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

The algebraic group (Formula presented.) arises from spinning collections of the numbers 1–9 on a (Formula presented.) 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.