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Towards an embodied, cultural, and material conception of mathematics cognition

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Abstract

In this paper I sketch an embodied, cultural, and material conception of cognition and discuss some of the implications for mathematics education. This approach, which I term sensuous cognition, rests on a cultural and historical dialectical materialist understanding of the senses, sensation, and the material and conceptual worlds. Sensation and matter are considered to be the substrate of mind, and of all psychic activity (cognitive, affective, volitional, etc.). I argue that human cognition can only be understood as a culturally and historically constituted multimodal sentient form of creatively responding, acting, feeling, transforming, and making sense of the world. To illustrate these ideas I briefly refer to a classroom episode involving 7- to 8-year-old students dealing with pattern generalization.

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References

  • Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa, Special Issue on Semiotics, Culture, and Mathematical Thinking (Guest Editors: L. Radford & B. D’Amore), pp. 267–299.

  • Bateson, G. (1973). Steps to an ecology of mind. Frogmore: Paladin.

    Google Scholar 

  • Bautista, A., & Roth, W.-M. (2012). Conceptualizing sound as a form of incarnate mathematical consciousness. Educational Studies in Mathematics, 79(1), 41–59.

    Article  Google Scholar 

  • Berkeley, G. (1710/1957). A treatise concerning the principles of human knowledge. New York: Liberal Arts Press.

  • Borba, M., & Villareal, M. (2006). Humans-with-media and the reorganization of mathematical thinking. New York: Springer.

    Google Scholar 

  • de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: The body in/of mathematics. Educational Studies in Mathematics, 83, 453–470.

    Article  Google Scholar 

  • Descartes, R. (1641/1982). Méditations touchant la première philosophie [Meditations concerning first philosophy]. In C. Adam & P. Tannery (Eds.), Oeuvres de Descartes [Descartes’ works] (Vol. 9). Paris: Vrin.

  • Eagleton, T. (1996). The illusions of postmodernism. Oxford: Blackwell.

    Google Scholar 

  • Eagleton, T. (1998). Body work. In S. Regan (Ed.), The Eagleton reader (pp. 157–162). Oxford: Blackwell.

    Google Scholar 

  • Edwards, L. (2009). Gestures and conceptual integration in mathematical talk. Educational Studies in Mathematics, 70(2), 127–141.

    Article  Google Scholar 

  • Edwards, L., Radford, L., & Arzarello, F. (Eds.) (2009). Gestures and multimodality in the teaching and learning of mathematics. Special issue of Educational Studies in Mathematics, 70(2), 91–215.

  • Fauconnier, G., & Turner, M. (2002). The way we think. New York: Basic Books.

    Google Scholar 

  • Feuerbach, L. (1843/1986). Principles of the philosophy of the future. Indianapolis: Hackett.

  • Freitag, M. (2002). Actualité de l’animal, virtualité de l’homme [Actuality of the animal, virtuality of man]. Conjonctures, 33–34, 99–154.

    Google Scholar 

  • Greenspan, S., & Shanker, S. (2004). The first idea: How symbols, language, and intelligence evolved from our primate ancestors to modern humans. Cambridge: Da Capo Press.

    Google Scholar 

  • Heath, L. (1910). Diophantus of Alexandria. A study in the history of Greek algebra (2nd ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  • Hegel, G. (1801/1977). The difference between Fichte’s and Schelling’s systems of philosophy. Albany: State University of New York Press.

  • Hegel, G. (1807/1977). Hegel’s phenomenology of spirit. Oxford: Oxford University Press.

  • Hegel, G. (1830/2009). Hegel’s logic (trans.: Wallace, W.). Pacifica, CA: MIA.

  • Hume, D. (1748/1921). An enquiry concerning human understanding. Chicago: Open Court.

  • Ilyenkov, E. V. (1977). Dialectical logic. Moscow: Progress Publishers.

    Google Scholar 

  • Kant, I. (1781/1929). Critique of pure reason. New York: Palgrave Macmillan.

  • Kant, I. (1790/2005). Critique of judgment. New York: Dover.

  • Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. New York: Basic Books.

    Google Scholar 

  • Le Breton, D. (2007). El sabor del mundo. Una antropología de los sentidos [The taste of the world. An anthropology of the senses]. Buenos Aires: Ediciones Nueva Visión.

  • Leibniz, G. W. (1705/1949). New essays concerning human understanding. La Salle, Ill: The Open Court.

  • Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Leont’ev [or Leontyev], A. N. (2009). Activity and consciousness. Pacifica, CA: MIA. http://www.marxists.org/archive/leontev/works/activity-consciousness.pdf. Accessed 28 April 2014.

  • Lewkowicz, D., & Lickliter, R. (1994). The development of intersensory perception. Hillsdale, NJ: Routledge.

    Google Scholar 

  • Lickliter, R., & Bahrick, L. E. (2000). The development of infant intersensory perception: advantages of a comparative convergent-operations approach. Psychological Bulletin, 126(2), 260–280. Retrieved from Google Scholar.

  • Luria, A. R., & Vygotsky, L. S. (1998). Ape primitive man and child. Essays in the history of behavior. Boca Raton, FL: CRC Press.

    Google Scholar 

  • Malafouris, L., & Renfrew, C. (2010). The cognitive life of things: archaeology, material engagement and the extended mind. In L. Malafouris & C. Renfrew (Eds.), The cognitive life of things: Recasting the boundaries of the mind (pp. 1–12). Cambridge: McDonald Institute.

    Google Scholar 

  • Marx, K. (1846/1998). The German ideology, including theses on Feuerbach and introduction to the critique of political economy. Amherst, NY: Prometheus.

  • Marx, K. (1932/1988). Economic and philosophic manuscripts of 1844. Amherst, NY: Prometheus.

  • McNeill, D. (2005). Gesture and thought. Chicago: University of Chicago Press.

    Book  Google Scholar 

  • Mithen, S. (1996). The prehistory of the mind. London: Thames & Hudson.

    Google Scholar 

  • Nicomachus of Geresa (1938). Introduction to arithmetic (trans.: D’Ooge, M. L.) Ann Arbor: University of Michigan Press.

  • Piaget, J. (1970). Genetic epistemology. New York, NY: Norton.

    Google Scholar 

  • Radford, L. (1995). La transformación de una teoría matemática: el caso de los números poligonales [The transformation of a mathematical theory: the case of polygonal numbers]. Mathesis, 11(3), 217–250.

    Google Scholar 

  • Radford, L. (2005). Body, tool, and symbol: Semiotic reflections on cognition. In E. Simmt & B. Davis (Eds.), Proceedings of the 2004 annual meeting of the Canadian Mathematics Education Study Group (pp. 111–117). Québec: Université Laval.

    Google Scholar 

  • Radford, L. (2006). Variables, unknowns, and parameters of mathematical generality. Mini-workshop on studying original sources in mathematics education. Oberwolfach, April 30th–May 6th, 2006. Report, 22(2006), 16–17.

    Google Scholar 

  • Radford, L. (2008). Semiotic reflections on medieval and contemporary graphic representations of motion. Working paper presented at the History and Pedagogy of Mathematics Conference (HPM 2008), 14–18 July 2008, Mexico City.

  • Radford, L. (2009a). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126.

    Article  Google Scholar 

  • Radford, L. (2009b). “No! He starts walking backwards!”: interpreting motion graphs and the question of space, place and distance. ZDM – The International Journal on Mathematics Education, 41, 467–480.

  • Radford, L. (2010). The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, 30(2), 2–7.

    Google Scholar 

  • Radford, L. (2012). On the development of early algebraic thinking. PNA, 6(4), 117–133.

    Google Scholar 

  • Radford, L. (2013a). Three key concepts of the theory of objectification: Knowledge, knowing, and learning. Journal of Research in Mathematics Education, 2(1), 7–44.

    Google Scholar 

  • Radford, L. (2013b). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, Online First. doi:10.1007/s13394-013-0087-2.

  • Radford, L., Edwards, L., & Arzarello, F. (2009). Beyond words. Educational Studies in Mathematics, 70(2), 91–95.

    Article  Google Scholar 

  • Sheets-Johnstone, M. (2009). The corporeal turn. Exeter: Imprint Academic.

    Google Scholar 

  • Thom, J., & Roth, W. (2011). Radical embodiment and semiotics: Towards a theory of mathematics in the flesh. Educational Studies in Mathematics, 77, 267–284.

    Article  Google Scholar 

  • Vygotsky, L. S. (1987a). Collected works (Vol. 1). New York, NY: Plenum.

    Google Scholar 

  • Vygotsky, L. S. (1987–1999). Collected works (Vols. 1–6). New York, NY: Plenum.

  • Vygotsky, L. S., & Luria, A. (1994). Tool and symbol in child development. In R. V. D. Veer & J. Valsiner (Eds.), The Vygotsky reader (pp. 99–174). Oxford: Blackwell.

    Google Scholar 

  • Yendovitskaya, Z., Zinchenko, V., & Ruzskaya, A. (1971). The development of sensation and perception. In A. Zaporozhets & D. Elkonin (Eds.), The psychology of preschool children (pp. 1–64). Cambridge, MA: MIT Press.

    Google Scholar 

  • Yoon, C., Thomas, M., & Dreyfus, T. (2011). Grounded blends and mathematical gesture spaces: Developing mathematical understandings via gestures. Educational Studies in Mathematics, 78, 371–393.

    Article  Google Scholar 

  • Zaporozhets, A. V. (2002). The development of sensations and perceptions in early and preschool childhood. Journal of Russian and East European Psychology, 40(2), 22–34.

    Article  Google Scholar 

  • Zaporozhets, A., & Elkonin, D. (Eds.). (1971). The psychology of preschool children. Cambridge, MA: MIT Press.

    Google Scholar 

Download references

Acknowledgments

This paper is a result of a research program funded by the Social Sciences and Humanities Research Council of Canada (SSHRC/CRSH). A previous version of it appeared in the Proceedings of ICME-12 Topic Study Group 22 (TSG22): Learning and cognition in mathematics (pp. 4536–4545), Seoul, South Korea. July 8–15, 2012. I am very grateful to the three ZDM reviewers for their thoughtful comments, suggestions, and criticism. I dedicate this paper to the memory of my friend and colleague Filippo Spagnolo who passed away on March 2, 2011.

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  1. Université Laurentienne, Sudbury, Canada

    Luis Radford

  2. The University of Manchester, Manchester, UK

    Luis Radford

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Radford, L. Towards an embodied, cultural, and material conception of mathematics cognition. ZDM Mathematics Education 46, 349–361 (2014). https://doi.org/10.1007/s11858-014-0591-1

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