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. Simply create a free My Rising Stars account and select Maths as your subject preference. If you've found this blog post interesting, make sure you sign up for e-updates to receive the latest blogs direct lyto your inbox. Therefore, it is suggested that a variety of manipulatives should be made available in the classroom, and not just for Key Stage 1 children. 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. Sometimes children will need to touch and manipulate, but at other times simply seeing or imagining the representation will be enough. Therefore, it is important that a variety of representations are available for children to use at all times. On a different occasion, a child may need to revisit a concrete representation before moving on to a pictorial or abstract one. CPA approach is a crucial strategy to teach maths for mastery in Singapore. Often marked as the concrete, representational, abstract framework, CPA was first proposed by the American psychologist Jerome Bruner. A child who uses abstract representations in one area may need concrete representations in another. Concrete, Pictorial, Abstract (CPA) is an effective method for teaching that offers a sustainable and deep understanding of maths to the students. There will be occasions when a particular child will use concrete, pictorial and abstract representations all in one session. It is important to realise that these are not stages gone through once, but a continuum. 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. As understanding develops, children move on to use some form of abstract representation. 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 the child’s experience and confidence grows, they may no longer need physical objects to actually move around. Whatever the objects are, they can be moved, grouped and rearranged to illustrate the problem. 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. Children will travel along this continuum again and again, often revisiting previous stages when a concept is extended. Rising Stars Mathematics is based on the belief that mathematical understanding is developed through using concrete, pictorial and abstract (or symbolic) representations. We asked Cherri Moseley, one of our Series Consultants and authors of Rising Stars Mathematics to explain how it works. You may have heard ‘the CPA approach’ referenced in the context of mathematics mastery and wondered what it really means.
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