ZDM

, Volume 45, Issue 2, pp 239–252 | Cite as

Virtual encounters: the murky and furtive world of mathematical inventiveness

  • Nathalie Sinclair
  • Elizabeth de Freitas
  • Francesca Ferrara
Original Article

Abstract

Based on Châtelet’s insights into the nature of mathematical inventiveness, drawn from historical analyses, we propose a new way of framing creativity in the mathematics classroom. The approach we develop emphasizes the social and material nature of creative acts. Our analysis of creative acts in two case studies involving primary school classrooms also reveals the characteristic ways in which digital technologies can occasion such acts.

References

  1. Burbules, N. C. (2006). Rethinking the virtual. In J. Weiss, et al. (Eds.), The International handbook of virtual learning environments (pp. 37–58). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  2. Châtelet, G. (1993). Les enjeux du mobile. Paris: Seuil.Google Scholar
  3. Châtelet, G. (2000). Figuring space: philosophy, mathematics and physics. (trans: Shore, R., & Zagha, M.). Dordrecht: KluwerGoogle Scholar
  4. Clagett, M. (1968). Nicole Oresme and the medieval geometry of qualities and motions. Madison: The University of Wisconsin Press.Google Scholar
  5. Davis, G. A., & Rimm, S. B. (2004). Education of the gifted and talented (5th ed.). Boston: Pearson Education.Google Scholar
  6. De Freitas, E., & Sinclair, N. (2012). Diagram, gesture, agency: theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80, 133–152.CrossRefGoogle Scholar
  7. Deleuze, G. (1994). Difference and repetition (trans: Patton, P.). New York: Columbia University Press.Google Scholar
  8. Ferrara, F., Pratt, D., & Robutti, O. (2006). The role and uses of technologies for the teaching of algebra and calculus. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 237–273). Rotterdam: Sense.Google Scholar
  9. Jackiw, N. (2006). Mechanism and magic in the psychology of dynamic geometry. In N. Sinclair, D. Pimm, & W. Higginson (Eds.), Mathematics and aesthetics: New approaches to an ancient affinity. New York: Springer.Google Scholar
  10. Leikin, R. (2009). Multiple proof tasks: Teacher practice and teacher education. In Proceedings of ICMI Study-19: Proofs and proving. Google Scholar
  11. Leikin, R., Berman, A., & Koichu, B. (Eds.) (2009). Creativity in mathematics and the education of gifted students. Rotterdam, The Netherlands: Sense.Google Scholar
  12. Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics, 70, 159–174.CrossRefGoogle Scholar
  13. Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. New York: Basic Books.Google Scholar
  14. Plucker, J. A., & Beghetto, R. A. (2004). Why creativity is domain general, why it looks domain specific, and why the distinction does not matter. In R. J. Sternberg, E. L. Grigorenko, & J. L. Singer (Eds.), Creativity: From potential to realization (pp. 153–168). Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  15. Rotman, B. (2008). Becoming beside ourselves: The alphabet, ghosts, and distributed human beings. Durham: Duke University Press.Google Scholar
  16. Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL: Scholastic Testing Service.Google Scholar
  17. Weil, A. (1992). The apprenticeship of a mathematician (trans: Gage, J.). Berlin: Birkhäuser.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2012

Authors and Affiliations

  • Nathalie Sinclair
    • 1
  • Elizabeth de Freitas
    • 2
  • Francesca Ferrara
    • 3
  1. 1.Simon Fraser UniversityBurnabyCanada
  2. 2.Adelphi UniversityGarden CityUSA
  3. 3.Università di TorinoTurinItaly

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