Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector

This article describes the design of a model-eliciting activity (MEA) that integrates GeoGebra drawing within the models and modeling perspective (MMP) and the action, process, object, and schema (APOS) theory to foster understanding of eigenvalues and eigenvectors. Insights from two pilot tests with linear algebra students led to refinement of the design to ensure alignment with the six principles of models and modeling theory, prior to its implementation with a group of university students in an introductory linear algebra course. Student work related to MEA generated during the implementation is analyzed using elements of genetic decomposition and modeling cycles. The reflections highlight the richness of the MEA, its potential to generate new situations and questions for further exploration of eigenvalues and eigenvectors, and its relevance for developing a more profound understanding of other fundamental concepts in linear algebra.