1.1 Progression in geometric thinking
A Dutch educator called Pierre van Hiele showed how children’s understanding of shape develops through increasing levels of sophistication.
At first, children learn to recognise shapes in a holistic way and to name them. This usually happens in early primary school. As they progress, children learn to describe shapes by their properties and to recognise a shape from a list of properties. These children tend to be older primary to younger secondary age, and some may never progress beyond this level.
In the third level, children or learners are able to reason more abstractly, to work out how one property of the shape generates other properties, and to construct a concise definition for a shape.
Later levels describe much more advanced geometrical reasoning which is appropriate for higher school and university study.