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

Larvor, Brendan (2018) Why ‘scaffolding’ is the wrong metaphor: the cognitive usefulness of mathematical representations. [Preprint]

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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 (and plausibly for others), 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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Larvor, Brendanb.p.larvor@herts.ac.uk0000-0003-0921-1659
Additional Information: In Synthese
Keywords: Mathematical cognition; enculturation; scaffolding; algebra; notation; diagrams; geometry
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Practice
Specific Sciences > Cognitive Science
Depositing User: Dr Brendan Larvor
Date Deposited: 27 Nov 2018 15:52
Last Modified: 27 Nov 2018 15:52
Item ID: 15375
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Practice
Specific Sciences > Cognitive Science
Date: 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15375

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