Schemes and Scheme Theory: Core Explanatory Constructs for Studying Mathematical Learning

We use this chapter to examine one of Piaget’s central explanatory constructs, schemes. We trace out important epistemological and historical developments related to schemes, situating them within Glasersfeld’s radical constructivism, and examining important developments mathematics education researchers have made to their use. We, then, turn to examining how schemes can be used to study mathematical learning by discussing assimilation, perturbation, and accommodation. The final two sections of the chapter discuss stages and levels in relation to schemes with the aim of situating mathematical learning within a broader framework for examining students’ mathematical cognition. Throughout, we provide empirical examples to illustrate the constructs under discussion.