PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Teaching eigenvalues and eigenvectors with a modeling approach
Page: 2-148
This investigation reports a classroom experience in which eigenvalues, eigenvectors, and eigenspaces were taught using Models and Modeling and APOS Theory. Models and Modeling was used to design a problem in a realistic context and, with the genetic decomposition of APOS Theory, activities were designed to help students make the mental constructions needed to have a better understanding. The research question is: Is it possible for students to construct an object conception of eigenvalues, eigenvectors, and eigenspaces when they are taught using a didactical design based on Models and Modeling and APOS Theory? Using one team as a case study, team A, we describe work done by students and show that two students were able to construct an object conception of these concepts. We also show that both theoretical frameworks can be used in an integrated way and students learned the mathematical concepts in a more meaningful way.