How to Teach Part 7

Thinking, then, is involved in any response which comes as a result of the conscious adaptation of means to end in a problematic situation.

Many of the processes of mental activity which have been given other names may involve this process. Habit formation--when the learner a.n.a.lyzes his progress or failure, when he tries to find a short cut, or when he seeks for an incentive to insure greater improvement--may serve as a situation calling for thinking. The process of apperceiving or of a.s.similation may involve it. Studying and trying to remember may involve it. Constructive imagination often calls for it. Reasoning, always requires it. In the older psychology reasoning and thinking were often used as synonyms, but more recently it has been accepted by most psychologists that reasoning is simply one type of thinking, the most advanced type, and the most demanding type, but not the only one.

Thinking may go on (as in the other processes just mentioned) without reasoning, but all reasoning must involve thinking. It is this lack of differentiation between reasoning and thinking, the attempt to make of all thinking, reasoning, that has limited teachers in their attempts to develop thinking upon the part of their pupils.

The essentials of the thinking process are three: (1) a state of doubt or uncertainty, resulting in suspended judgment; (2) an organization and control of mental states in view of an end to be attained; (3) a critical att.i.tude involving selection and rejection of suggestions offered. The recognition of some lack of adjustment, the feeling of need for something one hasn't, is the only stimulus toward thinking. This problematic situation, resulting in suspended judgment, caused by the inadequacy of present power or knowledge, may arise in connection with any situation. It is unfortunate that the terms "problematic situation"

and "feeling of inadequacy" have been discussed almost entirely in connection with situations when the result has some pragmatic value.

There is no question but what the situation arousing thinking must be a live one and a real one, but it need not be one the answer to which will be useful. It is true that with the majority of people, both children and adults, a problem of this type will be more often effective in arousing the thinking process than a problem of a more abstract nature, but it is not always so, nor necessarily so. Most children sometimes, and some children most of the time, enjoy thinking simply for the sake of the activity. They do not need the concrete, pragmatic situation--anything, no matter how abstract, that arouses their curiosity or appeals to their love of mastery offers enough of a problem. Sometimes children are vitally interested in working geometrical problems, translating difficult pa.s.sages in Latin, striving to invent the perpetual motion machine, even though there is no evident and useful result. It is not the particular type of situation that is the thing to be considered, but the att.i.tude that it arouses in the individual concerned. Educators in discussion of the situations that make for thinking must allow for individual differences and must plan for the intellectually minded as well as for others.

The thinker confronted by a situation for which his present knowledge is not adequate, recognizes the difficulty and suspends judgment; in other words, does not jump at a conclusion but undertakes to think it out. To do this control is continually necessary. He must keep his problem continually before him and work directly for its solution, avoiding delays, avoiding being side-tracked. This means, of course, the critical att.i.tude towards all suggestions offered. Each one as it comes must be inspected in the light of the end to be reached--if it does not seem to help towards that goal, it must be rejected. Criticism, selection, and rejection of suggestions offered must continue as long as the thinking process goes on. "To maintain the state of doubt and to carry on systematic and protracted inquiry--these are the essentials of thinking."

In order to maintain this critical att.i.tude to select and reject suggestions with reference to a goal, the suggestions as they come cannot be accepted as units and followed. Such a procedure is possible only when the mental process is not controlled by an end. Control by a goal necessitates a.n.a.lysis of the suggestions and abstraction of what in them is essential for the particular problem in hand. It is because no complete a.s.sociation at hand offers a satisfactory response to the situation that the need for thinking arises. Each a.s.sociation as it comes must be broken up, certain parts or elements emerge, certain relationships, implications, or functions are made conscious. Each of these is examined in turn; as they seem to be valueless for the purpose of the thinker, they are rejected. If one element or relationship seems significant for the problem, it is seized upon, abstracted from its fellows, and becomes the center of the next series of suggestions. A part, element, quality, or what not, of the situation is accepted as significant of it for the time being. The part stands for the whole--this is characteristic of all thinking. As a very simple ill.u.s.tration, consider the following one reported by Dewey:

"Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river, is a long white pole, bearing a gilded ball at its tip. It suggested a flag pole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flag pole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

"I then tried to imagine all possible purposes of such a pole, and to consider for which of these it was best suited: (_a_) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried like poles, this hypothesis was rejected. (_b_) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house, (_c_) Its purpose might be to point out the direction in which the boat is moving.

"In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it.

Moreover, the tip was enough higher than the base, so that, from the pilot's position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly."[8]

The problem was to find out the use of the flag pole. No adequate explanation came as the problem presented itself; it therefore caused a state of uncertainty, of suspended judgment, and a process of thinking in order to get an answer. Each suggestion that came was a.n.a.lyzed, its requirements and possibilities checked up by the actual facts and the goal. The suggestions that the pole was simply to carry a flag, was an ornament, was the terminal of a wireless telegraph, were examined and rejected. The final one, that the pole was to point out the direction in which the boat was moving, upon a.n.a.lysis seemed most probable and was accepted. The one characteristic of the pole, that it points direction, and its position, need to be accepted as the essential facts in the situation, for the particular problem. Without control of the process, without the two steps of a.n.a.lysis and abstraction, no conclusion could have been reached.

a.n.a.lysis and abstraction may be facilitated in three ways. First, by attentive piecemeal examination. The total situation is examined, element by element, attentively, until the element needed is reached or approximated. This method of procedure helps to emphasize minor bonds of a.s.sociation which the element possesses in the learner's experience but which he needs to have brought to his attention. It can only be used when the element is known to some degree. It is the method to use when elements are known in a hazy, incomplete, or indefinite way and need clearing up. Second, by varying the concomitant. An element a.s.sociated with many situations, which vary in other respects, comes to be felt and recognized as independent. This is the method to use when a new element in a complex is to be taught. Third, by contrast. A new element is brought into consciousness more quickly if it is set side by side with its opposite. Of course, this is only true provided the opposite has already been learned. To present opposites, both of which are new or only partially learned, confuses the a.n.a.lysis instead of facilitating it.

Reasoning, as the highest type of thinking, includes all that thinking in general does, and adds some particular requirement which differentiates it from the simpler forms. Further discussion of it, then, should make clearer the essential in thinking as a process, as well as make clear its most difficult form. Reasoning is defined by Miller as "controlled thinking,--thinking organized and systematized according to laws and principles and carried on by use of superior technique."[9] Reasoning, then, is the kind of thinking that deals directly with laws and principles. Much thinking may be carried on without any overt, definite use of laws and principles, as in constructive imagination or in apperception, but, if this is so, it seems better to call the thinking by one of the other names. Of course this cla.s.sification is somewhat arbitrary, but there can be no question that types of thinking do differ. As has already been noted, some psychologists have used the terms thinking and reasoning as synonyms, but such usage has resulted in confusion and has not been of practical value. It is only as the mental process desired becomes clearly conceived of, its connotations and denotation clearly defined, that it becomes a real goal towards Which a teacher or learner may strive. This, then, is the primary criterion of reasoning--that the thinker be dealing consciously with laws and principles. An acceptance of this first essential makes clear that the particular process of reasoning cannot be carried on in subjects which lack laws and principles. Spelling, elementary reading, vocabulary study, most of the early work in music and art, the acquisition of facts wherever found--these situations may offer opportunity for thinking, but little if any for reasoning. Because a teacher is using the development method does not mean necessarily that her students are reasoning. The two terms are not in any way synonymous.

The second essential in reasoning is the presence of a definite technique. This technique consists of two factors: first, certain definite mental states, and second, the use of the process of thinking by either the inductive or the deductive method.

First as to the mental states involved. The fact that the thinking deals with laws and principles necessitates the presence, in the thinking process, of constructive verbal or symbolic imagery, logical relationships, logical concepts, and explicit judgments. This does not at all exclude other types of these mental states and entirely different mental states. The kind of a.n.a.lysis involved simply necessitates the presence of these types, whatever others may be present. Constructive symbolic imagery has already been discussed. Logical relationships are those that are independent of accidental conditions, are not dependent on mere contiguity in time and s.p.a.ce, but are inherent in the a.s.sociation involved. Such relationships are those of likeness and difference, cause and effect, subject and object, equality, concession, and the like. Logical concepts are those which are the result of thinking, whose definite meaning has been brought clearly into consciousness so that a definition could be framed. A child has some notion of the meaning of tree, or man, or chemist, and therefore possesses a concept of some kind, but the exact meaning, the particular qualities necessary, are usually lacking, and so it could not be called a logical concept. Explicit judgments are those which contain within themselves the reasons for the inference. They, too, are the result of thinking. One may say that "cheating is wrong," or that "water will not rise above its source level," or that "cleanliness is necessary to health," or that "this is a Rembrandt"--as a matter of experience, habit, but without any reflection and with no reasons for such judgment.

If, on the other hand, the problems to which these judgments are answers had been a matter of thinking, the reasons or the ground for such judgment would have become conscious and the judgment then become explicit. It must be evident that in any problems dealing with laws and principles the mental states involved must be definite, clear cut, logically sound, and their implications thoroughly appreciated and understood.

The second element in the technique necessary in reasoning is the use of either the inductive or the deductive method in the process. Induction requires--a problem, search for facts with which to solve it, comparison and a.n.a.lysis of those facts, abstraction of the essential likenesses, and conclusion. Deduction requires--a problem, the a.n.a.lysis of the situation and abstraction of its essential elements, search for generals under which to cla.s.sify it, comparison of it with each general found, and conclusion. It is unfortunate that in the discussions of induction and deduction the differences have been so emphasized that they have been regarded as different processes, whereas the likenesses far outweigh the differences. An examination of the requirements of each as stated above shows that the process in the two is the same. Not only do both involve reasoning and therefore require the major steps of a.n.a.lysis and abstraction present in all thinking, but both also involve search and comparison. Both, of course, involve the same kind of mental states.

At times it is very difficult to distinguish between them. Although for practical purposes it is necessary, sometimes, to stress the differences, the inherent similarity should not be lost sight of.

The differences between these two methods of reasoning are, first, in the locus of the problem; second, in the order of the steps of the process; third, in the relative proportion of particulars and generals used; fourth, in the devices used, (1) In induction the problem is concerned with a general. In some situation a concept, law, or principle has proven inadequate as a response. The question is then raised as to what is wrong with it and the inductive process is instigated. The problem is solved when the principle or concept is perfected or enlarged--in other words, is made adequate. In deduction the problem is concerned with the individual situation. Some problem is raised by a particular fact or experience and is answered when it is placed under the law or concept to which it belongs. Deduction is, practically the cla.s.sification of particulars. (2) The order of steps is different. In induction, because present knowledge falls short, the major step of a.n.a.lysis necessary to abstraction of the essential is impossible, and therefore the search for new facts must come first, whereas in deduction, the a.n.a.lysis of the particular situation results in a search for generals and a cla.s.sification of the situation in question. (3) In induction many particular facts may be necessary before one concept or principle is made adequate, while in deduction many concepts or principles may be examined before one particular is cla.s.sified. (4) In induction the hypothesis is used as a device to make clear the possible goal; in deduction the syllogism is used as a device to make clear the conclusion which has been reached, to throw into relief the cla.s.sification and the result coming from it.

In this discussion, induction and deduction have been treated, for the sake of clearness, as if they acted independently of each other, as if a thinker might at one time use deduction and at another time induction.

They have been outlined in such a way that one might think that the movement of the mind in one process was such that it precluded the possibility of the other process. This is not so--the two are inextricably mingled in the actual process of reasoning, and further, induction as used in practical life always involves deduction at two points, as an initial starting point and as an end point. The knowledge that a certain principle is inadequate comes to consciousness through the attempt to cla.s.sify some particular experience under it. Failure results and the inductive process may then be initiated, but this initial attempt is deductive and if it had been successful there would have been no need of induction. After the inductive process is complete and the general principle has been cla.s.sified or perfected, the final step is testing it to see if it is adequate, first by applying it to the particular problem which caused the whole process, and then to new situations. If it tests, it is accepted,--if not, further induction is necessary. This again is deduction. Not only is induction not complete without deduction, but each deduction influences the principle which is applied, making it more sure and more flexible. Even in the process of induction, there are attempts to cla.s.sify these facts which are being gathered under suggested old principles, or half-formed new ones, before the process is completed. This is a deductive movement, even though it prove unsatisfactory or impossible. Dewey describes this interaction by saying, "There is thus a double movement in all reflection: a movement from the given partial and confused data to a suggested comprehension (or inclusive) entire situation; and back from this suggested whole--which as suggested is a meaning, an idea--to the particular facts, so as to connect these with one another and with additional facts to which the suggestion has directed attention."[10] However true this intermingling of induction and deduction may be, the fact still remains true that in any given case the major movement is in one direction or the other, and that therefore in order to insure effective thinking measures must be taken accordingly. As a child formulates his conception of a verb, or words the characteristic essentials of the lily-family, or frames the rule for addition of fractions or the action of a base on a metal, he is concerned primarily with the form of the reasoning process known as induction. When he cla.s.ses a certain word as a conjunction, a certain city as a trade center, a certain problem as one in percentage, he is using deduction. Complexes and gradual shadings of one state into another, not clearly defined and sharply differentiated processes and states, are characteristic of all mental life.

Another unfortunate statement with regard to induction and deduction is that the former "proceeds from particulars to generals" and the latter from "generals to particulars." Both of these statements omit the starting point and leave the thinker with no ground for either the particulars or the generals with which he works. The thinker is supposed, let us say, to collect specimens of flowers in order to arrive at a notion of the characteristics of a certain cla.s.s--but why collect these rather than any others? True, in the artificial situation of a schoolroom or college, the learner often collects in a certain field rather than another, simply because he is told to. But in daily life he would not be told to---the incentive must come from some particular situation which presents a problem and therefore limits the field of search. The starting point must be a particular experience or situation.

The same thing is true in deduction, although the syllogistic form has often been misleading. "Metals are hard; iron is a metal, therefore iron is hard." But why talk about metals at all--and if so why hardness rather than color or effect on bases or some other characteristic? Of course, here again it is some particular problem that defines the search for the general and directs attention to some cla.s.s characteristics rather than to others. Not only is the starting point of all reasoning some definite situation for which there is no adequate response, but the end point must naturally be the same. A particular problem demanding solution is the cause for reasoning, and, of course, the end of the process must be the solution of that problem.

From the foregoing it must not be concluded that the processes of induction and deduction are manifested only in connection with reasoning. In fact, their use as a conscious tool of technique in reasoning comes only after considerable experience of their use when there was no conscious purpose and no control. A little child's notion of dog, or tree, or city--in fact, all his psychological concepts necessitate the inductive movement, but it has taken place in his spontaneous thinking and the meanings have evolved after considerable experience without any definite control on his part. So with deduction.

As he recognizes this as a chestnut tree, that as a rocking chair, as he decides that this is wrong or that it is going to clear, he is cla.s.sifying things, or conduct, or conditions, and so is following the deductive movement. But the judgments may come as a result of past experience, may be spontaneous and involve no protracted controlled activity which has been defined as thinking. Man's mind works spontaneously both inductively and deductively, and hence the possibility of control of these operations later. Thinking is an outgrowth of spontaneous activity; reasoning is but an application of the natural laws of mental activity to certain situations.

The laws of readiness, exercise, and effect govern thinking just as they do all other mental processes. Thinking is not independent of habit; it is not a mysterious force other than a.s.sociation which deals with novel data. Thinking is merely an exhibition of the laws of habit under certain definite situations. At first sight this seems to be impossible, because, as has been emphasized throughout this chapter, thinking takes place when no satisfactory response is at hand and when nothing is offered by past experience which is adequate. As a result of the thinking, responses are reached which never before have occurred as a result of that situation. Just the same they are reached only because of the operation of the laws of habit. It must be borne in mind that the laws of a.s.sociation do not work in such a way that only gross total situations are bound to total responses. In man particularly, situations are being continually broken up into elements, and those elements connected with responses. Responses are being continually disintegrated, and elements, instead of the whole response, being bound to situations.

a.n.a.lysis is continually taking place merely as a result of the working of these laws. If the nervous mechanism of man were not of this hair-trigger variety, if elements did not emerge from a total complex as a result of bonds formed, of readiness of certain tracts, no willing, no attention on the part of the thinker, would ever bring about a.n.a.lysis.

This is made very vivid when one is met by a problem he cannot solve. If the situation does not break up, if the right element does not emerge, if the right cue is not given, he is helpless. All he can do is to hold fast to his problem and wait. As the a.s.sociations are offered, he can select and reject, but that is all. The marvelous power of the genius, the inventor, the reasoner in all fields, is merely an exhibition of the laws of a.s.sociation working with extremely subtle elements. It seems to transcend all experience because these elements and the bonds which experience has formed cannot be observed. A child fails in his thinking often because he uses his past experience and responds by a.n.a.logy--we note that fact and criticize him for it. But he succeeds for just the same reason and by the use of just the same laws. James long ago showed conclusively that a.s.sociation by similarity, which is one of the prominent types used in reasoning, was only the law of habit working with elements of novel data.

The fact that thinking is determined by its aim rather than by its antecedents has also been given a mysterious place as apart from a.s.sociation. The thinker who chose the right a.s.sociate, the one that led him towards his goal rather than some other, was called sagacious. But, after all, this being governed by an aim is nothing more than the operation of the law of readiness among intellectual bonds. One a.s.sociate is chosen and another rejected because one is more satisfying than another. Certain bonds are made more ready than others because of the general set or att.i.tude of the thinker, and therefore any a.s.sociate using those bonds brings satisfaction and is retained. "The power that moves the man of science to solve problems correctly is the same that moves him to eat, sleep, rest, and play. The efficient thinker is not only more fertile in ideas and more often productive of the 'right'

ideas than the incompetent is; he is also more satisfied by them when he gets them, and more rebellious against the futile and misleading ones.

We trust to the laws of cerebral nature to present us spontaneously with the appropriate idea, and also _to prefer that idea to others."_[11]

The reasons for failure of teachers and educators of all kinds to train people to think are numerous. (1) Scarcity of brains which work primarily in terms of connections between subtle elements, relationships, etc. (2) Lack of knowledge or incorrect knowledge, due to narrow experience or poor memory. (3) Lack of the necessary habits of attention and criticism. (4) Lack of power of the more abstract and intellectual operations to bring satisfaction, due partly to original equipment and partly to training. (5) Lack of power to do independent work, due to poor training. Schools cannot in any way make good the deficiency which is due to a lack of mental capacity. They can, and should, do something to provide knowledge which is well organized around experiences which have proved vital to pupils. Something can undoubtedly be done in the way of cultivating the habit of concentration of attention, and of making more or less habitual the critical att.i.tude.

Within the range of the ability which the individuals to be educated possess, the school may do much to give training which will make independent work or thinking more common in the experience of school pupils, and therefore much more apt to be resorted to in the case of any problematic situation.

Possibly the greatest weakness in our schools, as they are at present const.i.tuted, is in the dependence of both teachers and children upon text-books, laboratory manuals, lectures, and the like. In almost every field of knowledge which is presented in our elementary and high schools, more opportunity should be given for contact with life activities. Such contacts should, in so far as it is possible, involve the organization of the observations which are made with relation to problems and principles which the subject seeks to develop. In nature study or in geography in the elementary school many of the principles involved are never really mastered by children, by virtue of the fact that they merely memorize the words which are involved, rather than solve any of the problems which may occur, either by virtue of their intellectual interests, or on account of their meaning in everyday life.

The following of the instructions given in the laboratory manual does not necessarily result in developing the spirit of inquiry or investigation, nor even acquaint pupils with the method of the science which is supposed to be studied.

Possibly the greatest contribution which a teacher can make to the development of thinking upon the part of children is in discovering to them problems which challenge their attention, the solution of which for them is worth while. As has already been indicated, an essential element in thinking is constantly to select from among the many a.s.sociations which may be available that one which will contribute to the particular problem which we have in mind. The mere grouping of ideas round some topic does not satisfy this requirement, for such a reciting of paragraphs or chapters may amount simply to memorization and nothing more. If a teacher can in geography or in history send children to their books to find such facts as are available for the solution of a particular problem, she is stimulating thought upon their part, and may at the same time be giving them some command of the technique of inquiry or of investigation. The cla.s.s that starts to work, either in the discussion during the recitation period, or when they work at their seats, or at home, with a clear statement of the aim or problem may be expected to do much more in the way of thinking than will occur in the experience of those who are merely told to read certain parts of a book.

In a well-conducted recitation which involves thinking, the aim needs to be restated a number of times in order that the selection of those a.s.sociations which are important, and the rejection of those which are not pertinent, may continue over a considerable period.

In so far as it is possible, children should be made to feel responsibility for the progress which is made in the solution of their problems. They should be critical of the contributions made by each other. They should be sincere in their expression of doubt, and in questioning whenever they do not understand. Above all, if they are really thinking, they need to have an opportunity for free discussion.

In cla.s.srooms in which children are seated in rows looking at the backs of each other's heads and reciting to the teacher, the tendency is simply to satisfy what the pupils conceive to be the demands of the teacher, rather than to think and to attempt to resolve one's doubts. In cla.s.ses in which teachers provide not only for a statement of the problem which is to be solved during the study period, but also for a variety in a.s.signments, children may be expected to bring to cla.s.s differences in points of view and in the data which they have collected.

In such a situation discussion is a perfectly normal process, and thinking is stimulated.

As children pa.s.s through the several grades of the school system, they ought to become increasingly conscious of the process of reasoning. They should be asked to tell how they have arrived at their conclusions. They should give the reason for their judgments. A great deal of loose thinking would be avoided if we could in some measure establish the habit upon the part of boys and girls of asking, "Will it work in all cases?"; "What was a.s.sumed as a basis for arriving at the conclusion which I have accepted?"; "Are the data which have been brought together adequate?"; "To what degree have the fallacies which are more or less common in reasoning entered into my thinking?" It is not that one would hope to give a course in logic to elementary or to high school children, but rather that they should learn, out of the situations which demand thought, constantly to check up their conclusions and to verify them in every possible way. We may not expect by this method to create any unusual power of thought, but we may in some degree provide for the development of a critical att.i.tude which will enable these same boys and girls, both now and as they grow older, to discriminate between those who merely dogmatize, and those who present a sound basis for their reasoning, either in terms of a principle which can be accepted, or in terms of observations or experiments which establish the conclusions which they are asked to accept.

In all of the work which involves thinking, it is of the utmost importance that we preserve upon the part of pupils, in so far as it is possible, an open-minded att.i.tude. It is well to have children in the habit of saying with respect to their conclusions that in so far as they have the evidence, this or that conclusion seems to be justified. It may even be well to have them reach the conclusion in some parts of their work that there are not sufficient data available upon which to base a generalization, or that certain principles which are accepted as valid by some thinkers are questioned by others, and that the conclusions which are based upon principles which are not commonly accepted must always be stated by saying: it follows, if you accept a particular principle, that this particular conclusion will hold.

We need more and more to encourage the habit of independent work. We must hope as children pa.s.s through our school system that they will grow more and more independent in their statement of conclusions and of beliefs. We can never expect that boys and girls, or men and women, will reach conclusions on all of the questions which are of importance to them, but it ought to be possible, especially for those of more than usual capacity, to distinguish between the conclusions of a scientific investigation and the statements of a demagogue. The use of whatever capacity for independent thought which children possess should result in the development of a group of open-minded, inquiring, investigating boys and girls, eager and willing in confronting their common community problems to do their own thinking, or to be guided by those who present conclusions which are recognized as valid. They should learn to act in accordance with well-established conclusions, even though they may have to break with the traditions or superst.i.tions which have operated to interfere with the development of the social welfare of the group with which they are a.s.sociated.

QUESTIONS

1. How do children (and adults) most frequently solve their problems?

2. Under what conditions do children think and yet reach wrong conclusions? Give examples.

3. Can first-grade children think? Give examples which prove your contention.

4. What are the important elements to be found in all thinking?

5. Show how these elements may be involved in a first-grade lesson in nature study. In an eighth-grade lesson in geography. In the teaching of any high school subject.

6. When may habit formation involve thinking? Memorization?

7. Give five examples of problems which you believe will challenge the brightest pupils in your cla.s.s. Which would seem real and worth solving to the duller members of the group?

8. How may the a.n.a.lysis of such ideas as come to mind, and the abstraction of the part which is valuable for the solution of a particular problem, be facilitated?

9. How do you distinguish between thinking and reasoning?

10. What are the essential elements in reasoning? Give an example of reasoning as carried on by one solving a problem in arithmetic or geometry, in geography, physics, or chemistry.

11. In what respects are the processes of induction and deduction alike?

In what do they differ?

12. At what stage of the inductive process is deduction involved?