The Concrete, Pictorial and Abstract Approach
CPA Approach

This approach recognises that in order for pupils to understand abstract concepts, they must first learn mathematical concepts through the use of concrete resources and pictorial representation. 

Concrete is the ‘doing’ stage, using concrete objects to solve problems. It brings concepts to life as children have the opportunity to be hands on and use physical objects to aid them in developing their understanding. 

 
Pictorial is the ‘seeing’ stage, where representations of the objects are used to support learning.  This stage encourages children to make a mental connection between the physical object and abstract levels of understanding, by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem.

 
Abstract is the ‘symbolic’ stage, where children are able to use abstract symbols to model and solve maths problems.