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Teaching eigenvalues and eigenvectors using models and APOS theory. (English)
J. Math. Behav. 39, 100-120 (2015).
Summary: In this article we share the results of an investigation of a classroom experience in which eigenvalues, eigenvectors, and eigenspaces were taught using a modeling problem and activities based on APOS (Action, Process, Object, Schema) Theory. We show how a sample of 3 students were able to construct an object conception of these difficult concepts in one semester course ‒ something that existing literature had proven to be almost impossible to achieve. Using one team as a case study we describe the work done by a group of 30 students to show how eigenvectors and eigenvalues emerged in a group discussion. Furthermore, we present evidence on how, at least three students, were able to construct an object conception, demonstrating a deep understanding of these concepts. Finally, we validate the designed genetic decomposition. In summary, the results demonstrate the approach to be promising in the learning of eigenvalues and eigenvectors.
Classification: H65 M45
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