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On the Role of Corporeality, Affect, and Metaphoring in Problem-Solving

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Posing and Solving Mathematical Problems

Part of the book series: Research in Mathematics Education ((RME))

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Abstract

We explore the role of corporeality, affect, and metaphoring in problem-solving. Our experimental research background includes average and gifted Chilean high school students, juvenile offenders, prospective teachers, and mathematicians, tackling problems in a workshop setting. We report on observed dramatic changes in attitude toward mathematics triggered by group working for long enough periods on problem-solving, and we describe ways in which (possibly unconscious) metaphoring determines how efficiently and creatively you tackle a problem. We argue that systematic and conscious use of metaphoring may significantly improve performance in problem-solving. The effect of the facilitator ignoring the solution of the problem being tackled is also discussed.

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References

  • Arcavi, A., Kessel, C., Meira, L., & Smith, J. (1998). Teaching mathematical problem solving: A microanalysis of an emergent classroom community. In A. Schoenfeld, E. Dubinsky, & J. Kaput (Eds.), Research in collegiate mathematics education III (pp. 1–70). Providence, RI: American Mathematical Society.

    Chapter  Google Scholar 

  • English, L. (Ed.). (1997). Mathematical reasoning: Analogies, metaphors, and images. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Flessas, J. (1997). L’impact du style cognitive sur les apprentissages, Revue Éducation Francoph., 25, n° 2. Retrieved from http://www.acelf.ca/c/revue/revuehtml/25-2/r252-03.html

  • Flessas, J., & Lussier, F. (2005). La neuropsychologie de l’enfant. Paris, France: Dunod.

    Google Scholar 

  • Hannula, M. (2013). Affect in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 23–27). doi 10.1007/SpringerReference_331465

    Google Scholar 

  • Isoda, M., & Katagiri, S. (2012). Mathematical thinking: How to develop it in the classroom. Singapore, Singapore: World Scientific.

    Book  Google Scholar 

  • Isoda, M., & Nakamura, T. (2010). Mathematics education theories for lesson study: Problem solving approach and the curriculum through extension and integration. Journal of Japan Society of Mathematical Education, 92(11), 1–157.

    Google Scholar 

  • Järvinen, E.-M., & Twyford, J. (2000). The influences of socio-cultural interaction upon children’s thinking and actions in prescribed and open-ended problem solving situations. International Journal of Technology and Design Education, 10, 21–41. Dordrecht: Kluwer Academic Publishers.

    Article  Google Scholar 

  • Lakoff, G., & Nuñez, R. (2000). Where mathematics comes from. New York: Basic Books.

    Google Scholar 

  • Liljedahl, P. (2014). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices. New York, NY: Springer.

    Google Scholar 

  • Luria, A. (1973). The working brain. New York: Penguin.

    Google Scholar 

  • Pehkonen, E. (1995). Introduction: Use of open-ended problems. ZDM, 27(2), 55–57.

    Google Scholar 

  • Pólya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press. 2nd edition, 1957.

    Google Scholar 

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

    Google Scholar 

  • Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205–235). Rotterdam, Netherlands: Sense.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic.

    Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), The handbook of research on the teaching and learning of mathematics (pp. 334–370). New York: Macmillan.

    Google Scholar 

  • Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. New York: Routledge.

    Google Scholar 

  • Schoenfeld, A. (2012). Social dynamics for supporting creative mathematical thinking and problem solving, International Congress in Mathematical Education (pp. 4478–4487). Seoul, Korea, TSG22-6.

    Google Scholar 

  • Schwank, I. (1999). On predicative versus functional cognitive structures, European Research. In Proceedings of CERME 1 (The First Conference of The European Society for Research in Mathematics Education) (pp. 84–96).

    Google Scholar 

  • Sfard, A. (1997). Commentary: On metaphorical roots of conceptual growth. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 339–371). London, England: Erlbaum.

    Google Scholar 

  • Sfard, A. (2009). Metaphors in education. In H. Daniels, H. Lauder, & J. Porter (Eds.), Educational theories, cultures and learning : A critical perspective (pp. 39–50). New York: Routledge.

    Google Scholar 

  • Silver, E. A. (1985). Research on teaching mathematical problem solving: Some underrepresented themes and needed directions. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247–266). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Soto-Andrade, J. (2006). Un monde dans un grain de sable: Métaphores et analogies dans l’apprentissage des maths. Annales de Didactique et de Sciences Cognitives, 11, 123–147.

    Google Scholar 

  • Soto-Andrade, J. (2007). Metaphors and cognitive styles in the teaching-learning of mathematics. In D. Pitta-Pantazi, & J. Philippou (Eds.). Proceedings CERME 5 (pp. 191–200). Retrieved May 21, 2008, from http://ermeweb.free.fr/CERME5b/

  • Soto-Andrade J. (2013). Metaphors in mathematics education. In: Lerman S. (Ed.) Encyclopedia of mathematics education. Berlin, Germany: Springer. (pp. 447–453) Retrieved Oct 1, 2013, from (www.springerreference.com). DOI: 10.1007/SpringerReference_313292

  • Soto-Andrade, J., & Reyes-Santander, P. (2012) Mathematical cognition in juvenile offenders: A case study, en Proceedings ICME 12 (July 2012) (pp. 4721–4730). Seoul, Korea.

    Google Scholar 

  • Thurston, W. (1998). How to see 3-manifolds. Classical and Quantum Gravity, 15, 2545–2555.

    Article  Google Scholar 

  • Varela, F. J. (1987). Lying down a path in walking. In W. I. Thompson (Ed.), Gaia: A way of knowing (pp. 48–64). Hudson, NY: Lindisfarne Press.

    Google Scholar 

  • Varela, F. J. (1999). Ethical know-how: Action, wisdom, and cognition. Stanford, CA: Stanford University Press.

    Google Scholar 

  • vom Hofe, R. (1995). Grundvorstellungen mathematischer inhalte. Heidelberg, Germany: Spektrum Akademischer Verlag.

    Google Scholar 

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Acknowledgments

Support from University of Chile RIA Domeyko Project and funding from PIA-CONICYT Basal Funds for Centers of Excellence Project BF0003 is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Chile, Santiago, Chile

    Nicolás Libedinsky

  2. CIAE and Department of Mathematics, Faculty of Science, University of Chile, Santiago, Chile

    Jorge Soto-Andrade

Authors
  1. Nicolás Libedinsky
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  2. Jorge Soto-Andrade
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Corresponding author

Correspondence to Jorge Soto-Andrade .

Editor information

Editors and Affiliations

  1. University of Chile, Santiago, Chile

    Patricio Felmer

  2. University of Helskini, Helsinki, Finland

    Erkki Pehkonen

  3. University of Georgia, Athens, USA

    Jeremy Kilpatrick

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Libedinsky, N., Soto-Andrade, J. (2016). On the Role of Corporeality, Affect, and Metaphoring in Problem-Solving. In: Felmer, P., Pehkonen, E., Kilpatrick, J. (eds) Posing and Solving Mathematical Problems. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-28023-3_4

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  • DOI: https://doi.org/10.1007/978-3-319-28023-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28021-9

  • Online ISBN: 978-3-319-28023-3

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