Skip to main content
SpringerLink
Log in

Gestures and conceptual integration in mathematical talk

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

Abstract

Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately.

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

Similar content being viewed by others

References

  • Alibali, M. W., & diRusso, A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14, 37–56.

    Article  Google Scholar 

  • Alibali, M. W., Kita, S., & Young, A. (2000). Gesture and the process of speech production: We think, therefore we gesture. Language and Cognitive Processes, 15, 593–613.

    Article  Google Scholar 

  • Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigacion en Matemática Educativa, Numero Especial, 267–299.

  • Bazzini, L. (1991). From grounding metaphors to technological devices: A call for legitimacy in school mathematics. Educational Studies in Mathematics, 47, 259–271.

    Article  Google Scholar 

  • Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.) Handbook of research on mathematics teaching and learning (pp. 296–333). New York: Macmillan.

    Google Scholar 

  • Church, R. B., & Goldin-Meadow, S. (1986). The mismatch between gesture and speech as an index of transitional knowledge. Cognition, 23, 43–71.

    Article  Google Scholar 

  • Cobb, P., Gravemeijer, K., Yackel, E., McClain, K., & Whitenack, J. (1997). Symbolizing and mathematizing: The emergence of chains of signification in one first-grade classroom. In D. Kirshner, & J. A. Whitson (Eds.) Situated cognition theory: Social, semiotic, and neurological perspectives (pp. 151–233). Mahwah, NJ, USA: Lawrence Erlbaum.

    Google Scholar 

  • Edwards, L. (2003). A natural history of mathematical gesture. Paper presented at the Annual Meeting of the American Educational Research Association Annual Meeting, Chicago, April.

  • Fauconnier, G., & Turner, M. (2002). The way we think: Conceptual blending and the mind’s hidden complexities. New York: Basic Books.

    Google Scholar 

  • Goldin-Meadow, S. (2003). Hearing gestures: How our hands help us think. Chicago: University of Chicago Press.

    Google Scholar 

  • Goldin-Meadow, S., Kim, S., & Singer, M. (1999). What the teacher’s hands tell the student’s mind about math. Journal of Educational Psychology, 91(4), 720–730.

    Article  Google Scholar 

  • Goldin-Meadow, S., & Singer, M. (2003). From children’s hands to adults’ ears: Gesture’s role in teaching and learning. Developmental Psychology, 39, 509–520.

    Article  Google Scholar 

  • Graham, T. (1999). The role of gesture in children’s learning to count. Journal of Experimental Child Psychology, 74, 333–355.

    Article  Google Scholar 

  • Hutchins, E. (2005). Material anchors for conceptual blends. Journal of Pragmatics, 37, 1555–1577.

    Article  Google Scholar 

  • Jensen, G. (2003). Arithmetic for teachers: With applications and topics from geometry. Providence, RI: American Mathematical Society.

    Google Scholar 

  • Kendon, A. (1997). Gesture. Annual Review of Anthropology, 26, 109–128.

    Article  Google Scholar 

  • Kita, S. (2000). How representational gestures help speaking. In D. McNeill (Ed.) Language and gesture (pp. 162–185). Cambridge: Cambridge University Press.

    Google Scholar 

  • Kita, S. (Ed.). (2003). Pointing: Where language, culture and cognition meet. Mahwah, NJ, USA: Lawrence Erlbaum.

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

    Google Scholar 

  • Lamon, S. (1999). Teaching fractions and rational numbers for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ, USA: Lawrence Erlbaum.

    Google Scholar 

  • Lee, D. (2001). Cognitive linguistics: An introduction. Oxford: Oxford University Press.

    Google Scholar 

  • Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16–32.

    Article  Google Scholar 

  • McNeill, D. (1992). Hand and mind: What gestures reveal about thought. Chicago: University of Chicago Press.

    Google Scholar 

  • McNeill, D. (Ed.) (2000). Language and gesture. Cambridge: Cambridge University Press.

  • McNeill, D. (2005). Gesture and thought. Chicago: University of Chicago Press.

    Google Scholar 

  • Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and graphing. Cognition and Instruction, 16(2), 119–172.

    Article  Google Scholar 

  • Núñez, R. (2006). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. In R. Hersh (Ed.) 18 unconventional essays on the nature of mathematics (pp. 160–181). New York: Springer.

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • Parrill, F., & Sweetser, E. (2004). What we mean by meaning. Gesture, 4(2), 197–219.

    Article  Google Scholar 

  • Perry, M., Church, R. B., & Goldin-Meadow, S. (1988). Transitional knowledge in the acquisition of concepts. Cognitive Development, 3, 359–400.

    Article  Google Scholar 

  • Pimm, D. (1981). Metaphor and analogy in mathematics. For the Learning of Mathematics, 2, 47–50.

    Google Scholar 

  • Presmeg, N. (1992). Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595–610.

    Article  Google Scholar 

  • Presmeg, N. (1997). Reasoning with metaphors and metonymies in mathematical learning. In L. D. English (Ed.) Mathematical reasoning: Analogies, metaphors and images (pp. 267–279). Mahwah, NJ, USA: Lawrence Erlbaum.

    Google Scholar 

  • Presmeg, N. (2006). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163–182.

    Article  Google Scholar 

  • Radford, L. (2002). The seen, the spoken and the written: A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14–23.

    Google Scholar 

  • Radford, L. (2003). Gestures, speech and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37–70.

    Article  Google Scholar 

  • Radford, L., Demers, S., Guzmán, J., & Cerulli, M. (2003). Calculators, graphs, gestures, and the production of meaning. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.) Proceedings of the 2003 Joint Meeting of PME and PMENA, (Vol.4, pp. 55–62). Honolulu, HI, USA: University of Hawai’i.

    Google Scholar 

  • Reynolds, F., & Reeve, R. (2002). Gesture in collaborative mathematics problem solving. Journal of Mathematical Behavior, 20, 447–460.

    Article  Google Scholar 

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

    Google Scholar 

  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.

    Article  Google Scholar 

  • Smith, N. (2003). Gestures and beyond. A.B. Honors Thesis, University of California at Berkeley. Retrieved July 8 2008, from http://www.icsi.berkeley.edu/∼njs/thesis/.

  • Varela, F., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT Press.

    Google Scholar 

  • Walkerdine, V. (1988). The mastery of reason. London: Routledge.

    Google Scholar 

Download references

Acknowledgements

The research reported in this article was supported by a LaSallian Scholar grant from Saint Mary’s College; the writing took place during a scholarly leave at the University of California at San Diego funded by the Spencer Grant #200700151.

Author information

Authors and Affiliations

  1. Saint Mary’s College of California, 1928 Saint Mary’s Road, Moraga, CA, 94575, USA

    Laurie D. Edwards

Authors
  1. Laurie D. Edwards
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laurie D. Edwards.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(MOV 1.10 MB)

(MOV 1.06 MB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Edwards, L.D. Gestures and conceptual integration in mathematical talk. Educ Stud Math 70, 127–141 (2009). https://doi.org/10.1007/s10649-008-9124-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-008-9124-6

Keywords

Search

Navigation