Research output: Contribution to journal › Article

**Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations. .** / Larvor, Brendan.

Research output: Contribution to journal › Article

Larvor, B 2018, 'Why 'scaffolding' is the wrong metaphor: the cognitive usefulness of mathematical representations. ', *Synthese*. https://doi.org/10.1007/s11229-018-02039-y

Larvor, B. (2018). Why 'scaffolding' is the wrong metaphor: the cognitive usefulness of mathematical representations. . *Synthese*. https://doi.org/10.1007/s11229-018-02039-y

Larvor B. Why 'scaffolding' is the wrong metaphor: the cognitive usefulness of mathematical representations. . Synthese. 2018 Dec 4. https://doi.org/10.1007/s11229-018-02039-y

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title = "Why 'scaffolding' is the wrong metaphor: the cognitive usefulness of mathematical representations.",

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.",

keywords = "mathematical cognition, enculturation, scaffolding, algebra, notations, diagrams, Geometry",

author = "Brendan Larvor",

year = "2018",

month = "12",

day = "4",

doi = "10.1007/s11229-018-02039-y",

language = "English",

journal = "Synthese",

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N2 - 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.

AB - 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.

KW - mathematical cognition

KW - enculturation

KW - scaffolding

KW - algebra

KW - notations

KW - diagrams

KW - Geometry

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