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A social perspective on technology-enhanced mathematical learning: from collaboration to performance

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Abstract

This paper documents both developments in the technologies used to promote learning mathematics and the influence on research of social theories of learning, through reference to the activities of the International Commission on Mathematical Instruction (ICMI), and argues that these changes provide opportunity for the reconceptualization of our understanding of mathematical learning. Firstly, changes in technology are traced from discipline-specific computer-based software through to Web 2.0-based learning tools. Secondly, the increasing influence of social theories of learning on mathematics education research is reviewed by examining the prevalence of papers and presentations, which acknowledge the role of social interaction in learning, at ICMI conferences over the past 20 years. Finally, it is argued that the confluence of these developments means that it is necessary to re-examine what it means to learn and do mathematics and proposes that it is now possible to view learning mathematics as an activity that is performed rather than passively acquired.

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References

  • Afanasiev, A., & Crowe, D. (2008). Current problems and challenges in distance teaching and learning. In M. Niss (Ed.), ICME-10 Proceedings (pp. 534–537). Denmark: Roskilde University.

  • Beatty, R., & Geiger, V. (2009). Technology, communication and collaboration: Re-thinking communities of inquiry, learning and practice. In C. Hoyles, & J.-B. Lagrange (Eds.), Digital technologies and mathematics teaching and learning: Rethinking the terrain. New York: Springer.

    Google Scholar 

  • Beatty, R., & Moss, J. (2006). Connecting grade 4 students from diverse urban classrooms: virtual collaboration to solve generalizing problems. In C. Hoyles, J.-B. Lagrange, L. Hung Son, & N. Sinclair (Eds.), Technology revisited: proceedings of the seventeenth study conference of the International Commission on Mathematical Instruction (pp. 27–36). Hanoi: Hanoi Institute of Technology.

  • Bold, M. (2006). Use of wikis is graduate course work. Journal of Interactive Learning Research, 17(1), 5–14.

    Google Scholar 

  • Boorstin, J. (1990). The hollywood eye: what makes movies work. New York: Harper Collins Publishers.

    Google Scholar 

  • Borba, M. C. (2009). Potential scenarios for Internet use in the mathematics classroom. ZDM, 41(4), 453–465.

    Article  Google Scholar 

  • Borba, M., & Gadanidis, G. (2008). Virtual communities and networks of practising mathematics teachers: The role of technology in collaboration. In T. Wood (Series Editor), & K. Krainer (Volume Editor), International handbook of mathematics teacher education, Vol. 3: Participants in mathematics teacher education: individuals, teams, communities, and networks (pp 181–209). Rotterdam: Sense Publishers.

  • Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking. New York: Springer.

    Google Scholar 

  • Carss, M. (1986). Prodeedings of the 5th international conference on mathematics education. Boston: Birkhauser.

  • Churchhouse, R. F. (1986). The influence of computers and informatics on mathematics and its teaching. London: Cambridge University Press.

    Google Scholar 

  • Cobb, P., & Bauersfeld, H. (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: L. Erlbaum Associates.

    Google Scholar 

  • Drijvers, P., & Stacey, K. (2008). Technology in mathematics education. In M. Niss (Ed.), ICME-10 Proceedings (pp. 281–286). Denmark: ICMI.

  • Fey, J. T. (1993). Technology and mathematics education at ICME-7. In J. A. Dossey (Ed.), American perspectives on the seventh international congress on mathematical education (pp. 6–11). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Fraser, R., Meissner, H., Ralston, T., Roseveare, D., & Mohyla, J. (1986). In M. Carss (Ed.), Proceedings of the 5th international conference on mathematics education (pp. 159–176). Boston: Birkhauser.

  • Gadanidis, G., & Borba, M. (2008). Our lives as performance mathematicians. For the Learning of Mathematics, 28(1), 44–51.

    Google Scholar 

  • Gadanidis, G., Hughes, J., & Borba, M. (2008). Students as performance mathematicians. Mathematics Teaching in the Middle School, 14(3), 168–175.

    Google Scholar 

  • Gadanidis, G., Jardine, R., & Sedig, C. (2007). Designing digital windows into mathematics. In C. Montgomerie & J. Seale (Eds.), Proceedings of ED-Media 2007 (pp. 3532–3537). Cheseapeake, VA: Association for the advancement of computing in education.

  • Gaulin, C., Hodgson, B. R., Wheeler, D. H., & Egsgard, J. C. (Eds.). (1994). Proceedings of the 7th international congress on mathematical education. Ainte-Foy, Quebec: Presses de l’Universite Laval.

  • Geiger, V. (2005). Master, servant, partner and extension of self: A finer grained view of this taxonomy. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Theory, research and practice, proceedings of the 28th annual conference of the Mathematics Education Research Group of Australia (pp. 369–376). Sydney: MERGA.

  • Geiger, V. (2006). More than tools: mathematically enabled technologies as partner and collaborator. In C. Hoyles, J.-B. Lagrange, Le. Hung Son, & N. Sinclair (Eds.), Technology revisited: proceedings of the seventeenth study conference of the international commission on mathematical instruction (pp. 182–189). Hanoi: Hanoi Institute of Technology.

  • Goos, M., Galbraith, P., & Renshaw, P. (1999). Establishing a community of practice in a secondary mathematics classroom. In L. Burton (Ed.), Learning mathematics: From hierarchies to networks (pp. 36–61). London: Falmer Press.

    Google Scholar 

  • Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2000). Reshaping teacher and student roles in technology-enriched classrooms. Mathematics Education Research Journal, 12(3), 303–320.

    Google Scholar 

  • Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. Journal of Mathematical Behavior, 22(1), 73–89.

    Article  Google Scholar 

  • Grant, L. (2006). Using wikis in school: A case study. Futurelab. http://www.futurelab.org.uk/resources/publications_reports_articles/discussion_papers/Discussion_Paper258/. Accessed 12 June 2007.

  • Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.

    Article  Google Scholar 

  • Harada, M. (2008). Spherical geometry: Do parallel lines meet? Fields Institute. http://www.fields.utoronto.ca/mathwindows/sphere/. Accessed 1 October 2008.

  • Healy, L., & Kaput, J. (2008). The role and use of technology in the teaching and learning of mathematics. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematics education (pp. 355–358). Denmark: Roskilde University.

  • Hirst, A., & Hirst, K. (Eds.). (1988). Proceedings of the sixth international congress on mathematical education. Budapest: Janos Bolyai Mathematical Society.

  • Hoyles, C. (2008). Reflections and transformations: A mathematical autobiography. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematics education (pp. 255–265). Denmark: Roskilde University.

    Google Scholar 

  • Hoyles, C., & Lagrange, J.-B. (2009). Digital technologies and mathematics teaching and learning: Rethinking the terrain. New York: Springer.

    Google Scholar 

  • Hoyles, C., Lagrange, J.-B., Le Hung, Son., & Sinclair, N. (Eds.). (2006). Technology revisited: proceedings of the seventeenth study conference of the international commission on mathematical instruction. Hanoi: Hanoi Institute of Technology.

    Google Scholar 

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. J. Bishop (Ed.), Second international handbook of mathematics education (pp. 323–349). Dordrecht: Kluwer.

    Google Scholar 

  • Hughes, J. (2008). The performative pull of research with new media. International Journal of Qualitative Methods, 7(2), 16–34.

    Google Scholar 

  • Jarvis, D. H. (2006). On-line professional development for mathematics educators: Overcoming significant barriers to the modelling of reform-oriented pedagogy. In C. Hoyles, J.-B. Lagrange, Le. Hung Son, & N. Sinclair (Eds.), Technology revisited: proceedings of the seventeenth study conference of the international commission on mathematical instruction (pp. 246–252). Hanoi: Hanoi Institute of Technology.

    Google Scholar 

  • Kaput, J. (1992). Technology in mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). New York: Macmillan.

    Google Scholar 

  • Kemp, M., Kissane, B., & Bradley, J. (1996). Graphics calculator use in examinations: Accident or design? Australian Senior Mathematics Journal, 10(1), 36–50.

    Google Scholar 

  • Knight, G. (1994). Mathematics in distance learning. In C. Gaulin, B. R. Hodgson, D. H. Wheeler, & J. C. Egsgard (Eds.), Proceedings of the 7th international congress on mathematics education (pp. 211–225). Ainte-Foy, Quebec: Presses de l’Universite Laval.

    Google Scholar 

  • Landow, G. P. (2006). Hypertext 3.0. Critical theory and new media in a era of globalization. Baltimore, MD: The John Hopkins University Press.

    Google Scholar 

  • Lankshear, C., & Knobel, M. (2006). New literacies: Everyday practices and classroom learning (2nd ed.). London: Open University Press.

    Google Scholar 

  • Lankshear, C., & Knobel, M. (2007). Sampling “the new” in new literacies. In M. Knobel & C. Lankshear (Eds.), A new literacies sampler (pp. 1–24). New York: Peter Lang.

    Google Scholar 

  • Lerman, S. (2000). The socio-cultural turn in studying the teaching and learning of mathematics. In H. Fujita, Y. Hashimoto, B. Hodgson, P. Y. Lee, S. Lerman, & T. Sawada (Eds.), Proceedings of the ninth international congress on mathematical education (pp. 157–158). Tokyo: Kluwer.

  • Levy, P. (1997). Collective Intelligence. New York: Plenum.

    Google Scholar 

  • Li, J., & Wisenbaker, J. M. (2008). Research and development in the teaching and learning of probability and statistics. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematics education (pp. 337–340). Denmark: Roskilde University.

  • Lichtenberg, B. K. (1993). The impact of the calculator on the elementary school curriculum: Reflections on ICME-7. In J. A. Dossey (Ed.), American perspectives on the seventh international congress on mathematical education (pp. 19–20). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Mandelbrot, B. B. (1994). Fractals, the computer, and mathematics education. In C. Gaulin, B. R. Hodgson, D. H. Wheeler, & J. C. Egsgard (Eds.), Proceedings of the 7th international congress on mathematics education (pp. 77–98). Ainte-Foy, Quebec: Presses de l’Universite Laval.

  • Mariotti, M. (2002). The influences of technological advances on students’ mathematics learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 695–723). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Mayo, J. (1993). Just one more computer, please. In J. A. Dossey (Ed.), American perspectives on the seventh international congress on mathematical education (p. 18). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Niss, M. (Ed.). (2008). Proceedings of the 10th international congress on mathematics education. Denmark: Roskilde University.

    Google Scholar 

  • Noddings, N. (1990). Constructivism in mathematics education. In R. Davis, C. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and of learning of mathematics (pp. 7–18). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Pea, R. (1985). Beyond amplification: Using the computer to reorganize mental functioning. Educational Psychologist, 20(4), 167–182.

    Article  Google Scholar 

  • Pea, R. (1993a). Learning scientific concepts through material and social activities: Conversational analysis meets conceptual change. Educational Psychologist, 28(3), 265–277.

    Article  Google Scholar 

  • Pea, R. (1993b). Practices of distributed intelligence and designs for education. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations (pp. 47–87). Cambridge: Cambridge University Press.

    Google Scholar 

  • Richardson, W. (2006). Blogs, wikis, Podcasts and other powerful Web tools for classrooms. Thousand Oaks, California: Corwin Press.

    Google Scholar 

  • Schrage, M. (2001). The relationship revolution. http://web.archive.org/web/20030602025739/http://www.ml.com/woml/forum/relation.htm. Accessed 12 July 2008.

  • Shumway, R. (1989). Technology, mathematics and the international congress. In T. Cooney (Ed.), American perspectives on the sixth international congress on mathematical education (pp. 15–20). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Sloan, M., & Olive, J. (2006). Distance learning: mathematical learning opportunities for rural schools in the United States. In L. Son, N. Sinclair, J.-B. Lagrange, & C. Hoyles (Eds.), Technology revisited: proceedings of the seventeenth ICMI study conference (pp. 518–523). Hanoi: Hanoi Institute of Technology.

    Google Scholar 

  • Sprague, D., Maddux, C., Ferdig, R., & Albion, P. (2007). Online education: Issues and research questions. Journal of Technology and Teacher Education, 15(2), 157–166.

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Education, University of Western Ontario, London, ON, Canada

    George Gadanidis

  2. Faculty of Education, Australian Catholic University, Brisbane, QLD, Australia

    Vince Geiger

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  1. George Gadanidis
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  2. Vince Geiger
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Gadanidis, G., Geiger, V. A social perspective on technology-enhanced mathematical learning: from collaboration to performance. ZDM Mathematics Education 42, 91–104 (2010). https://doi.org/10.1007/s11858-009-0213-5

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