Construction of the diagonalizable linear operators based on the APOE theory
DOI:
https://doi.org/10.23925/1983-3156.2021v23i2p099-129Keywords:
Linear algebra, Mathematics education, APOS theoryAbstract
The understanding study of linear algebra concepts is an interesting research topic in mathematics education, mainly because of its abstraction and complexity. A goal concept for teaching linear algebra in a mathematics teaching degree course is that of a diagonalisable linear operator, therefore, based on APOS theory, a cognitive model that considers its construction as an object is given. A questionary was applied to five postgraduate students (25-30 years old) and a semi-structured interview. The results show two ways of construction followed by the students to construct the study concept, which required conjectured mental structures obtained from preliminary genetic decomposition. In addition, it was found that the students prefer to determine whether the matrix representation of the linear operator is similar to a diagonal matrix than to coordinate the ordered basis and eigenvectors processes in the eigenbasis process, with their conception process of similar matrix.
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