Abstract

Two refined genetic decompositions (DGs) are proposed, as a result of the application of the APOS Research Cycle, which describe mental struct ures and mechanisms for the concept of value and eigenvector in t wo case st udies. The f irst DG0 models the prior knowledge that high school st udents (14 – 16 years old) must achieve in R2 order to build this concept in the university —this model is based on vector rotation and the concept of scalar multiple—. The second DG1 models in R2 the const r uction of eigenvalue and eigenvector in f irst-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 R2.