Abstract

Two refined genetic decompositions (DGs) are proposed, as a result of the application of the APOS Research Cycle, which describe mental structures and mechanisms for the concept of value and eigenvector in two case studies. The first DG(0) models the prior knowledge that high school students (14 - 16 years old) must achieve in R-2 order to build this concept in the university -this model is based on vector rotation and the concept of scalar multiple-. The second DG(1) models in R-2 the construction of eigenvalue and eigenvector in first-year university students and shows how to rely on secondary education to structure that concept from relationships between the linear transformation and the scalar multiple vector as a generator of a line. The data analysis allows to validate the DG's and outline a cognitive path for learning the concept of eigenvalue and eigenvector in R-2.