Overall Commentary on Early Algebraization: Perspectives for Research and Teaching

Abstract

Using classroom episodes from grades 2–6, this chapter highlights four mathematical activities that underlie arithmetic and algebra and, therefore, provide a bridge between them. These are: • understanding the behavior of the operations, • generalizing and justifying, • extending the number system, and • using notation with meaning. Analysis of each episode provides insight into how teachers recognize the opportu- nities to pursue this content in the context of arithmetic and how such study both strengthens students’ understanding of arithmetic operations and enables them to develop ideas foundational to the study of algebra.