Intent

We believe that the language of mathematics is universal and develops a sense of COMMUNITY. The basic skills are fundamental for the life opportunities of our children. Therefore, we aim to ensure every child develops as confident and successful learners who show RESPONSIBILITY and have high aspirations to achieve in mathematics. We aspire to build fluent mathematicians who are able to TRUST their instincts and reason about key mathematical concepts and RESPECT other learners’ ideas. They can PERSEVERE and apply their mathematical knowledge to problems in a way that is meaningful to them and their everyday life to inspire them to have COURAGE to have a go. 

Our mathematics curriculum is structured, challenging and ambitious. We aim to promote the three key aims of the national curriculum: fluency, reasoning and problem-solving. Our mission is to enable all learners to enjoy and succeed in mathematics. 

We give children opportunities to develop fact fluency through varied and frequent practise with increasingly complex problems over time, which link to real life situations. This enables pupils to develop conceptual understanding and apply their mathematical thinking, allowing them to develop their ability to recall and apply knowledge rapidly and accurately. 

Throughout the school, we encourage children to develop high quality oracy skills in mathematics. We ensure mathematical thinking is a key element to enable learners to be responsible and confident. This ensures children can be systematic, generalise, make conjectures and seek out patterns in all areas of mathematical thinking. 

Planned opportunities for children to develop problem solving in mathematics provides a solid foundation for children to persevere and seek solutions.  Children are supported to make connections between their learning within and across curriculum areas especially when solving problems. 

To allow our children to be confident learners in mathematics and beyond, they need a mindset that facilitates the appreciation and celebration of making mistakes as a tool for growth. Our learning environments and teaching enable children to see the value of their mathematics learning, mistakes and all and how this contributes to their own mathematics journey. 

Implementation

source: ncetm.org.uk
Mathematics lessons are engaging, didactic and purposeful. In every lesson, we expose children to all three of the National Curriculum aims: fluency, reasoning and problem solving. We teach mathematics in blocks to develop a deeper understanding of key mathematical concepts, starting each year with place value; the fundamental building block which underpins all other mathematical knowledge and understanding. We use small steps to plan for teaching and learning of key concepts within each block.

 
On the whole, each lesson consists of 6 key areas of learning (although at a teachers’ discretion these may be split over two lessons or some parts may be revisited if misconceptions are highlighted):

•    Anchor Task- an open-ended question which allows all learners to participate at their own level and doesn’t put a ceiling on the learning. Examples include: what can you tell me about this number? What mathematics can you see? What’s the same and what’s different. This facilitates discussion and develops children’s oracy skills. 

•    Teach it- this is where the key concept and learning objectives are shared with the children. The teacher will identify the small steps within that lesson to enable all learners to succeed and become fluent in that concept. This will be done in line with the CPA approach- learners will have access to manipulatives as appropriate alongside pictorial images and the abstract mathematics. 
•    Practise it- working together as a class, children will have the opportunity to practise the key skill demonstrated by their teacher. This is will also include manipulatives where appropriate but allows the children to work collaboratively before independent learning takes place. 
•    Do it- independently, the children practise the key skill that has been taught, using manipulatives and jottings in their Maths books. This part of the lesson may also include conceptual or procedural variation to support the development of children’s knowledge. 
•    Twist it- the children have an opportunity to correct mistakes and explain their reasoning. They also begin to look for patterns and connections in calculations. Within this, they are expected to use reasoning to agree or disagree, or find the odd one out within various mathematical concepts. 
•    Deepen it- by applying their knowledge and skills, the children are expected to solve problems that may require deeper thinking. Problems such as how many ways and always, sometimes, never true, enable children to see a variety of answers and begin to explore answers in structured and systematic ways as well as giving another opportunity to explore mathematical reasoning and connections. 

     
The symbols, using communicate in print, allow all learners to see which part of the lesson they are on and provide them with a visual cue. 

Teachers also plan in opportunities for key instant recall facts (KIRFs) through Flashback Four, Times Tables Rockstars, Mastering Number and Morning Maths Activities which set the children up for the learning each day. 

Concrete-Pictorial-Abstract (CPA) 
We implement our approach through high quality teaching delivering appropriately challenging work for all individuals. To support this, we use a Concrete- Pictorial-Abstract (CPA) approach to teaching mathematical concepts. 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. 

•    Concrete - the doing: A pupil is introduced to an idea or a skill by acting it out with real objects. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding. 'Concrete' refers to objects such as Dienes apparatus, fraction tiles, counters, or other objects that can be physically manipulated. 
•    Pictorial - the seeing: A pupil may also begin to relate their understanding to pictorial representations, such as a diagram or picture of the problem. 
•    Abstract - the symbolic: A pupil is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6. This is the most formal and efficient stage of mathematical understanding. Abstract representations can simply be an efficient way of recording the Maths, without being the actual Maths. 

Impact
Through our teaching, questioning and use of 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 term using appropriate assessments for the cohort. Knowledge of children’s attainment and progress along with formative assessment data in EYFS, KS1 and KS2 contributes to discussions in termly pupil progress meetings and an update of our summative school tracker. The main purpose of all assessment is to always ensure that we are providing excellent provision for every child. In Reception, summative assessments take the form of termly 

‘Checkpoints’. Staff use their knowledge of the children alongside recorded evidence to make a judgement as to whether they are ‘On Track’ to reach the Early Learning Goal at the end of their Reception year. These judgements are accompanied by contextual discussions on children’s achievements and next steps for learning. 

Children 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. 

Pupil Voice
•    Through discussion and feedback, children talk coherently 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. 

Evidence in 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. 

Evidence in Skills
•    Pupils use acquired vocabulary in maths lessons. They have the skills to use methods independently and show resilience when tackling problems. 
•    They have the flexibility and fluidity to move between different contexts and representations of maths. 
•    Children show a high level of pride in the presentation and understanding of the work. 
•    They have the chance to develop the ability to recognise relationships and make connections in maths lessons. 
•    Children apply mathematical skills across different areas of the curriculum.