Conceptualizing Generalization

Abstract

The purpose of this paper is to encourage mathematics educators to refine their notions of generalizing and generalization. The paper describes generalization and how definitions of generalization have evolved from conceptions of transfer. In particular, the paper demonstrates how definitions of transfer have shaped definitions of generalizing, and specifically how constructivist learning perspectives have influenced definitions of mathematical generalization. Furthermore, the activity of generalizing is explained in the context of algebra as a way to support early algebra learning. Lastly, the final section offers tasks as a resource for mathematics educators who aim to promote generalizing in their classrooms.