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 ofmathematical 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-learningmight (ideally) produce “cultural use value” inmathematical 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. The Janet Duffin Award is made annually by the British Society for Research into LearningMathematics (BSRLM) to the author (or authors) of what is judged to be the most outstanding contribution – either research paper or essay review – published in the Society’s journal, Research in Mathematics Education (RME), during the preceding calendar year. All research papers or essay reviews published in RME during the calendar year in question are considered for the award. The award is made by voting amongst the membership and the RME Editorial Board. No authors can vote for their own paper. The author (or the nominee of multiple authors) is invited to attend one of the Society’s day conferences to receive the award, and to deliver the Janet Duffin Lecture. The award, and the lecture, is supported by the Janet Duffin Fund that was established by generous donation of the family of Janet Duffin, a longstanding and active member of BSRLM. For more information, see: http://www.bsrlm.org.uk/about/janet-duffin-award/ Julian Williams and Sophina Choudry received the award, and delivered the 2016 Janet Duffin Lecture, at the BSRLM conference on 10 June 2017 at the University of Oxford.

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2016 年珍妮特·达芬奖

数学教育需要更好地理解教育领域的主导权力结构：布迪厄的资本理论提供了一个很好的起点。我们从 Bourdieu 的角度认为，学校数学提供了经过精细调整的资本，可以按代复制社会结构，这些结构有助于保持强者的权力，同时确保弱小的群体被引导接受他们自己在数学上的失败。因此，布迪厄的观点突出了许多数学教育研究中的理论不足，因为它假定就提高所有人成就的“有效议程”达成共识。借鉴我们制造尴尬事实的一个案例，我们说明了布尔迪厄斯将数学资本解释为可再生的，以及其文化任意性的关键作用。然后，我们将布尔迪厄的“数学资本”概念批评为数学能力在实践中的价值，并建议扩展他的工具，以包括数学的相互矛盾的“使用”和“交换”价值：我们将展示这种概念化如何“超越布迪厄” ”，并有助于解释教学如何（理想情况下）产生“文化使用价值”的数学能力，同时仍然认识到教师和学习者面临的矛盾。最后，我们建议批判性教育研究通常如何从这个理论框架中受益：（1）暴露优势阶级的兴趣；但也 (2) 研究关键的教学替代方案，挑战正统的教育政策和实践，包括数学教育和更普遍的教育。珍妮特·达芬奖由英国学习数学研究学会 (BSRLM) 每年颁发给被认为是最杰出贡献的作者（或作者）——无论是研究论文还是论文评论——发表在该学会的期刊研究在数学教育（RME），在上一个日历年。在相关日历年期间在 RME 上发表的所有研究论文或论文评论都将被考虑获奖。该奖项由会员和 RME 编辑委员会投票决定。任何作者都不能为自己的论文投票。作者（或多位作者的提名人）受邀参加协会的一天会议以获奖，并发表珍妮特·达芬演讲。颁奖和演讲，由珍妮特·达芬 (Janet Duffin) 家族慷慨捐赠设立的珍妮特·达芬基金会 (Janet Duffin Fund) 支持，珍妮特·达芬 (Janet Duffin) 是 BSRLM 的长期活跃成员。欲了解更多信息，请参见：http://www.bsrlm.org.uk/about/janet-duffin-award/ Julian Williams 和 Sophina Choudry 获得了该奖项，并于 6 月 10 日在 BSRLM 会议上发表了 2016 年 Janet Duffin Lecture 2017 年在牛津大学。