Themes and Interplay of Beliefs in Mathematical Reasoning
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Upper secondary students’ task solving reasoning was analysed with a focus on arguments for strategy choices and conclusions. Passages in their arguments for reasoning that indicated the students’ beliefs were identified and, by using a thematic analysis, categorized. The results stress three themes of beliefs used as arguments for central decisions: safety, expectations and motivation. Arguments such as ‘I don’t trust my own reasoning’, ‘mathematical tasks should be solved in a specific way’ and ‘using this specific algorithm is the only way for me to solve this problem’ exemplify these three themes. These themes of beliefs seem to interplay with each other, for instance in students’ strategy choices when solving mathematical tasks.
Key wordsbeliefs mathematical reasoning upper secondary school
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- Ball, D. & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 27–44). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Frank, M. L. (1988). Problem solving and mathematical beliefs. Arithmetic Teacher, 35(5), 32–34.Google Scholar
- Fransisco, J. M. & Hähkiöniemi, M. (2011). Students’ ways of reasoning about nonlinear functions in guess-my-rule games. International Journal of Science and Mathematics Education. doi: 10.1007/s10763-011-9310-3.
- Furinghetti, F. & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In E. Pehkonen, G. C. Leder & G. Törner (Eds.), Beliefs: A hidden variable in Mathematics education? (pp. 39–57). Dordrecht: Kluwer.Google Scholar
- Green, T. F. (1971). The activities of teaching. New York: McGraw-Hill.Google Scholar
- Hannula, M.S. (2004). Affect in mathematical thinking and learning. PhD thesis, Finland: University of Turku.Google Scholar
- Hannula, M. S. (2006). Affect in mathematical thinking and learning: Towards integration of emotion, motivation and cognition. In J. Maasz & W. Schloeglmann (Eds.), New Mathematics Education Research and Practice (pp. 209–232). Rotterdam: Sense Publishers.Google Scholar
- Kloosterman, P. (2002). Beliefs about mathematics and mathematics learning in the secondary school. In E. Pehkonen, G. C. Leder & G. Törner (Eds.), Beliefs: A hidden variable in Mathematics education? (pp. 39–57). Dordrecht: Kluwer.Google Scholar
- Lester, F. K., Garofalo, J. & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving. A new perspective (pp. 75–88). New York: Springer.CrossRefGoogle Scholar
- McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning (pp. 575–596). New York: Macmillan Publishing Company.Google Scholar
- National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: The Council.Google Scholar
- Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In Third Mediterranean conference on mathematics education (pp. 115–124).Google Scholar
- Op’t Eyende, P., De Corte, E. & Verschaffel, L. (2006). “Accepting emotional complexity”: A socio-constructivist perspective on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, 35(2), 189–206.Google Scholar
- Pólya, G. (1945). How to solve it. Princeton: Princeton University Press.Google Scholar
- Presmeg, N. C. (1993). Mathematics—‘A bunch of formulas’? Interplay of beliefs and problem solving styles. In I. Hirabayashi, N. Nohda, K. Shigematsu & F.-L. Lin (Eds.), Proceedings of the 17th PME International Conference, 3 (pp. 57–64)Google Scholar
- Schoenfeld, A. (1985). Mathematical problem solving. Orlando: Academic.Google Scholar
- Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning (pp. 334–370). New York: Macmillan Publishing Company.Google Scholar
- Skemp, R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9–15.Google Scholar
- Thompson, A. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning (pp. 127–146). New York: Macmillan Publishing Company.Google Scholar