Research mathematicians’ practices in selecting mathematical problems

Morten Misfeldt, Mikkel Willum Johansen

    Research output: Contribution to journalJournal articleResearchpeer-review

    10 Citations (Scopus)

    Abstract

    Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to what extent our results can be used to inform, criticize, and develop educational practice at various levels. Selecting and posing problems is far from simple. In fact, it is considered hard, complex, and of crucial importance. A number of criteria concerning personal interest, continuity with previous work, the danger of getting stuck, and how fellow mathematicians will respond to the findings are considered when mathematicians think about whether to approach a specific problem. These results add to previous investigations of mathematicians’ practice and suggest that mathematics education research could further investigate how students select and develop problems, work with multiple problems over a longer period of time, and use the solutions to problems to support the development of new problems. Furthermore, the negative emotional aspects of being stuck in problem solving and students’ conceptions of solvability and relevance of or interest in a mathematical problem are areas of research suggested by our study.
    Original languageEnglish
    JournalEducational Studies in Mathematics
    Volume89
    Issue number3
    Pages (from-to)357-373
    Number of pages17
    ISSN0013-1954
    DOIs
    Publication statusPublished - 1 Jul 2015

    Keywords

    • Mathematical practice
    • Mathematicians
    • Problem choice
    • Problem solving

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