Research-based guidance and classroom activities for teachers of mathematics

Geometric proof

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

In school mathematics, geometrical reasoning is often taken to mean primarily, or even solely, deductive proving. Yet this ignores the process by which new mathematics is created through posing and solving problems, analysing examples, making and revising conjectures, and searching for classes of counter-examples.

Classroom-based research points to approaches that incorporate the use of logical arguments that build on learners' prior knowledge in order to demonstrate the truth of some geometrical result; preferably one that has some element of surprise and is based around something previously conjectured by learners after conducting a well-chosen ‘experiment’.

This is what is sometimes called local deduction, where learners can utilise geometrical properties that they already know to deduce or explain other facts or results. The idea is that fluency with local deduction should provide a foundation on which to build knowledge of systematic axiomatisation at a later stage of their mathematics education. An important thread in the research concerns the impact of using Dynamic Geometry Software (DGS) on the teaching and learning of proof in geometry.