top of page

The CPA Approach

The Concrete, Pictorial, Abstract approach (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.

At a glance

  • An essential technique of maths mastery that builds on a child’s existing understanding

  • A highly effective framework for progressing pupils to abstract concepts like fractions

  • Involves concrete materials and pictorial/representational diagrams

  • Based on research by psychologist Jerome Bruner

  • Along with bar modelling and number bonds, it is an essential maths mastery strategy

and multi-link cubes are more commonly used in the UK. However, concrete materials are frequently shelved by the time children reach KS2 — many teachers believe them to be too childish or distracting. Removing concrete materials exposes children to abstract concepts too early. As a result, they miss out on the opportunity to build a conceptual mathematical understanding that can propel them through their education.

It is important to recognise that the CPA model is a progression. By the end of KS1, children need to be able to go beyond the use of concrete equipment to access learning using either pictorial representations or abstract understanding. What is important, therefore, is that all learners, however young, can see the connections between each representation.

9 views0 comments

Recent Posts

See All


Common Challenges Year 9-13 Students Face in School Students in Year 9-13 often encounter a range of challenges that can impact their academic performance and overall school experience. These challeng


At Raena Learning Centre, we believe in a personalized and student-centered approach to education. Our teaching philosophy is built on the following core principles: Individualized Learning Pathways W


bottom of page