Throughout KS1, composition and subitising is taught through concrete resources, pictorials representations and then abstract form. We encourage children to explore numbers in many ways so children have part and whole awareness. We thrive for pupils from Reception to year 2 to master numbers in order to build a solid foundation before KS2. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Maths mastery is implemented as a daily starter. Children are given opportunities to explore numbers using concrete resources such as recandrecs and explaining their answers using full sentences. Maths Mastery continues our ethos on rich vocabulary and by explaining your understanding behind the answer.
More information on NCETM
Our maths is based around the concrete, pictorial, abstract (CPA) which is a highly effective approach to teaching that develops a deep and sustainable understanding of maths. We believe that children’s chances of succeeding in education and life will be maximised if they develop deep and lasting procedural and conceptual mathematical understanding.
We are aware that children can find maths difficult because it is often abstract. The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way.
Concrete is the ‘doing’ stage, using concrete objects to solve problems. It brings concepts to life by allowing children to handle physical objects themselves. Every new abstract concept is learned first with a ‘concrete’ or physical experience. For example:
There are 8 flowers in the vase. Hannah has 2 flowers in her hand. How many flowers are there altogether?
In this problem, the children might first handle actual flowers – the concrete stage – before progressing to handling counters or cubes (like Numicon) which are used to represent the flowers.
Pictorial is the ‘seeing’ stage, using representations of the objects involved in maths problems. 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.
Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.
For example, for the above problem, the pictorial stage would involve using drawings of flowers, or pictures of objects such as multi-link blocks or counters, to represent the actual object.
Abstract is the ‘symbolic’ stage, where children are able to use abstract symbols to model and solve maths problems.
Once a child has demonstrated that they have a solid understanding of the ‘concrete’ and ‘pictorial’ representations of the problem, the teacher can introduce the more ‘abstract’ concept, such as mathematical symbols.
Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, / to indicate addition, multiplication, or division.
So, for the following problem:
Jim has 12 cookies. Julie has 8 cookies. How many do they have altogether?
Children at the abstract stage would be able to solve the problem by writing it out as 12 + 8 = 20.