Research-based guidance and classroom activities for teachers of mathematics

Symmetry and transformations

Symmetry and transformations is a theme within spatial and geometrical reasoning. Links to relevant activities and resources are on the right hand side of this page. 

There are many reasons why a focus on symmetries is a good idea in geometry education. This is not to say that symmetry is simple or uncomplicated to teach.

Research with suitable digital technologies is providing examples of how students can gain a multi-faceted appreciation of symmetry. Switching attention from symmetries of geometric objects to invariants of transformations of those objects can be a fruitful way to study congruency and similarity (the former involving an isometry, or distance-preserving transformation, the latter a transformation which preserves shape but not necessarily size).