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Commentary on Problem Solving Heuristics, Affect, and Discrete Mathematics: A Representational Discussion

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Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

The chapter by Goldin in this volume can be viewed as an attempt to suggest one future direction of problem solving in school mathematics. The major theme in Goldin’s chapter is that the domain of discrete mathematics has a great potential to increase students’ interest in exploring mathematics and develop problem-solving heuristics. In this commentary, I would like to situate my discussion of his chapter in the context of future directions of mathematical problem-solving research. I will start with a discussion of Goldin’s idea about discrete mathematics as a content domain to solve problems, then I will specifically discuss instructional objectives and problem-solving heuristics in the discrete mathematical domain. I end this commentary by pointing out a future direction for problem-solving research.

Preparation of this chapter has been supported in part by a grant from the National Science Foundation (ESI-0454739). Any opinions expressed herein are those of the author and do not necessarily represent the views of the National Science Foundation. I am very grateful for helpful discussion with Frank Lester in various occasions.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, USA

    Jinfa Cai

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  1. Jinfa Cai
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Correspondence to Jinfa Cai .

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Editors and Affiliations

  1. Dept. Mathematical Sciences, University of Montana-Missoula, Missoula, 59812-0864, U.S.A.

    Bharath Sriraman

  2. Centre for Learning Innovation, Queensland University of Technology, Victoria Park Road, Kelvin Grove, 4059, Australia

    Lyn English

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Cai, J. (2010). Commentary on Problem Solving Heuristics, Affect, and Discrete Mathematics: A Representational Discussion. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_25

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  • DOI: https://doi.org/10.1007/978-3-642-00742-2_25

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