A look at the linear algebra’s textbooks in the light of the theory of representation of records semiotics

Abstract

This article presents the results of a survey on the main textbook Linear Algebra, adopted in undergraduate courses in mathematics, using as lens the Theory of Semiotics Representation Registers of Raymond Duval. Our objective was to investigate the types of representations and recorded more treatments or conversions in the solved exercises of the four chosen books. The results indicate that the symbolic-algebraic representation registration system is the most used and that the symbolic-matrix type, geometric, figural or graphic are the least used. Regarding treatments and conversions presented in the resolution of exercises, we note that most are resolved with treatment operations. Among the implications of these results we highlight that it is necessary to propose tasks that fix the representation and vary the content and vice versa, always analyzing the relationship between the mathematical content of the representation and the representation itself.