# Examining Students’ Procedural and Conceptual Understanding of Eigenvectors and Eigenvalues in the Context of Inquiry-Oriented Instruction

## Abstract

This study examines students’ reasoning about eigenvalues and eigenvectors as evidenced by their written responses to two open-ended response questions. This analysis draws on data taken from 126 students whose instructors received a set of supports to implement a particular inquiry-oriented instructional approach and 129 comparable students whose instructors did not use this instructional approach. In this chapter, we offer examples of student responses that provide insight into students’ reasoning and summarize broad trends observed in our quantitative analysis. In general, students in both groups performed better on the procedurally oriented question than on the conceptually oriented question. The group of students whose instructors received support to implement the inquiry-oriented approach outperformed the other group of students on the conceptually oriented question and performed equally well on the procedurally oriented question.

## Keywords

Eigenvalues Eigenvectors Linear algebra Inquiry-oriented instruction Student thinking## Notes

### Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant Numbers DRL 0634099, 0634074; DUE 1245673, 1245796, 1246083, and 1431393. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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