Volume 2, Issue 4, August 2014, Page: 137-140
A Result in the Theory of Determinants from a Semiotic Viewpoint
Michael F. Otte, Universidade Anhanguera de São Paulo (UNIAN) Programa de Pós-graduação em Educação Matemática, São Paulo, Brasil
Tânia M. M. Campos, Universidade Anhanguera de São Paulo (UNIAN) Programa de Pós-graduação em Educação Matemática, São Paulo, Brasil
Luiz G. X. de Barros, Universidade Anhanguera de São Paulo (UNIAN) Programa de Pós-graduação em Educação Matemática, São Paulo, Brasil
Geslane F. S. Santana, Universidade Federal do Mato Grosso (UFMT), Cuiabá, Brasil
Received: Aug. 21, 2014;       Accepted: Aug. 30, 2014;       Published: Sep. 20, 2014
DOI: 10.11648/j.sjedu.20140204.16      View  1980      Downloads  101
Abstract
We present a conceptual proof of the Cauchy-Binet theorem about determinants to show how much one can gain by investing a bit more in conceptual development, comparing this treatment with the usual one in terms of laborious matrix calculations. The purpose is to stimulate a conceptual understanding and to overcome the usual empiricism, which is an obstacle to a real understanding of mathematical knowledge. The article also aims to show that mathematical terms could be understood as dynamic processes, based on the interaction between intensional and extensional aspects. As it is not really possible to answer any question about the nature of mathematical objects definitively, much less to limit the possible interpretations of mathematical concepts, processes of concept evolution are of great importance to mathematics as a human activity.
Keywords
Mathematics Education, Semiotics, Determinants
To cite this article
Michael F. Otte, Tânia M. M. Campos, Luiz G. X. de Barros, Geslane F. S. Santana, A Result in the Theory of Determinants from a Semiotic Viewpoint, Science Journal of Education. Vol. 2, No. 4, 2014, pp. 137-140. doi: 10.11648/j.sjedu.20140204.16
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