Exploring dihedral groups with the Dihedral Group Explorer: a multi-representational approach

Abstract This report describes a teaching and learning experience centred on the Dihedral Group Explorer (DGE) applet, used to investigate the symmetries of regular polygons—specifically the dihedral groups ${D}_3$ and ${D}_4$ (comprising six and eight elements, respectively). Drawing on the coordination of visual and analytic strategies, I report on a pedagogical approach where DGE-based tasks are used to scaffold the transition from geometric intuition to formal group theory. The report demonstrates that this activity-based approach enables learners to coordinate visual, algebraic, symbolic and verbal representations, thereby unpicking the specific role of digital interactivity in developing a deeper understanding of abstract algebraic structures.