Abstract
In the first part of this chapter I sketch an approach where human cognition is conceptualized in non-dualistic, non-representational, and non-computational terms. The basic idea is that cognition is a feature of living material bodies characterized by a capacity for responsive sensation. The sketched approach, which I term sensuous cognition, refers precisely to this view where sensation is considered to be the substrate of mind, and all psychic activity (cognitive, affective, volitional, etc.). I argue that, as far as humans are concerned, responsive sensation evolves—both at the phylogenetic and ontogenetic levels—interwoven with the material culture in which individuals live and growth. As a result, human cognition can only be understood as a culturally and historically constituted sentient form of creatively responding, acting, feeling, transforming, and making sense of the world. In the second part of the chapter, I present classroom experimental data involving 7–8-year-old students dealing with pattern recognition. The classroom data allow me to illustrate the interplay of the various sensuous modalities in mathematical cognition. I end the chapter suggesting that a sensuous-based materialistic monistic view of cognition needs to attend not only to the plethora of sensorial modalities that teachers and students display while engaging in mathematical activities, but also to the manner in which sensorial modalities come to constitute more and more complex psychic wholes of sensorial and artifactual units.
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Notes
- 1.
For some embodied perspectives in mathematics education, see the special isssue of Educational Studies in Mathematics edited by Edwards, Radford, and Arzarello (2009), and the special issue edited by Radford, Schubring, and Seeger (2011) in the same journal. See also Bautista and Roth (2011) and the seminal book of Lakoff and Núñez (2000).
- 2.
My use of the adjective objective does not refer to claims about truth. It is rather a claim about something that is distinct from the organism, something that objects the organism; in other words, the term objective refers to something that we can term Otherness.
References
Bautista, A., & Roth, W.-M. (2011). Conceptualizing sound as a form of incarnate mathematical consciousness. Educational Studies in Mathematics, 79, 1–19.
Bateson, G. (1973). Steps to an ecology of mind. Frogmore, UK: Paladin.
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
Gee, J. P. (2003). What video games have to teach us about learning and literacy. New York: Palgrave Macmillan.
Gehlen, A. (1988). Man. His nature and place in the world. New York: Columbia University Press.
Gómez, J. C. (2004). Apes, monkeys, children, and the growth of mind. Cambridge, MA: Harvard University Press.
Gogtay, N., Giedd, J., Lusk, L., Hayashi, K., Greenstein, D., Vaituzis, A., et al. (2004). Dynamic mapping of human cortical development during childhood through early adulthood. Proceedings of the National Academy of Sciences of the United States of America, 101(21), 8174–8179.
Hegedus, S., & Moreno-Armella, L. (2011). The emergence of mathematical structures. Educational Studies in Mathematics, 77(2–3), 369–388.
Humphrey, G. (1962). Introduction. In J.-M.-G. Itard (Ed.), The wild boy of Aveyron (pp. v–xxiv). New York: Meredith Publishing Company.
Hyppolite, J. (1961). Logique et existence [logic and eistence]. Paris: Presses Universitaires de France.
Itard, J.-M.-G. (1962). The wild boy of Aveyron. New York: Meredith Publishing Company.
Kant, I. (1787). Critique of pure reason. New York: St. Marin’s Press (Second Printing, 1965).
Köhler, W. (1951). The mentality of apes. New York/London: The Humanities Press/Routledge & Kegan Paul.
Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. New York: Basic Books.
Le Breton, D. (2009). El sabor del mundo. Una antropología de los sentidos [The taste of the world. An anthropology of the senses]. Buenos Aires, Argentina: Ediciones Nueva Visión.
Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.
Leontyev [or Leont’ev], A. N. (2009). Activity and consciousness. Pacifica, CA: MIA. Retrieved August 29, 2009, from http://www.marxists.org/archive/leontev/works/activity-consciousness.pdf
Lewkowicz, D., & Lickliter, R. (Eds.). (1994). The development of intersensory perception. Hillsdale, NJ: Routledge.
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.
Luria, A. R. (1984). Sensación y percepción [Sensation and perception]. Barcelona, Spain: Ediciones Martínez Roca.
Luria, A. R., & Vygotsky, L. S. (1998). Ape primitive man and child. Essays in the history of behavior. Boca Raton, FL: CRC Press LLC.
Malafouris, L., & Renfrew, C. (Eds.). (2010). The cognitive life of things: Archaeology, material engagement and the extended mind. In The cognitive life of things: Recasting the boundaries of the mind (pp. 1–12). Cambridge, UK: McDonald Institute.
Marks, L. U. (2000). The skin of the film: Intercultural cinema, embodiment, and the senses. Durham, UK/London: Duke University Press.
Maturana, H., & Varela, F. (1998). The tree of knowledge. Boston: Shambhala. (Original work published 1987).
McLuhan, M. (1962). The Gutenberg galaxy: The making of typographic man. Toronto, ON, Canada: University of Toronto Press.
Peirce, C. S. (1931). Collected papers (Vol. I-VIII). Cambridge, MA: Harvard University Press.
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.
Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM – The International Journal on Mathematics Education, 40(1), 83–96.
Radford, L. (2009). “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. (2010a). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1–19.
Radford, L. (2010b). The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, 30(2), 2–7.
Radford, L. (2011a). Embodiment, perception and symbols in the development of early algebraic thinking. In Proceedings of the 35th conference of the international group for the psychology of mathematics education (pp. 17–24). Ankara, Turkey: PME.
Radford, L. (2011b). Grade 2 students’ non-symbolic algebraic thinking. In J. Cai & E. Knuth (Eds.), Early algebraization (pp. 303–322). Berlin, Germany: Springer.
Radford, L. (2011c, November 2–3). Phenomenological mediations: Changing the subject (and the object!). Working Paper presented at the Phenomenology and Mathematics Education φ-ME First Meeting, Turin.
Radford, L. (2012). On the development of early algebraic thinking. PNA, 6(4), 117–133.
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.
Radford, L., Demers, S., Guzmán, J., & Cerulli, M. (2003). Calculators, graphs, gestures, and the production meaning. In P. Pateman, 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). University of Hawaii, PME.
Radford, L., Edwards, L., & Arzarello, F. (2009). Beyond words. Educational Studies in Mathematics, 70(2), 91–95.
Radford, L., & Roth, W.-M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2–3), 227–245.
Radford, L., Schubring, G., & Seeger, F. (Eds.). (2011). Signifying and meaning-making in mathematics thinking, teaching and learning: Semiotic perspectives. Special Issue of Educational Studies in Mathematics, 77(2–3), 149–397.
Sheets-Johnstone, M. (2009). The corporeal turn. Exeter, Devon, UK: imprint-academic.com.
Seitz, J. A. (2000). The bodily basis of thought. New Ideas in Psychology, 18, 23–40.
Stephens, M. (1998). The rise of the image the fall of the world. New York: Oxford University Press.
Trend, D. (2010). The end of reading. From Gutenberg to grand theft auto. New York: Peter Lang.
Varela, F. (1999). Ethical know-how. Stanford, CA: Stanford University Press. (Original work published 1992).
Vygotsky, L. S. (1987–1999). Collected works. New York: Plenum Press.
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, UK: Blackwell Publishers.
Wilson, F. (1998). The hand. How its use shapes the brain, language, and human culture. New York: Pantheon Books.
Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636.
Wessnitzer, J., & Webb, B. (2006). Multimodal sensory integration in insects—Towards insect brain control architectures. Bioinspiration & Biomimetics, 1(3), 63–75.
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.
Acknowledgements
This chapter is a result of a research program funded by the Social Sciences and Humanities Research Council of Canada (SSHRC/CRSH). A previous version was presented at the ICME-12 Topic Study Group 22 (Learning and cognition in mathematics, co-chaired by Hsin-Mei Huang and Gaye William), South Korea, July 2012.
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Radford, L. (2013). Sensuous Cognition. In: Martinovic, D., Freiman, V., Karadag, Z. (eds) Visual Mathematics and Cyberlearning. Mathematics Education in the Digital Era, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2321-4_6
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