Why ‘scaffolding’ is the wrong metaphor: the cognitive usefulness of mathematical representations

Synthese:1-14 (2018)
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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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Brendan Larvor
University of Hertfordshire

Citations of this work

The Tools of Enculturation.Richard Menary & Alexander Gillett - 2022 - Topics in Cognitive Science 14 (2):363-387.
A Pattern Theory of Scaffolding.Albert Newen & Regina E. Fabry - forthcoming - Review of Philosophy and Psychology:1-26.

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References found in this work

Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: 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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