Abstract

PARRAGUEZ GONZALEZ, Marcela; ROA-FUENTES, Solange; JIMENEZ ALARCON, Raúl  and  BETANCUR SANCHEZ, Alexander. Mental structures and mechanisms that from a geometric perspective model and articulate the learning of eigenvalue and eigenvector in ℝ². Relime [online]. 2022, vol.25, n.1, pp.63-92.  Epub June 19, 2023. ISSN 2007-6819.  https://doi.org/10.12802/relime.22.2513.

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 DG0 models the prior knowledge that high school students (14 - 16 years old) must achieve in ${\mathbb{R}}^2$ order to build this concept in the university -this model is based on vector rotation and the concept of scalar multiple-. The second DG1 models in ${\mathbb{R}}^2$ 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 ${\mathbb{R}}^2$.

Keywords : Eigenvalue; Eigenvector; Rotation; Scalar Product; APOS Theory.