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An introduction to inferentialism in mathematics education

Derry, J; (2017) An introduction to inferentialism in mathematics education. Mathematics Education Research Journal 10.1007/s13394-017-0193-7. (In press). Green open access

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Abstract

This paper introduces the philosophical work of Robert Brandom, termed inferentialism, which underpins this collection and argues that it offers rich theoretical resources for reconsidering many of the challenges and issues that have arisen in mathematics education. Key to inferentialism is the privileging of the inferential over the representational in an account of meaning; and of direct concern here is the theoretical relevance of this to the process by which learners gain knowledge. Inferentialism requires that the correct application of a concept is to be understood inmterms of inferential articulation, simply put, understanding it as having meaning only as part of a set of related concepts. The paper explains how Brandom’s account of the meaning is inextricably tied to freedom and it is our responsiveness to reasons involving norms which makes humans a distinctive life form. In an educational context norms function to delimit the domain in which knowledge is acquired and it is here that the neglect of our responsiveness to reasons is significant, not only for Brandom but also for Vygotsky, with implications for how knowledge is understood in mathematics classrooms. The paper explains the technical terms in Brandom’s account of meaning, such as deontic scorekeeping, illustrating these through examples to show how the inferential articulation of a concept, and thus its correct application, is made visible. Inferentialism fosters the possibility of overcoming some of the thorny old problems that have seen those on the side of facts and disciplines opposed to those whose primary concern is the meaning making of learners.

Type: Article
Title: An introduction to inferentialism in mathematics education
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s13394-017-0193-7
Publisher version: http://dx.doi.org/ 10.1007/s13394-017-0193-7
Language: English
Additional information: © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Philosophy of Education, Mathematics Education, Inferentialism, Pedagogy, Knowledge
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Education
UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education
UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education > IOE - Education, Practice and Society
URI: https://discovery.ucl.ac.uk/id/eprint/1541289
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