TY - JOUR
T1 - Material representations in mathematical research practice
AU - Willum Johansen, Mikkel
AU - Misfeldt, Morten
PY - 2020/9/1
Y1 - 2020/9/1
N2 - Mathematicians’ use of external representations, such as symbols and diagrams, 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.
AB - Mathematicians’ use of external representations, such as symbols and diagrams, 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.
KW - mathematical practice
KW - mathematical cognition
KW - embodied cognition
KW - distributed cognition
KW - cognitive semantics
KW - enculturation
KW - external representations
KW - diagrams
KW - Mathematical practice
KW - Mathematical cognition
KW - Embodied cognition
KW - Distributed cognition
KW - Cognitive semantics
KW - Enculturation
KW - External representations
KW - Diagrams
U2 - 10.1007/s11229-018-02033-4
DO - 10.1007/s11229-018-02033-4
M3 - Journal article
SN - 0039-7857
SP - 1
EP - 21
JO - Synthese
JF - Synthese
ER -