Endomorphisms in R2 : change of basis and ways of thinking in Linear Algebra

Abstract

The objective of this research work was to contribute to the understanding of the Base Change in Endomorphisms of R², through the implementation of the theory of modes of thinking: Synthetic-Geometric, Analytical-Arithmetic and Analytical-Structural proposed by Anna Sierpinska (2000) and induced by the Geometric, Arithmetic and Algebraic languages. For this, didactic activities were designed where these languages are articulated that allow the transition between the different modes of thinking about the change of base in endomorphisms of R². A quantitative approach with posttest only was used. Two groups were randomly selected: the experimental and the control. For the purpose of evaluating the design, the post-test was implemented in both groups. In the experimental group a greater mastery of the subject of study was demonstrated, which resulted in a more solid geometric interpretation in R², as well as a precise use of definition and properties, with very good performance in the manipulation of matrices associated with endomorphism in different bases. On the other hand, the students of the control group will not be able to establish a connection between the modes of thinking, which had an impact on the understanding of the subject under study.