Embodied Interaction as Designed Mediation of Conceptual Performance

  • Dragan Trninic
  • Dor Abrahamson
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 1)


Can conceptual understanding emerge from embodied interaction? We believe the answer is affirmative, provided that individuals engaged in embodied-interaction activity enjoy structured opportunities to describe their physical actions using instruments, language, and forms pertaining to the targeted concept. In this chapter, we draw on existing literature on embodiment and artifacts to coin and elaborate on the construct of an embodied artifact—a cognitive product of rehearsed performance such as, for example, an arabesque penchée in dance or a flying sidekick in martial arts. We argue that embodied artifacts may encapsulate or “package” cultural knowledge for entry into disciplinary competence not only in explicitly embodied domains, such as dance or martial arts, but also implicitly embodied domains, such as mathematics. Furthermore, we offer that current motion-sensitive cyber-technologies may enable the engineering of precisely the type of learning environments capable of leveraging embodied artifacts as both means of learning and means for studying how learning occurs. We demonstrate one such environment, the Mathematical Imagery Trainer for Proportion (MIT–P), engineered in the context of a design-based research study investigating the mediated emergence of mathematical notions from embodied-interaction instructional activities. In particular, we discuss innovative features of the MIT–P in terms of the technological artifact as well as its user experience. We predict that embodied interaction will become a focus of design for and research on mathematical learning.


Embodied interaction Sociocultural theory Educational technology Learning sciences Mathematics Proportion Embodied artifact 



The notion of an embodied artifact originates in Abrahamson’s earlier publications on the Mathematical Imagery Trainer. We gratefully appreciate Mira-Lisa Katz for her comments on an earlier draft. This research was supported by a UC Berkeley Committee on Research Faculty Research Grant and an Institute of Education Sciences pre-doctoral Research Training grant R305B090026.


  1. Abrahamson, D. (2009a). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27–47.CrossRefGoogle Scholar
  2. Abrahamson, D. (2009b). Orchestrating semiotic leaps from tacit to cultural quantitative reasoning – The case of anticipating experimental outcomes of a quasi-binomial random generator. Cognition and Instruction, 27(3), 175–224.CrossRefGoogle Scholar
  3. Abrahamson, D., Gutiérrez, J. F., Lee, R. G., Reinholz, D., & Trninic, D. (2011, April 8–12). From tacit sensorimotor coupling to articulated mathematical reasoning in an embodied design for proportional reasoning. In R. Goldman (Chair), H. Kwah, & D. Abrahamson (Organizers), & R. P. Hall (Discussant), Diverse perspectives on embodied learning: what’s so hard to grasp? Symposium presented at the annual meeting of the American Educational Research Association (SIG Advanced Technologies for Learning). New Orleans.Google Scholar
  4. Alač, M., & Hutchins, E. (2004). I see what you are saying: Action as cognition in fMRI brain mapping practice. Journal of Cognition and Culture, 4(3), 629–661.CrossRefGoogle Scholar
  5. Antle, A. N., Corness, G., & Droumeva, M. (2009). What the body knows: Exploring the benefits of embodied metaphors in hybrid physical digital environment. Interacting with Computers, 21(1/2), 66–75.CrossRefGoogle Scholar
  6. Barsalou, L. W. (2010). Grounded cognition: Past, present, and future. Topics in Cognitive Science, 2, 716–724.CrossRefGoogle Scholar
  7. Birchfield, D., & Johnson-Glenberk, M. C. (2010). A next gen Interface for embodied learning: SMALLab and the geological layer cake. International Journal of Gaming and Computer-Mediated Simulation, 2(1), 49–58.CrossRefGoogle Scholar
  8. Brooks, R. A. (1991). Intelligence without representation. Artificial Intelligence, 47, 139–159.CrossRefGoogle Scholar
  9. Campbell, S. R. (2003). Reconnecting mind and world: Enacting a (new) way of life. In S. J. Lamon, W. A. Parker, & S. K. Houston (Eds.), Mathematical modeling: A way of life (pp. 245–256). Chichester, England: Horwood Publishing.Google Scholar
  10. Chemero, A. (2009). Radical embodied cognitive science. Cambridge, MA: The MIT Press.Google Scholar
  11. Clinton, K. A. (2006). Being-in-the-digital-world: how videogames engage our pre-linguistic sense-making abilities. Unpublished doctoral dissertation. Madison, WI: University of Wisconsin.Google Scholar
  12. Collins, A. (1992). Toward a design science of education. In E. Scanlon & T. O’Shea (Eds.), New directions in educational technology (pp. 15–22). New York: Springer.CrossRefGoogle Scholar
  13. Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process. Boston: D.C. Heath.Google Scholar
  14. Dourish, P. (2001). Where the action is: The foundations of embodied interaction. Cambridge, MA: MIT Press.Google Scholar
  15. Dove, G. (2009). Beyond perceptual symbols: A call for representational pluralism. Cognition, 110(3), 412–431.CrossRefGoogle Scholar
  16. Dreyfus, H. L., & Dreyfus, S. E. (1999). The challenge of Merleau-Ponty’s phenomenology of embodiment for cognitive science. In G. Weiss & H. F. Haber (Eds.), Perspectives on embodiment: The intersection of nature and culture. New York: Routledge.Google Scholar
  17. Ericsson, K. A. (2002). Attaining excellence through deliberate practice: Insights from the study of expert performance. In M. Ferrari (Ed.), The pursuit of excellence in education (pp. 21–55). Hillsdale, NJ: Erlbaum.Google Scholar
  18. Feldman, M. S., & Pentland, B. T. (2003). Reconceptualizing organizational routines as a source of flexibility and change. Administrative Science Quarterly, 48, 94–118.CrossRefGoogle Scholar
  19. Fischer, U., Moeller, K., Bientzle, M., Cress, U., & Nuerk, H.-C. (2011). Sensori-motor spatial training of number magnitude representation. Psychonomic Bulletin & Review, 18(1), 177–183.CrossRefGoogle Scholar
  20. Fodor, J. A. (1975). The language of thought. Cambridge, MA: Harvard University Press.Google Scholar
  21. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, the Netherlands: D. Reidel Publishing Company.Google Scholar
  22. Fuson, K. C., & Abrahamson, D. (2005). Understanding ratio and proportion as an example of the apprehending zone and conceptual-phase problem-solving models. In J. Campbell (Ed.), Handbook of mathematical cognition (pp. 213–234). New York: Psychology Press.Google Scholar
  23. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.Google Scholar
  24. Gokhale, E. (2008). 8 steps to a pain-free back. Stanford, CA: Pendo Press.Google Scholar
  25. Goldstone, R. L., Landy, D. H., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2, 265–284.CrossRefGoogle Scholar
  26. Howison, M., Trninic, D., Reinholz, D., & Abrahamson, D. (2011). The Mathematical Imagery Trainer: From embodied interaction to conceptual learning. In G. Fitzpatrick, C. Gutwin, B. Begole, W. A. Kellogg & D. Tan (Eds.), Proceedings of the annual meeting of The Association for Computer Machinery Special Interest Group on Computer Human Interaction: ``Human Factors in Computing Systems'' (CHI 2011), Vancouver, May 7--12, 2011 (Vol. ``Full Papers'', pp. 1989--1998). New York: ACM Press.Google Scholar
  27. Karmiloff-Smith, A., & Inhelder, B. (1975). If you want to get ahead, get a theory. Cognition, 3(3), 195–212.CrossRefGoogle Scholar
  28. Kirsh, D. (2009). Projection, problem space and anchors. In N. Taatgen, H. van Rijn, & L. Schomaker (Eds.), Proceedings of the Cognitive Science Society 2009 (pp. 2310–2315). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  29. Kirsh, D. (2010). Thinking with the body. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the Cognitive Science Society 2010 (pp. 2864–2869). Austin, TX: Cognitive Science Society.Google Scholar
  30. Kirsh, D., & Maglio, P. (1994). On distinguishing epistemic from pragmatic action. Cognitive Science, 18(4), 513–549.CrossRefGoogle Scholar
  31. Kiverstein, J., & Clark, A. (Eds.). (2009). Introduction: Mind embodied, embedded, enacted: One church or many? Topoi, 28(1), 1--7.Google Scholar
  32. Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). Charlotte, NC: Information Age Publishing.Google Scholar
  33. Lee, J. C. (2008). Hacking the Nintendo Wii Remote. IEEE Pervasive Computing, 7(3), 39–45.CrossRefGoogle Scholar
  34. Leontiev, A. N. (1981). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in soviet psychology (pp. 37–71). Armonk, NY: M.E. Sharpe.Google Scholar
  35. Melser, D. (2004). The act of thinking. Cambridge, MA: The MIT Press.Google Scholar
  36. Namirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of PME 2003 (Vol. 1, pp. 105–109). Columbus, OH: Eric Claringhouse.Google Scholar
  37. Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26(2–3), 165–190.CrossRefGoogle Scholar
  38. Rosenbaum, D. A., Kenny, S. B., & Derr, M. A. (1983). Hierarchical control of rapid movement sequences. Journal of Experimental Psychology: Human Perception and Performance, 9, 86–102.CrossRefGoogle Scholar
  39. Roth, W.-M., & Thom, J. S. (2009). Bodily experience and mathematics conceptions: from classical views to phenomenological reconceptualization. In L. Radford, L. Edwards, & F. Arzarello (Eds.), Gestures and multimodality in the construction of mathematical meaning [Special issue]. Educational Studies in Mathematics, 70(2), 175–189.Google Scholar
  40. Salomon, G., Perkins, D. N., & Globerson, T. (1991). Partners in cognition: Extending human intelligences with intelligent technologies. Educational Researcher, 20(3), 2–9.Google Scholar
  41. Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18(1), 253–286.CrossRefGoogle Scholar
  42. Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1991). Learning: The microgenetic analysis of one student’s evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (pp. 55–175). Hillsdale, NJ: Erlbaum.Google Scholar
  43. Schön, D. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.Google Scholar
  44. Sheets-Johnstone, M. (1990). The roots of thinking. Philadelphia, PA: Temple University Press.Google Scholar
  45. Trninic, D., Gutiérrez, J. F., & Abrahamson, D. (2011). Virtual mathematical inquiry: Problem solving at the gestural-symbolic interface of remote-control embodied-interaction design. In G. Stahl, H. Spada, N. Miyake, & N. Law (Eds.), Proceedings from CSCL 2011 (Vol. 1, pp. 272–279). Hong Kong: International Society of the Learning Sciences.Google Scholar
  46. Tulving, E. (1983). Elements of episodic memory. New York: Oxford University Press.Google Scholar
  47. Varela, F. J., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: The MIT Press.Google Scholar
  48. Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.CrossRefGoogle Scholar
  49. Vygotsky, L. (1987). Thinking and speech. In R. Rieber & A. Carton (Eds.), The collected works of L.S. Vygotsky (Vol. 1, pp. 39–285). New York: Plenum Press.Google Scholar
  50. Winograd, T., & Flores, F. (1987). Understanding computers and cognition: A new foundation for design. Boston: Addison-Wesley Professional.Google Scholar
  51. Yin, R. K. (2009). Case study research: design and methods. London: Sage.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Embodied Design Research Laboratory, Graduate School of EducationUniversity of California at BerkeleyBerkeleyUSA

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