Relevant research

In the field of research into children’s geometric learning, an influential framework has been that developed is called the Van Hiele levels of geometric reasoning. There are five levels, of which only the first three are relevant to primary school-age range.

Level 1 Visualisation

Children can name and recognise shapes but cannot specifically identify properties of shapes or use characteristics of shapes for recognition and sorting.

Level 2 Analysis

Children begin to identify properties of shapes and learn to use appropriate vocabulary related to these properties.

Level 3 Informal Deduction

Children are able to recognise relationships between and among properties of shapes or classes of shapes and are able to follow logical arguments using these properties.

The implication of this framework is that geometry taught in the primary school should be informal and exploratory, aimed at moving children from visualisation through analysis. Only the more able pupils will move into level three.

Children’s experience should begin with play, investigating plane and solid shapes, building and taking apart, drawing and talking about shapes in the world around them. This early informal experience is seen to be essential.