Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue

  • David PlaxcoEmail author
  • Michelle Zandieh
  • Megan Wawro
Part of the ICME-13 Monographs book series (ICME13Mo)


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. Students’ 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.


Linear algebra Eigenvector Eigenvalue Realistic mathematics education Inquiry oriented curriculum 


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Clayton State UniversityMorrowUSA
  2. 2.Arizona State UniversityTempeUSA
  3. 3.Virginia TechBlacksburgUSA

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