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Improving of Mathematical Problem-Solving: Some New Ideas from Old Resources

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Posing and Solving Mathematical Problems

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

Abstract

The main focus of this chapter is on improvement of teaching of problem-solving.

In the introduction important and to some extent neglected issues of teaching problem-solving will be presented and discussed.

On this background the following questions and possible answers will be addressed:

How to combine the traditional mathematical curriculum with problem-solving, understanding, and creativity?

Pupils can construct rules for calculating with fractions themselves, conjectures as well as proofs of the Pythagorean and related theorems.

How history might help to better understand and foster mathematical problem-solving processes?

Observed problem-solving processes of pupils involved in well-known problems from calculating the area of a circle, fractions and calculus can be interpreted as reinvention of old and important heuristic strategies.

Finally, some recommendations are made for teacher education and teachers.

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Authors and Affiliations

  1. Friedrich-Schiller-University of Jena, Schwartauer Allee 6 b, Lübeck, 23554, Germany

    Bernd Zimmermann

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  1. Bernd Zimmermann
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Correspondence to Bernd Zimmermann .

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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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Zimmermann, B. (2016). Improving of Mathematical Problem-Solving: Some New Ideas from Old Resources. 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_6

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  • DOI: https://doi.org/10.1007/978-3-319-28023-3_6

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  • Online ISBN: 978-3-319-28023-3

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