Estructuras mentales para modelar el aprendizaje de los valores y vectores propios en R2: El caso de enseñanza media

Abstract

Based on the APOS theory as a theoretical and methodological framework, we investigate from a cognitive stance, mental structures needed to model the cognitive construction of eigenvalues and eigenvectors in R² as an object. In order to analyze how middle school students learn it, a genetic decomposition (DG) was designed for this purpose. The testing of this DG in high school students through a questionnaire (together with the comments they made their answers) showed that elements from the geometric field –the rotation 180° with center at the origin and the homothecy– are relevant mathematical concepts to build the
concept value/eigenvector as an object in R².