Diagram, gesture, agency: theorizing embodiment in the mathematics classroom

Abstract

In this paper, we use the work of philosopher Gilles Châtelet to rethink the gesture/diagram relationship and to explore the ways mathematical agency is constituted through it. We argue for a fundamental philosophical shift to better conceptualize the relationship between gesture and diagram, and suggest that such an approach might open up new ways of conceptualizing the very idea of mathematical embodiment. We draw on contemporary attempts to rethink embodiment, such as Rotman's work on a "material semiotics," Radford's work on "sensuous cognition", and Roth's work on "material phenomenology". After discussing this work and its intersections with that of Châtelet, we discuss data collected from a research experiment as a way to demonstrate the viability of this new theoretical framework.

The Interplay Between Mathematicians’ Conceptual and Ideational Mathematics about Continuity of Complex-Valued Functions

“…Following other researchers (Châtelet 2000;de Freitas and Sinclair 2012;Nemirovky et al 2012) we view learning and experience within an environment as inherently inseparable. For us, knowing is doing, and is observable.…”

New opportunities in geometry education at the primary school

“…It is worth noting that in much of the research on children's drawing, there is an epistemological assumption that these drawings reflect children's internal representations of shapes. However, more contemporary theoretical perspectives attempt to avoid the implied dichotomy, preferring instead to view diagrams (and speech, gestures and other actions) as the active space for thinking itself, rather than infer any mental structures or schemas (see Châtelet, 2000;de Freitas & Sinclair, 2012;Thom & McGarvey, this issue).…”

Reasoning on the complex plane via inscriptions and gesture

“…The study of diagrams has become a growing field in mathematics education (de Freitas & Sinclair, 2012;Gibson, 1998;Samkoff, Lai, & Weber, 2012). The findings of Gibson and Samkoff indicate students and mathematicians use diagrams to help them comprehend the information available to them, to reason about the truthfulness of an assertion, to discover new ideas, to make conjectures, and to help them communicate their own ideas.…”

“…In the past decade there has been an outgrowth of research related to the role of gesture in undergraduate mathematics (de Freitas & Sinclair, 2012;Garcia & Engelke, 2012;Keene, Rasmussen, & Stephan, 2012;Marrongelle, 2007;Rasmussen, Stephan, & Allen, 2004;Sinclair & Tabaghi, 2010). Keene et al (2012) and Rasmussen et al (2004) show how instructors' and students' gestures can influence understanding of differential equations content and how gestures can be taken-as-shared in the classroom.…”