Estructuras mentales que modelan el aprendizaje de un teorema del álgebra lineal: Un estudio de casos en el contexto universitario

In this paper, a qualitative research that explores how Chilean and Colombian university students learn a linear algebra theorem, called Matrix Linear Transformation theorem, MALT, is presented. For this, a cognitive model is defined in terms of the structures and mechanisms proposed by the APOS theory (Action, Process, Object, and Schema) to interpret the advanced mathematical thinking. Furthermore, the levels of Intra, Inter and trans evolution of the MALT theorem and its development indicators in terms of relationships, transformations and invariants are described. The results of this research show on the one hand, that the construction of the matrix representation of a linear transformation as object is essential for first year students to understand the MALT theorem; and on the other hand that such an object must be assimilated by the linear transformation schema.