Using the Spin_{3 × 3} Virtual Manipulative to Introduce Group Theory

Abstract

The algebraic group ${\mathrm{Spin}}_{3\times 3}$ arises from spinning collections of the numbers 1–9 on a $3\times 3$ game board. The authors have been using this group, as well as a corresponding online application, to introduce undergraduate students to core concepts in group theory. We discuss the benefits of using this deceptively simple, toy-like puzzle in terms of student learning and engagement. Practical exercises as well as use cases outside the abstract algebra classroom are provided at the end.

Keywords:

• Group theory
• virtual manipulatives
• apps
• inquiry-based learning
• IBL

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Dana C. Ernst

Dana C. Ernst received his BS from George Mason University, an MS from Northern Arizona University, and completed his PhD at the University of Colorado at Boulder in 2008. He is currently an associate professor at Northern Arizona University in Flagstaff, AZ. Furthermore, Ernst is a Project NExT national fellow and co-director for the Academy of Inquiry-Based Learning. His primary research interests are in the interplay between combinatorics and algebraic structures. In addition, Ernst is passionate about mathematics education and his scholarly activities include topics in this area with a specialization in inquiry-based learning.

Jeffrey Slye

Jeffrey Slye graduated with a BA in Mathematics with Teaching Certification from Messiah University (formerly Messiah College) in 2010, and an MA and PhD in Mathematics from the University of Kentucky in 2019. Slye works as an assistant professor at SUNY Oswego. He is a 2020 Project NExT fellow and holds a permanent certification in Mathematics 7–12 Education in the state of Pennsylvania. Slye enjoys researching mathematics students' thinking and learning and creating digital applications that support that learning.