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Reformulating: Approaching Mathematical Problem Solving as Inquiry

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Posing and Solving Mathematical Problems

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

Abstract

The Gestalt psychologist Karl Duncker (1903–1940) characterized problem solving as getting from where you are to where you want to be through successive reformulations of the problem until it becomes something you can manage. That view can be seen in a recent European project to promote inquiry as a means of learning mathematics and attracting students to its study. It can also be seen in increased research efforts to study problem formulation in mathematics. Considerations of how to educate teachers of mathematics to approach problem solving as inquiry should include attention to questions of metacognition and to the cognitive demand of a problem—in much the same manner as George Pólya (1887–1985) promoted such attention. For Duncker and Pólya, we solve problems by replacing our unsuccessful efforts by successful ones through a heuristic inquiry process.

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Authors and Affiliations

  1. University of Georgia, 105 Aderhold, Athens, GA, 30602-7124, USA

    Jeremy Kilpatrick

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  1. Jeremy Kilpatrick
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Correspondence to Jeremy Kilpatrick .

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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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Kilpatrick, J. (2016). Reformulating: Approaching Mathematical Problem Solving as Inquiry. 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-28023-3_5

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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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