1.3 The visual or physical representation of shapes

If you consider a shape, such as a square or a circle, you have a mind’s-eye picture of the shape which includes the ‘squareness’, or the ‘circleness’, and this shape may be filled in (with colour) in your mind, and it may have a particular orientation. You may draw a diagram of this shape with a pencil and the outside edges are likely to have some width (or you could not see them). If you have a square or circular tile then the tile will have depth (or you could not pick it up).

The diagram and the tile are representations of the shape and as such are examples of what the shape can look like. In contrast, the mathematical shape itself is entirely abstract and is described using its geometric properties. Orientation and thick pencil lines are not included in those properties. However, teachers and learners need to work with representations of shapes as if they are mathematical objects because it is all they have to work with. It is worth being aware of the differences because learners’ attention may be distracted by particular features of the physical representations of the shapes.