ABSTRACT
This chapter describes a theoretical framework for thinking about algebra and algebraic thinking. It argues that thinking about how individuals create their own mathematical certainty is an important part of representational thinking and a neglected route to making mathematics more connected, more general, and more explicit in Nemirovsky's terms. The chapter describes an approach to building student's understanding of functions that is applicable in the elementary years that builds on students' sense-making activities around constructing units, working toward an understanding of linear functions reflecting a longitudinal approach to the function strand of algebra. Finally, the chapter argues that occupied context plays an important role in connecting mathematical certainty with functional thinking—that is, in allowing functional thinking to become part of the algebraic process of enriching our mathematical experience.
