Genetic Epistemology as a Complex and Unified Theory of Knowing

The purpose of this chapter is to bring together constructs introduced in Part I of the book, integrating them within Piaget’s unifying theory of mathematical knowing and learning. The chapter draws heavily on Piaget’s untranslated tome on mathematical thought: Volume 1 of Introduction à l’épistémologie génétique. That work describes Piaget’s historicocritical and psychogenetic approach to answering the chief question motivating his genetic epistemology: how is knowledge—and mathematical thought in particular—possible? As researchers of mathematics education, we build models of students’ mathematical thought. These models depend upon theoretical constructs such as schemes, operations, reflective abstraction, groupings, units coordination, and covariational reasoning. This chapter reviews those constructs, as introduced in prior chapters, with Piaget’s chief question in mind. The chapter concludes with additional questions that might guide future research in mathematics education.