\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015e.00708}
\itemau{Salgado, Hilda; Trigueros, Mar\'{\i}a}
\itemti{Teaching eigenvalues and eigenvectors using models and APOS theory.}
\itemso{J. Math. Behav. 39, 100-120 (2015).}
\itemab
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.
\itemrv{~}
\itemcc{H65 M45}
\itemut{eigenvalues; eigenvectors; case study; APOS theory; models}
\itemli{doi:10.1016/j.jmathb.2015.06.005}
\end