Generalization

Abstract

Generalization as a principle of teaching mathematics is often neglected. We are not thinking here of generalization as simply a process of passing from particulars to generals; rather we wish to consider that attitude of mind which continually gives attention to the relations and significance of facts. Learning is a continuous process, a growth, a development, a passing from one thing to something else. In the process of learning there must be concrete particulars; these particulars are the means to intellectual growth and form the material of which knowledge is made. But so long as they remain just isolated particulars they are of little value, they are mere excitations and possible irritations. To be of value these particulars must be related, organized, given meaning and significance. The mere encyclopaedic collection of facts is not our conception of valuable learning; rather it is the interpreting and application of facts, the relation and organization of facts, the careful study of the meaning and significance of particulars which rounds out and carries forward the learning process. This continual seeking for significance and organization is generalization.