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Duality between formalism and meaning in the learning of linear algebra

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Published in R. Göller, R. Biehler, R. Hochmuth, H.-G. Rück. Didactics of Mathematics in Higher Education as a Scientific Discipline. Hannover (Germany) - 1-4 December 2015 - Kassel (Germany): Universitätsbibliothek Kassel. 2016
Abstract In the French tradition of Bourbaki, the theory of vector spaces is usually presented in a very formal setting, which causes severe difficulties to many students. The aim of this talk is to analyze the un-derlying reasons of these difficulties and to suggest some ways to make the first teaching of the the-ory of vector spaces less inefficient for many students. From a mathematical analysis with a historical perspective, we analyze the teaching and the apprehension of vector space theory in a new ap-proach. I particular, we w show that mistakes made by many students can be interpreted as a result of a lack of connection between the new formal concepts and their conceptions previously acquired in more restricted, but more intuitively based areas.
Keywords Mathematics educationLinear algebraLinear independenceFormalismRankVector
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Research group Didactique des mathématiques à Genève (DiMaGe)
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DORIER, Jean-Luc. Duality between formalism and meaning in the learning of linear algebra. In: R. Göller, R. Biehler, R. Hochmuth, H.-G. Rück (Ed.). Didactics of Mathematics in Higher Education as a Scientific Discipline. Hannover (Germany). Kassel (Germany) : Universitätsbibliothek Kassel, 2016. https://archive-ouverte.unige.ch/unige:85576

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Deposited on : 2016-07-29

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