Introduction to the Concrete Pictorial Abstract Approach (CPA)
What is CPA?
Pictorial
Abstract
P (Pictorial)
A (Abstract)
C (Concrete)
Concrete
Introduces an idea, skill or concept
Uses real-examples and objects
Pupils use pictures or diagrams
Drawing of the concrete object previously used
Numerals
Mathematical symbols
Any other mathematical notation
The bar model is often used as a pictorial representations as it can be used to show proportions
Children will often use bar models when they have become more comfortable drawing pictures of manipulatives they were using in the concrete stage
Numerals
Mathematical symbols
Any other mathematical notations
The concrete and pictorial representations are there to help children to understand the abstract mathematics.
A good idea to show concrete pictorial and abstract representations side by side so that children can begin to make links between them.
The ultimate goal is for children to be able to access stage of learning the more opportunities that they have to make leaks between the different representations and the easier for educators familiar with the approach will understand when to move back and forth between the stages to reinforce learning and investigate concepts.
The approach is not linear
Not all of the stages need to be covered in one lesson
All pupils can benefit from the approach