An Innovative Activity for Learning Groups of Symmetries in Abstract Algebra

Abstract

In many cases, group theory is the first axiomatic mathematics taught, and so is abstract algebra. Thus, the way teachers teach and students learn group theory is considered the foundation with respect to the development of mathematical abilities and attitudes towards mathematics at the higher level. It has been realised that the permutation group (S3) is the most common example throughout group theory, and students need to remember elements and their compositions. Review of different solution initiatives with practical perspectives, such as inclusion of seminar, visual and analytical approach, collaborative approach with Interactive Set Language ( ISETL) and penny moving, etc., and theoretical perspectives such as inquiry-based mathematics education, linking informal knowledge to formal mathematics and constructivist learning became helpful in this innovation. This innovative hands-on activity was developed by following a design thinking approach with a view to bringing changes in the learning of a group of symmetries at the undergraduate level. This hands-on activity has two parts: one on the regular polygon (equilateral triangle and square) and permutation using these polygons, including five worksheets to facilitate learning.