Skip to main content
SpringerLink
Log in

Mathematical imagination and embodied cognition

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing displacements, and (2) articulating necessary cases. The discussion elaborates on the significance of these phenomena and draws relationships with the perspectives of embodied cognition and intersubjectivity.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa, 9 (Special issue on semiotics, culture and mathematical thinking), 267–299.

  • Casey, E. (1979). Imagining. Bloomington: Indiana University Press.

    Google Scholar 

  • Erickson, F. (2004). Talk and social theory. Cambridge, UK: Polity Press.

    Google Scholar 

  • Ferrara, F. (2006). Remembering and Imagining: Moving back and forth between motion and its representation. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.) Proceedings of the Thirtieth Conference of the International Group for the Psychology of Mathematics Education, (vol. 3, pp. 65–72). Prague: Charles University

    Google Scholar 

  • Gallese, V. (2003). The roots of empathy: The shared manifold hypothesis and the neural basis of intersubjectivity. Psychopathology, 36(4), 171–180. doi:10.1159/000072786.

    Article  Google Scholar 

  • Gallese, V. (2007). Before and below ‘theory of mind’: Embodied simulation and the neural correlates of social cognition. Philosophical Transactions of the Royal Society B, 362(1480), 659–669. doi:10.1098/rstb.2006.2002.

    Article  Google Scholar 

  • Gallese, V., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22(3–4), 455–479. doi:10.1080/02643290442000310.

    Article  Google Scholar 

  • Husserl, E. (1983). Ideas pertaining to a pure phenomenology and to a phenomenological philosophy—First Book (R. Rojcewicz & A. Schuwer, Trans.). The Hague: Martinus Nijhoff Publishers.

  • Hutchins, E. (2005). Material anchors for conceptual blends. Journal of Pragmatics, 37(10), 1555–1577. doi:10.1016/j.pragma.2004.06.008.

    Article  Google Scholar 

  • Johnson, M. (1987). The body in the mind: The bodily basis of meaning, imagination, and reason. Chicago: University of Chicago Press.

    Google Scholar 

  • Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.

    Google Scholar 

  • Noble, T. (2007). Body Motion and Physics: How elementary school students use gesture and action to make sense of the physical world. Unpublished Doctoral Dissertation, Tufts University, Medford, MA.

  • Radford, L. (2006). Elements of a cultural theory of objectification. Revista Latinoamericana de Investigación en Matemática Educativa, 9 (Special Issue on Semiotics, Culture and Mathematical Thinking), 103–129.

  • Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: A semiotic–cultural perspective on mathematical thinking. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th International Group for the Psychology of Mathematics Education (vol. 4, pp. 113–122). Melbourne, Australia.

  • Robutti, O. (2006). Motion, technology, gesture in interpreting graphs. International Journal of Computer Algebra in Mathematics Education, 13, 117–126.

    Google Scholar 

  • Roth, W.-M., & Welzel, M. (2001). From activity to gestures and scientific language. Journal of Research in Science Teaching, 38(1), 103–136. doi:10.1002/1098-2736(200101)38:1<103::AID-TEA6>3.0.CO;2-G.

    Article  Google Scholar 

  • Sabena, C. (2007). Body and signs: A multimodal semiotic approach to teaching–learning processes in early calculus. Unpublished Doctoral Dissertation, Università degli Studi di Torino, Torino.

  • Vygotsky, L. S. (1986). Thought and language. Cambridge, MA: MIT Press.

    Google Scholar 

Download references

Acknowledgments

This research has been supported by the Math in Motion project (NSF REC-0087573). Opinions expressed are those of the authors and not necessarily those of the Foundation. We would like to thank the students in Mr. Barros’s class for all that they have taught us. We would also like to thank the members of the “Math in Motion” group, Djalita Oliveira-Ramos for her help in translating and analyzing the data for this paper, and Laurie Edwards for her feedback on a previous version. We extend our acknowledgements to three anonymous reviewers and Luis Radford for their invaluable feedback

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, GMCS Building, Room 503, San Diego, CA, 92182-7720, USA

    Ricardo Nemirovsky

  2. Center for Research in Mathematics and Science Education (CRMSE), 6475 Alvarado Rd. Suite 206, San Diego, CA, 92120-5013, USA

    Ricardo Nemirovsky

  3. Dipartimento di Matematica, Università di Torino, Turin, Italy

    Francesca Ferrara

Authors
  1. Ricardo Nemirovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesca Ferrara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ricardo Nemirovsky.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nemirovsky, R., Ferrara, F. Mathematical imagination and embodied cognition. Educ Stud Math 70, 159–174 (2009). https://doi.org/10.1007/s10649-008-9150-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-008-9150-4

Keywords

Search

Navigation