Educational Studies in Mathematics

, Volume 70, Issue 2, pp 111–126 | Cite as

Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings

Article

Abstract

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed “sensuous cognition.” The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal “material” conception of thinking. The very texture of thinking, it is suggested, cannot be reduced to that of impalpable ideas; it is instead made up of speech, gestures, and our actual actions with cultural artifacts (signs, objects, etc.). As illustrated through an example from a Grade 10 mathematics lesson, thinking does not occur solely in the head but also in and through a sophisticated semiotic coordination of speech, body, gestures, symbols and tools.

Keywords

Cognition Gestures Graphs Objectification Multimodality Mathematical meaning Semiotics 

Notes

Acknowledgment

I wish to thank the three reviewers for their insightful comments on a previous version of this paper.

References

  1. Alibali, M., Bassok, M., Solomon, K. O., Syc, S. E., & Goldin-Meadow, S. (1999). Illuminating mental representations through speech and gesture. Psychological Science, 10(4), 327–333.CrossRefGoogle Scholar
  2. Arzarello, F. (2006a). Mathematical landscapes and their inhabitants: Perceptions, languages, theories. In: M. Niss (Ed.), Proceedings of the 10th International Congress on Mathematical Education (pp. 158–181). Copenhagen, Denmark, July 4–11, 2004. Roskilde University, Denmark.Google Scholar
  3. Arzarello, F. (2006b). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa, 9, 267–299 (Special issue on semiotics, culture, and mathematical thinking. Guest editors: L. Radford & B. D’Amore).Google Scholar
  4. Arzarello, F., & Robutti, O. (2004). Approaching functions through motion experiments. Educational Studies in Mathematics, 57(3) (PME special issue “Approaching functions through motion experiments,” edited by R. Nemirovsky, M. Borba, & C. DiMattia. CD-Rom, chapter 1).Google Scholar
  5. Cushing, F. H. (1892). Manual concepts: A study of the influence of hand-usage on culture-growth. The American Anthropologist, 4, 289–318.CrossRefGoogle Scholar
  6. Deacon, T. W. (1997). The symbolic species. New York: W. W. Norton.Google Scholar
  7. Eagleton, T. (1998). Body work. In S. Regan (Ed.), The Eagleton reader (pp. 157–162). Oxford: Blackwell.Google Scholar
  8. Fischbein, E. (1989). Tacit models and mathematical reasoning. For The Learning of Mathematics, 9(2), 9–14.Google Scholar
  9. Freedman, N. (1977). Hands, words and mind: On the structuralization of body movements during discourse and the capacity for verbal representation. In N. Freedman, & S. Grand (Eds.), Communicative structures and psychic structures: A psychoanalytic approach (pp. 109–132). New York: Plenum.Google Scholar
  10. Garber, P., & Goldin-Meadow, S. (2002). Gesture offers insight into problem-solving in adults and children. Cognitive Science, 26, 817–831.CrossRefGoogle Scholar
  11. Geertz, C. (1973). The interpretation of cultures. New York: Basic.Google Scholar
  12. Gehlen, A. (1988). Man. His nature and place in the world. New York: Columbia University Press.Google Scholar
  13. Goldin-Meadow, S. (2003). Hearing gesture. How our hands help us think. Cambridge, MA: Belknap.Google Scholar
  14. Goldin-Meadow, S., Nusbaum, H., Kelly, S. D., & Wagner, S. (2001). Explaining math: Gesturing lightens the load. Psychological Science, 12(6), 516–522.CrossRefGoogle Scholar
  15. Gómez, J. C. (2004). Apes, monkeys, children, and the growth of mind. Cambridge, MA: Harvard University Press.Google Scholar
  16. Kendon, A. (Ed.) (1981). Current issues in the study of nonverbal communication. Selections from Semiotica. Hague: Mouton.Google Scholar
  17. Kendon, A. (Ed.) (1993). Human gesture. Cambridge, MA: Cambridge University Press.Google Scholar
  18. Kendon, A. (2004). Gesture: Visible action as utterance. Cambridge, MA: Cambridge University Press.Google Scholar
  19. Kenneally, C. (2007). The first word. New York: Viking.Google Scholar
  20. Kita, S. (2000). How representational gestures help speaking. In D. McNeill (Ed.), Language and gesture (pp. 162–185). Cambridge: Cambridge University Press.Google Scholar
  21. Kita, S. (2003). Pointing. Where language, culture, and cognition meet. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  22. Köhler, W. (1951). The mentality of apes. London: Routledge & Kegan Paul.Google Scholar
  23. Laborit, E. (2003). Le cri de la mouette. Paris: Éditions Pocket Jeunesse.Google Scholar
  24. Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh. New York: Basic.Google Scholar
  25. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. New York: Basic.Google Scholar
  26. Lemke, J. (2003). Mathematics in the middle: Measure, picture, gesture, sign, and word. In M. Anderson, A. Sáenz-Ludlow, S. Zellweger, & V. Cifarelli (Eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 215–234). Ottawa: Legas.Google Scholar
  27. McNeill, D. (1992). Hand and mind. Chicago, IL: Chicago of University Press.Google Scholar
  28. McNeill, D. (Ed.) (2000). Language and gesture. Cambridge, MA: Cambridge University Press.Google Scholar
  29. McNeill, D. (2005). Gesture and thought. Chicago, IL: University of Chicago Press.Google Scholar
  30. Nemirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In P. N. B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27 Conference of the International Group for the Psychology Of Mathematics Education (Vol. 1, pp. 105–109). Hawaii: University of Hawaii.Google Scholar
  31. Núñez, R. (2007). Understanding abstraction in mathematics education: Meaning, language, gesture, and the human brain. Conference delivered at the 31st Annual Meeting of the Canadian Mathematics Education Study Group. Fredericton, University of New Brunswick, June 8–12, 2007.Google Scholar
  32. Núñez, R., Edwards, L., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1–3), 45–65.CrossRefGoogle Scholar
  33. Radford, L. (2002). The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14–23.Google Scholar
  34. Radford, L. (2003). Gestures, speech and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37–70.CrossRefGoogle Scholar
  35. Radford, L. (2004). Cose sensibili, essenze, oggetti matematici ed altre ambiguità [Sensible things, essences, mathematical objects and other ambiguities]. La Matematica e la Sua Didattica, 1, 4–23 (English version available at: http://laurentian.ca/educ/lradford/).Google Scholar
  36. Radford, L. (2006a). Elements of a cultural theory of objectification. Revista Latinoamericana de Investigación en Matemática Educativa, 9, 103–129 (Special issue on semiotics, culture and mathematical thinking. Available at: http://laurentian.ca/educ/lradford/).Google Scholar
  37. Radford, L. (2006b). The anthropology of meaning. Educational Studies in Mathematics, 61, 39–65.CrossRefGoogle Scholar
  38. Radford, L. (2008). Towards a cultural theory of learning. In L. Radford, G. Schubring & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture. Rotterdam: Sense (in press).Google Scholar
  39. Radford, L., Bardini, C., & Sabena, C. (2007). Perceiving the general: The multisemiotic dimension of students’ algebraic activity. Journal for Research in Mathematics Education, 38, 507–530.CrossRefGoogle Scholar
  40. Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: A semiotic–cultural perspective on mathematical thinking. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 129–136). Australia: University of Melbourne.Google Scholar
  41. Radford, L., Cerulli, M., Demers, S., & Guzmán, J. (2004). The sensual and the conceptual: Artefact-mediated kinesthetic actions and semiotic activity. In M. J. Høines, & A. B. Fuglestad (Eds.), Proceedings of the 28 Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 73–80). Norway: Bergen University College.Google Scholar
  42. Radford, L., Demers, S., Guzmán, J., & Cerulli, M. (2003). Calculators, graphs, gestures, and the production meaning. In P. N. B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27 Conference of the International Group for the Psychology Of Mathematics Education (Vol. 4, pp. 55–62). Hawaii: University of Hawaii.Google Scholar
  43. Robutti, O. (2006). Motion, technology, gesture in interpreting graphs. International Journal for Technology in Mathematics Education, 13(3), 117–126.Google Scholar
  44. Roth, M.-W. (2001). Gestures: Their role in teaching and learning. Review of Educational Research, 71(3), 365–392.CrossRefGoogle Scholar
  45. Sabena, C. (in press). On the semiotics of gestures. In L. Radford, G. Schubring & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture. Rotterdam: Sense.Google Scholar
  46. Savage-Rumbaugh, S., & Lewin, R. (1994). Kanzi. New York: Wiley.Google Scholar
  47. Seitz, J. A. (2000). The bodily basis of thought. New Ideas in Psychology, 18, 23–40.CrossRefGoogle Scholar
  48. Tomasello, M., & Call, J. (1997). Primate cognition. New York: Oxford University Press.Google Scholar
  49. Vygotsky, L. S. (1986). In A. Kozulin (Ed.), Thought and language. Cambridge, MA: MIT.Google Scholar
  50. Wertsch, J. V. (1991). Voices of the mind. A sociocultural approach to mediate action. Cambridge, MA: Harvard University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.École des Sciences de l’ÉducationUniversité LaurentienneSudburyCanada

Personalised recommendations