You may have heard ‘the CPA approach’ referenced in the context of mathematics mastery and wondered what it really means. We asked Cherri Moseley, one of our Series Consultants and authors of Rising Stars Mathematics to explain how it works.
Rising Stars Mathematics is based on the belief that mathematical understanding is developed through using concrete, pictorial and abstract (or symbolic) representations. Children will travel along this continuum again and again, often revisiting previous stages when a concept is extended. Children use concrete objects to help them make sense of the concept or problem; this could be anything from real or plastic fruit, to straws, counters, cubes or something else meaningful.
Whatever the objects are, they can be moved, grouped and rearranged to illustrate the problem. As the child’s experience and confidence grows, they may no longer need physical objects to actually move around. Instead, they draw them. These simple pictures to represent the problem could be pictures of real objects they have used in the past, objects mentioned in the problem or something else meaningful. As understanding develops, children move on to use some form of abstract representation. This could be giving values to rectangular bars (bar model) to identify what is known and what is unknown, using a symbol to stand for a number or something else.
It is important to realise that these are not stages gone through once, but a continuum. There will be occasions when a particular child will use concrete, pictorial and abstract representations all in one session. A child who uses abstract representations in one area may need concrete representations in another. On a different occasion, a child may need to revisit a concrete representation before moving on to a pictorial or abstract one. Therefore, it is important that a variety of representations are available for children to use at all times. Sometimes children will need to touch and manipulate, but at other times simply seeing or imagining the representation will be enough.
Using the CPA approach, understanding is likely to be developed more quickly where children are encouraged to start from modelling a problem with concrete objects, before moving on to pictorial and abstract representations. Therefore, it is suggested that a variety of manipulatives should be made available in the classroom, and not just for Key Stage 1 children.
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Interested in discovering more about the CPA approach? Take a guided tour of Rising Stars Mathematics, a complete mastery textbook programme that has been written for the new curriculum.
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