The Aims of Mathematical Education

Abstract

Education is a complex process involving a variety of experiences gained through both school and out-of-school activities. Each subject of the curriculum should make its definite contribution to this experience, but we must be sure that the result is a unit. An investigation of conditions in most of our high schools will show that a child is under the instruction of perhaps four or five teachers, all of whom are working independently of each other. Very seldom docs one teacher know what the others are trying to do. In order to avoid such conditions and to insure a unified education for each individual, it is necessary that the aim of each subject shall be determined in the light of the general definition of education. Only by this means can the subject matter of each course be so selected and presented that there is neither useless overlapping on the one hand nor the omission of important elements on the other hand. Hence, in discussing the aim of mathematical education, we shonld consider the general meaning of education and then determine what contribution mathematics can make most effectively. For this purpose we shall accept Ruediger’s definition, namely, “… to educate a person means to adjust him to those elements of his environment that are of concern in modern life, and to develop, organize, and train his powers so that he may make efficient and proper use of them.”1 This definition consists of two parts. One of these is concerned with the adjustment of the individual to his environment; this is the objective side. The other is concerned with the development of the powers of the individual; this is the subjective side of education. However, one’s powers are developed only by contact with and adjustment to his environment, and he is adjusted to his environment only through his powers and abilities. Thus, a child’s power to think correctly is developed most effectively when he is brought face to face with a real situation the solution of which is vital to his welfare; but he can successfully master the situation only by the use of his reasoning power or such other abilities as may be involved. Hence, the two parts of this definition are not independent and we need not consider them separately; when one is satisfied in the most effective way the other will be. At present we shall confine our attention to the objective phase of education.