What it teaches
The names of flat shapes, and the property that gives each one its name. A pentagon is not a shape to be recognised on sight — it is the shape with five sides, and a child who counts will never be caught out by a pentagon drawn at an angle.
Counting sides and corners is also the first time a child describes a shape by a rule instead of by its appearance, which is the beginning of geometry proper.
How it works
A shape appears and the answers are names. The shapes are drawn at different sizes and turned to different angles on purpose: a triangle standing on its point is still a triangle, and plenty of children are not sure of that.
On a wrong answer the sides are counted out one at a time on the shape itself.
What to look for
The rotated shapes are the ones worth watching. A child who gets every upright square right and hesitates on a tilted one has learned the picture rather than the rule.