Singapore Maths Unpacked: A Closer Look at the Concrete-Pictorial-Abstract (CPA) Approach

The CPA approach, as championed by Singapore Maths and exemplified in the S.A.M program, holds great potential in shaping the future of mathematics education. By focusing on developing a deep and holistic understanding of mathematical concepts, the CPA approach provides a strong foundation for students to build upon as they progress in their academic journey.

In recent years, Singapore mathematics, or more commonly known as Singapore Maths, has gained international acclaim for its innovative and effective teaching approach. With countries like the USA, UK, and Australia adopting its principles, the spotlight is on Singapore’s maths methodology. One of the key reasons for its success lies in the Concrete-Pictorial-Abstract (CPA) approach, an integral part of the Singapore Maths framework.

What is the CPA Approach?

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The CPA approach is a three-step instructional approach, rooted in the theories of renowned psychologist Jerome Bruner, which encourages a gradual progression in students’ mathematical understanding. It consists of three interconnected stages:

Concrete: In this stage, students begin with hands-on experiences using physical objects to represent mathematical concepts. Manipulatives such as counting cubes, number lines, and base-10 blocks are employed to make abstract concepts tangible.

Pictorial: After grasping the idea through concrete materials, students transition to pictorial representations of the same concept. They use diagrams, drawings, and charts to visualise and further explore the mathematical ideas.

Abstract: As students gain a better understanding, they move on to the abstract stage, where mathematical symbols and notations are introduced to represent the concepts without relying on physical objects or pictures.

This sequential progression helps students develop a deep understanding of mathematical concepts, allowing them to connect the tangible with the abstract, and to gain mastery over the subject.

The Impact of CPA on Singapore Maths

The success of Singapore Maths can largely be attributed to the thoughtful application of the CPA approach in its curriculum. It focuses on providing students with a strong foundation in number sense and problem-solving skills, building upon each level of understanding before progressing to the next.

S.A.M – Seriously Addictive Mathematics

S.A.M, or Seriously Addictive Mathematics, is a program designed to engage students with Singapore Maths in a fun and meaningful way. S.A.M emphasises the CPA approach, providing learners with a comprehensive and multi-dimensional perspective on mathematics.

S.A.M’s engaging and interactive lessons enable students to explore mathematical concepts at their own pace, while providing instructors with a toolkit to facilitate effective learning. This allows students to enjoy the process of learning maths, leading to greater interest and enthusiasm in the subject.


Singapore Maths, underpinned by the CPA approach, is an effective instructional method that encourages students to develop a deep understanding of mathematical concepts. Its success is evident in its adoption by various countries and the widespread appreciation for its contribution to raising the bar in maths education.

S.A.M, with its emphasis on the CPA approach and its engaging lessons, is a great way to introduce students to the world of Singapore Maths, fostering a love for the subject and encouraging them to become lifelong learners.