As with most of the high performing nations, Jerome Bruner’s (USA) CPA approach plays a significant part of their success. Bruner’s research suggests that the most natural way for us to learn is to go through a Concrete-Pictorial-Abstract (CPA) approach and this can be thought of by using an analogy I read in a research paper.
If you imagine a baby, at the early stages we give the baby toys and name the toys, say a toy Car. We keep saying this is a car, here is your car, would you like to play with your car – whilst pointing or holding or emphasising the concrete car. This happens until the baby decided to call the car a car! Later on, the baby may then see a picture of a car in a book and conclude this is also a car which means they have moved onto recognising the pictorial representation. Finally, after a few more months, the baby may be able to decode C-A-R is also car! They have now reached the final stage of the process, the full on Abstract phase and hence concluding the CPA approach.
So why is the CPA approach so important when teaching, especially at primary level?
The CPA approach allows pupils to “see” the maths happening and therefore understand complex written and formal methods much better. We’ve seen this various times over many year groups and myriads of topics too. It allows the teacher to create more, low floor – high ceiling, tasks which enable slower learners to grasp a challenging concept using concrete materials and then slowly be able to transfer that learning as a pictorial representation before moving onto the abstract.
CPA Approach in Action – NCETM Maths Hub (North and East London) and MUA Consultancy
We’ve chosen to show you this question that Mohi attempts with some Year 3 children from Elmhurst Primary School, a school we at MUA Consultancy have been working closely with as part of the work we do for NCETM Maths Hub (North and East London). You can see that all four children attempt this division question in their own way, with an interesting discussion at the end!