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Four Mathematical Miniatures on Problem Posing

In: Problem Posing and Solving for Mathematically Gifted and Interested Students

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  • Lukas Baumanns

    (University of Cologne, Faculty of Mathematics and Natural Sciences, Institute of Mathematics Education)

Abstract

Understanding problem posing as an inherently mathematical activity has gained importance in recent years within mathematics education. Numerous empirical studies show a wide range of different problem-posing activities. This paper highlights the diversity of problem-posing activities based on considerations on subject-matter didactics. Based on definitions and conceptions of problem posing in mathematics education, four different problem-posing activities are first identified: 1) Problem posing as generating new problems, 2) problem posing as reformulating a given problem for problem solving, 3) problem posing as reformulating a given problem for investigation, and 4) problem posing as constructing tasks for others. Subsequently, each of these four problem-posing activities is illustrated by a mathematical miniature. In addition, the empirical research on each of these four problem-posing activities is summarized.

Suggested Citation

  • Lukas Baumanns, 2023. "Four Mathematical Miniatures on Problem Posing," Springer Books, in: Deniz Sarikaya & Lukas Baumanns & Karl Heuer & Benjamin Rott (ed.), Problem Posing and Solving for Mathematically Gifted and Interested Students, pages 3-25, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-41061-2_1
    DOI: 10.1007/978-3-658-41061-2_1
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