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THE PSYCHOLOGY OF NUMBER.

CHAPTER I.

WHAT PSYCHOLOGY CAN DO FOR THE TEACHER.

THE value of any fact or theory as bearing on human activity is, in the long run, determined by practical application—that is, by using it for accomplishing some definite purpose. If it works well-if it removes friction, frees activity, economizes effort, makes for richer results-it is valuable as contributing to a perfect adjustment of means to end. If it makes no such contribution it is practically useless, no matter what claims may be theoretically urged in its behalf. To this the question of the relation between psychology and education presents no exception. The value of a knowledge of psychology in general, or of the psychology of a particular subject, will be best made known by its fruits. No amount of argument can settle the question once for all and in advance of any experimental work. But, since education is a rational process, that is a process in harmony with the laws of psychical development, it is plain that the educator need not and should not depend upon vague inductions from a practice not grounded upon principles. Psychology can not dispense with ex

perience, nor can experience, if it is to be rational, dispense with psychology. It is possible to make actual practice less a matter of mere experiment and more a matter of reason; to make it contribute directly and economically to a rich and ripe, because rational, experience. And this the educational psychologist attempts to do by indicating in what directions help is likely to be found; by indicating what kind of psychology is likely to help and what is not likely; and, finally, by indicating what valid reasons there are for anticipating any help at all.

I. As to the last point suggested, that psychology ought to help the educator, there can be no disagreement. In the first place the study of psychology has a high disciplinary value for the teacher. It develops the power of connected thinking and trains to logical habits of mind. These qualities, essential though they are in thorough teaching, there is a tendency to undervalue in educational methods of the present time when so much is made of the accumulation of facts and so little of their organization. In our eager advocacy of “facts and things" we are apparently forgetting that these are comparatively worthless, either as stored knowledge or for developing power, till they have been subjected to the discriminating and formative energy of the intelligence. Unrelated facts are not knowledge any more than the words of a dictionary are connected thoughts. And so the work of getting "things" may be carried to such an extent as to burden the mind and check the growth of its higher powers. There may be a surfeit of things with the usual consequence of an impaired mental digestion. It is pretty generally conceded that the num

ber of facts memorized is by no means a measure of the amount of power developed; indeed, unless reflection has been exercised step by step with observation, the mass of power gained may turn out to be inversely proportional to the multitude of facts. This does not mean that there is any opposition between reflection and true observation. There can not be observation in the best sense of the word without reflection, nor can reflection fail to be an effective preparation for observation.

It will be readily admitted that this tendency to exalt facts unduly may be checked by the study of psychology. Here, in a comparatively abstract science, there must be reflection-abstraction and generalization. In nature study we gather the facts, and we may reflect upon the facts: in mind study we must reflect in order to get the facts. To observe the subtle and complex facts of mind, to discriminate the elements of a consciousness never the same for two successive moments, to give unity of meaning to these abstract mental phenomena, demands such concentration of attention as must secure the growth of mental power-power to master, and not be mastered by, the facts and ideas of whatever kind which may be crowding in upon the mind; to resolve a complex subject into its component parts, seizing upon the most important and holding them clearly defined and related in consciousness; to take, in a word, any "chaos" of experience and reduce it to harmony and system. This analytic and relating power, which is an essential mark of the clear thinker, is the prime qualification of the clear teacher.

But, in the second place, the study of psychology is

of still more value to the teacher in its bearing upon his practical or strictly professional training.

Every one grants that the primary aim of education is the training of the powers of intelligence and will— that the object to be attained is a certain quality of character. To say that the purpose of education is "an increase of the powers of the mind rather than an enlargement of its possessions"; that education is a science, the science of the formation of character; that character means a measure of mental power, mastery of truths and laws, love of beauty in nature and in art, strong human sympathy, and unswerving moral rectitude; that the teacher is a trainer of mind, a former of character; that he is an artist above nature, yet in harmony with nature, who applies the science of education to help another to the full realization of his personality in a character of strength, beauty, freedom-to say this is simply to proclaim that the problem of education is essentially an ethical and psychological problem. This problem can be solved only as we know the true nature and destination of man as a rational being, and the rational methods by which the perfection of his nature may be realized. Every aim proposed by the educator which is not in harmony with the intrinsic aim of human nature itself, every method or device employed by the teacher that is not in perfect accord with the mind's own workings, not only wastes time and energy, but results in positive and permanent harm; running counter to the true activities of the mind, it certainly distorts and may possibly destroy them. To the educator, therefore, the only solid ground of assurance that he is not setting up impossible or artificial aims, that he

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