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Challenges and Strategies in Teaching Linear Algebra

Sepideh Stewart, Christine Andrews-Larson, Avi Berman, and Michelle Zandieh, editors
Publication Date: 
Number of Pages: 
ICME-13 Monographs
[Reviewed by
Michele Intermont
, on

The 2016 International Conference on Mathematics Education included a discussion group focused on teaching linear algebra. This monograph is a result of those discussions. It collects almost 20 articles intentionally drawn from experiences in several countries, and from those involved in education research on linear algebra as well as those simply involved in teaching the subject.

The volume is divided into four parts. The first, “Theoretical Perspectives Elaborated Through Tasks” is very … theoretical. All the articles make reference to APOS theory (action, process, object schema) which even this reader understands is a common framework for mathematics education. However, the section as a whole is dense with terminology and not particularly illuminating for the uninitiated.

The second part of the text is entitled “Analyses of Learners’ Approaches and Resources”. The articles in this section document several studies. The studies, done in Mexico, Uruguay, Zimbabwe, and in the U.S., explore how students understand — and mis-understand — determinants, subspaces, and systems of linear equations.

“Dynamic Geometry Approaches” is the third section of the text. As the title suggests, these articles focus on the role of visualization software in learning linear algebra. One article highlights the Geogebra package; another examines more generally how interactive software should be used to be effective.

Part IV is entitled “Challenging Tasks with Pedagogy in Mind”. This contains some nice problems that could be tailored for use in various classrooms. I found this the easiest section to read and the most useful for my role as one who often teaches linear algebra.

If I were looking for some possible research questions in mathematics education, this would be a good volume to peruse. In fact, a few avenues for future research are explicitly stated. Several of the studies analyzed seemed too small (less than 30 students) to be particularly significant, and this might also provide inspiration for future work. I had hoped to find more articles which might lay open pedagogical considerations in accessible language or, such as those in Part IV, might be fairly immediately useful in the classroom. Perhaps a more thoughtful reader than this one will have better success in culling insights from this volume.

Michele Intermont is Associate Professor of Mathematics at Kalamazoo College.

See the table of contents on the publisher's web page.