Activity Theoretic Approaches

Abstract

9.1 Introduction Activity theory 1 (AT) is an approach to the study of human practices—any human practice and human practice in itself. It warrants a chapter in this book on tools and mathematics because artefacts/tools 2 are intrinsic to its approach and many math-ematics educators use theoretic approaches to study mathematical practices. I first consider this approach in general but then focus on the practices of doing, learning and teaching mathematics, and the light that activity theoretic approaches shed on tool use in these mathematical practices. The roots of AT go back to early Soviet approaches and the section on Vygotsky in Sect. 7.2 serves as an introduction to these roots. This chapter has four sections. Section 9.1 provides an overview of AT. Section 9.2 traces early influences of AT in mathematics education research. Section 9.3 considers foci of a set of mathematics education papers recent at the time of writing. Section 9.4 explores emphases and tensions in papers considered in Sects. 9.2 and 9.3. 1 As will soon become apparent, there are a number of schools of thought within what is called 'activity theory' and I use the term 'activity theoretic approaches' as a collective noun for these different approaches. 2 A note for readers who are reading this as a 'stand alone chapter'. In Sect. 1.3.1 I stated my distinction between and artefact and a tool as, an artefact becomes a tool when it is used by an agent to do something. I use this distinction in this chapter. For example, a compass as a metal thing which holds a pencil and rests on a desk is an artefact but when it is picked up by someone to draw a circle it is a tool. When its status is ambiguous I use the term 'artefact/tool'.