Synthese 197 (9):3743-3756 (2020)

Authors
Brendan Larvor
University of Hertfordshire
Abstract
The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least, scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.
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DOI 10.1007/s11229-018-02039-y
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References found in this work BETA

Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
Mathematics and Plausible Reasoning.George Polya - 1954 - Princeton: Princeton University Press.
The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.

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