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@article{a1346d2b2d7a4aba80d9e71b141cb495,
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",
issn = "0039-7857",
publisher = "Springer Netherlands",

}

RIS

TY - JOUR

T1 - Why 'scaffolding' is the wrong metaphor

T2 - the cognitive usefulness of mathematical representations.

AU - Larvor, Brendan

PY - 2018/12/4

Y1 - 2018/12/4

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

UR - http://www.scopus.com/inward/record.url?scp=85057714199&partnerID=8YFLogxK

U2 - 10.1007/s11229-018-02039-y

DO - 10.1007/s11229-018-02039-y

M3 - Article

JO - Synthese

JF - Synthese

SN - 0039-7857

ER -