Maths

White Rose Maths at West Wycombe School

Intent

At West Wycombe, we make sure that our students develop a life-long love of Maths. Mathematics is an important creative discipline that helps us to understand and change the World. We want all pupils at West Wycombe to experience the beauty, power and enjoyment of mathematics and develop a sense of curiosity about the subject.

At West Wycombe School, we foster a growth mindset attitude and believe that everyone can learn and achieve in mathematics and teach for secure and deep understanding of concepts. We use mistakes and misconceptions as an essential part of learning and provide challenge through rich and sophisticated problems before acceleration through new content. Our children are proud of our school values and discussed how they show these within our Maths lessons. They think they show these by: working hard; never giving up; looking after equipment; helping someone who is struggling; saying if we are stuck; not copying each other’s work; encouraging each other; have belief in ourselves; and being happy that we can learn from our mistakes.

Implementation

At West Wycombe School, Maths is taught in classes every day. We have a Maths lesson each day with covers the small steps children need in order to progress in their learning.

• Staff use White Rose Maths as a starting point in order to develop a coherent and comprehensive conceptual pathway through the mathematics. The focus is on the whole class progressing together
• We use a Concrete, Pictoral, Abstract (CPA) approach to teach concepts- for more on this, see below
• We focus on times tables practice, effective intervention and ambitious progression- see Cracking Times Tables below for more
• Learning is broken down into small, connected steps, building from what pupils already know.
• Difficult points and potential misconceptions are identified in advance and strategies to address them planned.
• Key questions are planned, to challenge thinking and develop learning for all pupils.
• Contexts and representations and resources are carefully chosen to develop reasoning skills and to help pupils link concrete ideas to abstract mathematical concepts.
• The use of high quality materials and tasks to support learning and provide access to the mathematics, is integrated into lessons.

In a typical lesson, teachers use Flashback 4 questions to review prior learning. Children follow steps to success to show them how to achieve in their learning. Teachers scaffold and challenge work appropriately to the needs of the learners in their class. When the children have completed their independent work, they are given opportunities to self-mark and correct any misconceptions they have come across. All children are encouraged to reflect on their learning and think about their next steps.

Children are assessed regularly using formative and summative assessments. Teachers use their formative assessments to plan the next steps in learning for their class. Each term, children take a PiXL assessment to show how their learning has progressed. Analysis of these helps teachers to plan the next stages in the learning for their class.

Concrete, Pictoral, Abtract

So what is the CPA approach?

Children and adults can find maths difficult because it is 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. This approach is proven to be highly effective around the world. 

Concrete

Concrete is the “doing” stage, using concrete objects to model problems. Instead of the traditional method of maths teaching, where a teacher demonstrates how to solve a problem, the CPA 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.

Pictoral

Pictorial 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.

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.

Abstract

Abstract 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.

Although we’ve presented CPA has three distinct stages, a skilled teacher will go back and forth between each representation to reinforce concepts.

Our approach encourages teachers to vary the apparatus the children use in class, for example, one day they might use counters, another day they might use a ten frame. Likewise, children are encouraged to represent the day’s maths problem in a variety of ways, for example, drawing an array, a number bond diagram or a bar model. By systematically varying the apparatus and methods they use to solve a problem, we help children to make quicker mental connections between the concrete, pictorial and abstract phases.

When teaching young children, exposing to abstract concepts too early may mean that children are missing out on the opportunity to build the conceptual mathematical understanding which they need to take them through their education. However, it should never be a case of concrete ‘good’, abstract ‘bad’. It is important to recognise that the CPA model is a progression. By the end of KS1, children need to be able to go beyond the use of concrete equipment to access learning using either pictorial representations or abstract understanding. What is important, therefore, is that all learners, however young, can see the connections between each representation.

Impact

As a result of Maths teaching at West Wycombe School, our pupils:

• enjoy and are engaged in lessons;
• take an active role in their learning;
• demonstrate resilience when attempting to solve problems, and are able to choose the equipment and strategies they think are best suited to each problem;
• develop skills in being able to reason verbally, pictorially and in written form;
• are confident talking about maths using appropriate mathematical vocabulary;
• can recognise relationships and make connections in maths lessons;
• demonstrate mastery of mathematical concepts or skills through independently applying concepts to new problems in unfamiliar situations;
• achieve high outcomes in maths at the end of Key Stage 2.

In the 2022 statutory assessments at the end of Key Stage 2, 79.2% of our Year 6 pupils achieved Expected standard in maths and 33% achieved Greater Depth standard. We have set ambitious targets for the 2023 outcomes in maths at the end of Key Stage 2. We are aiming for 82% of our Year 6 pupils to achieve Expected standard in maths and 32% to achieve Greater Depth standard. 

Page last updated: 27/04/24