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Views of cognition: different lenses for ‘looking-in’ on classrooms

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Abstract

The evolution of different theories of cognition over the years has given mathematics education researchers new tools for highlighting particular characteristics of classroom issues to enable more detailed investigation of how students learn mathematics. In the past there has been a strong dominance of the dualistic view separating body and mind. In recent times, however, the body has been given a more central role in shaping the mind. This has led to the situation where some long-standing conundrums of mathematics education have become more tractable to researchers. Similarly, using older ideas in new ways, light is being shone on what is possible at different stages of development or different levels of schooling. In this issue different views of cognition have been mined by the authors of different articles to frame studies and analyses or invent and apply new tools. They bring new lenses for looking-in on classrooms, a fresh view with old lenses and new methodological tools to the fore. Using a small selection of the articles of the issue the empowerment that differing views of cognition have enabled for mathematics education research is demonstrated.

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References

  • Anderson, J. R. (1995). Cognitive psychology and its implications (4th ed.). New York: Freeman.

    Google Scholar 

  • Ernest, P. (2010). Reflections on theories of learning. In B. Sriraman & L. D. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 39–52). Heidelberg: Springer.

    Chapter  Google Scholar 

  • Funahashi, Y., & Hino, K. (2014). Teacher’s role in guiding children’s mathematical ideas toward meeting lesson objectives. ZDM—The International Journal on Mathematics Education, 46(3) (this issue). doi:10.1007/s11858-014-0592-0.

  • Keene, K. A., Rasmussen, C., & Stephan, M. (2012). Gestures and a chain of signification: The case of equilibrium solutions. Mathematics Education Research Journal, 24(3), 347–369.

    Article  Google Scholar 

  • Luria, A. R. (1966). Human brain and psychological processes. (Trans. B. Haigh) New York: Harper & Row.

  • Luria, A. R. (1973). The working brain: An introduction to neuropsychology. (Trans. B. Haigh) London: Penguin.

  • Massaro, D. W., & Cowan, N. (1993). Information processing models: Microscopes of the mind. Annual Review of Psychology, 44, 175–200.

    Article  Google Scholar 

  • Neisser, U. (1967). Cognitive psychology. New York: Appleton-Century-Crofts.

    Google Scholar 

  • Nunes,T., Bryant, P., Evans, D., Gottardis, L., & Terlesti, M.-E. (2014). The cognitive demands of understanding the sample space. ZDM—The International Journal on Mathematics Education, 46(3) (this issue). doi:10.1007/s11858-014-0581-3.

  • Pegg, J., & Tall, D. (2010). The fundamental cycle of concept construction underlying various theoretical frameworks. In B. Sriraman & L. D. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 173–192). Heidelberg: Springer.

    Chapter  Google Scholar 

  • Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126.

    Article  Google Scholar 

  • Radford, L. (2014). Towards an embodied, cultural, and material conception of mathematics cognition. ZDM—The International Journal on Mathematics Education, 46(3) (this issue). doi:10.1007/s11858-014-0591-1.

  • Rumelhart, D. E., & McCelland, J. L. (1986). Parallel distributed processing: Explorations in the microstructures of cognition (Vol. 1). Cambridge: MIT Press.

    Google Scholar 

  • Schoenfeld, A. H. (1987). Cognitive science and mathematics education. Hillsdale: Erlbaum.

    Google Scholar 

  • Stillman, G. A., & Galbraith, P. L. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157–195.

    Article  Google Scholar 

  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.

    Article  Google Scholar 

  • Vygotsky, L. S., & Luria, A. (1994). Tool and symbol in child development. In R. V. D. Veer & J. Valsiner (Eds.), The Vygotsky reader (pp. 99–174). Oxford: Blackwell.

    Google Scholar 

  • Wawro, M. (2014). Student reasoning about the invertible matrix theorem in linear algebra. ZDM—The International Journal on Mathematics Education, 46(3) (this issue). doi:10.1007/s11858-014-0579-x.

  • Williams, G. (2006). Autonomous looking-into support creative mathematical thinking: Capitalising on activity in Australasian LPS classrooms. In D. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 221–236). Rotterdam: Sense.

    Google Scholar 

  • Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Education and Arts, Australian Catholic University, 1200 Mair Street, Ballarat, VIC, 3350, Australia

    Gloria Ann Stillman

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  1. Gloria Ann Stillman
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Correspondence to Gloria Ann Stillman.

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Stillman, G.A. Views of cognition: different lenses for ‘looking-in’ on classrooms. ZDM Mathematics Education 46, 493–496 (2014). https://doi.org/10.1007/s11858-014-0601-3

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  • DOI: https://doi.org/10.1007/s11858-014-0601-3

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