Mathematics capital in the educational field: Bourdieu and beyond

ABSTRACT

Mathematics education needs a better appreciation of the dominant power structures in the educational field: Bourdieu's theory of capital provides a good starting point. We argue from Bourdieu's perspective that school mathematics provides capital that is finely tuned to generationally reproduce the social structures that serve to keep the powerful in power, while ensuring that less powerful groups are led to accept their own failure in mathematics. Bourdieu's perspective thereby highlights theoretical inadequacies in much mathematics education research, insofar as it presumes a consensus about a ‘what works agenda’ for improving achievement for all. Drawing on one case where we manufactured awkward facts, we illustrate a Bourdieusian interpretation of mathematics capital as reproductive, and the crucial role of its cultural arbitrary. We then criticise the Bourdieusian concept of ‘mathematical capital’ as the value of mathematical competence in practice and propose to extend his tools to include the contradictory ‘use’ and ‘exchange’ values of mathematics instead: we will show how this conceptualisation goes ‘beyond Bourdieu’ and helps explain how teaching-learning might (ideally) produce ‘cultural use value’ in mathematical competence, while still recognising the contradictions teachers and learners face. Finally, we suggest how critical education research generally can benefit from this theoretical framework: (1) in exposing the interest of the dominant classes; but also (2) in researching critical pedagogic alternatives that challenge orthodoxy in educational policy and practice both in mathematics education and more generally.

KEYWORDS:

• Bourdieu
• mathematical capital
• use and exchange value

Acknowledgements

We acknowledge the support of the ESRC-TLRP Widening Participation Programme (under grant RES-139-25-0241) and Transmaths research projects, (including grants RES-062-23-1213, RES-189-25-0235, and RES-000-22-2890, for further details visit www.transmaths.org) and continuing work in Teleprism (ESRC grant: RES-061-25-0538). We also would like to acknowledge Maria Pampaka's help in preparing Figure 2 especially for this paper.

Notes

1 Footnotes too, contextualise most of Bourdieu's writing. It is annoying but at the same time Bourdieu has a strong point: in fact, critics do quote passages of Bourdieu one-sidedly, reading his objectivism as too deterministic, notwithstanding his efforts.

2 We are not aware of anyone making this point: implicit here is our suggestion that the structure of a ‘relatively static’ field may not need to be explicitly formulated as such, and that the ‘practices of the field’ may be more likely to be sufficient to understand how habitus develops.

3 This view of capital is more consistent with those of Putnam or Coleman.

4 The new English Baccalaureate measures school performance by accounting for the number of students getting grade C and above at the end of their school year exams in core subjects.

5 English school league table compare how secondary schools perform across England in their GCSE examinations.

6 By sleight of hand we are earlier and here introducing the concept of ‘use’ as in competence, and functional use, which will be counterposed to exchange value and capital later, as in Williams (2011b).

7 We are aware that Bourdieu himself occasionally preferred to say he offered “thinking tools” and denied “having a theory”, at least in the sense of grand theory that one would apply mechanistically to model new situations and contexts. But his thinking tools clearly only make sense as a system for analysis of social practice (as is obvious in the title of his 1977 book) and we take it that this point was made to emphasise that his system offers tools that need developing with and through data in the best dialectical, social scientific (and not natural science) Hegelian sense.