Maths

Calculation Policy 

What do we mean by Concrete, Pictorial and Abstract (CPA) in mathematics?

The CPA approach in maths is a style of learning that uses physical objects and visual representations to enable a pupil to develop a meaningful and deeper understanding of abstract topics. 

When being introduced to a new mathematical concept, teachers and pupils will use concrete resources such as household items or maths resources such as dienes, counters or numicon. The pupils will be encouraged to manipulate/use the objects when exploring the concept to help them solve problems. The concrete objects pupils have experienced are also represented as a picture or diagram. The pupils will use these drawings or their own to solve maths problems. As pupils develop their understanding of the concept they will move to the abstract stage. The teacher will model the concept using numbers, notation and maths symbols.

By using this consistent approach, we provide a maths framework that enables students to build on what they already know, creating meaningful connections between concrete, pictorial and abstract levels of mathematical thinking.

Within a teaching group, the students will be working at different stages of their mathematical thinking and therefore at different stages of the CPA model and will move onto the next stage when appropriate. This approach is not linear. At times, when developing a deeper understanding, it will be appropriate for teachers and students to return to using concrete apparatus or pictorial representations. As pupils transition from the Primary phase through to Key Stages 3 and 4, teachers and pupils will continue to use the Concrete, Pictorial and Abstract approach when working on new concepts or building on existing knowledge, skills and understanding.

This ensures all students continue to develop their mathematical thinking and understanding to a deeper level.