Early years maths mastery: introducing the CPA approach
Editor’s Note:
This is an updated version of a blog post published on January 22, 2020.
Are you teaching the CPA approach in the early years? Find out why it’s best to focus on C and P. Here’s how to use concrete and pictorial representations effectively.
The CPA model works brilliantly in the primary years but for the youngest learners, moving onto abstract concepts too early causes difficulties. Spending as much time as possible with concrete objects and pictorial representations will help them master number skills.
By the time they reach Key Stage 2, children need to develop their understanding of numbers by being able to visualise what the concrete looks like in their heads. That’s why it’s great that the EYFS framework is changing the focus of the curriculum with just numbers to 10. This lets teachers focus on counting, number bonds, additions and subtractions to just 10… phew!
If learners develop a deep understanding of numbers to 10, the chances of children understanding numbers beyond significantly increases. So, how can you use the CP stages to help your early years learners master numbers to 10?
C is for concrete
Concrete is the “doing” stage. During this stage, students use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects.
Spending time with real-life objects
The theorist Jerome Bruner (1966) stresses the importance of children spending time learning maths through tangible items. Spending lots of time using real-life objects, solving real-life problems, and manipulating abstract concrete objects (when ready) such as cubes and counters is essential in the early years.
My Reception class loves counting out fruit for snack time, comparing, sorting and counting a range of different buttons, pasta, and even ‘magic beans’ linked to our topics.
Supporting a mastery mindset
When children can confidently solve problems and count using concrete objects, they can then progress to pictorial representations, and finally to more abstract numbers. It may be as simple as sharing pasta between a group of dolls in the home corner. Is there enough for every doll to have an equal amount? How do you know? Is there any pasta left over? Why?
How to use number frames
Giving children time to understand numbers is key. Introducing five frames in nursery and playing key songs such as five currant buns (with children physically standing in a large five frame) can progress to introducing ten frames in Reception and building on their prior knowledge of number.
Supporting a mastery mindset
Ten frames can be used in provision in a number of ways. Here’s an example for you. My Reception class begins by showing the amount of different numbers on a ten frame. Once they are confident, they start to explore the ways of making different number bonds. For example, how many ways can we make 10?
The great thing is you can make ten frames in different ways. Try using egg boxes, lollipop sticks, or even create a large ten frame made out of masking tape on the carpet!
If you need some inspiration for your own DIY frames, check out these creative maths educators.
A homemade five frame
Imagine a little learner with a huge grin saying ‘Can I do more math please? Pleeeease!?!’ We were having fun with our homemade #fiveframes and #tenframes and had an idea for a six frame! #ldsb #mtbos #welovemath #playingmath #mathisexciting #iteachmath #collaboration pic.twitter.com/SVLsC2GCme
— Kat Hendry (@GoslinK123) October 31, 2018
Ten frames on the carpet
Nailed it!❤ #Inaction #Tenframes #Buildingfluency pic.twitter.com/WeGoWCuMVx
— Ms. Gallow (@GallowCintel) September 11, 2018
Ten frames made of recycled materials
Using #tenframes and recycled marker lids to explore #addition in #fdk @McKeeSchool #mathfun #looseparts @EcoSchoolsTDSB @Crayola pic.twitter.com/qCZcKzQXgm
— Hosna (@hosna_w) May 9, 2017
P is for pictorial
Pictorial is the ‘seeing’ stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they were just handling and the abstract pictures, diagrams, or models that represent the objects from the problem.
How to use the part-whole model in Reception
Reception is also a good time for children to explore the part-whole model . Do this by creating a number of the week and focusing on different ways of making the number, for example, how many ways can you make 5?
Supporting a mastery mindset
Provide children with real-life objects to manipulate (dry pasta is a great and cheap resource) and explore using a part-whole model. This really helps with understanding before moving onto cubes or counters.
How to introduce pictorial images
Once children are confident using a part-whole model with concrete resources, you can begin to introduce pictorial images.
For instance, you can replace three pictures of cars in one part and two pictures of cars in the other part. Can the children visualise 3 and 2 coming together to make 5 in the ‘whole’? Encourage children to draw the amount of the missing part-whole model. I suggest laminating a range of missing part-whole models with pictorial images on so that children can solve the missing parts using a whiteboard pen which can simply rub off again.
Supporting a mastery mindset
Provide children with pictorial images on ten frames. Ask yourself if the children can count and match it to the numbers? Showing children pictorial images of ten frames and letting them represent it on their own ten frames with cubes helps learners transition from the concrete methods to understanding the pictorial methods too.
These small steps in the early years build skills to solve abstract concepts like missing number problems and equations. Spend as much time as you need helping early learners visualise and understand numbers before moving onto the abstract concepts. Once a child gathers mathematical understanding, everything else follows.
References
Bruner, J. (1967). Toward a theory of instruction. Cambridge, Mass.: Belknap Press.
Haylock, D. and Cockburn, A. (2003). Understanding mathematics in the lower primary years. London: Paul Chapman.
Foundations — Your Reception Solution
This Early Years mastery programme encourages learning through play and sets children on a path to a deep understanding of maths.
