The structure of Mathematics




Why is it that it is in the subject of mathematics that learners show the widest occurrence and the greatest extent of backlogs?

This is because mathematics is a subject where concepts build on earlier concepts. Understanding of progressive concepts depends on an understanding of earlier concepts.

The famous Harvard Professor of Mathematics, William Thurston, said:

“Mathematics is a tall subject. The structure is like a scaffolding, with many interconnected supports. Once the scaffolding is in place, it is not hard to build it higher but it is impossible to build a layer before previous layers are in place.”

Unfortunately, these connections and dependencies are often not evident to learners (or even maybe teachers) and this is due to the way the mathematics curriculum is designed and how its implementation is enforced.

Classroom practise is governed by policy. For example, the SA CAPS curriculum, the Cambridge International curriculum, Common Core in the U.S., even the Montessori curriculum – they all follow a spiral design. Spiral learning comes out of valuable work by the theorist, Jerome Bruner. Bruner believed that early teaching of a subject should emphasise an intuitive understanding of basic ideas and then the curriculum should revisit these ideas, building upon them incrementally until a learner understands them fully.

BUT … the success of a spiral curriculum depends on an initial understanding of these basic ideas and the connections between them.



  1. Mathematical Education – by William Thurston