Maths At Pucklechurch
At Pucklechurch we believe that all children can be successful mathematicians. We follow the National Curriculum's aims and plan learning activities to ensure that all pupils:
- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non- routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
In Pucklechurch Primary School, we follow the White Rose Scheme of Work that sets out clear small progressive steps per term, per year group. Each small step requires our children to demonstrate explicit skills in calculations, through reasoning and in problem solving. Across the curriculum, we seek to provide children with learning opportunities that will utilise and embed maths skills learned during core maths lessons.
We use a CPA (Concrete, Pictorial and Abstract) approach to our maths learning. This is a highly effective approach that develops a deep and sustainable understanding of maths. 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: this is the “doing” stage, using concrete objects to model problems. This approach brings concepts to life by allowing children to experience and handle physical objects themselves. Every new abstract concept is learned first with a “concrete” or physical experience.
For example, if a problem is about adding up four baskets of fruit , the children might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit.
Pictorial: This is the “seeing” stage, using representations of the objects to model 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.
Abstract: this is the “symbolic” stage, where children are able to use abstract symbols to model problems. Only once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, can the teacher 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.
Through maths, children will go back and forth between each representation to reinforce concepts.
We encourage children to use different resources for example, one day they might use counters, another day they might use a dienes. By varying the resources and methods they use to solve a problem, we help children to make quicker mental connections between the concrete, pictorial and abstract phases.
This is our calculation policy at Pucklechurch Primary school.