Title: Getting mathematical concepts and learning proofs by computer aided linear algebra

Authors: Wolfgang Fraunholz

Addresses: University in Koblenz, Institute for Mathematics, Universitatsstrasse 1, D-56070 Koblenz, Germany

Abstract: Two of the most important aims of learning mathematics are to get the exact mathematical concepts and to learn how to make proofs. To achieve these aims, first year students need many examples and exercises as well as visualisations. Especially, visualisations were the targets which should be realised by the computer learning environment for linear algebra. This article will show many visualisations for concepts within the linear algebra. In the computer learning environment, there are besides mere visualisations experimental pages provided, where the students may try out many cases (e.g. of mappings in two or three dimensions, for finding fixed points or eigenvectors). Helping students to learn many proofs are shown in their clear layout and all explanations to the essential reasons of the steps of deduction are shown by display upon mouse over.

Keywords: linear mappings; linear mapping composition; computer aided learning; CAL; eigenvalues; eigenvectors; fixed points; interactive learning; learning proofs; linear algebra; three-dimensional solids; visualisation; mathematics teaching; learning maths; mathematics education.

DOI: 10.1504/IJCEELL.2008.022167

International Journal of Continuing Engineering Education and Life-Long Learning, 2008 Vol.18 No.5/6, pp.547 - 563

Available online: 22 Dec 2008 *

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