At Thorney Close Primary School, we’ve embraced the new approach to deepening children’s understanding of Maths and have developed our teaching using the White Rose Maths Hub’s resources. The mastery approach to the teaching and learning of Mathematics enables our children to grown into competent and independent mathematicians as well as creative problem solvers. Our curriculum is designed to enable our pupils to develop a secure understanding of each area of mathematics, recognising the rich and varied connections between them. It is our intention to ensure that all children are fluent in the fundamentals of mathematics. Children are encouraged to be flexible and adaptable, applying their learning to investigate, reason and solve increasingly sophisticated problems.
All children access a daily maths lesson, which is engaging and accessible for all. Through mathematical talk, children will develop the ability to articulate, discuss and explain their thinking. Maths lessons will be meaningful with an emphasis on the application of mathematics to real life examples and to develop an understanding of the value of money. We aspire to develop a natural curiosity and love of Maths, where children are equipped with the confidence, resilience and resourcefulness needed to use Maths within all aspects of everyday life.
We believe Maths is a journey from which many start at different places. However, our intention is that children foster a love of mathematical learning, whatever their ability or starting place and that they are able to confidently use and apply mathematical concepts across a variety of situations. We expect children to clearly articulate their ideas and thoughts and reasoning processes, enabling deeper learning. We expect children to make mistakes, analyse them and learn from them, justifying and explaining as they do this. At each stage of learning, children should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.
How we Teach Maths at Thorney Close Primary School
We aim to provide all pupils with some direct teaching every day, which is oral, interactive and stimulating. Teaching styles and lesson structure provide opportunities for pupils to consolidate their previous learning, use and apply their knowledge, understanding and skills, pose and ask questions, investigate mathematical ideas, reflect on their own learning and make links with other work. A typical lesson will comprise of a ‘Memory Jogger’ and ‘Guided Practice’ followed by independent work, often adapted from the White Rose Maths resources.
In line with the 2014 National Curriculum for mathematics, Thorney Close Primary School aims 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 have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
- 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.
Mathematics is a diverse subject in which pupils need to be able to confidently move fluently between mathematical ideas. The programmes of study are, by necessity, organised into distinct areas, but pupils will be taught to develop their own rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They will also apply their mathematical knowledge to science and other subjects.
The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace – becoming masters in each key concept as they do. However, decisions about when to progress will always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly will be challenged through being offered rich and sophisticated problems before any acceleration through new content. Mastery teaching provides our children with the time to acquire a deep and transferable understanding of mathematical concepts. Children in the bottom 20% of the school population will make good progress due to staff considering and planning steps to allow them to overcome their learning barriers.
We have high aspirations for all learners, and each child’s learning in Maths is centred around a growth mindset. Our children fully believe that, regardless of their ability, they can develop their skills through dedication and hard work. This view of Maths creates a love of learning and a resilience that is essential for deep, challenging learning and ultimate success. As such, pupils are taught through whole-class, interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time. This ensures that all can master concepts before moving to the next part of the curriculum sequence. Differentiation is through depth and not breadth. Pupils who grasp concepts rapidly are challenged through rich problems that encourage them to explore a concept in greater depth, reason about their learning or make new connections.
Sequencing of Lessons
Lessons are sequenced in small steps, following the guidance offered by the White Rose Maths Hub’s recommendations. Topics are taught in appropriately sequenced blocks to allow children to acquire a depth of understanding in each area of Maths before moving on, and although these have been allocated specific teaching weeks, we have built in the opportunity for teachers to extend learning where necessary. Significant time is spent developing a deep knowledge of the key ideas that are needed to underpin future learning. The same mathematical models and vocabulary is used across school to ensure consistent progression between year groups. All topics are regularly revisited in ‘morning maths’ fluency sessions, and are applied to other areas of learning, making cross curricular links where relevant, to ensure the retention of knowledge over time. The structure and connections within the mathematics are emphasised, so that pupils develop deep learning that can be sustained.
Representation and Structure
Concrete and pictorial resources are used to introduce new learning and are revisited regularly to ensure children have strong number sense and procedural understanding, and to help develop their understanding of new concepts as well as make links between embedded and new learning. Scaffolds (such as new vocabulary and representations should be included on the Maths Working Wall).
The Concrete Step of CPA
Concrete is the “doing” stage. During this stage, children 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. 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.
The 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.
The Abstract Step of CPA
Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Children 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, subtraction, multiplication or division.
Although CPA is understood as three distinct stages, a skilled teacher will go back and forth between each stage to reinforce concepts.
It is our intention to ensure that all children are fluent in the fundamentals of mathematics. Procedural fluency and conceptual understanding are developed in tandem because we recognise that each supports the development of the other. Gaining fluency with key number facts and mathematical procedures forms an integral part of our daily Maths teaching. This includes helping children to learn to recall key facts automatically. Children are encouraged to work flexibly, recognising that calculations can be solved in a variety of ways.
Teachers make use of resources provided by the White Rose Maths Hub to sequence learning in small steps and to teach with variation. Teaching with variation involves presenting the same concept in different ways in order to encourage children to make connections and comparisons. For example, they may be asked to consider ‘What’s the same?’ and ‘What’s different?’ about two different representations of the same concept. This helps to deepen children’s understanding of the mathematical concepts they are taught, so that they can be flexible in their thinking and adapt their learning to new contexts.
Mathematical talk and discussion are used to provide opportunities for children to reason mathematically. Children are encouraged to spot patterns, make connections and use mathematical language to justify their views. Our children are taught to apply their knowledge of mathematics to help them solve routine and non-routine problems with increasing sophistication, and are encouraged to be both flexible and resilient when seeking solutions.
How we Evaluate Learning
- Learners who can clearly explain their reasoning and justify their thought processes
- Quick recall of facts and procedures
- The flexibility and fluidity to move between different contexts and representations of mathematics.
- The ability to recognise relationships and make connections in mathematics.
- Happy, confident, articulate and autonomous learners with a life-long passion for learning
At Thorney Close Primary School, we believe a mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations.
Assessment is woven into Maths lessons so that teachers have a clear idea of what has been mastered and what each child’s next steps are. However, we also complete a termly summative assessment using resources designed in line with The White Rose Maths Hub's approach. Planning is responsive – teachers plan to meet children’s gaps on a daily, weekly and termly basis. All assessment is low-stakes and takes place as a normal part of the maths lesson routine. Children have access to any equipment that may help them to be successful and are encouraged to self-select what they need. In this way, pupils are taught to be reflective and are involved in seeing their progress and their next steps.
Long Term Overview