Abstract

This paper aims to critique and develop neo-Vygotskian work in mathematics education from (i) within the Vygotskian and activity theoretic tradition, and where necessary from (ii) a Bourdieusian perspective. First, I critique Roth and Radford’s (2011) version of Cultural-historical Activity Theory, suggesting that a classroom episode presented as developmental might be seen as a process of alienation. I trace this to the institutional structure of schooling, in which curriculum and pedagogy are alienated from the learner’s everyday sense. Next, I examine and critique the Vygotskian ‘Funds of Knowledge’ approach to critical mathematics education, which seeks to overcome alienation by subjecting the curriculum to the needs of the poor communities the school serves. Here, the critical point on alienation in the Vygotskian approach is better argued in Bourdieu’s perspective on educational institutions as reproductive of class domination. Finally, the paper discusses the extent to which these critiques pertain to Vygotskian activity theory in general or only to these versions in particular and draws implications for the development of a critical mathematics education perspective in a synthesis of perspectives from Vygotsky and Bourdieu.

Highlights

  • The present paper aims to develop the critical, neo-Vygotskian, cultural-historical activity theory (ChAT) approach to mathematics education: it will do so through a process of critique of existing Vygotskian approaches to mathematics education, mainly from within the Vygotskian ChAT perspective but, where necessary, from Bourdieu’s sociology of ‘schooling’

  • I previously argued for a synthesis of neo-Vygotskian ChAT with Bourdieusian perspectives, by relating the ‘use value’ of mathematically competent labour to Vygotsky’s true concepts, the ‘exchange value’ of mathematics to Bourdieu’s cultural capital, and its arbitrary use in schooling for selection

  • In Roth and Radford (2011)—abbreviated here to R&R—one finds a detailed account of a Vygotskian-inspired developmental classroom understood by R&R as affording a zone of proximal development (ZPD) for mathematics: I choose this study to critique due to its Vygotskian inspiration and because it provides an admirable degree of detail of the classroom process that makes the praxis visible

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Summary

Introduction

The present paper aims to develop the critical, neo-Vygotskian, cultural-historical activity theory (ChAT) approach to mathematics education: it will do so through a process of critique of existing Vygotskian approaches to mathematics education, mainly from within the Vygotskian ChAT perspective but, where necessary, from Bourdieu’s sociology of ‘schooling’. I previously argued for a synthesis of neo-Vygotskian ChAT with Bourdieusian perspectives, by relating the ‘use value’ of mathematically competent labour to Vygotsky’s true concepts, the ‘exchange value’ of mathematics to Bourdieu’s cultural capital, and its arbitrary use in schooling for selection (see Williams, 2011, 2012). In Roth and Radford (2011)—abbreviated here to R&R—one finds a detailed account of a Vygotskian-inspired developmental classroom understood by R&R as affording a zone of proximal development (ZPD) for mathematics: I choose this study to critique due to its Vygotskian inspiration and because it provides an admirable degree of detail of the classroom process that makes the praxis visible. I will argue that Bourdieu’s perspective proves to be much sharper, insofar as it explains why schools and teachers may identify the ‘capital’ in these funds more readily than its critical ‘use’ in supporting the poor and underprivileged

Zone of proximal development or a moment in the process of alienation?
A funds of knowledge approach to mathematics education
Conclusions: is there a problem with alienation in activity theory?

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