Comprensión del concepto de base de un espacio vectorial desde el punto de vista de la teoría APOE

this paper addresses the question of how students learn the concept of basis of a vector space. based on apos theory (action-process-object-schema) we present a genetic decomposition of this concept in it, the set of mental constructions that students might make in order to give meaning to the concept of basis are described. we center our attention on the concept of basis of in linear algebra, since it is of fundamental importance in the study of vector spaces and their applications and at the same time students have many difficulties when trying to learn it. in order to test the viability of the proposed mental constructions we designed an interview which was helpful in analyzing students' responses in terms of the constructions they had made after taking a linear algebra course. results of the analysis show the specific difficulties associated with the construction of this concept.