Examining Students’ Procedural and Conceptual Understanding of Eigenvectors and Eigenvalues in the Context of Inquiry-Oriented Instruction Khalid Bouhjar, Christine Andrews-Larson, Muhammad Haider and Michelle Zandieh Abstract This study examines students’ reasoning about eigenvalues and eigen- vectors 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 instruc- tional 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 con- ceptually oriented question and performed equally well on the procedurally oriented question. Keywords Eigenvalues ⋅ Eigenvectors ⋅ Linear algebra ⋅ Inquiry-oriented instruction ⋅ Student thinking Linear algebra is a mandatory course for many science, technology, engineering, and mathematics (STEM) students. The theoretical nature of linear algebra makes it a dif ficult course for many students because it may be their first time to deal with abstract and conceptual content (Carlson, 1993). Carlson (1993) also posited that this dif ficulty arises from the prevalence of procedural and computational emphases K. Bouhjar ⋅ C. Andrews-Larson ( ✉ ) ⋅ M. Haider Florida State University, Tallahassee, FL, USA e-mail: cjlarson@fsu.edu M. Zandieh Arizona State University, Mesa, AZ, USA e-mail: zandieh@asu.edu © Springer International Publishing AG 2018 S. Stewart et al. (eds.), Challenges and Strategies in Teaching Linear Algebra, ICME-13 Monographs, https://doi.org/10.1007/978-3-319-66811-6_9 193