The concrete, pictorial and abstract (CPA) approach to learning maths

2 min read

Maths can often be a source of contention at home. The University of Cambridge found that 40% of students are anxious about maths at least some of the time. This, combined with the methods of teaching being continually being revised, can make it difficult to know how you can support your child at home. 

One of the biggest developments in maths teaching has been the widespread understanding of the CPA method. CPA simply stands for concrete, pictorial, abstract. It’s the process through which children are now introduced to concepts in such a way as to make it less intimidating. 

With this in mind, we look at how this method is being used in schools, and how this can help you support your child’s maths learning. 

C is for Concrete

This is the stage of ‘doing’. In the concrete phase, children should be almost acting out the maths problem. If I have four pencils and someone gives me three more, how many do I have? With this maths problem, children should be counting out their four pencils and then a further three. This is ensuring children become familiar with the language being used and are physically engaging with the question.

Once children have used the real objects mentioned in the question, they can also start using physical representations, such as cubes or counters which still allow them to manipulate the resource. Children should use concrete items until they have a strong understanding of what is being asked of them.

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P is for Pictorial

Once children are confident with the concrete stage of the topic, they can move on to pictorial representations. This means that we can start drawing bar models or diagrams to support the learning.

Perhaps I used chocolate buttons on day 1 to count out number bonds to 10 and picked it up easily, so then changed to counters on day 2. On day 3, I can now draw dots or circles to represent the buttons. I can still see the items and I have that link between the physical objects I was moving yesterday and the ones I have drawn today to help me embed my understanding. 

A is for Abstract

Once children have developed a solid understanding of the CP stages, introduce the abstract concepts. As mathematical symbols or numbers are abstract, this is where children often start to struggle with maths. Having used the concrete and pictorial stages, children should have developed a strong understanding of the topic at hand. 

If your child is struggling with a particular maths concept, why not see if you can take it back to the concrete stage to build their confidence? If your child is learning about negative numbers, using thermometers or water can be a great way to introduce the concept. Half fill a jug with water and then float a toy in it. This toy is now at zero – what would happen if you lifted the toy up a bit? What if you moved it further down the jug?

You can then use the experience of physically doing it to draw pictorial representations to support your child and then as they become more confident, they’ll find they need to rely on their diagrams less and less, but they still have the option if they feel they need it. 

 

Encourage your child to use these stages throughout their education to help ensure that they have a strong understanding of maths concepts and flit back and forth between the stages as necessary to reinforce comprehension.

Article by Emma Hall

Doodle empowers learners to achieve confidence in maths and English. Our intelligent technology creates individual work programmes which are motivational, affordable and convenient to use.