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Relooking ‘look back’: a student’s attempt at problem solving using Pólya’s model. (English)
Int. J. Math. Educ. Sci. Technol. 43, No. 3, 357-369 (2012).
Summary: Against the backdrop of half a century of research in mathematics problem solving, Pólya’s last stage is especially conspicuous - by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, Conditions for promoting reasoning in problem solving: Insights from a longitudinal study, J. Math. Behav. 24(3-4) (2005), pp. 361-372 see ME 2007c.00117; J.A. Taylor and C. Mcdonald, Writing in groups as a tool for non-routine problem solving in first year university mathematics, Int. J. Math. Educ. Sci. Technol. 38(5) (2007), pp. 639-655, see ME 2008a.00250.), with little or no successful attempts at following through with the subjects. In this article, we describe a case study of how the innovation of a ‘Practical Worksheet’ within a new paradigm of a ‘Mathematics Practical’ enabled a high-achieving student to push beyond getting a solution for a problem to extending, adapting and generalizing his solution. The findings from this study indicate promise in achieving the learning of Polya’s model with notable success in the fourth stage, Look Back.
Classification: D53
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