Abstract
This paper examines how a person’s gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures to construct a graphical anti-derivative while working on a professional development task in a calculus modelling activity. Results indicate that mathematical gesture spaces can encourage mathematical experimentation, lighten the cognitive load for students and can be limited by a person’s physical constraints.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alexander, J. C. (2008). Mathematical blending. Retrieved on February 22, 2010, from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1404844.
Alibali, M., & diRusso, A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14, 37–56.
Arzarello, F., & Paola, D. (2007). Semiotic games: The role of the teacher. In J-H. Woo, H-C. Lew, K-S. Park, & D-Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 17–24). Seoul: PME.
Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97–109.
Arzarello, F., & Robutti, O. (2008). Framing the embodied mind approach within a multimodal paradigm. In L. English (Ed.), Handbook of international research in mathematics education (pp. 720–749). New York: Routledge.
Arzarello, F., Thomas, M. O. J., Corballis, M. C., Hamm, J. P., Iwabuchi, S., Lim, V. K., et al. (2009). Didactical consequences of semantically meaningful mathematical gestures. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 57–64). Thessaloniki, Greece: PME.
Bjuland, R., Cestari, M. L., & Borgersen, H. E. (2008). The interplay between gesture and discourse as mediating devices in collaborative mathematical reasoning: A multimodal approach. Mathematical Thinking and Learning, 10, 271–292.
Broaders, S., Cook, S. W., Mitchell, Z., & Goldin-Meadow, S. (2007). Making children gesture brings out implicit knowledge and leads to learning. Journal of Experimental Psychology. General, 136, 539–550.
Bruner, J. S. (1966). The process of education: Towards a theory of instruction. New York: Norton.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–604.
Diénès, Z. P. (1960). Building up mathematics (4th ed.). London: Hutchinson.
Diénès, Z. P. (1963). An experimental study of mathematics learning. London: Hutchinson.
Edwards, L. D. (2009). Gestures and conceptual integration in mathematical talk. Educational Studies in Mathematics, 70, 127–141.
Fauconnier, G. (1998). Mental spaces, language modalities, and conceptual integration. In M. Tomasello (Ed.), The new psychology of language (pp. 251–279). Mahwah: Erlbaum.
Fauconnier, G., & Turner, M. (2002). How we think: Conceptual blending and the mind’s hidden complexities. New York: Basic Books.
Goodwin, C. (2000). Gesture, aphasia, and interaction. In D. McNeill (Ed.), Language and gesture (pp. 84–98). Cambridge: Cambridge University Press.
Haviland, J. (2000). Pointing, gesture spaces, and mental maps. In D. McNeill (Ed.), Language and gesture (pp. 13–47). Cambridge: Cambridge University Press.
Kendon, A. (1988). How gestures can become like words. In F. Poyatos (Ed.), Cross-cultural perspectives in nonverbal communication (pp. 131–141). Toronto: Hogrefe.
Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591–646). Mahwah: Erlbaum.
Liddell, S. K. (1996). Spatial representation in discourse: Comparing spoken and signed language. Lingua, 98, 145–167.
Liddell, S. K. (1998). Grounded blends, gestures and conceptual shifts. Cognitive Linguistics, 9(3), 283–314.
Liddell, S. K. (2000). Blended spaces and deixis in sign language discourse. In D. McNeill (Ed.), Language and gesture (pp. 331–357). Cambridge: Cambridge University Press.
Lim, V. K., Wilson, A. J., Hamm, J. P., Phillips, N., Iwabuchi, S., Corballis, M. C., et al. (2009). Semantic processing of mathematical gestures. Brain and Cognition, 71, 306–312.
McNeill, D. (1992). Hand and mind: What gestures reveal about thought. Chicago: The University of Chicago Press.
McNeill, D. (2005). Gesture and thought. Chicago: University of Chicago Press.
Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and graphing. Cognition and Instruction, 16(2), 119–172.
Núñez, R. (2004). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. In F. Iida, R. Pfeifer, L. Steels, & Y. Kuniyoshi (Eds.), Embodied artificial intelligence (pp. 54–73). Berlin: Springer.
Parrill, F., & Sweetser, E. (2004). What we mean by meaning. Gesture, 4(2), 197–219.
Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126.
Reynolds, F., & Reeve, R. (2002). Gesture in collaborative mathematics problem-solving. Journal of Mathematical Behavior, 20, 447–460.
Roth, W.-M. (1994). Thinking with hands, eyes, and signs: Multimodal science talk in a grade 6/7 unit on simple machines. Interactive Learning Environments, 4(2), 170–187.
Sfard, A. (2000). Steering (dis)course between metaphors and rigor: Using focal analysis to investigate an emergence of mathematical objects. Journal for Research in Mathematics Education, 31(3), 296–327.
Sinclair, N., & Tabaghi, S. G. (2010). Drawing space: Mathematicians’ kinetic conceptions of eigenvectors. Educational Studies in Mathematics, 74, 223–240.
Sweetser, E. (2007). Looking at space to study mental spaces. In M. Gonzalez-Marquez, I. Mittelberg, S. Coulson, & M. J. Spivey (Eds.), Methods in cognitive linguistics (pp. 201–224). Philadephia: John Benjamins North America.
Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4, 295–312.
Tall, D. O. (2004). Building theories: The three worlds of mathematics. For the Learning of Mathematics, 24(1), 29–32.
Tall, D. O. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20(2), 5–24.
Tall, D. O., Thomas, M. O. J., Davis, G., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behavior, 18(2), 223–241.
Yoon, C., Dreyfus, T., & Thomas, M. O. J. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, 22(2), 141–157.
Yoon, C., Thomas, M. O. J., & Dreyfus, T. (2009). Gestures and virtual space. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 409–416). Thessaloniki, Greece: PME.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yoon, C., Thomas, M.O.J. & Dreyfus, T. Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures. Educ Stud Math 78, 371–393 (2011). https://doi.org/10.1007/s10649-011-9329-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-011-9329-y