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

Alexander Betancur-Sánchez; Solange Roa-Fuentes

doi:10.29333/ejmste/18127

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Alexander Betancur-Sánchez ¹ ² ^* , Solange Roa-Fuentes ¹

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¹ Universidad Industrial de Santander, Bucaramanga, COLOMBIA² Bucaramanga Education Secretariat, Bucaramanga, COLOMBIA^* Corresponding Author

Abstract

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.

Keywords

MEA
APOS
MMP
linear algebra
eigenvalues
eigenvectors

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 22, Issue 4, April 2026, Article No: em2805

https://doi.org/10.29333/ejmste/18127

Publication date: 01 Apr 2026

Online publication date: 15 Mar 2026

Article Views: 82

Article Downloads: 18

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How to cite this article

APA

Betancur-Sánchez, A., & Roa-Fuentes, S. (2026). Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector. Eurasia Journal of Mathematics, Science and Technology Education, 22(4), em2805. https://doi.org/10.29333/ejmste/18127

Vancouver

Betancur-Sánchez A, Roa-Fuentes S. Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector. EURASIA J Math Sci Tech Ed. 2026;22(4):em2805. https://doi.org/10.29333/ejmste/18127

AMA

Betancur-Sánchez A, Roa-Fuentes S. Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector. EURASIA J Math Sci Tech Ed. 2026;22(4), em2805. https://doi.org/10.29333/ejmste/18127

Chicago

Betancur-Sánchez, Alexander, and Solange Roa-Fuentes. "Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector". Eurasia Journal of Mathematics, Science and Technology Education 2026 22 no. 4 (2026): em2805. https://doi.org/10.29333/ejmste/18127

Harvard

Betancur-Sánchez, A., and Roa-Fuentes, S. (2026). Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector. Eurasia Journal of Mathematics, Science and Technology Education, 22(4), em2805. https://doi.org/10.29333/ejmste/18127

MLA

Betancur-Sánchez, Alexander et al. "Designing a model-eliciting activity (MEA) to foster understanding of eigenvalues and eigenvector". Eurasia Journal of Mathematics, Science and Technology Education, vol. 22, no. 4, 2026, em2805. https://doi.org/10.29333/ejmste/18127