At Barrowford St Thomas, we believe in maths being fun and exciting for our pupils whilst teaching them to become fluent in the fundamentals of mathematics. We aim for all our pupils to develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
They are taught to reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
Our pupils are taught to 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.
We occasionally use schemes such as 'Busy Ant' and we encourage all our children to take part in 'Times Table Rock Stars' to improve their times table knowledge and their speed of recall. Most importantly we are aiming to improve the teaching of mathematics at Barrowford St Thomas by establishing the CPA approach and in order to achieve this we have purchased a wide variety of age-appropriate concrete resources which are sorted into maths boxes in all classrooms. This is to ensure that all pupils as a class will be able to access and use the most appropriate resource to explore a concept.
At Barrowford St Thomas, we believe that CPA (Concrete - Pictorial - Abstract) is a highly effective approach to teaching that develops a deep and sustainable understanding of mathematics in pupils.
Children (and adults!) can find maths difficult because it is abstract. The CPA approach builds on children’s existing knowledge by introducing abstract concepts in a concrete and tangible way. It involves moving from concrete materials, to pictorial representations, to abstract symbols and problems.
Concrete Step of CPA
Concrete is the “doing” stage. During this stage, our pupils use concrete objects to model problems. The CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. Every abstract concept is first introduced using physical, interactive concrete materials.
For example, if a problem involves adding pieces of fruit, children can first handle actual fruit. From there, they can progress to handling abstract counters or cubes which represent the fruit.
Pictorial step of CPA
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 just handled and the abstract pictures, diagrams or models that represent the objects from the problem.
Building or drawing a model makes it easier for children to grasp difficult abstract concepts (for example, fractions). Simply put, it helps our pupils visualise abstract problems and make them more accessible.
Abstract step of CPA
Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Students will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages of the problem. The abstract stage involves the teacher introducing abstract concepts (for example, 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.
To further improve standards, establishing the CPA approach in mathematics will become a key priority of our School Improvement Plan for 2019 - 20.
The maths subject leader is Mrs Jill Beswick
Key Stage 1
During key stage 1: The principal focus of mathematics teaching in key stage 1 is to ensure that our pupils develop confidence and mental fluency with whole numbers, counting and place value. This involves working with numerals, words and the four operations, including with practical resources (for example, concrete objects and measuring tools). They will develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. They will use a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.
Key Stage 2
During key stage 2: In Years 3 and 4 we teach our pupils to become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. They will develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. By the end of year 4, pupils should have learnt their multiplication tables up to and including the 12 multiplication table and the associated division facts. In Years 5 and 6 we ensure that pupils extend their understanding of the number system and place value to include larger whole numbers (integers). Pupils develop connections that are made between multiplication and division with fractions, decimals, percentages and ratio. By the end of year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.
We endeavour to provide the children with opportunities to apply their mathematical skills across the curriculum in areas such as science.