## Abstract

In this chapter, we document the reasoning students exhibited when engaged in an instructional sequence designed to support student development of notions of eigenvectors, eigenvalues, and the characteristic polynomial. Rooted in the curriculum design theory of Realistic Mathematics Education (RME; Gravemeijer, 1999), the sequence builds on student solution strategies from each problem to the next. Studentsâ€™ used their knowledge of how matrix multiplication transforms space to engage in problems involving stretch factors and stretch directions. In working through these problems students reinvented general strategies for determining eigenvectors, eigenvalues, and the characteristic polynomial.

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Plaxco, D., Zandieh, M., Wawro, M. (2018). Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue. In: Stewart, S., Andrews-Larson, C., Berman, A., Zandieh, M. (eds) Challenges and Strategies in Teaching Linear Algebra. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-66811-6_8

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