Technological Supports for Mathematical Thinking and Learning: Co-action and Designing to Democratize Access to Powerful Ideas

Part of the ICME-13 Monographs book series (ICME13Mo)


The enterprise of understanding and supporting processes of mathematical cognition is both epistemologically deep and politically urgent. We cannot ignore that new technology-mediated learning environments have the potential to democratize access to powerful ideas. The importance of technology in this respect is bound up with the essential nature of mathematical objects as symbolic entities that can only be expressed and conjured up through the mediation of representations. A key question for the design of technology-enhanced learning environments is whether the cognitive tools—material and digital-symbolic—that have been developed in recent decades might offer learners access to modes of activity with disciplinary structures that have historically been achievable only by ‘maestros’ of the discipline. In this article we elaborate the construct of “co-action” as a means of describing humans’ mathematical interactions with the support of such tools.


Technological infrastructure Co-action Collaboration Mathematical representations 


  1. Baldwin, M. (1896). A new factor of evolution. The American Naturalist, 30, 441–451, 536–553.CrossRefGoogle Scholar
  2. Cole, M. (1996). Cultural psychology: A once & future discipline. Cambridge, MA: Harvard University Press.Google Scholar
  3. Donald, M. (2001). A mind so rare: The evolution of human consciousness. New York: Norton.Google Scholar
  4. Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3–26). Cuernavaca: Mexico.Google Scholar
  5. Forster, E. M. (1927). Aspects of the novel. London: Edward Arnold.Google Scholar
  6. Gibson, J. J. (2014). The ecological approach to visual perception. New York: Psychology Press.Google Scholar
  7. Gleick, J. (1993). Genius: Richard Feynman and modern physics. New York: Pantheon.Google Scholar
  8. Hegedus, S. J., & Moreno-Armella, L. (2009). Intersecting representation and communication infrastructures. ZDM, 41(4), 399–412.CrossRefGoogle Scholar
  9. Luria, A. R. (1928). The problem of the cultural development of the child. Genetic Psychology, 35, 493–506.Google Scholar
  10. Moreno-Armella, L., & Hegedus, S. J. (2009). Co-action with digital technologies. ZDM, 41(4), 505–519.CrossRefGoogle Scholar
  11. Rabardel, P. (1995). Les hommes et les technologies: Approche cognitive des instruments contemporains. Paris: Armand Colin.Google Scholar
  12. Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.Google Scholar
  13. Wertsch, J. V. (1991). Voices of the mind: A sociological approach to mediated action. Cambridge, MA: Harvard University Press.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  2. 2.Vanderbilt UniversityNashvilleUSA

Personalised recommendations