evaluations. A comparison of these with those made by the teacher shows him whether he is right or wrong. Moreover, he probably not only follows the teacher's reasoning but observes as well the latter's method, and then either consciously or unconsciously imitates it or, if he thinks it is a poor one, may purposely avoid it. The total amount of training received by a class from following the teacher's reasoning is probably too small to make this an important basis for such training except in the case of advanced or superior students.

4. Properly constructed books may provide good opportunities for reasoning. The fourth kind of opportunity for training in reflective thinking, namely, following and supplementing the reasoning outlined in a book, has possibilities that are not generally appreciated. It is generally assumed that a book provides primarily opportunities for acquiring information, but the possibilities of providing also for training in reasoning approximate in some subjects the possibilities of providing for the independent individual reasoning discussed above (p. 200, § 1). An excellent example of such a book is the textbook on economics from which a quotation was made at the beginning of this chapter (see p. 172). Another good example is E. L. Thorndike's "Principles of Teaching," in which two thirds of the book is taken up with exercises intended to give students training in thinking about problems of teaching. Other examples of books which tend to provide for reasoning instead of mere acquisition of facts or ideas are the recent "suggestive" geometries, which place the emphasis upon the solution of exercises instead of on the memorizing of proofs of propositions. One of the best arguments in favor of this tendency is found in A. Schultze's "Teaching of Mathematics in Secondary Schools." It reads in part as follows:

The most common error of geometric instruction is the fact that the knowledge of book demonstrations is made the chief object of the study.

The study of geometry should be primarily a course in the solution of originals and general methods of attack. The regular textbook propositions should be treated as exercises, with this difference, that the facts stated by them should be remembered.

Exercises, however, should be studied not in order to be remembered but in order that the student may familiarize himself with geometric working methods, which will enable him to do other and more complex reasoning.

The student's ability and progress in the subject can be measured only by his ability to solve exercises that are original to him, and not by his ability to repeat well-known facts. (21: 103)

This quotation suggests not only the possibility of organizing geometry books in which problem-solving is emphasized, but also calls attention to the fact that the ordinary methods of teaching the subject do not give exercise in reasoning, but simply require the memorizing of a series of statements.

Kind of mental activity determined by method, not by subject matter. These facts concerning the teaching of geometry suggest the general principle that the character of the subject matter does not necessarily assure a certain type of mental activity on the part of the pupil. Often it is the method of teaching the subject matter which determines the type of mental activity. The same point is well illustrated in the teaching of natural science, which, like geometry, has ordinarily been supposed to train in reasoning. The distinction between learning the body of scientific subject matter and using methods of scientific reasoning has been discussed at length by Dewey (13:121–127) and Karl Pearson (19: 9–12). It has already been considered in this book in connection with the distinction between the logical and psychological methods of organizing subject matter. (Review page 91.)

Summary of problem-solving aspect of reflective thinking. This will conclude our discussion of the first phase of reflective thinking, namely, problem-solving. We have

considered the opportunities for problem-solving which occur in various subjects; the types of problems with which persons are confronted in ordinary life; the nature of the process of reflective thinking in solving problems; the methods which a teacher might use in stimulating and assisting pupils in solving problems; and the relative value of independent reasoning by the individual pupil as compared with reasoning as a member of a group, or following and supplementing the reasoning of the teacher, or solving a series of problems outlined in a book.

In the next section of the chapter we shall take up reflective thinking from a slightly different point of view, namely, from the standpoint of the part played in reflective thinking by the process of acquiring clearly defined abstract and general meanings or ideas.

SECTION II. ACQUIRING ABSTRACT AND GENERAL

MEANINGS

Closely

Plays a large part in high-school instruction. related to the first phase of reflective thinking which we have been considering, namely, problem-solving, is the learning of abstract and general meanings. This process plays a very large part in high-school instruction. This may be illustrated by the following list of a few of the general or abstract terms, the meanings of which are learned in high school or in the upper grades of the elementary school.

In linguistic studies: ablative, accordance, appositive, concession, conditional subjunctive, diæresis, ellipsis, genitive, gerund, hyperbole, metonymy, moods, pleonasm, pluperfect tense, vocatives.

In mathematics: abscissa, binomial, conditional equations, constants, coördinates, determinant, exponents, geometric progression, indeterminate equations, logarithms, mean proportional, reciprocal, surd.

In physics: aberration, acceleration, adhesion, capillarity, centrifugal, conduction, dialysis, diathermous, diatonic, endosmose, index of refraction, viscosity.

In botany: absorption, adaptation, bacteria, chloroplasts, chromosomes, fertilization, palisade cells, parthenogenesis, tropism, xerophytes.

Similarly, in chemistry, economics, psychology, and other subjects there are hundreds of abstract or general meanings which must be learned in order to understand the discussions or to do reflective thinking in the various subjects. Examples of general propositions studied. In addition to the meanings of single terms there are many abstract and general propositions, statements, rules, or laws that have to be studied, understood, and learned. Examples of these are the following:

From grammar: A verb agrees with its subject in number. In German" the subjunctive mode is used in all conditional sentences when the supposition is contrary to fact, and it occurs in both the condition and the conclusion."

From mathematics: To reduce a fraction to its lowest terms, divide both its numerator and its denominator by all of their common factors or by their highest common factor.

From physics: The value of the greatest resistance that can be overcome with a combination of pulleys is obtained by multiplying together the effort that is applied and the number of cords that support the movable pulley.

From botany: It has been observed that the chloroplasts in these palisade cells are able to assume various positions in the cell, so that when the light is very intense, they move to the more shaded depths of the cell, and when it becomes less intense, they move to the more external region of the cell. The stomata, or breathing pores, which are developed in the epidermis, are also great regulators of transpiration.

Contrasting methods used in textbooks. As we examine the various methods of teaching abstract or general meanings and propositions which are used in textbooks, we find striking

differences. For example, contrast the two following quotations from chemistries, which are intended to teach the meaning of chemical change.

The matter of the universe is constantly changing. Sometimes the change temporarily modifies the special properties of the matter under examination, but often the change is permanent and another substance or kind of matter is the result. When the properties of a given portion of matter are so changed that a different kind of matter is formed, then the change is called a chemical change. If the properties are temporarily changed, then the substance has undergone a physical change. (18: 15)

The second example of methods of teaching the meaning of chemical change reads as follows :

Introductory. Those things which are most familiar to us are apt to be regarded with least wonder and to occasion the least thought. Take, for example, the changes included under the head of fire. Unless we have studied these changes with care, what can we make of them? We see substances destroyed by fire. They apparently disappear. We feel the heat produced by the burning. We know that this heat disappears, and we have nothing left in the place of the substance burned. Take as another example the rusting of iron. We all know that iron when exposed to moist air undergoes a serious change, becoming covered with a reddish-brown substance which we call rust. If the piece of iron is comparatively thin and it is allowed to lie in the air long enough, it will be completely changed to the reddish-brown substance and no iron as such will be left. If a spark is brought in contact with gunpowder, there is a flash and the powder disappears, dense smoke appearing in its place. What are the causes of these remarkable changes? Can we learn anything about them by study?

Chemical changes. In those changes which have been referred to, the substances changed disappear as such. After the fire, the wood or the coal or whatever may have been burned is no longer to be found. The gunpowder after the flash is no longer gunpowder. The rusted iron is no longer iron, and no matter how long the rust is allowed to be unmolested, it will not return to the form of iron.