Skip to main content

Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education

  • Chapter
  • First Online:
Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

This chapter reports on an initiative in educational research in mathematics education that is augmenting traditional methods of educational research with methods of cognitive neuroscience and psychophysiology. Background and motivation are provided for this initiative—referred to here as mathematics educational neuroscience. Relations and differences between cognitive neuroscience and educational neuroscience are proposed that may have some bearing as to how this area unfolds. The key role of embodied cognition as a theoretical framework is discussed in some detail, and some methodological considerations are presented and illustrated as well. Overall, mathematics educational neuroscience presents exciting new opportunities for research in mathematics education and for educational research in general.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, J. R., Reder, L. M., & Simon, H. A. (2000, Summer). Applications and misapplications of cognitive psychology to mathematics education. Texas Educational Review. On-line at http://act-r.psy.cmu.edu/papers/misapplied.html.

  • Ansari, D., & Dhital, B. (2006). Age-related changes in the activation of the intraparietal sulcus during non-symbolic magnitude processing: an event-related fMRI study. Journal of Cognitive Neuroscience, 18, 1820–1828.

    Article  Google Scholar 

  • Ausubel, D. P. (1968). Educational Psychology: A Cognitive View. New York: Holt, Rinehart and Winston.

    Google Scholar 

  • Bauersfeld, H. (1992). Integrating theories for mathematics education. For the Learning of Mathematics, 12(2), 19–28.

    Google Scholar 

  • Bereiter, C. (1991). Implications of connectionism for thinking about rules. Educational Researcher, 20(3), 10–16.

    Google Scholar 

  • Berninger, V. W., & Corina, D. (1998). Making cognitive neuroscience educationally relevant: Creating bi-directional collaborations between educational psychology and cognitive neuroscience. Educational Psychology Review, 10(3), 343–354.

    Article  Google Scholar 

  • Blakemore, S. J., & Frith, U. (2005). The learning brain: Lessons for education, A précise. Developmental Science, 8(6), 459–465.

    Article  Google Scholar 

  • Brown, L., & Reid, D. (2006). Embodied cognition: Somatic markers, purposes and emotional orientations. Educational Studies in Mathematics, 63(2), 179–192.

    Article  Google Scholar 

  • Bruer, J. T. (1997). Education and the brain: A bridge too far. Educational Researcher, 26(8), 4–16.

    Google Scholar 

  • Butterworth, B. (1999). The Mathematical Brain. London, UK: Macmillan.

    Google Scholar 

  • Byrnes, J. P. (2001). Minds, Brains, and Learning: Understanding the Psychological and Educational Relevance of Neuroscientific Research. New York: The Guilford Press.

    Google Scholar 

  • Campbell, S. R. (1993). The embodied mind and worlds without ground. Unpublished manuscript.

    Google Scholar 

  • Campbell, S. R. (1998). Preservice Teachers’ Understanding of Elementary Number Theory: Qualitative Constructivist Research Situated Within a Kantian Framework for Understanding Educational Inquiry. Burnaby, BC: Simon Fraser University. (263 pp.)

    Google Scholar 

  • Campbell, S. R. (2001). Enacting possible worlds: Making sense of (human) nature. In J. F. Matos, W. Blum, S. K. Houston, & S. P. Carreira (Eds.), Modelling and Mathematics Education (pp. 1–14). Chichester, UK: Horwood Publishing.

    Google Scholar 

  • Campbell, S. R. (2002a). Constructivism and the limits of reason: Revisiting the Kantian problematic. Studies in Philosophy and Education, 21(6), 421–445.

    Article  Google Scholar 

  • Campbell, S. R. (2002b). Coming to terms with division: Preservice teachers’ understanding. In S. R. Campbell & R. Zazkis (Eds.), Learning and Teaching Number Theory: Research in Cognition and Instruction (pp. 15–40). Westport, CT: Ablex.

    Google Scholar 

  • Campbell, S. R. (2003a). Dynamic tracking of preservice teachers’ experiences with computer-based mathematics learning environments. Mathematics Education Research Journal, 15(1), 70–82.

    Google Scholar 

  • Campbell, S. R. (2003b). Reconnecting mind and world: Enacting a (new) way of life. In S. J. Lamon, W. A. Parker, & S. K. Houston (Eds.), Mathematical Modelling: A Way of Life (pp. 245–253). Chichester, UK: Horwood Publishing.

    Google Scholar 

  • Campbell, J. I. D. (Ed.) (2004a). The Handbook of Mathematical Cognition. New York, NY: Psychology Press.

    Google Scholar 

  • Campbell, S. R. (2004b). Forward and inverse modelling: Mathematics at the nexus between mind and world. In H.-W. Henn & W. Blum (Eds.), ICMI Study 14: Applications and Modelling in Mathematics Education—Pre-conference Volume (pp. 59–64). Dortmund, Germany: University of Dortmund.

    Google Scholar 

  • Campbell, S. R. (2005a). Specification and rationale for establishing a mathematics educational neuroscience laboratory. Paper presented at the meeting of the American Educational Research Association, Montreal, QC, Canada (12 pp.).

    Google Scholar 

  • Campbell, S. R. (2005b). Educational neuroscience: Keeping learners in mind. In G.G. Hruby (Ed.), Peril and Promise in Educational Neuroscience. Symposium conducted at the meeting of the American Educational Research Association, Montreal, QC, Canada (12 pp.).

    Google Scholar 

  • Campbell, S. R. (2006a). Educational neuroscience: New horizons for research in mathematics education. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for Psychology in Mathematics Education (PME) (Vol. 2, pp. 257–264). Prague: PME.

    Google Scholar 

  • Campbell, S. R. (2006b). Defining mathematics educational neuroscience. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for Psychology in Mathematics Education (PME-NA) (Vol. 2, pp. 442–449). Mérida, México: Universidad Pedagógica Nacional.

    Google Scholar 

  • Campbell, S. R. (2006c). Understanding elementary number theory in relation to arithmetic and algebra. In R. Zazkis & S. R. Campbell (Eds.), Number Theory in Mathematics Education: Perspectives and Prospects (pp. 19–40). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Campbell, S. R. (2008a). Connecting brain and behavior in educational research. In A. J. Spink, M. R. Ballintijn, N. D. Bogers, F. Grieco, L. W. S. Loijens, L. P. J. J. Noldus, G. Smit, & P. H. Zimmerman (Eds.), Proceedings of Measuring Behavior 2008: 6th International Conference on Methods and Techniques in Behavioral Research (Maastricht, The Netherlands, August 26–29, 2008) (pp. 127–128). Maastricht, The Netherlands: Noldus Information Technology.

    Google Scholar 

  • Campbell, S. R. (2008b). Mathematics educational neuroscience: Origins, applications, and new opportunities. In P. Liljedahl (Ed.), Proceedings/2007 Annual Meeting for the Canadian Mathematics Education Study Group (pp. 71–78). Simon Fraser University, BC: CMESG/GCEDM.

    Google Scholar 

  • Campbell, S. R., & Dawson, A. J. (1995). Learning as embodied action. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery with Computers in Mathematics Education (pp. 233–249). Berlin: Springer.

    Google Scholar 

  • Campbell, S. R., & Handscomb, K. (April, 2007). An embodied view of mind-body correlates. Paper presented to the American Educational Research Association: Brain, Neuroscience, and Education SIG. Chicago, IL, U.S.A.

    Google Scholar 

  • Campbell, S. R., & the ENL Group (2007). The ENGRAMMETRON: Establishing an educational neuroscience laboratory. SFU Educational Review, 1, 17–29.

    Google Scholar 

  • Campbell, S. R., & Zazkis, R. (2002). Learning and Teaching Number Theory: Research in Cognition and Instruction. Westport, CT: Ablex Publishing.

    Google Scholar 

  • Campbell, S. R., Cimen, O. A., & Handscomb, K. (2009a, April). Learning and understanding division: A study in educational neuroscience. Paper presented to the American Educational Research Association: Brain, Neuroscience, and Education SIG (San Diego, CA). 10 pp. (ED505739).

    Google Scholar 

  • Campbell, S. R., Handscomb, K., Zaparyniuk, N. E., Sha, L., Cimen, O. A., & Shipulina, O. V. (2009b, April). Investigating image-based perception and reasoning in geometry. Paper presented to the American Educational Research Association: Brain, Neuroscience, and Education SIG (San Diego, CA). 24 pp. (ED505740).

    Google Scholar 

  • CNS (Cognitive Neuroscience Society) (2007). On-line at http://www.cogneurosociety.org.

  • Cohen, J. D., & Tong, F. (2001). The face of controversy. Science, 293, 2405–2407.

    Article  Google Scholar 

  • Davis, R. B. (1984). Learning Mathematics: The Cognitive Science Approach to Mathematics Education. Norwood, NJ: Ablex.

    Google Scholar 

  • Davis, R. B. (1986). The convergence of cognitive science and mathematics education. Journal of Mathematical Behaviour, 5(3), 321–333.

    Google Scholar 

  • Davis, R. B. (1992). Reflections on where mathematics education now stands and on where it may be going. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 724–734). New York, NY: Macmillan Publishing Company.

    Google Scholar 

  • Davis, B. (1995a). Hearing otherwise and thinking differently: Enactivism and school mathematics. JCT: An Interdisciplinary Journal of Curriculum Studies, 11(4), 31–56.

    Google Scholar 

  • Davis, B. (1995b). Why teach mathematics? Mathematics education and enactivist theory. For the Learning of Mathematics, 15(2), 2–8.

    Google Scholar 

  • Davis, B., & Sumara, D. (2007). Complexity science, ecology, and enactivism. In J. Kincheloe & R. A. Horn Jr. (Eds.), The Praeger Handbook of Education and Psychology (pp. 464–473). Westport, CT: Praeger.

    Google Scholar 

  • Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. New York, NY: Oxford University Press.

    Google Scholar 

  • Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2004). Three parietal circuits for number processing. In J. Campbell (Ed.), The Handbook of Mathematical Cognition (pp. 433–453). New York: Psychology Press.

    Google Scholar 

  • Ebisawa, Y. (1998). Improved video-based eye-gaze detection method. IEEE Transactions on Instrument and Measurement, 47(4), 948–955.

    Article  Google Scholar 

  • Egan, K. (1997). The Educated Mind: How Cognitive Tools Shape Our Understanding. Chicago: University of Chicago Press.

    Google Scholar 

  • English, L. D., & Halford, G. S. (1995). Mathematics Education: Models and Processess. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Fingelkurts, A. A., & Fingelkurts, A. A. (2001). Operational architectonics of the human brain biopotential field: Towards solving the mind-brain problem. Brain and Mind, 2, 261–296.

    Article  Google Scholar 

  • Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.

    Article  Google Scholar 

  • Gardner, H. (1985). The Mind’s New Science: A History of the Cognitive Revolution. New York, NY: Basic Books Inc.

    Google Scholar 

  • Gazzaniga, M. S. (2004). The Cognitive Neurosciences III. Cambridge, MA: MIT Press.

    Google Scholar 

  • Geake, J. G. (2005). Educational neuroscience and neuroscientific education: In search of a mutual middle way. Research Intelligence, 92(3), 10–13.

    Google Scholar 

  • Geake, J., & Cooper, P. (2003). Cognitive neuroscience: Implications for education? Westminster Studies in Education, 26(1), 7–20.

    Article  Google Scholar 

  • Gerofsky, S., & Gobel, J. S. (2007). A conversation on embodiment at the heart of abstraction in mathematics education and music education. Journal of the Canadian Association for Curriculum Studies, 5(1), 49–68.

    Google Scholar 

  • Gibbons, M., Limoges, C., Nowotny, H., Schwartzman, S., Scott, P., & Trow, M. (1994). The New Production of Knowledge. London: Sage.

    Google Scholar 

  • Gordon, J. A., & Hen, R. (2004). Genetic approaches to the study of anxiety. Annual Review of Neuroscience, 27, 193–222.

    Article  Google Scholar 

  • Goswami, U. (2004). Neuroscience and education. British Journal of Educational Psychology, 74, 1–14.

    Article  Google Scholar 

  • Grouws, D. A. (Ed.) (1992). Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics. New York, NY: Macmillan Publishing Company.

    Google Scholar 

  • Gutiérrez, A., & Boero, P. (2006). Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future. Rotterdam: Sense Publishers.

    Google Scholar 

  • Hackenberg, A., & Sinclair, N. (2007). Talking about embodiment and caring in relation to computer use in mathematics education. For the Learning of Mathematics, 27(3), 12–16.

    Google Scholar 

  • Hinrichs, H., & Machleidt, W. (1992). Basic emotions reflected in EEG-coherences. International Journal of Psychophysiology, 13(3), 225–232.

    Article  Google Scholar 

  • Hutchinson, T. E. (1989). Human-computer interaction using eye-gaze input. IEEE Transactions on System, Man, and Cybernetics, 19(6), 1527–1533.

    Article  Google Scholar 

  • Iannece, D., Mellone, M., & Tortora, R. (2006). New insights into learning processes from some neuroscience issues. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for Psychology in Mathematics Education (PME) (Vol. 3, pp. 321–328). Prague: PME.

    Google Scholar 

  • Jackendoff, R. (1987). Consciousness and the Computational Mind. Cambridge, MA: MIT Press.

    Google Scholar 

  • John, E. R. (2002). The neurophysics of consciousness. Brain Research Reviews, 39(1), 1–28.

    Article  Google Scholar 

  • Jung-Beeman, M. J., Bowden, E. M., Haberman, J., Frymiare, J. L., Arambel-Liu, S., Greenblatt, R. E., Reber, P. J., & Kounios, J. (2004). Neural activity when people solve verbal problems with insight. PLoS Biology, 2(4), 500–510.

    Article  Google Scholar 

  • Kant, I. (1933). Immanuel Kant’s Critique of Pure Reason. London: MacMillan and Co., Ltd. (N.K. Smith, Trans.). (Original work published 1787).

    Google Scholar 

  • Kieren, T. E. (2004). Mathematics knowing as fully embodied. For the Learning of Mathematics, 24(3), 23.

    Google Scholar 

  • Kieren, T., & Simmt, E. (2001). A model for observing mathematics knowing in action. In S. Gunn & A. Begg (Eds.), Mind, Body and Society: Emerging Understandings of Knowing and Learning (pp. 125–133). Victoria, Australia: University of Melbourne.

    Google Scholar 

  • Kirshner, D., & Whitson, J. A. (Eds.) (1997). Situated Cognition: Social, Semiotic, and Psychological Perspectives. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Klimesch, W. (1999). EEG alpha and theta oscillations reflect cognitive and memory performance: A review and analysis. Brain Research Reviews, 29(2–3), 169–195.

    Article  Google Scholar 

  • Lakoff, G., & Johnson, M. (1980). Metaphors We Live By. Chicago: University of Chicago Press.

    Google Scholar 

  • Lakoff, G. & Johnson, M. (1999). Philosophy in the Flesh. New York: Basic Books.

    Google Scholar 

  • Lakoff, G., & Núñez, R. E. (2000). Where Mathematics Comes from: How the Embodied Mind Brings Mathematics Into Being. New York, NY: Basic Books, Inc.

    Google Scholar 

  • Lee, K. (2003). Neuroscience and education: Promises and pitfalls. Asia-Pacific Journal of Education, 23, 109–120.

    Article  Google Scholar 

  • Lee, K., Lim, Z. Y., Yeong, S. H. M., Ng, S. F., Venkatraman, V., & Chee, M. W. L. (2007). Strategic differences in algebraic problem solving: Neuroanatomical correlates. Brain Research, 1155, 163–171.

    Article  Google Scholar 

  • Liu, C., Lin, F.-L., & Dai, C.-N. (2006). New approach of neurocognition in mathematical education research and further implications. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for Psychology in Mathematics Education (PME) (Vol. 1, p. 286). Prague: PME.

    Google Scholar 

  • Lutz, A., & Thompson, E. (2003). Neurophenomenology: Integrating subjective experience and brain dynamics in the neuroscience of consciousness. Journal of Consciousness Studies, 10, 31–52.

    Google Scholar 

  • McCandliss, B. D., Kalchman, M., & Bryant, P. (2003). Design experiments and laboratory approaches to learning: Steps towards collaborative exchange. Educational Researcher, 32(1), 14–16.

    Article  Google Scholar 

  • McClelland, J. L., Rumelhart, D. E., & the PDP Research Group (1987). Parallel distributed processing: Explorations in the microstructure of cognition. In J. A. Feldman, P. J. Hayes, & D. E. Rumelhart (Eds.), Computational Models in Cognition and Perception Series (Vol. 2). Cambridge, MA: MIT Press.

    Google Scholar 

  • McVee, M. B., Dunsmore, K., & Gavelek, J. R. (2005). Schema theory revisited. Review of Educational Research, 75(4), 531–566.

    Article  Google Scholar 

  • Merleau-Ponty, M. (1962). Phenomenology of Perception. London, UK: Routledge and Kegan Paul.

    Google Scholar 

  • Merleau-Ponty, M. (1968). The Visible and the Invisible. Evanston, IL: Northwestern University Press.

    Google Scholar 

  • Niebur, E. (2002). Electrophysiological correlates of synchronous neural activity and attention: A short review. Biosystems, 67(1–3), 157–166.

    Article  Google Scholar 

  • NRC (National Research Council) (2000). How People Learn: Brain, Mind, Experience and School. Washington, DC: National Academy Press.

    Google Scholar 

  • NRC (National Research Council) (2002). Scientific Research in Education. Washington, DC: National Academy Press.

    Google Scholar 

  • Núñez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1–3), 45–65.

    Article  Google Scholar 

  • OECD (Organisation for Economic Co-operation and Development) (2002). Understanding the Brain: Towards a New Learning Science. Paris, France: OECD.

    Google Scholar 

  • Pea, R. D. (1987). Cognitive Technologies for Mathematics Education. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Pfurtscheller, G., & Aranibar, A. (1977). Event-related cortical desynchronization detected by power measurement of scalp EEG. Electroencephalography and Clinical Neurophysiology, 42, 817–826.

    Article  Google Scholar 

  • Phillips, D. C. (1995). The good, the bad, and the ugly: The many faces of constructivism. Educational Researcher, 24(7), 5–12.

    Google Scholar 

  • Reid, D. (1996). Enactivism as a methodology. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the Twentieth Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 203–210). Valencia, Spain.

    Google Scholar 

  • Reid, D., & Drodge, E. (2000). Embodied cognition and the mathematical emotional orientation. Mathematical Thinking and Learning, 2(4), 249–267.

    Article  Google Scholar 

  • Sacks, O. (1989). Seeing Voices: A Journey Into the World of the Deaf. Berkeley, CA: University of California Press.

    Google Scholar 

  • Sacks, O. (1990). The Man Who Mistook His Wife for a Hat: And Other Clinical Tales. New York, NY: Harper Perennial Library.

    Google Scholar 

  • Sacks, O. (1995). An Anthropologist on Mars: Paradoxical Tales. New York, NY: Vintage.

    Google Scholar 

  • Schoenfeld, A. H. (1987). Cognitive Science and Mathematics Education. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Schoenfeld, A. H. (1992a). Comments from the guest editor: Research methods in and for the learning sciences. The Journal of the Learning Sciences, 2(2), 137–139.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1992b). On paradigms and methods: What do you do when the ones you know don’t do what you want them to? Issues in the analysis of data in the form of videotapes. The Journal of the Learning Sciences, 2(2), 179–214.

    Article  Google Scholar 

  • Sfard, A. (2008). Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Shipulina, O. V., Campbell, S. R., & Cimen, O. A. (2009, April). Electrooculography: Connecting mind, brain, and behavior in mathematics education research. Paper presented at the Brain, Neuroscience, and Education SIG at 2009 AERA Annual Meeting (San Diego, CA) (16 pp.). (ED505692).

    Google Scholar 

  • Sierpinska, A., & Kilpatrick, J. (Eds.) (1998). Mathematics Education as a Research Domain: A Search for Identity—An ICMI Study (2 vols.). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Simmt, E., & Kieren, T. (2000). On being embodied in the body of mathematics: consequences for mathematics knowing in action. In M. Fernandez (Ed.), Proceedings of the Twenty-Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 205–212).

    Google Scholar 

  • Steffe, L. P., von Glasersfeld, E., & Cobb, P. (1983). Children’s Counting Types: Philosophy, Theory, and Application. New York, NY: Praeger.

    Google Scholar 

  • Sugioka, A., Ebisawa, Y., & Ohtani, M. (1996). Nonconstant video-based eye-gaze detection method allowing large head displacements. In IEEE International Conference on Medicine and Biology Society (pp. 948–955).

    Google Scholar 

  • Szücs, D., & Csépe, V. (2004). Access to number representations is dependent on the modality of stimulus presentation in mental addition: A combined behavioral and ERP study. Cognitive Brain Research, 19(1), 10–27.

    Article  Google Scholar 

  • Uttal, W. R. (2001). The New Phrenology: The Limits of Localizing Cognitive Processes in the Brain. Cambridge, MA: The MIT Press.

    Google Scholar 

  • van Nes, F., & de Lange, J. (2007). Mathematics education and neurosciences: Relating spatial structures to the development of spatial sense and number sense. The Montana Mathematics Enthusiast, 4(2), 210–229.

    Google Scholar 

  • van Nes, F., & Gebuis, T. (2006). Mathematics education and neurosciences (MENS). In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for Psychology in Mathematics Education (PME) (Vol. 1, p. 352). Prague: PME.

    Google Scholar 

  • Varela, F. J. (1996). Neurophenomenology: A methodological remedy to the hard problem. Journal of Consciousness Studies, 3, 330–350.

    Google Scholar 

  • Varela, F. J., & Shear, J. (1999). First-person accounts: Why, what, and how. In F. J. Varela & J. Shear (Eds.), The View from Within: First-Person Approaches to the Study of Consciousness (pp. 1–14). Thorveton, UK: Imprint Academic.

    Google Scholar 

  • Varela, F. J., Thompson, E., & Rosch, E. (1991). The Embodied Mind: Cognitive Science and Human Experience. Cambridge, MA: MIT Press.

    Google Scholar 

  • Varma, S., McCandliss, B. D., & Schwartz, D. L. (2008). Scientific and pragmatic challenges for bridging education and neuroscience. Educational Researcher, 37(3), 140–152.

    Article  Google Scholar 

  • von Glasersfeld, E. (1982). An interpretation of Piaget’s constructivism. Review Internationale de Philosophy, 142-3, 612–635.

    Google Scholar 

  • von Glasersfeld, E. (1991). Radical Constructivism in Mathematics Education. Boston, MA: Kluwer.

    Google Scholar 

  • Ward, L. M. (2003). Synchronous neural oscillations and cognitive processes. TRENDS in Cognitive Sciences, 7(12), 553–559.

    Article  Google Scholar 

  • Wertsch, J. V. (1991). Voices of the Mind: A Sociocultural Approach to Mediated Action. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Wigner, E. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics, 13, 1–14.

    Article  Google Scholar 

  • Zazkis, R., & Campbell, S. R. (Eds.) (2006). Number Theory in Mathematics Education: Perspectives and Prospects. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stephen R. Campbell .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Campbell, S.R. (2010). Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00742-2_31

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00741-5

  • Online ISBN: 978-3-642-00742-2

  • eBook Packages: Humanities, Social Sciences and LawEducation (R0)

Publish with us

Policies and ethics