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ERIC Number: EJ1039965
Record Type: Journal
Publication Date: 2014-Jan
Pages: 18
Abstractor: As Provided
ISSN: ISSN-0926-7220
La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy
Cable, John
Science & Education, v23 n1 p223-240 Jan 2014
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A