Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures

Abstract

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for each of these claims drawn from the gestures that teachers and learners produce when they explain mathematical concepts and ideas. We argue that (a) pointing gestures reflect the grounding of cognition in the physical environment, (b) representational gestures manifest mental simulations of action and perception, and (c) some metaphoric gestures reflect body-based conceptual metaphors. Thus, gestures reveal that some aspects of mathematical thinking are embodied.

ACKNOWLEDGMENTS

This work was funded by Grant No. R305H060097 from the Institute of Education Sciences and by Grant No. DRL-0816406 from the National Science Foundation.

We would like to thank Matthew Wolfgram, Breckie Church, and Eric Knuth for their contributions to this line of research. We are also grateful to many others for their contributions to our thinking about these issues, especially Julia Evans, Arthur Glenberg, Susan Goldin-Meadow, Rogers Hall, Autumn Hostetter, Sotaro Kita, David McNeill, and Ricardo Nemirovsky.

Notes

¹This example is drawn from the data set reported in Alibali (1999), an experimental study of how children's explanations of equations change in response to different types of instruction.

FIGURE 1 Pointing in a student's explanation of a mathematical equation. Accompanying speech is indicated under each frame.

²This example is drawn from an unpublished corpus of 18 middle school mathematics lessons collected in order to document teachers' use of gesture in naturalistic instructional settings (Alibali, Nathan, Wolfgram, Church, Knuth, Johnson, Jacobs, & Kim, 2010).

³This example is drawn from the data set reported by Alibali et al. (1999), which addressed relations between adults' problem representations and their strategy use.