Maths - Intent
The purpose of mathematics at Withycombe Raleigh C of E Primary School is to ensure that children develop and associate enjoyment, motivation and enthusiasm with learning Maths that will stay with them throughout their lives.
We understand that by being taught Maths effectively, children are able to develop a logical and methodical mind-set and show increased resilience and focus in their approaches to problem solving. Maths at WRPS sets out to deliver ‘The Education Inspection Framework’s’ advice, in providing a Maths curriculum which ‘helps pupils to gain enjoyment through a growing self-confidence in their ability’
Maths is a life skill that is used on a daily basis. Therefore, mathematics forms an important part of our broad and balanced curriculum, permeating through many foundation subjects whilst also being taught discretely.
At Withycombe Raleigh CofE Primary School, we believe that unlocking mathematical fluency is essential for all learners and is a prerequisite to being able to reason and solve problems mathematically.
Children will have opportunities to develop their mathematical skills by applying their knowledge to real life situations through reasoning and problem solving. In doing so, children will be able to connect their learning to the real world. Our aim is to develop a positive culture of deep understanding, confidence and competence in Maths that produces strong, secure learning foundations upon which children can continue to build throughout their education and into adult life.
We recognise how and when Cognitive Load Theory and Rosenshine’s Ten Principles of Instruction can be applied to create effective learning opportunities by employing teaching and learning methods that reflect this. We want children to develop links to their prior learning both in Maths and across the curriculum in order to improve their understanding.
Opportunities are planned to develop children’s spiritual, moral, social and cultural development, including through the school’s GRACE values. We encourage the children at Withycombe Raleigh C of E Primary School to delve deeper into their understanding of Maths and how it relates to the world around them. Sequences, patterns, measures and ultimately the entire study of Maths was created to make sense of the world around us and we aim to enable children to use Maths as a tool to explore its wonder more fully.
The moral development of children in Maths is an important thread which runs throughout our mathematics curriculum; children apply and explore the skills required in a variety of real-life contexts, being made aware of the fact that the choices they make will have consequences.
At WRPS we ensure that foundational knowledge, particularly a proficiency in number, gives pupils the ability to progress through the curriculum more effectively later on in their primary education. We are mindful of the journey that our individual pupils take and their readiness for achieving greater problem-solving proficiency.
Problem solving skills and teamwork are fundamental to Maths, and are encouraged through creative thinking, discussion, explaining and presenting ideas with others. Mathematics is a universal language with a myriad of cultural inputs throughout the ages which we aim to reflect in our mathematics provision at Withycombe Raleigh C of E Primary School.
It is our intention that children will unlock their critical thinking and potential for problem solving through the development of basic number skills and the deep understanding of mathematical concepts. We therefore place great emphasis on the use of concrete resources and pictorial representations at all ages, to enable children to fully understand the concepts and principles, when presented with abstract calculations and questions.
At Withycombe Raleigh C of E Primary, our Maths curriculum is progressive. In Key Stage One, it is designed to develop competencies to equip children for Key Stage Two where they will build on their knowledge, make connections and solve increasingly sophisticated problems.
In ensuring high standards of teaching and learning in mathematics, we implement a curriculum that is progressive throughout the whole school. Our curriculum provides breadth and balance, is relevant and engaging and is differentiated to match the needs and abilities of all our children to ensure that all pupils are able to excel.
The White Rose Scheme of Work builds upon children’s prior knowledge, understanding and skills over time. Systematic and coherent planning resources are provided, while still providing teachers with a freedom to choose how to teach. The core content of the curriculum has been sequenced effectively and it is taught in a way that links together knowledge of facts with methods. Pupils are increasingly able to access their familiarity with the facts and methods to learn strategies for solving problems more proficiently and with greater automaticity.
Maths lessons at Withycombe include a recap of prior learning which encompasses strategies to support Rosenshine’s Principles of Instruction (2010). The four strands (Reviewing Material, Questioning, Explaining and Modelling and Practising) suggested by Rosenshine are embedded throughout. Using methods such as the daily use of ‘Flashback 4’ ensures that previous concepts are revisited and children are given ample opportunities for retrieval practice in order to lighten the cognitive load. This allows children to develop their own schema, committing learning to their deep processing and semantic memory. This is carefully thought-out and designed by teachers, allowing them to draw upon previous successes and content (whether in the previous lesson, the previous week, the previous term or the previous year), preparing children for what they are about to learn in the current teaching session. We are also careful not to overload children’s thinking by presenting them too much content in one session; using a small steps approach ensures that children can fully understand and access their learning.
At Withycombe Raleigh CofE Primary School, we believe in the importance of following the concrete-pictorial approach as a means of developing a solid understanding of mathematical concepts which can be applied in a variety of contexts through reasoning and problem solving challenges. The White Rose Scheme of Work uses pictorial representations to scaffold and develop a deep understanding of mathematical ideas. This, alongside the use of a wide range of manipulatives, enables our children to explore their understanding and develop strong connections before moving onto more abstract concepts.
Our Maths curriculum is also supported through the implementation of carefully selected, high quality resources from Classroom Secrets, Deepening Understanding and other sources such as NRich to develop fluency, reasoning and problem solving. White Rose and Classroom Secrets break down the teaching sequences into small achievable steps which carefully build childrens’ deep and thorough understanding of the concept being taught.
Teachers help pupils develop their automatic recall of core ‘declarative knowledge’ (fact retrieval) rather than relying on guesswork.
Times tables play an important part in our Maths learning, with children developing their fluency in rapid recall of tables up to 12 x 12 by the end of Year 4. While the rapid recall of times tables are being developed, children are also learning how to apply and manipulate their understanding of this to reason and solve problems. Times tables facts underpin several mathematical areas, including fractions, decimals, percentages as well as ratio and proportion, meaning that children require a solid understanding and quick recall of facts to be able to fully access these areas.
Retention and application of prior knowledge are identified via regular retrieval practice and through start-of-unit elicitation tasks. Progress across a unit is measured by daily formative assessment, through live and verbal feedback during lessons and marking. This is supported by end of unit assessments. Longer-term retention is also assessed summatively through end-of-term arithmetic and reasoning assessments.
From EYFS to Year 6, we adhere to our calculation policy which outlines the progression of strategies and methods to be taught. Strategies, such as the use of the number-line, are developed across the school to ensure that children’s understanding of numbers is secure and that these skills can then be applied to other areas of Maths (e.g. algebra in Year Six).
From the onset, teachers ensure the best possible start for pupils by closing school-entry gaps in knowledge of the early Maths including: facts, concepts, subject vocabulary and symbols.
As they progress, older pupils are taught efficient, systematic and accurate mathematical ‘procedural’ methods as well as facts which they can use for more complex calculations (‘conditional’ learning, where children begin to choose strategies) and in their next stages of their Maths education.
At WRPS we recognise the importance of ensuring that our children are helped in such a way that leads to a journey from success to motivation. We do so by focusing on early proficiency and success. This proficiency-first approach will also prevent many pupils developing anxiety about ‘struggling in Maths.’
Where children require additional support, ‘scaffolds’ are used to support children further to ensure that they have secured the small step before moving on. These ‘scaffolds’ may be in the form of returning to concrete resources or pictorial representations. For children who understand a concept quicker, challenges are used to deepen their understanding.
We also recognise that some children may achieve greater proficiency when teachers respond to their interests and by ensuring that they are given dedicated time to learn and rehearse mathematics every day. It is important to us that children who struggling or at risk of falling behind are given more time to complete tasks, allowing them to commit core facts and methods to their long-term memory. Where children require additional support in addition to their lessons, the necessary interventions are targeted specifically to meet the needs of children. Where appropriate, pre-teaching is used to assign competence and build confidence prior to the lesson itself.
Progression documents such as our calculation policy are carefully used to ensure that children are not being stretched outside their year group but rather deepened within it.
Children’s Maths knowledge is developed and used where appropriate across our wider school curriculum – we believe that ‘real life’ learning can help children to develop their knowledge, skills and understanding and become motivated to learn through interconnected topics.
Our pupils are given every opportunity to participate in a wide range of mathematical learning experiences beyond their classroom. These experiences include: trips, visitors, involvement in project weeks (‘Inspirational Maths’), the use of our outdoor and local environment and opportunities to participate in Maths competitions. These opportunities encourage more positive attitudes towards Mathematics. We believe that by extending children’s ‘Cultural Capital’ and extending their essential knowledge that children will be better prepared for their future success, becoming valued contributors to society.
Maths Leads and School Leaders organise regular opportunities to observe Maths. At WRPS we have school-wide approaches developing staff subject knowledge and to learn valuable ways of teaching from each other. This way we ensure that teachers have sufficient knowledge to deliver topics effectively.
The impact of quality first teaching in mathematics will ensure that children have a lifelong love of learning for Maths. They will understand its applications in real life situations and its relevance beyond the classroom.
Through discussion and feedback children talk enthusiastically about their Maths and speak about how they love to learn about and from Maths.
They know about different ways that Maths can be used to support their future potential and have the flexibility and fluidity to move between different contexts and representations in Maths. They can articulate the context in which Maths is being taught and relate this to real-life situations.
We aspire for our children have secured strong fundamental knowledge in Maths, developing early proficiency, particularly around ‘number’.
Children show confidence and believe that they can learn about a new Maths area and apply the knowledge and skills they already have.
The children remain motivated and can also celebrate their mistakes, learning from each and every one that they make.
Our children are able to review their successes in achieving the lesson objectives and are actively encouraged to identify their own areas of development. This response to their own learning can take many forms and progress throughout the school, starting with a simple ‘smiley face’ system in Year One, ranging to a full written feedback based on the children’s perception of their confidence and attainment within the learning objective in Year Six.
They are therefore well-prepared for assessments, having learned the key facts, methods and strategies that are likely to be tested. At the end of each year, we expect the children to have achieved Age Related Expectations (ARE) for their year group. Some children will have progressed further and achieved Greater Depth (GDS).
Children who have gaps in their knowledge receive appropriate support and interventions. All children secure a long-term, deep and adaptable understanding of Maths which they can apply in a range of contexts. We aim that children make outstanding progress over time from their own starting points and that teachers endeavour to clearly know and assess what children have learnt and what might need to be reviewed or re-taught as they progress.
Progress is monitored by class teachers, Maths Leads and the Senior Leadership Team. Monitoring is multi-faceted and is used to ensure the best possible outcomes for all children.
Lesson observations and feedback, learning walks, pupil conferencing, monitoring of planning, frequent book looks and termly data analysis all contribute to the rigorous monitoring cycle at Withycombe Raleigh CofE Primary School. Triangulated data is collected termly and reported to the Senior Leadership Team. This is discussed at termly monitoring meetings where in-year and across key stage data and progress are analysed in order to provide additional support where needed, identifying children at risk of not making good progress or meeting age-related expectations and focusing on next steps.
At the end of Year Six, as they make the transition to secondary school, we aspire that a Withycombe Raleigh mathematician will have developed a bank of efficient and accurate knowledge and skills that can be used to calculate and problem-solve effectively. These will have been underpinned by the Concrete-Pictorial-Abstract process so that children understand rather than just do, which ultimately will allow children to identify when answers do not make mathematical sense. Their understanding is relational rather than instrumental which ensures that children will be able to apply these calculation skills and understanding of other mathematical concepts to become confident and resilient problem-solvers with the ability to reason and articulate their ideas mathematically.