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the arts of calculation involved in trade and the arts; culture value in its enlargement of the imagination in dealing with the most general relations of things; even religious value in its concept of the infinite and allied ideas. But clearly mathematics does not accomplish such results, because it is endowed with miraculous potencies called values; it has these values if and when it accomplishes these results, and not otherwise. The statements may help a teacher to a larger vision of the possible results to be effected by instruction in mathematical topics. But unfortunately, the tendency is to treat the statement as indicating powers inherently residing in the subject, whether they operate or not, and thus to give it a rigid justification. If they do not operate, the blame is put not on the subject as taught, but on the indifference and recalcitrancy of pupils.
This attitude toward subjects is the obverse side of the conception of experience or life as a patchwork of independent interests which exist side by side and limit one another. Students of politics are familiar with a check and balance theory of the powers of government. There are supposed to be independent separate functions, like the legislative, executive, judicial, administrative, and all goes well if each of these checks all the others and thus creates an ideal balance. There is a philosophy which might well be called the check and balance theory of experience. Life presents a diversity of interests. Left to themselves, they tend to encroach on one another. The ideal is to prescribe a special territory for each till the whole ground of experience is covered, and then see to it each remains within its own boundaries. Politics, business, recreation, art, science, the learned professions, polite intercourse, leisure, represent such interests. Each of these ramifies into many branches: business into manual occupations, executive positions, bookkeeping, railroading, banking, agriculture, trade and commerce, etc., and so with each of the others. An ideal education would then supply the means of meeting these separate and pigeon-holed interests. And when we look at the schools, it is easy to get the impression that they accept this view of the nature of adult life, and set for themselves the task of meeting its demands. Each interest is acknowledged as a kind of fixed institution to which something in the course of study must correspond. The course of study must then have some civics and history politically and patriotically viewed: some utilitarian studies; some science; some art (mainly literature of course); some provision for recreation; some moral education; and so on. And it will be found that a large part of current agitation about schools is concerned with clamor and controversy about the due meed of recognition to be given to each of these interests, and with struggles to secure for each its due share in the course of study; or, if this does not seem feasible in the existing school system, then to secure a new and separate kind of schooling to meet the need. In the multitude of educations education is forgotten.
The obvious outcome is congestion of the course of study, overpressure and distraction of pupils, and a narrow specialization fatal to the very idea of education. But these bad results usually lead to more of the same sort of thing as a remedy. When it is perceived that after all the requirements of a full life experience are not met, the deficiency is not laid to the isolation and narrowness of the teaching of the existing subjects, and this recognition made the basis of reorganization of the system. No, the lack is something to be made up for by the introduction of still another study, or, if necessary, another kind of school. And as a rule those who object to the resulting overcrowding and consequent superficiality and distraction usually also have recourse to a merely quantitative criterion: the remedy is to cut off a great many studies as fads and frills, and return to the good old curriculum of the three R's in elementary education and the equally good and equally old-fashioned curriculum of the classics and mathematics in higher education.
The situation has, of course, its historic explanation. Various epochs of the past have had their own characteristic struggles and interests. Each of these great epochs has left behind itself a kind of cultural deposit, like a geologic stratum. These deposits have found their way into educational institutions in the form of studies, distinct courses of study, distinct types of schools. With the rapid change of political, scientific, and economic interests in the last century, provision had to be made for new values. Though the older courses resisted, they have had at least in this country to retire their pretensions to a monopoly. They have not, however, been reorganized in content and aim; they have only been reduced in amount. The new studies, representing the new interests, have not been used to transform the method and aim of all instruction; they have been injected and added on. The result is a conglomerate, the cement of which consists in the mechanics of the school program or time table. Thence arises the scheme of values and standards of value which we have mentioned.
This situation in education represents the divisions and separations which obtain in social life. The variety of interests which should mark any rich and balanced experience have been torn asunder and deposited in separate institutions with diverse and independent purposes and methods. Business is business, science is science, art is art, politics is politics, social intercourse is social intercourse, morals is morals, recreation is recreation, and so on. Each possesses a separate and independent province with its own peculiar aims and ways of proceeding. Each contributes to the others only externally and accidentally. All of them together make up the whole of life by just apposition and addition. What does one expect from business save that it should furnish money, to be used in turn for making more money and for support of self and family, for buying books and pictures, tickets to concerts which may afford culture, and for paying taxes, charitable gifts and other things of social and ethical value? How unreasonable to expect that the pursuit of business should be itself a culture of the imagination, in breadth and refinement; that it should directly, and not through the money which it supplies, have social service for its animating principle and be conducted as an enterprise in behalf of social organization! The same thing is to be said, mutatis mutandis, of the pursuit of art or science or politics or religion. Each has become specialized not merely in its appliances and its demands upon time, but in its aim and animating spirit. Unconsciously, our course of studies and our theories of the educational values of studies reflect this division of interests. The point at issue in a theory of educational value is then the unity or integrity of experience. How shall it be full and varied without losing unity of spirit? How shall it be one and yet not narrow and monotonous in its unity? Ultimately, the question of values and a standard of values is the moral question of the organization of the interests of life. Educationally, the question concerns that organization of schools, materials, and methods which will operate to achieve breadth and richness of experience. How shall we secure breadth of outlook without sacrificing efficiency of execution? How shall we secure the diversity of interests, without paying the price of isolation? How shall the individual be rendered executive in his intelligence instead of at the cost of his intelligence? How shall art, science, and politics reinforce one another in an enriched temper of mind instead of constituting ends pursued at one another's expense? How can the interests of life and the studies which enforce them enrich the common experience of men instead of dividing men from one another? With the questions of reorganization thus suggested, we shall be concerned in the concluding chapters.
Summary.
Fundamentally, the elements involved in a discussion of value
have been covered in the prior discussion of aims and interests. But since educational values are generally discussed in connection with the claims of the various studies of the curriculum, the consideration of aim and interest is here resumed from the point of view of special studies. The term "value" has two quite different meanings. On the one hand, it denotes the attitude of prizing a thing finding it worth while, for its own sake, or intrinsically. This is a name for a full or complete experience. To value in this sense is to appreciate. But to value also means a distinctively intellectual act—an operation of comparing and judging—to valuate. This occurs when direct full experience is lacking, and the question arises which of the various possibilities of a situation is to be preferred in order to reach a full realization, or vital experience.
We must not, however, divide the studies of the curriculum into the appreciative, those concerned with intrinsic value, and the instrumental, concerned with those which are of value or ends beyond themselves. The formation of proper standards in any