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

© The Author 2016. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. This article presents a teaching proposal that emphasizes onvisualization and physical applications in the study of eigenvectors and eigenvalues. More concretely, these concepts were introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposalwas designed after observing architecture students difficulty grasping the meaning of eigenvectors and eigenvalues from a geometric point of view. The aim of this research is to determine whether the designed teaching proposal allows students to give a geometrical meaning to the concepts of eigenvectors and eigenvalues. To this end, the responses given to a test by the students attending the teaching proposal and others attending a traditional course with no emphasis on visualization were analysed. Aclassification of the students reasoning was established in order 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, it was observed that in the traditional group, no responses reasoned in the embodied world ofmathematics were found, whereas in the group attending the teaching proposal responses were found in each of the three worlds of mathematics provided by Tall: embodied, symbolic and formal.