Exploring symmetry in professional development courses for mathematics teachers

Abstract

In a way, mathematics can be generally described as a science that studies structure, relations, order or patterns through its own language, in order to help us better understand the world we live in. Structure, relations, order and patterns are also fundamental in art and therefore it is not surprising that mathematics and art share a long historical relationship. Mathematics has inspired several artists and art works are sometimes a good motivation for mathematical reasoning or learning. Combining artistic creativity and mathematical reasoning turns out to be a very appealing way to explore several mathematical topics, in particular symmetry. Learning the mathematical principles of symmetry by first looking at art works and exploring one's own creativity has proven to be a very powerful and attractive strategy. During the last years I have explored symmetry with mathematics teachers of all grades through several professional development courses. In these courses teachers had the opportunity to create their own art works using different materials. The topics explored in these courses covered all types of symmetry in the plane: rosettes, friezes and wallpaper patterns. In this paper we shall present some results of three of these courses, involving about 50 primary and secondary school teachers (grades 1 to 12). In all courses we studied symmetry and the groups of symmetry of plane figures. We produced applications using two specific crafts techniques: patchwork/quilting and ceramics.