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

- 1.3k Downloads
- 17 Citations

## 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.

## Keywords

Gesture Diagram Agency Embodiment## References

- Bartolini-Bussi, M., & Boni, M. (2003). Instruments for semiotic mediation in primary school classrooms.
*For the Learning of Mathematics, 23*(2), 12–19.Google Scholar - Bennett, J. (2010).
*Vibrant matter: A political ecology of things*. Durham: Duke University Press.Google Scholar - Châtelet, G. (1993).
*Les enjeux du mobile*. Paris: Seuil [English Translation by R. Shore & M. Zagha:*Figuring space: Philosophy, mathematics and physics*. Dordrecht: Kluwer, 2000].Google Scholar - Châtelet, G. (2000).
*Figuring Space: Philosophy, Mathematics, and Physics*. (R. Shore & M. Zagha, Trans.). Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar - de Freitas, E. (2010). Making mathematics public: Aesthetics as the distribution of the sensible
*Educational Insights, 13*(1). (Available: http://www.ccfi.educ.ubc.ca/publication/insights/v13n01/articles/defreitas/index.html). - De Landa, M. (2006).
*A new philosophy of society: Assemblage theory and social complexity*. London: Continuum.Google Scholar - Deleuze, G. (1990).
*The logic of sense. (Trans. M. Lester)*. New York: Columbia University Press.Google Scholar - Deleuze, G. (1993).
*The fold: Leibniz and the Baroque*. Minneapolis: Regents of University of Minnesota Press.Google Scholar - Deleuze, G., & Guattari, F. (1987).
*A thousand plateaus: Capitalism and schizophrenia*. Minneapolis: University of Minnesota Press.Google Scholar - Gough, N. (2004). Rhizomantically becoming cyborg: Performing posthuman pedagogies.
*Educational Philosophy and Theory, 36*, 253–265.CrossRefGoogle Scholar - Grawemeyer, B. & Cox, R. (2008). The effects of users’ background diagram knowledge and task characteristics upon information display selection. In: G. Stapleton, J. Howse & J. Lee (Eds.),
*Diagrammatic representation and inference, 5th international conference, diagrams 2008*. Lecture notes in computer science, Vol. 5223 (pp. 321–334). Springer-Verlag.Google Scholar - Hughes, M. (1986).
*Children and number: Difficulties in learning mathematics*. Oxford: Blackwell.Google Scholar - Knoespel, K. (2000). Diagrammatic writing and the configuration of space. Introduction to Gilles Châtelet,
*Figuring Space: Philosophy, Mathematics, and Physics*(pp. ix-xxiii). Dordrecht, The Netherlands: Kluwer Academic Publishers. Google Scholar - Latour, B. (2005).
*Reassembling the social: An introduction to Actor-Network-Theory*. Oxford: Oxford University Press.Google Scholar - Leibniz, G. W. (1973). In G. H. R. Parkinson (Ed.),
*Philosophical writings. (Trans. M. Morris & G.H.R. Parkinson)*. London: Everyman’s Library.Google Scholar - Leibniz, G. W. (2005).
*Discourse on metaphysics and the monadology. (Trans. G. R. Montgomery)*. Mineola: Dover Publications.Google Scholar - Maclure, M. (2010). Facing Deleuze: Affect in education and research. Presentation at the
*American Educational Research Association*. Denver, CO. May 4, 2010.Google Scholar - McNeill, D. (2005).
*Gesture and thought*. Chicago: University of Chicago Press.Google Scholar - Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition.
*Educational Studies in Mathematics, 70*, 159–174.CrossRefGoogle Scholar - Netz, R. (1999).
*The shaping of deduction in Greek mathematics: A study in cognitive history*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Núñez, R. (2006). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. In R. Hersh (Ed.),
*18 Unconventional essays on the nature of mathematics*(pp. 160–181). New York: Springer.CrossRefGoogle Scholar - Nunokawa, K. (2004). Solvers’ making of drawings in mathematical problem solving and their understanding of the problem situations.
*International Journal of Mathematical Education in Science and Technology, 35*, 173–183.CrossRefGoogle Scholar - Nunokawa, K. (2006). Using drawings and generating information in mathematical problem solving processes.
*Journal of Mathematics, Science and Technology Education, 2*(3), 33–54.Google Scholar - Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization.
*Mathematical Thinking and Learning, 5*(1), 37–70.CrossRefGoogle Scholar - Ringrose, J. (2010). Beyond discourse: Using Deleuze and Guattari’s schizoanalysis to explore affective assemblages, heterosexually striated space, and lines of flight online and at school.
*Educational Philosophy and Theory, 43*(6), 1–21.Google Scholar - Roth, W.-M. (2010). Incarnation: Radicalizing the embodiment of mathematics.
*For the Learning of Mathematics, 30*(2), 8–17.Google Scholar - Rotman, B. (2008).
*Becoming beside ourselves: The alphabet, ghosts, and distributed human beings*. Durham: Duke University Press.Google Scholar - Semetsky, I. (2006).
*Deleuze, education, and becoming*. Rotterdam: Sense Publishers.Google Scholar - Sinclair, N., & Gol Tabaghi, S. (2010). Drawing space: Mathematicians’ kinetic conceptions of eigenvectors.
*Education Studies in Mathematics, 74*(3), 223–240.CrossRefGoogle Scholar - Singer, M. A., & Goldin-Meadow, S. (2005). Children learn when their teachers’ gestures and speech differ.
*Psychological Science, 16*, 85–89.Google Scholar - Stylianou, D. A., & Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences.
*Mathematical Thinking and Learning, 6*(4), 353–387.CrossRefGoogle Scholar - Tahta, D. (1980). About geometry.
*For the learning of mathematics, 1*(1), 2–9.Google Scholar - Webb, T. (2008). Remapping power in educational micropolitics.
*Critical Studies in Education, 49*(2), 127–142.CrossRefGoogle Scholar