Maths

Key Intentions

Within each unit of work children will follow a structured lesson sequence which include each of the following key intentions.

Intent:

The intention of the maths curriculum at Bradfield Dungworth is for children to master Maths by acquiring and achieving a deep, long-term, secure and adaptable understanding of the subject. We strive to embed the skills and processes necessary to enable children to use and apply their Maths learning in a variety of contexts. We achieve thus we aim to:

deliver an inspiring and engaging mathematics curriculum, taught by highly-enthusiastic and knowledgeable staff, which sparks curiosity and excitement and which nurtures confidence in maths.
create a vocabulary rich environment by modelling and supporting mathematical talk so that children will develop the ability to articulate and discuss their thinking.
Instil the mind-set in every child and staff member that everyone can do maths and that mistakes are learning tools that help us to grow.
teach in a way that develops children's ability to work both independently and collaboratively as part of a team.
teach fluency (conceptual understanding) so that all pupils to become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, which link to real life situations.
teach reasoning (mathematical thinking) to support children to develop mathematical ‘habits of mind’- to be systematic, generalise, make conjectures and seek out patterns.
Teach problem solving so that pupil can apply their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Implementation

At Bradfield Dungworth, we recognise that in order for pupils to progress to deeper and more complex problems, children need to be confident and fluent across each yearly objective. We provide age-appropriate fluency tasks for our pupils: in turn, practising key skills and allowing children be become confident when working on key strategies, calculations or methods. To ensure our pupils acquire a deeper understanding in their mathematical learning journey, we supplement our fluency resources by using the White Rose Maths Hub schemes of learning to support the teaching of mathematics.

Within the Maths Hub schemes of learning, each National Curriculum objective is broken down into fluency, reasoning and problem solving; our teachers use the learning challenges to teach for mastery - an approach to extend and deepen the understanding of pupils within each year group. Our teaching staff use these documents in conjunction with a range of high quality resources (such as NRich and NCETM) to support, stretch and challenge all learners within the classroom.

The content and principles underpinning the 2014 Mathematics curriculum and the Maths curriculum at Bradfield Dungworth reflect those found in high-performing education systems internationally. These principles and features characterise this approach and convey how our curriculum is implemented:

Teachers reinforce an expectation that all children are capable of achieving high standards in Mathematics and the vast majority of children progress through the curriculum content at the same pace with differentiation being achieved by emphasising deep knowledge and through individual support and intervention.
Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons and resources to foster deep conceptual and procedural knowledge.
To support the delivery of high quality teaching, a CPA (Concrete-Pictorial-Abstract) approach is taken. Reinforcement of learning is achieved by going back and forth between these representations, building pupils' conceptual understanding instead of an understanding based on completing mathematical procedures.
Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts. Spaced learning activities are planned for to ensure previously taught themes are revisited regularly.
Teachers use precise questioning in class to test conceptual and procedural knowledge and assess children regularly to identify those requiring intervention, so that all children keep up.
Maths meetings are used to consolidate key learning away from curriculum time. Each Maths Meeting lasts between 10 and 20 minutes and they happen regularly throughout the week (usually during assembly times). Each year group in school from Reception to Year 6 participates in Maths Meetings. Maths Meetings are a fantastic way for staff to support children with consolidating their knowledge and pre-teaching upcoming concepts, ensuring they are confident with skills required for the upcoming lesson.
Through our teaching, questioning and use of pre-unit and post-unit quizzes, we continuously monitor pupils’ progress against expected attainment for their age, making formative assessment notes where appropriate and using these to inform our teaching. Summative assessments are completed at the end of each half term using appropriate assessments for the cohort. We predominately use end of unit assessments from White Rose and Maths Frame. Whilst White Rose assessments include similarly styled questions and content to what is taught and completed in lessons, Maths Frame offers a more SATS style assessment which organises questions into National Curriculum criteria; this can be used to identify specific gaps, misconceptions and areas for improvement for each pupil.
Pupils are given time and opportunities to fully explore mathematical concepts. The challenge comes from investigating ideas in new and complex ways – rather than accelerating through new topics. While there is only one curriculum, we recognise that not all learners come to each lesson at the same starting point. Therefore, teachers adapt tasks by increasing/decreasing scaffolding and may put constraints in place to ensure each child is working at the correct level of challenge to maximise their personal potential.
We use a range of online tools: Times Tables Rock Stars for multiplication practise, application and consolidation; Numbots to support a foundation in maths in Key Stage 1; Maths Frame for maths games that link to specific curriculum objectives; Seesaw to allow us to set weekly maths homework that can be completed online.
We strive for continual professional development to further improve practice and frequently share ideas and strategies that have been particularly effective. This includes a Teaching for Mathematics project completed during 2022/2023 with NCETM.

Impact

There are a number of ways that the impact of our Mathematics Curriculum can be seen:

Pupil Voice

Through discussion and feedback, children talk articulately using mathematical language and vocabulary about their maths lessons and speak with enthusiasm about their love of learning in maths. They can talk about the context in which maths is being taught and relate this to real life purposes.
Children show confidence and believe they can learn about a new mathematical concept and apply the knowledge and skills they already have.

Learning walks

Provide clear evidence of successful practice: children’s confident use of concrete resources across school; opportunities for reasoning and problem solving; effective use of working walls to support and consolidate knowledge; appropriate vocabulary used throughout school; evidence of differentiation; evidence of developing number sense and derivation throughout school ; evidence of CPA alongside each other; evidence of variation theory; outdoor learning; staff adjusting planning and teaching to needs of children; evidence of staff confidently using concrete resources to support teaching and learning; peer support where children discuss work and support each others understanding; more consistent teaching practices that are well-known to be more effective for pupil progress long term, evident across school

Moderation

Cross-school moderation highlights the high level of challenge for all ability groups, evident throughout topics through reasoning and problem solving activities
Teacher assessment of the depth of learning is also increasingly accurate
Book looks show a progression throughout school and a consistency in what is taught and how.

Evidence of Knowledge

Pupils know how and why maths is used in the outside world and in the workplace. They know about different ways that maths can be used to support their future potential.
Mathematical concepts or skills are 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.
Children are engaged and all challenged to their full potential.
Children demonstrate a quick recall of facts and procedures. This includes the recollection of the times tables.

Concrete, pictorial, abstract

Objects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they’ve learnt.

All pupils, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. Pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.

Concrete – children have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.

Pictorial – children then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems.

Abstract – With the foundations firmly laid, children can move to an abstract approach using numbers and key concepts with confidence.

Links to long term planning for maths

Fawn

Aims of Calculation policy

This policy outlines progression through calculation strategies for addition, subtraction, multiplication and division in line with the new National Curriculum commencing September 2014 A school wide policy helps to ensure consistency of approach, enabling children to progress stage by stage through models and representations they recognise from previous teaching, allowing for deeper conceptual understanding and fluency. As children move at the pace appropriate to them, teachers will be presenting strategies and equipment appropriate to children’s level of understanding. However, it is expected that the majority of children in each class will be working at age-appropriate levels as set out in the National Curriculum 2014 and in line with school policy.

Each of the four operations build on a solid understanding of place value, the connections between the four number operations and number sense, such as: whether they are odd or even, whether they are close to multiples of ten or if they are close together:

Children need to use correct mathematical terminology in context and be able to verbalise their calculation strategies.
Children need to make considered decisions as to the most appropriate methods to make mathematics more functional. They need to choose the most appropriate, fluent, efficient and accurate method to do a particular calculation.
Children need to use concrete resources before they progress to pictorial and abstract representations. This CPA (concrete, pictorial and abstract) approach needs to be available to children throughout school, as and when necessary. Use of manipulatives (numicon, Cuisenaire, dienes, HTO counters etc.) helps reinforce understanding and provides support when calculating mentally, mentally with jottings, using expanded methods and formal written methods. Use of the bar model, number lines and partpart whole diagrams are recommended.
Children should progress between the stages working towards formal written methods (where appropriate), once they have mastered each stage. However, they should not be hurried and, after the method has been taught, children should still be able to make their preferred choice of the most appropriate, efficient and accurate method for them. Previous stages may need to be revisited to consolidate understanding when introducing a new strategy.
As new methods of calculations are introduced, children should have the opportunity to examine them, alongside the method they have consolidated, to make connections between the methods and establish the similarities and differences between them. This policy includes sections on: Addition, Subtraction, Multiplication and Division. It outlines progression in teaching, from mental through to formal written methods.

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Links for Parent/Carers

Below are some links to help Parents/Carers with maths at home

Calculating with Fractions

Multiplication

Subtraction

Times Tables