Research-based guidance and classroom activities for teachers of mathematics

Geometric diagrams

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

A central idea in geometry education is that of the ‘figural concept’. As such, it is important to acknowledge the influence on learners of what are generally called prototypical geometric diagrams, such as an isosceles triangle seeming to need to stand on its short side.

One approach might be the use of ‘only just’ examples and ‘very nearly’ non-examples of geometrical shapes, with an ‘only just’ example being one for which any change causes it to become a non-example, and a ‘very nearly’ non-example needing but one further adjustment in order to become an example.

Evidence suggests that coupling ‘only just’ examples with ‘very nearly’ non-examples is more effective that solely providing examples. Asking learners to construct such boundary examples by adding or removing constraints is also useful.

Activities and resources

Where are they?