Emphasizing visualization and physical applications in the study of eigenvectors and eigenvalues

Abstract

In this paper, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. More concretely, we introduce these concepts using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was designed after observing that architecture students had problems grasping the meaning of eigenvectors and eigenvalues from a geometric point of view. The aim of this research is to determine if the designed teaching proposal allows students to give a geometrical meaning to the concepts of eigenvectors and eigenvalues. To this end, we analyze the responses given to a test by the students attending the teaching proposal and others attending a traditional course with no emphasis on visualization. We classify their reasoning to check differences between both groups. As our findings show, the students who attended the course where the teaching proposal was developed, obtained better results in questions formulated from a visual point of view than those attending the traditional course. Moreover, we observe that whereas in the traditional group we did not find responses reasoned in the embodied world of mathematics, in the group attending the teaching proposal we found students giving responses in each of the three worlds of mathematics provided by Tall: embodied, symbolic and formal.