not raise the latch sufficiently from its slot-case of insufficient elevation-raise door bodily on hinges! Or door sticks at top by friction against lintel-press it bodily down! . . . By many measurements of triangles one might find their area always equal to their height multiplied by half their base, and one might formulate an empirical law to that effect. But a reasoner saves himself all this trouble by seeing that it is the essence of a triangle to be the half of a parallelogram whose area is the height into the entire base. To see this he must invent additional lines; and the geometer must often draw such to get at the essential property he may require in a figure. The essence consists in some relation of the figure to the new line, a relation not obvious at all until they are put in. The geometer's sagacity lies in the invention of the new lines. 3. The Reflective Thought Process [DEWEY, John, How We Think, pp. 12-13. New York, D. C. Heath & Co., 1910.] We may recapitulate by saying that the origin of thinking is some perplexity, confusion, or doubt. Thinking is not a case of spontaneous combustion; it does not occur just on "general principles." There is something specific which occasions and evokes it. General appeals to a child (or to a grown-up) to think, irrespective of the existence in his own experience of some difficulty that troubles him and disturbs his equilibrium, are as futile as advice to lift himself by his boot-straps. Given a difficulty, the next step is suggestion of some way out --the formation of some tentative plan or project, the entertaining of some theory which will account for the peculiarities in question, the consideration of some solution for the problem. The data at hand cannot supply the solution; they can only suggest it. What, then, are the sources of the suggestion? Clearly past experience and prior knowledge. If the person has had some acquaintance with similar situations, if he has dealt with material of the same sort before, suggestions more or less apt and helpful are likely to arise. But unless there has been experience in some degree analogous, which may now be represented in imagination, confusion remains mere confusion. There is nothing upon which to draw in order to clarify it. Even when a child (or a grown-up) has a problem, to urge him to think when he has no prior experiences involving some of the same conditions, is wholly futile. If the suggestion that occurs is at once accepted, we have uncritical thinking, the minimum of reflection. To turn the thing over in mind, to reflect, means to hunt for additional evidence, for new data, that will develop the suggestion, and will either, as we say, bear it out or else make obvious its absurdity and irrelevance. Given a genuine difficulty and a reasonable amount of analogous experience to draw upon, the difference, par excellence, between good and bad thinking is found at this point. The easiest way is to accept any suggestion that seems plausible and thereby bring to an end the condition of mental uneasiness. Reflective thinking is always more or less troublesome because it involves overcoming the inertia that inclines one to accept suggestions at their face value; it involves willingness to endure a condition of mental unrest and disturbance. Reflective thinking, in short, means judgment suspended during further inquiry; and suspense is likely to be somewhat painful. As we shall see later, the most important factor in the training of good mental habits consists in acquiring the attitude of suspended conclusions, and in mastering the various methods of searching for new materials to corroborate or to refute the first suggestions that occur. To maintain the state of doubt and to carry on systematic and protracted inquiry-these are the essentials of thinking. 4. Induction and Deduction: Two Related Kinds of Thinking [LYMAN, R. L., The Mind at Work: In Studying, Thinking, and Reading, pp. 136-140. Chicago, Scott Foresman & Co., 1924.] Dr. Lyman has succeeded very well indeed in making concrete the distinction between and the relationship of the two kinds of thinking. The entire book from which this selection is taken should be read by the student. It will clarify much that is difficult in the field of educational psychology. McMurry says that the investigations into the causes of yellow fever employed two different kinds of thinking, called induction and deduction. These are types of thinking differing from each other, and at the same time closely related to each other, which every one should understand. The Meaning of the Two Words.-Induction comes from two Latin words, in and duco, which mean respectively in and lead; induction, then, is a leading in. Obviously, deduction, coming from de and duco, means similarly a leading out. A Graphic Representation.-Suppose we imagine a large reservoir with pipes leading into it and out of it. in leading reservoir out- If these passageways and this receptacle contained a liquid, we could readily see that one set of pipes, a,a, was designed to fill the reservoir, and the other, b,b, to empty it. But in speaking of inductive and deductive thinking, we are not considering a physical substance like a liquid. We have for consideration streams of thinking flowing into and out of the body of thought. Our diagram may then be changed. How the Study of Yellow Fever Involved Both Induction and Deduction.-From the investigations and experiments named at the left of the diagram, certain judgments or conclusions flowed into a reservoir of thought, at the right, gath ering there the data for an intelligent guess, an hypothesis, as to the cause of yellow fever. In short, the cause of yellow fever was determined experimentally by inductive thinking. Thus in science laboratories the inductive processes are used for the discovery of new truth. But... the hypothesis had to be very widely and repeatedly tested, in order that the investigators might be positive that the right cause had been found. We may therefore picture the testing processes as follows: Here we have deduction. Drawn out of the general reservoir on one side are certain features that go back for further testing; drawn out of it on the other are certain elements of judgment, certain inferences which result in conclusions. Thus we may represent the conclusion-Destroy mosquitoes and prevent yellow fever as the result of a joint process of inductive and deductive thinking. Relation Between Induction and Deduction.-Induction and deduction are not to be considered separate and distinct forms of thinking; they are mutually dependent upon one another. Thus in the last diagram, we must not think of the flow of thought as being only in one direction, viz., from the in-going pipes to the reservoir, and away from the reservoir along the out-going pipes. The flow of thought is in both directions, from the out-going to the in-going pipes of the reservoir as well. When we are in doubt about the truth in the reservoir, the outgoing pipes become the in-going pipes and the in-going pipes become the out-going pipes. There is constant flowing of thought back and forth, forth and back, along our line of thinking, so that the reservoir of truth is never at a standstill when we are thinking. Truth is in the making for us; and we, by questioning and testing, become important factors in the making of that truth. The content of our minds is not in the form of a solid, but rather in the form of a fluid, and thinking sets the fluid in motion, This ought to make us realize the importance of thinking in all our daily life of school and home. If we accept the materials before us without question and learn them by heart, our reservoir of knowledge is not disturbed except for the addition of new portions of truth. Its contents become solidified and take the form of blocks rather than remain in the fluid state. On the other hand, when we think about what we are studying and reading, the content of our study is set in motion and we become factors in shaping the course of events. Thus the boys who really think about their courses in physics are not satisfied with the mere addition of various items to their store of information One plans a new radio apparatus at home or a modification of the old one. One sets up an electric light in the furnace room or changes the connection of his mother's door bell from dry cells to the current carried by the city wires. Girls adjust some of the operations of their own garment-making or the preparation of food at home, in the light of new principles revealed to them in their domestic science courses. Thus do we count for something when the contents of our minds are not solid but fluid, growing, diminishing, changing, as we read, study, think, judge, apply. To continue our diagram of mental activity, this movement of thinking, considered as a fluid rather than a solid, may be sketched as follows: Homely Examples of Induction and Deduction.-(1) A boy repeatedly trying to throw a curve ball, experimenting about how to hold and how to deliver it, is performing an inductive experiment. His thinking is also inductive. A boy pitching in a game, and applying the principles of throwing curves is using |