Mental constructs associated with eigenvalues and eigenvectors: refining a cognitive model

Authors

DOI:

https://doi.org/10.35763/aiem22.4005

Keywords:

Eigenvalues and Eigenvectors, APOS theory, Genetic decomposition, Linear transformation, Linear algebra

Abstract

Empirical evidence is presented on the mental structures and mechanisms necessary for learning the concept of eigenvalue and eigenvector from the linear transformation, using the research paradigm of the APOE (Action, Process, Object, Scheme) theory. The data of the study are the result of the implementation of teaching based on a cognitive model (Genetic Decomposition) located in a regular linear algebra course of a public university in Colombia. The empirical evidence allows to show a refined cognitive model in relation to the key structures and mechanisms, to account for the Processes underlying the eigenvalue and eigenvector Process and to generate discussion in relation to the whole Process. The recommendations for teaching specify the importance of providing various situations involving the linear transformation and its coordination with the Processes: zero vector - not an eigenvector; solution set of T(v)=)=λ_0v; null space and determinant.

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References

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Published

2022-10-31

How to Cite

Betancur Sánchez, A. ., Roa, S., & Parraguez, M. . (2022). Mental constructs associated with eigenvalues and eigenvectors: refining a cognitive model. Advances of Research in Mathematics Education, (22), 23–46. https://doi.org/10.35763/aiem22.4005

Issue

No. 22 (2022)

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Artículos

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Copyright (c) 2022 Solange Roa (Autor); Alexander Betancur Sánchez, Marcela Parraguez

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