What is the CPA approach in maths?

By Jemma Z Smith

CPA (concrete, pictorial, abstract) is a maths teaching approach that has grown in popularity in recent years. It involves using tangible objects for children to add, subtract, multiply or divide. They then progress to using pictorial representations of the objects and ultimately, abstract symbols.

This way of learning is one of the foundations of Singaporean maths, now being adopted in the UK.

Concrete

The tangible, ‘handling’ stage uses physical objects to solve problems. For example:

There are four buttons in the pot. Stanley has two buttons in his hand. How many buttons are there altogether?

In this problem, the children might first count out actual buttons before moving on to non-related objects such as counters.

Of course, almost anything can be used to help a child master this stage from pencils to plastic pots, to counting beans and coins. You don’t need to spend money on concrete resources to support learning.

Pictorial

The next step is for learners to move on to making their own representations.

Returning to the buttons example, these could be drawn as four circles on one part of the paper and two more on another part, representing the pot and the hand. Kids can then count each small circle, getting the same answer as with the buttons READ

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