Teaching for Mastery
At Wild Bank Primary School, 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. Mastery of mathematics is something that we want all pupils to acquire, and continue acquiring, throughout their school lives, and beyond. We use the phrase 'teaching for mastery' to describe a range of elements of classroom practice and school organisation that combine to give pupils the best chances of mastering mathematics. Mastering maths means acquiring a deep, long-term, secure and adaptable understanding of the subject. At any one point in a pupil's journey through school, achieving mastery is taken to mean acquiring a solid enough understanding of the maths that's been taught to enable them to move on to more advanced material.
Teaching is designed to enable a coherent learning progression through the curriculum, providing access for all pupils to develop a deep and connected understanding of mathematics that they can apply in a range of contexts.
Representation and Structure
Teachers carefully select representations of mathematics to expose mathematical structure. The intention is to support pupils in ‘seeing’ the mathematics, rather than using the representation as a tool to ‘do’ the mathematics. These representations become mental images that students can use to think about mathematics, supporting them to achieve a deep understanding of mathematical structures and connections.
Mathematical thinking is central to how pupils learn mathematics and includes looking for patterns and relationships, making connections, conjecturing, reasoning, and generalising. Pupils should actively engage in mathematical thinking in all lessons, communicating their ideas using precise mathematical language.
Efficient, accurate recall of key number facts and procedures is essential for fluency, freeing pupils’ minds to think deeply about concepts and problems, but fluency demands more than this. It requires pupils to have the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections, and to choose appropriate methods and strategies to solve problems.
The purpose of variation is to draw closer attention to a key feature of a mathematical concept or structure through varying some elements while keeping others constant.
- Conceptual variation involves varying how a concept is represented to draw attention to critical features. Often more than one representation is required to look at the concept from different perspectives and gain comprehensive knowledge.
- Procedural variation considers how the student will ‘proceed’ through a learning sequence. Purposeful changes are made in order that pupils’ attention is drawn to key features of the mathematics, scaffolding students’ thinking to enable them to reason logically and make connections.
(Taken from The Five Big Ideas first published by the NCETM in 2017)
Click here to read the Maths Curriculum Statement.
Early Years Foundation Stage:
In EYFS, we have implemented Mastering Number from the NCETM with Shape, Space and Measure threaded through continuous provision based on planning from White Rose maths. Mastering Number aims to secure firm foundations in the development of good number sense for all children in EYFS as they start their mathematical journey in our school. We aim to ensure that children leave EYFS and make their way into KS1 with improved fluency in calculation and a greater confidence and flexibility with number.
Click here for an overview of the EYFS Mastering Number content.
Click here to read our Reception Calculation Policy.
Click here to for more information on the EYFS end of year expectations for Maths via the Early Learning Goals.
Key Stage 1 and Key Stage 2:
Power Maths is a whole-class mastery programme designed to spark curiosity and excitement and help pupils nurture confidence in maths. Power Maths is a mastery programme perfectly aligned to the White Rose Maths progressions and schemes of learning. It’s written specifically for UK classrooms by leading mastery experts, and is recommended by the DfE and is used from Year 1 to Year 6.
P = Pictorial. This uses pictorial representations and diagrams of objects to ‘see’ what maths problems look like. This might be drawn counters which represent each child in the maths problem.
A = Abstract. The ultimate goal is for children to understand abstract mathematical concepts and symbols.
What is the CPA approach?
Children 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, 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. With the CPA framework, 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 students 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.