot be too much emphasized, and that is that it is not the comparison of things or situations which present striking likenesses which gives rise to the highest type of thinking. To look at a dozen horses and then to conclude that all horses have four legs is merely a matter of classification; to observe that the sun, chemical action, electricity, and friction produce heat, and to arrive at the generalization from these cases, apparently so unlike, that heat is a mode of motion is the work of a genius. In general, it is safe to say that we would greatly strengthen our teaching if we were only more careful to see to it that our basis for generalization is found in situations presenting as many variations as possible. For example, if we want to teach a principle in arithmetic, the way to fix it and to make it available for further use by our pupils is not to get a number of problems all of which are alike in form and statement; but rather we should seek as great a variety as is possible in the language used or symbols employed that is compatible with the application of the principle to be taught. In an interesting article on reasoning in primary arithmetic, Professor Suzzallo has pointed out the fact that children’s difficulty in reasoning is often one of language.[8] The trouble has been that teachers have always used a set form, or a very few forms of expression, when they described situations which involved any one of the arithmetical processes. Later when the child is called upon to solve a problem involving this process he does not know which process to apply because he is unfamiliar with the form of expression used. To succeed in teaching children when to add involves the presentation of the situations which call for addition with as great a variation as is possible, i.e. by using not one form, but all of the words or phrases which may be used to indicate summation. In like manner in other fields the examples for comparison will be valuable in proportion as they present variety rather than uniformity in those elements which are not essential. Equally good illustration can be had from any other field. If we want pupils to get any adequate conception of the function of adjectives, we should use examples which involve a variety of adjectives in different parts of sentences. In geography the concept “river” will be clear only when the different types of rivers have been considered and the non-essential elements disregarded.

Generalization: When we feel that we have solved the problem, we are ready to state our generalization. There is considerable advantage in making such a statement. One can never be quite sure that he has solved his problem until he finds himself able to state clearly the results of his thinking. To attempt to define or to generalize is often to realize the inadequacy of our thought on the problem. Children should be encouraged to give their own definition or generalization before referring to that which is provided by the teacher or the book. Indeed, the significance of a generalization for further thinking or later action depends not simply upon one’s ability to repeat words, but rather upon adequate realization of the significance of the conclusion reached. The best test of such comprehension is found in the ability of the pupil to state the generalization for himself.

There is very great danger, if definitions or generalizations are given ready-made to children, that they will learn to juggle with words. The parrot-like repetition of rules of syntax, or principles of arithmetic, never indicates real grasp of these subjects. Children think most when the requirement for thinking is greatest, and none are readier than they to take advantage of laxness on the part of the teacher in this respect. It is not only when the formal statement of principles or definitions is called for that the teacher needs to be on her guard. At any stage of the process, if the teacher will only take their words and read meaning into them, some children will be found ready to substitute words for thought. It is really a mistake to tell a child that you know what he means even though he did not say it. Language is the instrument which he employs in thinking, and, if his statement lacked clearness or definiteness, the chances are very great that his thinking has failed in these same particulars. Instead of encouraging children in loose thinking by accepting any statement offered, it would be much better to raise the question of the real significance of the statement, to inquire just what was meant by the words used. Such procedure will help to make children more careful in expressing themselves, and will inevitably tend to clearer thinking.

Application: Whatever conclusions we have reached, whatever truths we have satisfactorily established, influence us in our later thought and action. But even though this is true, there is a decided advantage in providing for a definite application of the results of the thinking which children have done as soon as possible and in as many different ways as is feasible. In the first place, such application makes clearer the truth itself, and helps to fix it in mind. Again, the conclusion arrived at to-day is chiefly significant as a basis for our thinking of to-morrow, and it is as we apply our conclusions that new problems arise to stimulate us to further thought. Then, too, the satisfaction which comes when one feels his power over situations as a result of thinking is the very best possible stimulus to further intellectual activity. Finally, we need to show children the application of that which they have learned to the life which they live outside of the school. We are not apt to err on the side of too frequent or too varied application of the generalizations we have led children to make. Rather we shall have to study diligently to provide enough applications to fix for the child the habit of verification by an appeal to experience.

A few words by way of caution concerning the inductive lesson may not be out of place.

First: Not all school work can be undertaken on this general plan. There are times when the end to be accomplished is distinctly not the discovery of some new truth, but rather the fixing of some habit. There are exercises which are distinctively deductive, some which aim to produce habits, and others which seek to secure appreciation. But more of this is in the succeeding chapters.

Second: Even when we seek to establish truth, we cannot always develop it by an appeal to the experience of children nor to observations which they can make. We shall have, on some occasions, to supply the data, and in still other cases it will be most economical to demonstrate the truth of the position which we desire to have them take. There are occasions when the solution of the problem is not possible for children. In this last instance we shall have to provide the authoritative statement. Indeed, it may be argued that one of the lessons which we all need to learn is respect for the expert. We cannot settle all of the problems which arise, but we may choose from among those who profess to have found a solution. Our education ought to help us to avoid the quack and the charlatan. The habit of logical thinking on the part of children, and expert knowledge in some field, however small, is the only protection which the school can give against the pretensions of those who represent themselves as the dispensers of truth.[9]

Third: There is a grave danger that we may help children too much. Some teachers interpret the inductive development lesson to mean that each step in the thinking required must be carefully prepared for and quickly passed. They consider that they have taught the best lesson when there has been no hitch in the progress from the statement of aim to the wording of the generalization. The suggestive question which makes thinking on the part of children unnecessary is a favorite measure employed. If we stop to consider what thinking means, we cannot fail to see the fallacy of such work. We all do our best thinking, not when the problem to be solved is explained by some one else and all of the difficulties removed, but rather when we find the problem most difficult of solution.

If children are at work on problems which are vital to them, we may expect them to continue to work even though they make mistakes. Indeed, the best recitation may be the one that leaves the children not with a solution skillfully supplied for them by the teacher, but rather with a keen realization of the problem, and with a somewhat clearer idea of the direction in which the solution may be sought. It is the teacher’s work to help the child to see the problem, and, seeing the problem herself from the child’s point of view, to stimulate the child to his best effort. The teacher must know not only the pupil’s attitude of mind toward the problem and how his mind is most likely to react, but also the mental activity required to master properly the issue that has been raised. On the one hand, the teacher’s equipment consists of a knowledge of the minds of the children whom she teaches, and on the other a knowledge of the subject to be taught, not simply as a body of knowledge more or less classified or organized, but as a mode of mental growth.[10] What the teacher needs is a clear realization of the difficulties which the pupils must meet, and the way in which childish minds may best overcome these obstacles. When such sympathy exists between teacher and pupil, we may expect that pupils will constantly grow stronger in their ability to think logically, instead of becoming more and more dependent upon the teacher. And this is our great work as teachers, to render our services unnecessary.

Fourth: No teacher should attempt to outline her work on the basis of the steps indicated in the discussion of the inductive method without a clear realization of the fact that these steps cannot be sharply differentiated, that they are not mutually exclusive. To define a problem adequately may mean that we have passed through the whole process. At any step in the process after the problem is defined, and some hypothesis formed, we may wish to verify our guess by an appeal to known facts, and often we shall find it necessary to abandon the hypothesis already formed and provide another as a basis for further thinking. It is true that the natural movement of the mind is roughly indicated by the steps named; but it must be remembered that no mind can possibly arrive at the solution of a real problem by adhering to a fixed order of procedure. We do not by our teaching create the power of logical thought; we rather guide a mind that naturally operates logically. We can never teach children to reason, but we can provide the occasion for logical thinking, and can guard against the common fallacies. Our success will depend upon a clear realization of the possibilities of the child mind and of the subjects we teach as part of their growth and development.

Teaching by Types: Teaching by means of types is sometimes discussed as a separate method, while in reality it is simply one form of the inductive process. As was indicated in our discussion of observation above, there are times when the consideration of a single situation or object in detail may be worth more than a thousand careless observations. It is especially true that a thoroughly adequate knowledge of one object or case of a class prepares in the best possible way for future observations of members of the same class. Familiarity with the life history of one animal or plant will help us greatly to understand other animals and plants, because that which is most essential in all has been carefully observed in the case considered. Now let us suppose that several plants and animals have been studied. If the cases which are considered are truly typical, it may be possible for the student to appreciate not simply the individuals belonging to the classes studied, but also something of the interrelation of the several classes. This illustration, given because it represents in a general way something of the method followed in the study of science, represents a very common method of procedure in the ordinary affairs of life. None of us can hope to support our conclusions by a careful scrutiny of all possible cases. We take something on authority; namely, that the individual case considered is representative of a large group, then after we have investigated the one case we apply our conclusions to the whole group. Of course there is one great danger. We may be overhasty in our generalizations. No fallacy is more common than the emphasis placed upon non-essentials by those whose observations have been limited. The stories of the traveler who generalizes, after seeing one red-headed child or after eating at one hotel, concerning the children and hotels of the country visited, are too common to need repetition here. Where observations are necessarily limited, the important consideration is to get cases that seem as different as possible in order that that which is essential may be differentiated from the non-essential or accidental.

Teaching by types in our ordinary school work has been applied most frequently to the subject of geography. Applying the principle stated above, we shall be careful in teaching rivers, mountains, cities, commerce, or any other geographical notion to see to it that the individual cases considered are as widely different as possible. To teach New York City, Philadelphia, and Chicago only would give children a very erroneous idea of the concept “city.” They are all exceptionally large, all American, all modern. There are cities smaller, with peculiarities due to age, to location, and to the ideas and resources of the people building them. A better selection would be New York City, London, Tokyo, Venice, Cairo, and Munich. Objection could still very well be offered that this list is too short to include all classes. There can be no doubt that to have taught any city carefully will aid greatly in understanding the notion “city” and in appreciating other cities, but manifestly any final generalization concerning cities must wait until our knowledge of geography has been widely extended. The same conclusion would be reached were any other notion of geography, or any other study, subjected to the same test. There is, however, no harm in forming tentative judgments. Indeed, we must all do this every day of our lives. The main issue is to see to it that there is no mistake as to the tentative character of the conclusions reached, that the open-minded attitude be preserved.