A Study on the Function of Generalization in Learning Mathematics: Focusing on its Ordered Structure

Abstract

　　 Generalization is very important knowing process in mathematics learning.  However, its purpose, meaning and usefulness (we call, the function of generalization) are not so clear for not only students but also mathematics educators.  In fact, even very young children has ability to generalize something (Vinner, 2011), nevertheless generalization does not appear just by performing in mathematics class (cf. Tatsis & Tatsis, 2012).  This problem should not simply be attributed to students’ cognitive ability, but also that they may not realize the function of generalization.

　　 In our previous study, we identified six functions of generalization: purification, valiablization, unification, discovery, association, and socialization.  In this study, we focus and analize their epistemological ordered structure between two functions.  Of course, their actual relationship in mathematics learning is more complex and tangled.  However, relationship between two functions is the most simple structure.  Thus, our analysis provide the basis for understanding the function of generalization in learning mathematics.