An introduction to inferentialism in mathematics education

Mathematics Education Research Journal, Feb 2017

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 in terms 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.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2Fs13394-017-0193-7.pdf

An introduction to inferentialism in mathematics education

An introduction to inferentialism in mathematics education Jan Derry 0 0 UCL Institute of Education, University College London , Bedford Way, London WC1H 0AL , UK 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 in terms 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. Inferentialism; Epistemology; Pedagogy; Vygotsky; Brandom; Philosophy of mind - special issue, it is interesting to note that it was developed by a philosopher, Robert Brandom, who majored in mathematics for his first degree and who was excited by the idea that mathematical languages could be extended to understand meanings in natural languages, including literary uses. Our interest here is of course mathematics education but the ideas treated below apply equally well to all areas of education. This paper is intended to serve as an introduction to the theory of inferentialism itself. Brandom’s work on inferentialism is now being applied across a broad range of disciplines including law, political theory, history as well as education studies (Bakker & Derry, 2011; Canale & Tuzet, 2007; Erman, 2010; Klatt, 2008; Marshall, 2013). The task of providing concrete examples and working through the implications of the theoretical approach is relatively recent. Locating inferentialism among the various theories relevant to mathematics education is not at all straightforward. Simply put it is a theory of meaning but this fails to do full justice to its theoretical reach. It is a theory which forms part of a move in thought which sees mind as inseparable from world and language Bnot as a formal structure but as a feature of the natural history of beings like us^ (Williams & Brandom, 2013, p. 372). Our understanding of the human mind was transformed over half a century ago when the cognitive revolution in psychology responded to the Bscience of behaviour^ that had come to define psychology (Miller, 2003). The revolution in psychology acted as a counter attempt to bridge the gap between brain and mind by the development of a new interdisciplinary field; it was in a large part driven by interest in developments in artificial intelligence. By contrast, inferentialism attends to what is distinctively human. As it is has been developed by Brandom, inferentialism is a systematic theory which offers the possibility of thinking through old problems in refreshingly new ways. In keeping with other recent developments in philosophy, it places emphasis on activity and the development of meaning. With Vygotsky, it shares a Hegelian inheritance and as such it is concerned with the movement of thought rather than with snapshots that fail to do justice to the nature of thought. The idea of the movement of thought in the articulation of meaning is central to inferentialism since it shows that the meaning of a concept, rather than being fixed, is fleshed out by the inferential connections that constitute it. As these connections change, so the meanings of concepts alter. Although this may seem to be restricted to historical or philosophical concerns about how knowledge itself develops through inferential articulation (Rouse, 2011), these ideas can be extended to the pedagogical and educational domain (cf. Bransen, 2002). Most importantly, here for mathematics educators, inferentialism offers a powerful analytical tool to examine human activity through a more fine-grained account than is generally available within social scientific research. Indeed, Ste (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs13394-017-0193-7.pdf

Jan Derry. An introduction to inferentialism in mathematics education, Mathematics Education Research Journal, 2017, pp. 1-16, DOI: 10.1007/s13394-017-0193-7