White Rose Maths at West Wycombe School

West Wycombe's maths curriculum ensures a solid foundation in early years, focusing on counting, number recognition, and essential measurement. As students progress through the years, they revisit these foundational concepts with increasing complexity, ensuring that each new layer of learning builds on previous knowledge. This spiral approach helps students retain and deepen their understanding of mathematical principles, preparing them for more advanced studies and practical applications.

The curriculum is structured to provide a balanced mix of theoretical knowledge and practical problem-solving skills. By the time students reach Year 6, they are equipped with a comprehensive understanding of mathematics that they can apply in real-world scenarios, ensuring they are well-prepared for secondary education and beyond.

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 which 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, Pictorial, 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, 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 Recap and Recall 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. 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 help teachers to plan the next stages in the learning for their class.

Concrete, Pictorial, Abstract

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.

Pictorial

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.

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.

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.

The mathematics curriculum from Reception to Year 6 is designed to build on foundational skills progressively, ensuring that students develop a deep and comprehensive understanding of mathematical principles.

Here are the key links and progression of skills throughout the years:

Reception

Autumn Term:

• Matching, Sorting, and Comparing: Basic skills include matching objects, sorting by type and comparing amounts. These activities lay the groundwork for understanding classification, grouping, and numerical comparison.

Spring Term:

• Numbers 6, 7, and 8: Identifying, representing and understanding the relationships between these numbers, including concepts of one more, one less and composition. This introduces early number sense and basic arithmetic operations.

Summer Term:

• Addition and Subtraction: Engaging in adding and subtracting small quantities, tracking changes and understanding the effects of these operations. This reinforces counting and basic arithmetic.

Year 1

• Counting Techniques: Counting in 2s, 5s, and 10s, recognising and adding equal groups. These skills are foundational for understanding multiplication and division.

• Basic Arithmetic: Simple addition and subtraction, understanding number bonds and beginning to solve problems involving these operations.

Year 2

• Place Value: Understanding tens and ones, comparing and ordering numbers up to 100 and using place value to solve problems.

• Addition and Subtraction: Building on Year 1 skills with more complex issues and introducing mental calculation strategies.

• Multiplication and Division: Introduction to multiplication and division, including arrays, repeated addition and sharing.

Year 3

• Addition and Subtraction: Adding and subtracting 2-digit and 3-digit numbers, understanding complements to 100 and estimating answers.

• Multiplication and Division: Multiplying and dividing 2-digit numbers by 1-digit numbers, understanding the relationship between multiplication and division and solving problems involving these operations.

• Fractions: Introduction to fractions, including understanding parts of a whole and equivalent fractions.

Year 4

• Multiplication and Division: Multiplying and dividing larger numbers, including 3-digit numbers, by 1-digit numbers and solving correspondence problems.

• Fractions: Building on Year 3 skills with more complex fractions, including adding and subtracting fractions with the same denominator.

• Measurement: Understanding and converting between different units of measure, including length, mass, volume and time.

Year 5

• Place Value: Understanding numbers up to 1,000,000, including reading, writing, comparing and rounding large numbers.

• Addition, Subtraction, Multiplication, and Division: Advanced techniques, including long multiplication and division and solving multi-step problems.

• Fractions, Decimals, and Percentages: Understanding the relationship between fractions, decimals and percentages and solving problems involving these concepts.

Year 6

• Place Value: Understanding numbers up to 10,000,000, including reading, writing, comparing and rounding large numbers.

• Addition, Subtraction, Multiplication, and Division: Advanced techniques, including long division, multi-step problems and using factors and multiples.

• Fractions, Decimals, and Percentages: Solving complex problems involving fractions, decimals, and percentages, including converting between these forms.

• Ratio and Proportion: Introduction to ratios, scale factors, and similar shapes and solving problems involving proportional relationships.

• Geometry: Advanced study of shapes, including properties of quadrilaterals, angles, and symmetry and exploring transformations such as reflection and translation.

• Statistics: Interpret and represent data using charts, graphs, and tables, as well as analyse data to draw conclusions.

Key Links and Progression

• Number Sense and Place Value: From recognizing and comparing small numbers in Reception to understanding large numbers and their properties in Year 6.

• Arithmetic Operations: Starting with basic addition and subtraction, progressing to multiplication and division, and culminating in complex multi-step problems.

• Geometry and Spatial Reasoning: Beginning with simple shape recognition and building up to advanced concepts like transformations and properties of shapes.

• Measurement and Data Handling: From basic measurement and tracking changes to interpreting complex data and solving real-world measurement problems.

• Fractions, Decimals, and Ratios: Gradual introduction and deepening understanding of parts of a whole, equivalent fractions and proportional reasoning.

This structured and incremental approach ensures that students build on their prior knowledge, reinforcing and expanding their understanding of mathematical concepts year by year. The curriculum is designed to develop both procedural fluency and conceptual understanding, preparing students for more advanced mathematical studies and real-world applications.

Maths SATS results 2024: The overall performance of the whole cohort was strong, with 90% of students meeting age-related expectations (EXS) and 57% achieving greater depth (GDS).