Research-based guidance and classroom activities for teachers of mathematics

Spatial and geometrical reasoning

We have identified six themes within the key idea of spatial and geometrical reasoning: spatial relations, 3D geometry, symmetry and transformations, similarity and congruence, geometric diagrams, and geometric proof.

Each theme page has links to relevant online activities and resources. A full list of all activities for spatial and geometrical reasoning is on the right hand side of this page.

Two aspects of geometry

Geometry education at the school level should attend to two closely-entwined aspects of geometry: the spatial aspects and the aspects that relate to reasoning with geometrical theory. These twin aspects of geometry, the spatial and the deductive, are not separate; but interlocked. Just as geometry and algebra have been called the “twin pillars” of mathematics, spatial and geometric reasoning are the yin-yang of geometry education. Both are interconnected and inter-dependent in such a way that each gives rise to the other.