Concrete Pictorial Abstract (CPA)

'Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding' - William Paul Thurston.  

The Concrete Pictorial Abstract (CPA) approach is heavily used in the vast majority of our Maths lessons here at Mangotsfield. Whether in EYFS or Year 6, Maths is taught using the CPA approach. CPA is a system of learning that utilises concrete and visual aids to build a child's understanding of abstract topics. 

Each new mathematical concept is introduced with concrete or pictorial resources. Concrete resources allow children to use physical objects (such as Dienes, counters etc.) to solve mathematical problems. Pictorial representations use pictures or drawings to solve problems. Solving maths problems abstractly means to only solve questions using numbers. 

The aim is for children to work through the CPA approach with the end goal of being able to work abstractly in every mathematical concept.  

 Why CPA?

The CPA approach has been proven to have many benefits to our young learners. It allows pupils to have a deeper understanding of the mathematical concepts and not rely on a process to get the correct answer. This is most evident when tackling reasoning questions where children are required to have a deeper level of knowledge. 

CPA has also been proven to aid retention through the pupils actively engaging in processes to acquire new knowledge. 

What does CPA look like in our classrooms?

As mentioned previously, CPA is used widely across all key stages. Our Maths lessons are engaging and show children actively participating in their learning through a variety of resources. This 'doing' leads to a deeper level of understanding as there is not a focus on the process. CPA is also used as a tool to support learning as well as to introduce new concepts.