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Idealisierungsprozesse — ihr logisches Verständnis und ihre didaktische Funktion

Idealisierungsprozesse — ihr logisches Verständnis und ihre didaktische Funktion Idealisation is a most important process of concept formation (besides recursion and abstraction) mainly known from the construction of ideas in physics. First, the considerations proposed below contain an attempt to make sense of applying a more general notion of idealisation to mathematics, too. Its features are discussed by examples from elementary algebra, probability, and geometry supplemented by a proposal for giving a more formalized definition. Second, some didactical functions of ‘ideative’ concept formation are considered, that is opening up the real world, pointing out the purposes behind mathematical ideas, understanding concepts and methods genetically. As a special case, the author formulates a principle of operative concept formation in geometry teaching. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal für Mathematik-Didaktik Springer Journals

Idealisierungsprozesse — ihr logisches Verständnis und ihre didaktische Funktion

Journal für Mathematik-Didaktik , Volume 1 (2) – Dec 20, 2013

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References (41)

Publisher
Springer Journals
Copyright
Copyright
Subject
Education; Mathematics Education; Mathematics, general; Science Education; History of Mathematical Sciences
ISSN
0173-5322
DOI
10.1007/BF03338630
Publisher site
See Article on Publisher Site

Abstract

Idealisation is a most important process of concept formation (besides recursion and abstraction) mainly known from the construction of ideas in physics. First, the considerations proposed below contain an attempt to make sense of applying a more general notion of idealisation to mathematics, too. Its features are discussed by examples from elementary algebra, probability, and geometry supplemented by a proposal for giving a more formalized definition. Second, some didactical functions of ‘ideative’ concept formation are considered, that is opening up the real world, pointing out the purposes behind mathematical ideas, understanding concepts and methods genetically. As a special case, the author formulates a principle of operative concept formation in geometry teaching.

Journal

Journal für Mathematik-DidaktikSpringer Journals

Published: Dec 20, 2013

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