“Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is number.” Shakuntala Devi
At All Saints School, we believe that mathematics is essential to everyday life (critical to science, design, sport, technology & engineering, and vital for financial literacy.) One of our fundamental beliefs is that students deserve a creative and ambitious mathematics curriculum, rich in skills and knowledge, which ignites curiosity and prepares them well for everyday life and future employment. Our ethos is that all children can be successful in the study of mathematics. We do not accept that ‘some children cannot do Maths’ or that children should be limited by prior attainment. Maths is for everyone!
The ‘Intent’ of our mathematics curriculum has been derived from the aims of National Curriculum for Mathematics:
- Fluency: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately;
- Reasoning: reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;
- Problem Solving: 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.
Through our curriculum design, we ensure that all children can develop the mathematical skills and knowledge needed to become successful citizens of the world. Our ‘Teaching for Mastery’ approach enables children to be numerate, creative, independent, inquisitive, enquiring and confident. Children are taught not be afraid to make mistakes and fully embrace the fact that mistakes are part of learning! A mastery curriculum promotes a long-term, secure and adaptable understanding of the subject, so that children become fluent in the fundamentals of mathematics, develop conceptual understanding, the acquisition of reasoning skills and the ability to recall and apply knowledge rapidly and accurately. This ensures that those pupils beginning their education at school can access age-appropriate ideas as detailed in the DfE ‘Mathematics guidance: key stages 1 and 2’ (2020) publication, and do not see gaps open in their learning over time. The intention of the Maths curriculum at All Saints is for children to be excited about Maths! Developing a positive attitude to this subject is essential. Teachers promote children’s enjoyment of maths and provide opportunities for children to build a conceptual understanding before applying their knowledge to everyday problems and challenges. We ensure that challenge is provided for all children, whatever their understanding. Children are encouraged to be brave and push the boundaries, deepening their understanding further. The only way to learn mathematics is by doing mathematics!
The decisions taken in terms of curriculum design and intended learning/teaching practice are inextricably linked to necessary Continuing Professional Development (CPD) for teaching staff. School leaders ensure a range of CPD is made available, which means that strong consistency in practice is enabled across Years 1-6, whilst colleagues in Early Years are also aware about the mastery agenda and adopt relevant approaches to support the effective implementation of our mathematics curriculum offer.
We have developed the ‘All Saints School Maths Non Negotiables’ which are followed consistently across the school. In every lesson, there are opportunities for children to:
- Participate in active discussions giving reasons for their opinions
- Practise and rehearse the precise use of mathematical language
- Explore concepts through concrete, pictorial and abstract approaches
- Dig deeper, reason, learn from mistakes and misconceptions
- Be challenged through questioning
- Develop understanding and independence through teacher modelled activities, guided work and independent application of concepts
- Evaluate their understanding
- Find mathematics engaging and challenge through appropriately pitched lessons taught at the correct pace to facilitate optimum learning.
Differentiation is likely to appear very subtle. Scaffolding is the key tool which teachers will use to ensure that all pupils can make progress through the learning point based on their individual starting points. Varied use of practical resources/models and images, plus questioning that requires deeper reasoning, are used to ensure that all children are supported/challenged appropriately. Further challenge is also provided to all children through problem solving, including those linked with real-life contexts.
We understand the need for pupils to achieve key objectives for their current stage of learning but are aware that some children will have gaps in their pre-requisite knowledge. Consequently, in lessons, teachers use precise and purposeful questioning to check conceptual and procedural knowledge. They formatively assess in order to identify need within the class or individuals/groups of pupils who require intervention. This can include by making adaptations to lessons, in-class support or by attending same day intervention, meaning that all pupils are expected to ‘keep up’ rather than ‘catch-up’. When interventions are used, they focus on ensuring that pupils are helped to keep up by revisiting concepts and/or being provided with prior learning in advance of lessons. Where children have vulnerability factors, other targeted/specialist intervention is provided by skilled practitioners.
Through pupils’ learning experiences, teachers promote connections within and across Key Stage 1 and 2 National Curriculum domains, so that children are taken deeper with their understanding over time and recognise the interconnectedness of concepts. Pupils revisit concepts, for example, multiplication within area when presented as an array model, which means they absorb learning within their long-term memory. To secure firm foundations in early mathematics learning, those children in Early Years benefit from daily adult directed teaching experiences, which are then supplemented through opportunities to further engage because of child-initiated learning.
It should be noted that varied use of practical resources, structures and representations, plus questioning that requires deeper reasoning is used to ensure all children are supported/challenged appropriately. A progression in key representations and structures, leading to understanding of sometimes complex and abstract concepts, is exemplified in the school’s calculation policy. This in turn supports the delivery of consistent approaches and equity of access for learners.
The attainment and progress of pupils’ learning is tracked by class teachers and senior leaders so that swift interventions can be put into place and may include the use of pre-teaching.
In cases where children’s learning is most effectively being deepened, the following descriptors can be seen in their learning:
Depth Greater Depth
The school’s Marking and Feedback policy allows children’s levels of independence to be evident, as instances where pupils have the most secure knowledge and skills can most easily be recognised when they’ve applied learning independently and in a range of ways, including across different areas of the curriculum. On occasions when such extended depth has yet to be developed, an expected impact of our curriculum offer is that children are, at least, ready to move on to the next key stage of learning. This can be judged by each pupil’s capacity to access age appropriate ready-to-progress criteria in Years 1-6 as detailed in the ‘Mathematics guidance: key stages 1 and 2’ publication. In Reception, we implement the latest Early Years Framework, which became statutory in September, 2021, and the impact of our increasing emphasis on progressive learning is that increasing proportions of children secure understanding of all concepts and skills detailed in progression charts related to the six key areas of early mathematics learning. This is expected to further impact by in turn allowing them to attain the Early Learning Goals (ELGs) for mathematics.
Throughout our Maths teaching, teachers assess the impact of what has been learnt through classroom feedback and marking of work. Teachers then plan and deliver lessons to address the needs of all pupils with the use of scaffolding, skilful questioning, rapid intervention and carefully designed enriching activities. The vast majority of pupil’s progress through the programmes of study at broadly the same pace. Pupils who grasp concepts rapidly are challenged by being offered rich and sophisticated problems before any acceleration to new content. Those who are not sufficiently fluent with earlier material consolidate their understanding, including through additional practice, before moving on. Teachers aim to rapidly address gaps in children’s understanding within the lesson and through targeted intervention outside of the lesson. Consistency in teaching mathematics across the entire school is achieved by teachers planning and delivering lessons with the aid of high-quality and rich resources including primarily The NCETM Curriculum Prioritisation in Primary Maths and other resources such as Maths No Problem, White Rose, NRICH.
Assessment is used purposefully to plan subsequent maths lessons, identifying intervention support for children who may require it for a particular point in time and support accurate teacher assessment judgements. Teachers assess continuously throughout the learning journey using a broad range AfL techniques. The rationale behind assessment in Maths is to give an accurate picture of children’s attainment and progress against that which has been taught rather than over-relying on pre-produced assessments which give a snapshot of coverage from across the curriculum. The impact of our curriculum on pupils’ development of mathematical knowledge and skills is measured formatively and summatively.
Regular and ongoing assessment by teachers and the use of rapid intervention, support and enable the success of each child. Senior Leaders and the Mathematics Lead rigorously monitors teaching and learning to ensure that pupils make good progress across the school. These factors ensure that we are able to maintain high standards in mathematics, with achievement at the end of Key Stage One and Key Stage Two being in line or above the national average. In the Early Years, a mixture of child-initiated and quality teacher-led learning enables the vast majority of pupils to progress seamlessly onto the National Curriculum by achieving their Early Learning Goals in mathematics. Upon completion of Year 6, our curriculum enables pupils to be fully prepared and equipped to successfully continue their mathematical learning journey at secondary school and in their later lives.
How can I support my child with Maths?
Advice for Parents from Professor Jo Boaler, Professor of Mathematics Education at the Stanford Graduate School of Education.
- Encourage children to play maths puzzles and games. Puzzles and games – anything with a dice really – will help children enjoy maths, and develop number sense, which is critically important.
- Always be encouraging and never tell children they are wrong when they are working on maths problems. Instead find the logic in their thinking – there is always some logic to what they say. For example, if your child multiplies 3 by 4 and gets 7, say – “Oh I see what you are thinking, you are using what you know about addition to add 3 and 4, when we multiply we have 4 groups of 3…”
- Never associate maths with speed. It is not important to work quickly, and we now know that forcing children to work quickly on maths can cause maths anxiety for children. Instead of speed drills use visual, fun activities.
- Be positive about maths… even if your feelings about your own maths education is not!
- Encourage number sense. What separates high and low achievers is number sense – having an idea of the size of numbers and being able to separate and combine numbers flexibly. For example, when working out 29 + 56, if you take one from the 56 and make it 30 + 55, it is much easier to work out. The flexibility to work with numbers in this way is what is called number sense and it is very important.
- Perhaps most important of all – encourage a “growth mindset” let your children know that they have unlimited maths potential and that being good at maths is all about working hard. When children have a growth mindset, they do well with challenges and do better in school overall. When children have a fixed mindset and they encounter difficult work, they often conclude that they are not “a maths person”. One way in which parents encourage a fixed mindset is by telling their children they are “clever” when they do something well. That seems like a nice thing to do, but it sets children up for difficulties later because when children’s fail at something they will inevitably conclude that they aren’t clever after all. Instead, use growth praise such as “It is great that you have learned that!”, “I really like you’re thinking about that!”. When they tell you something is hard for them, or they have made a mistake, tell them: “That’s wonderful, your brain is growing!”