Material representations in mathematical research practice

Mikkel Willum Johansen, Morten Misfeldt

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Mathematicians’ use of external representations constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical basis of the article consists of a qualitative interview study we conducted with active research mathematicians. In our analysis of the empirical material, we primarily used the empirically based frameworks provided by distributed cognition and cognitive semantics as well as the broader theory of cognitive integration as an analytical lens. We conclude that research mathematicians engage in generative feedback loops with material representations, that they use representations to facilitate the use of experiences of handling the physical world as a resource in mathematical work, and that their use of representations is socially sanctioned and enabled. These results verify the validity of the cognitive frameworks used as the basis for our analysis, but also show the need for augmentation and revision. Especially, we conclude that the social and cultural context cannot be excluded from cognitive analysis of mathematicians’ use of external representations. Rather, representations are socially sanctioned and enabled in an enculturation process.
Original languageEnglish
JournalSynthese
Pages (from-to)1-21
Number of pages21
ISSN0039-7857
DOIs
Publication statusE-pub ahead of print - 2020

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Keywords

  • Mathematical practice
  • Mathematical cognition
  • Embodied cognition
  • Distributed cognition
  • Cognitive semantics
  • Enculturation
  • External representations
  • Diagrams

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