Chapter 1: Social Bodies and Mathematical Cognition: An Introduction

In this book, two bodies of literature come together: mathematical knowing in communities of practice and the embodied nature of mathematical knowing. The purpose of this introductory chapter is to (a) set an ever-so-brief historical context of developments in the late twentieth-century; (b) provide a philosophical context for the debate about the nature of mathematical knowing as idealist or embodied; and (c) articulate cultural-historical activity theory as dialectical materialist alternative that can be used to integrate into a single framework the two literatures emphasizing the embodied and social nature of mathematical knowing.

Over the past two decades, the theoretical interests of mathematics educators have changed substantially—as any brief look at the titles and abstracts of articles in relevant journals shows. In the 1980s, mathematical knowing and learning were explained in psychological models, focusing on motivation, interest, abilities, information processing, and conceptual (including alternative) frameworks. Jean Piaget’s concepts of accommodation and assimilation reigned as a pair of key theoretical concepts that many mathematics educators have drawn on to explain observations made in individual interviews, teaching experiments, and quantitative Classroom studies. His work alerted mathematics educators to the role of bodily experiences in the elaboration of mind especially drawing also on the concept of reflective abstraction. Piaget’s perspective, however, is somewhat limited because he operated from Kantian principles attempting to identify formal knowledge that exists in excess of practical knowledge of the world without providing a framework how this might go. Moreover, Piaget did not address a well-known learning paradox, which questions the possibility of “constructing” abstract (formal) representations and forms of reasoning when the tools, objects, and material ground on and with which this construction occurs all are of lower complexity (e.g., Bereiter, 1985). He further did not address the question of how students can intend to learn something when they do not yet have the knowledge required to formulate the object of this intention. How can anyone who stands in a clearing (knowing) intend to learn the unseen in the surrounding dark without already knowing it?