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Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration

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Abstract

This study examines the consequences of whole-body, multi-party activity for mathematics learning, both in and out of the classroom. We develop a theoretical framework that brings together contemporary theories related to social space, embodied cognition, and mathematical activity. Then, drawing on micro-ethnographic and case-comparative techniques, we examine and juxtapose two cases of implementing whole-body, collaborative movement to engage learners in the mathematics of number sense and ratio and proportion. Analytically foregrounding the interdependence among setting, embodied activity, and mathematical tools and practices, we illustrate how whole-body collaboration can transform how learners experience learning environments and make sense of important mathematical ideas. The analysis enriches our understanding of the changing spatial landscapes for learning and doing mathematics as well as how re-instating bodies in mathematics education can open up new forms of collective mathematical sense-making and activity.

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References

  • Abrahamson, D., & Sánchez-García, R. (2016). Learning is moving in new ways: The ecological dynamics of mathematics education. Journal of the Learning Sciences, 25(2), 203–239.

    Article  Google Scholar 

  • Alibali, M. W., & DiRusso, A. 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., & Nathan, M. J. (2012). Embodiment in mathematics teaching and learning: Evidence from learners’ and teachers’ gestures. Journal of the Learning Sciences, 21(2), 247–286.

    Article  Google Scholar 

  • Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70, 97–109.

    Article  Google Scholar 

  • Becker, H. S. (2014). What about Mozart? What about murder? Reasoning from cases. Chicago: The University of Chicago Press.

    Book  Google Scholar 

  • Church, R. B., & Goldin-Meadow, S. (1986). The mismatch between gesture and speech as an index of transitional knowledge. Cognition, 23(1), 43–71.

    Article  Google Scholar 

  • Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1&2), 113–163.

    Article  Google Scholar 

  • de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: The body in/of mathematics. Educational Studies in Mathematics, 83(3), 453–470.

    Article  Google Scholar 

  • Ferrara, F., & Ferrari, G. (2017). Agency and assemblage in pattern generalization: A materialist approach to learning. Educational Studies in Mathematics, 94(1), 21–36.

    Article  Google Scholar 

  • Foucault, M. (1979). Discipline and punish: The birth of the prison. New York: Vintage.

    Google Scholar 

  • Gerofsky, S. (2010). Mathematical learning and gesture: Character viewpoint and observer viewpoint in students’ graphs of functions. Gesture, 10(2), 321–343.

    Google Scholar 

  • Hall, R., & Nemirovsky, R. (2012). Introduction to the special issue: Modalities of body engagement in mathematical activity and learning. Journal of the Learning Sciences, 21(2), 207–215.

    Article  Google Scholar 

  • Hutchins, E. (2010). Enaction, imagination, and insight. In J. Stewart, O. Gapenne, & E. A. Di Paolo (Eds.), Enaction: Toward a new paradigm for cognitive science (pp. 425–450). Cambridge: MIT Press.

    Chapter  Google Scholar 

  • Jordan, B., & Henderson, A. (1995). Interaction analysis: Foundations and practice. Journal of the Learning Sciences, 4, 39–103.

    Article  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 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Lave, J., Murtaugh, M., & de la Rocha, O. (1984). The dialectic of arithmetic in grocery shopping. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context (pp. 67–94). Cambridge: Harvard University Press.

    Google Scholar 

  • Leander, K. M., Phillips, N. C., & Taylor, K. H. (2010). The changing social spaces of learning: Mapping new mobilities. Review of Research in Education, 34, 329–394.

    Article  Google Scholar 

  • Ma, J. Y. (2016). Designing disruptions for productive hybridity: The case of walking scale geometry. Journal of the Learning Sciences, 25, 335–371.

    Article  Google Scholar 

  • Ma, J. Y. (2017). Multi-party, whole-body interactions in mathematical activity. Cognition and Instruction, 35, 141–164.

    Article  Google Scholar 

  • Ma, J. Y., & Munter, C. (2014). The spatial production of learning opportunities in skateboard parks. Mind, Culture, and Activity, 21, 238–258.

    Article  Google Scholar 

  • Marghetis, T., Edwards, L. D., & Núñez, R. (2014). More than mere handwaving. In L. D. Edwards, F. Ferrara, & D. Moore-Russo (Eds.), Emerging perspectives on gesture and embodiment in mathematics (pp. 227–246). Charlotte: Information Age Publishing.

    Google Scholar 

  • Massey, D. (1999). Space-Time, ‘science’ and the relationship between physical geography and human geography. Transactions of the Institute of British Geographers, 24(3), 261–276.

    Article  Google Scholar 

  • Massey, D. (2005). For space. London: Sage Publications Limited.

    Google Scholar 

  • Meyer, C., Streeck, J., & Jordan, J. S. (Eds.). (2017). Intercorporeality: Emerging socialities in interaction. New York: Oxford University Press.

    Google Scholar 

  • Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics, 70(2), 159–174.

    Article  Google Scholar 

  • Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2012). Gesture and imagination: On the constitution and uses of phantasms. Gesture, 12(2), 130–165.

    Article  Google Scholar 

  • Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2013). Playing mathematical instruments: Emerging perceptuomotor integration with an interactive mathematics exhibit. Journal for Research in Mathematics Education, 44(2), 372–415.

    Article  Google Scholar 

  • Nemirovsky, R., Rasmussen, C., Sweeney, G., & Wawro, M. (2012). When the classroom floor becomes the complex plane: Addition and multiplication as ways of bodily navigation. Journal of the Learning Sciences, 21(2), 287–323.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nespor, J. (1997). Tangled up in school: Politics, space, bodies, and signs in the educational process. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Nespor, J. (2000). School field trips and the curriculum of public spaces. Journal of Curriculum Studies, 32(1), 25–43.

    Article  Google Scholar 

  • Noble, T., DiMattia, C., Nemirovsky, R., & Barros, R. (2006). Making a circle: Tool use and the spaces where we live. Cognition and Instruction, 24(4), 387–437.

    Article  Google Scholar 

  • Pink, S. (2011). From embodiment to emplacement: Re-thinking competing bodies, senses and spatialities. Sport, Education and Society, 16, 343–355.

    Article  Google Scholar 

  • Radford, L. (2009a). ‘No! He starts walking backwards!’: Interpreting motion graphs and the question of space, place and distance. ZDM, 41(4), 467–480.

    Article  Google Scholar 

  • Radford, L. (2009b). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies of Mathematics, 70, 111–126.

    Article  Google Scholar 

  • Radford, L., Arzarello, F., Edwards, L., & Sabena, C. (2017). The multimodal material mind: Embodiment in mathematics education. In J. Cai (Ed.), The compendium for research in mathematics education (pp. 700–721). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Roth, W. M. (2001). Gestures: Their role in teaching and learning. Review of Educational Research, 71(3), 365–392.

    Article  Google Scholar 

  • Saltman, K. J. (2017). Scripted bodies: Corporate power, smart technologies, and the undoing of public education. New York: Routledge.

    Google Scholar 

  • Sfard, A. (2009). What’s all the fuss about gestures? A commentary. Educational Studies in Mathematics, 70, 191–200.

    Article  Google Scholar 

  • Stevens, R. (2012). The missing bodies of mathematical thinking and learning have been found. Journal of the Learning Sciences, 21, 337–346.

    Article  Google Scholar 

  • Streeck, J., & Mehus, S. (2005). Microethnography: The study of practices. In K. L. Fitch & R. E. Sanders (Eds.), Handbook of language and social interaction (pp. 381–404). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Winter, B., Marghetis, T., & Matlock, T. (2015). Of magnitudes and metaphors: Explaining cognitive interactions between space, time, and number. Cortex, 64, 209–224.

    Article  Google Scholar 

  • Yin, R. K. (2009). Case study research: Design and methods (5th ed.). Thousand Oaks, CA: Sage Publications.

    Google Scholar 

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Acknowledgments

All opinions expressed are those of the authors and do not necessarily represent the foundation. We would like to thank Max Ray, Malke Rosenfeld, Sarah Radke, and our research participants for their contributions to this work. We also thank Nicole Ferry for copy-editing and formatting assistance.

Funding

This research was supported by the National Science Foundation (DRL-0840320 and DRL-0816406) and New York University.

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Author notes

  1. Both authors contributed equally to this article and are listed alphabetically.

Authors and Affiliations

  1. Department of Teaching and Learning, Washington State University, Cleveland Hall 321, Pullman, WA, 99164-2132, USA

    Molly L. Kelton

  2. New York University, 239 Greene St., 4th Floor, New York, NY, 10003, USA

    Jasmine Y. Ma

Authors
  1. Molly L. Kelton
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  2. Jasmine Y. Ma
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Correspondence to Molly L. Kelton.

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The authors declare that they have no conflict of interest.

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Kelton, M.L., Ma, J.Y. Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration. Educ Stud Math 98, 177–196 (2018). https://doi.org/10.1007/s10649-018-9805-8

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  • DOI: https://doi.org/10.1007/s10649-018-9805-8

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