Thinking and learning to think

by Nathan Christ Schaeffer

Cognition is not complete until the knowledge has been or can be applied. At times there may be a division of labor and glory in the discovery and application of truth. The discoveries of Professor Henry which made the electric telegraph possible involved thinking quite as valuable as the invention of Professor Morse. The achievement of Cyrus W. Field in laying the Atlantic cable involved thinking quite as important as the researches and experiments of Lord Kelvin which made the cable successful. Interesting examples of such division of labor in thinking cannot justify neglect of the applications after a general truth has been evolved and stated.

The instruction may sometimes begin with a statement of applications, in order to prepare the mind for the thinking that issues in knowing. The applications of color in the railway service, in navigation, and in the arts will create an interest in the study of color without which the presentation of the fundamental ideas may be in vain. Several lecturers have admitted that they failed, in the presentation of color lessons, to hold the attention of their pupil-teachers until they excited an interest in color by indicating important applications. This statement of applications by way of preparation must, however, not be confounded with the applications which should follow the framing of general propositions and the cognition of general truths.

The hypotheses of the scientist correspond to the general truths and principles which instruction always aims to reach. In all except the most advanced investigations, the pupil should work under the guidance of principles that have risen above the hypothetical stage. He should think under the inspiration of well-established truths. He should master the known in his chosen field before he seeks to enlarge the boundaries of human knowledge by invasions into the realm of the unknown. Sad is the spectacle of a talented mind wasting its strength in fruitless efforts to rediscover what is already well established.

The formulation of truths.

Similarity in diversity.

The formulation of truths in mathematical studies is sometimes carried to extremes. The pupil may at times be allowed to work under the guidance of principles which he knows by implication, and which he has never had occasion to formulate in explicit statements. The formulation of the principles of algebra can be carried into the statement of hundreds of general propositions. If the pupil is asked to fix all these in the crystallized or specific form given in the text-book, it may result in a prodigious waste of time. Furthermore, the effort to follow invariably any formal steps in the order of instruction is apt to make the instruction unduly formal and lifeless. No thinker can afford to think in the set forms of the syllogism while evolving a train of thought. Conscious conformity to these hinders progress in the spontaneous evolution of germinal ideas. In like manner, although the student of pedagogy may find a guide in the rules and principles of his science while preparing the subject-matter of a lesson, yet, in giving the instruction, the truth must be the object of chief regard, the centre of attention in consciousness. Constant thought of prescribed steps makes the teaching stiff and formal, and dissipates the joyous interest which accompanies free and spontaneous thinking. Formal rules are very often like hobbles on the feet of the horse. They impede his speed, rob him of half his power and energy, and spoil his enjoyment of the open field. Bearing this in mind, the young teacher will perhaps not be harmed by the advice that in his teaching he should ever seek to lead the learner to clear and distinct perception of likenesses and differences in the subject-matter of each and every lesson. The newer methods of teaching a beginner to read, wisely draw attention to the points of similarity and difference in the shapes and sounds of the letters of the alphabet. They even go to the extreme of comparing sounds with the noises of animals, with which the child in the larger cities is totally unfamiliar. This error is not half so bad as the opposite extreme. Very much of the bad teaching by which the schools are afflicted arises from the assumption that the learner sees the points of agreement and difference which are so very obvious to the mature mind of the teacher. The consequence is mental confusion and loss of the joy of definite thinking. The detection of likeness in objects having many points of diversity gives the mind an agreeable surprise. This emotion is an element in the pleasure afforded by the various forms of wit, metaphor, and allegory. Professor Bain has shown how greatly progress in science and art is indebted to the discovery of similarity in the midst of great diversity.[49] Much of the child’s progress in knowledge must be ascribed to the same principle. Children notice points of similarity that often escape older persons. On seeing the picture of a tiger, they call it a cat. A mother who showed her little daughter, just beginning to talk, the caricature of a man prominent in the public eye, was surprised to hear the child exclaim, “Papa.” It was the child’s word for man, as she afterwards discovered. Where she saw contrast, the child only noticed the points of similarity between one man and another. As the power of discrimination advances, the mind pays more attention to points of difference than to points of likeness. Indistinguishableness gives way to clear and distinct knowledge. With the further growth of intelligence the mind seeks the hidden resemblances in objects far removed from one another in space and time, or by surface appearances. At first sight the bat seems like a bird, because it can fly. Scientific discrimination assigns it to the class of mammals. The identification of the lightning in the clouds with the sparks of the electric machine gave Franklin world-wide reputation as a philosopher. The identification of the force which causes bodies to fall to the earth with the force which holds the moon in its orbit, and with the kind of force by which the sun attracts the bodies of the solar system, has been justly called the greatest example of the power to detect likeness in the midst of diversity. The power of detecting similarity in diversity should be appealed to whenever it is helpful either for purposes of illustration or discovery. Algebra is shorn of half its difficulty as soon as the learner is led to see that the operations in multiplication, division, involution and evolution of monomials turn on signs, coefficients, and exponents. Let him grasp the thought that the words add, subtract, multiply, and divide respectively express the law of exponents in the four operations above named; and he will not only escape the perplexities of the average student in the more difficult operations of ordinary algebra, but he will also see at a glance the beautiful truth which underlies the manipulation of logarithms.

The thinking that ripens into knowing.

Thinking that ripens in knowing involves comparison, discrimination, and formation of judgments. Through the detection of likeness and unlikeness in objects and their relations, judgments are formed, inferences are made, and conclusions are drawn, which mark the transition from thinking to knowing. Discrimination, identification, judgment, reasoning, definition, division, and classification mark the stages through which the mind passes in thinking things, their relations, more especially their causes, effects, laws, and ends. Analysis and synthesis, induction and deduction, are the processes by which the intellect explores the content and extent of concepts, and passes to general principles and truths, and to their applications in thought and action. As processes of mental activity, these are discussed in detail by the psychologist. The laws of thought to which they must conform in order to be correct are set forth in treatises on logic. It would be a mistake to underestimate the value of a knowledge of logic and psychology; but neither of them can supply the place and function of the living teacher. He who would learn to think in some special line of research should go to a master of that specialty, learn of him what is well established in the chosen field of study, imbibe his methods of work, think his thoughts, catch his spirit, and follow his advice until the hour for independent investigation comes. Great is the tonic effect of a university atmosphere; but greater still is the bracing influence of the atmosphere created by a specialist who is both a master in his department and a master in the art of teaching. The choice of a teacher is of more account than the choice of a university, either at home or abroad.

Knowing involves more than mere thinking.