A teaching experience of eigenvalues, eigenvectors, and eigenspaces based on apos Theory

Hilda Salgado y María Trigueros

Abstract:When teaching Linear Algebra, given the complexity and high level of abstraction of the concepts involved in its learning, several problems arise. Eigenvalues, eigenvectors, and eigenspaces are very abstract concepts, but due to their multiples applications are important to learn. This paper reports on the results of a research project that studies students’ learning of these concepts in a course that followed a specific didactical design based on apos Theory. The results obtained permited to validate the designed genetic decomposition. The analysis of students’ work related to the above mentioned concepts shows evidence of students’ learning. In particular, they show the possibility of building an object conception of the studied concepts and the construction of a process conception by most students.

Keywords: eigenvalue, eigenvector, eigenspace, apos Theory, genetic decomposition.


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