Modes of description and indicators of formalism in students' descriptions of eigenvectors

Abstract

In the study presented in this paper, we investigate students' concepts of eigenvectors in an early stage of their education on linear algebra. The different descriptions used by the students for eigenvectors are analysed with respect to both their chosen representations of the mathematical objects (algebraic, geometric, or abstract), and the indicators of formalism used in these descriptions. We find that while the modes of description presented to them seem to influence their own choice of description, students still show their ability to switch between different representations and descriptions and provide individual concept images. However, some shortcomings concerning formalism and preciseness of their descriptions indicate that some mathematical properties and logical relations in the context of learning about eigentheory require particular attention in teaching and learning activities.

Modes of description and indicators of formalism in students' descriptions of eigenvectors