A Summary of the Singapore Maths Model of teaching

Concrete, Pictorial, Abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. Often referred to as the concrete, representational, abstract framework, CPA was developed by American psychologist Jerome Bruner. It is an essential technique within the Singapore method of teaching maths for mastery.

The approach to maths education in Primary Schools used in Singapore since 1981 is based on the work of Jerome Bruner – an American psychologist.

Bruner developed a technique called “CPA” which stands for Concrete, Pictorial, Abstract”.


This means that children are first introduced to maths using concrete objects such as cubes, balls and the wonderful Cuisenaire rods developed in the 1950’s.


Once children have established a mathematical understanding of shapes, sizes and their relation with each other they can move on to Pictorial, which means drawings such as geometric shapes used in workbooks.

The pictorial phase also includes the ability to read charts and understand fractions and ratio’s visually.


The final stage is abstract, which means that maths is reduced to symbols which represent numbers, shapes and operators etc. This includes algebra but also includes things like degrees of a circle, fractions and percentages etc.

Visual Learning

All this reinforces the case for visual learning which is delivered very well by online tutoring.

Still not convinced?

In the fifteen years since Singapore adopted Concrete, Pictorial, Abstract approach it has topped the global Maths achievement tests in 1995, 1999, 2003 and 2007 and in all other years come very close to the top.