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In Search of Structures: How Does the Mind Explore Infinity?

In Search of Structures: How Does the Mind Explore Infinity? When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g‐structures), arithmetic (a‐structures), fractal‐type (f‐structures), and density‐type (d‐structures). Students select different problem‐solving strategies depending on the structure they recognize within the problem domain. They naturally search for structures in challenging learning contexts. This tendency to search for structure might be a characteristic of human cognition and a necessary condition for human knowledge development. For example, specific fractal structures are intrinsic to concepts such as the numerical system that have been developed by the human race over a long period of time. When these structures are emphasized within teaching, they can facilitate the deep understanding of several basic concepts, in mathematics and beyond. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mind, Brain, and Education Wiley

In Search of Structures: How Does the Mind Explore Infinity?

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Publisher
Wiley
Copyright
© 2010 the Authors. Journal Compilation © 2010 International Mind, Brain, and Education Society and Blackwell Publishing, Inc.
ISSN
1751-2271
eISSN
1751-228X
DOI
10.1111/j.1751-228X.2010.01087.x
Publisher site
See Article on Publisher Site

Abstract

When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g‐structures), arithmetic (a‐structures), fractal‐type (f‐structures), and density‐type (d‐structures). Students select different problem‐solving strategies depending on the structure they recognize within the problem domain. They naturally search for structures in challenging learning contexts. This tendency to search for structure might be a characteristic of human cognition and a necessary condition for human knowledge development. For example, specific fractal structures are intrinsic to concepts such as the numerical system that have been developed by the human race over a long period of time. When these structures are emphasized within teaching, they can facilitate the deep understanding of several basic concepts, in mathematics and beyond.

Journal

Mind, Brain, and Education – Wiley

Published: Jun 1, 2010

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