Purpose of study
Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
The national curriculum for mathematics 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 develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
- 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 an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should 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. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.
We believe mathematics is an important part of children’s development throughout school, right from an early age. We intend to deliver a curriculum with a mastery approach that has three key principles: deep understanding, mathematical thinking and mathematical language, with problem solving at the heart.
- Gives each pupil a chance to BELIEVE in themselves as mathematicians and develop the power of resilience and perseverance when faced with mathematical challenges.
- Recognises that mathematics underpins much of our daily lives and therefore is of paramount importance in order that children ASPIRE to develop their mathematical understanding.
- Through high quality teaching and learning opportunities they strive to ACHIEVE their full potential.
- Makes rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems.
- Provides equal opportunities for children to apply their mathematical knowledge to other subjects (cross-curricular links).
- Is in line with the expectations in the National Curriculum 2014. .
EWe implement our curriculum intent in the following ways:
- Our planning and teaching is informed by Mathematics Mastery materials (EYFS to Y6) to promote the three principles of our mastery approach.
- A calculation policy is used within school to ensure a consistent approach to teaching the four operations so over time pupils make rich connections.
- To promote the accurate use of mathematical vocabulary we introduce key words at the beginning of each topic and ensure these are regularly revisited and displayed. We ensure language acquisition develops meaningfully over time through making connections, representations and providing contexts through Big Pictures in some year groups.
- Children are taught through clear modelling and have the opportunity to develop their knowledge and understanding of mathematical concepts. The mastery approach incorporates using concrete manipulatives, pictures, words and numbers to help children explore and demonstrate mathematical ideas; enrich their learning experience and deepen understanding at all levels.
Every Mathematics Mastery lesson provides opportunities for pupils to communicate and develop mathematical language through:
- Modelling clear sentence structures and expecting pupils to respond using a full sentence;
- Talk Task activities, allowing pupils to discuss their thinking and reasoning of the concepts being presented;
- We promote reasoning by asking ‘why’ so children have to explain their mathematical thinking.
Our intent to include problem solving opportunities in all we do is implemented by providing opportunities for pupils to:
- Explore, recognise patterns, hypothesise and be empowered.
- Let problem solving take them on new and unfamiliar journeys.
- Explore problems that have different possible solutions and get them to compare their approaches.
We develop our intent of pupils believing and achieving by:
- Children work on the objective at whatever entrance stage they are assessed as being at. Children can ACQUIRE the skill, APPLY the skill or DEEPEN the skill within the lesson.
- Through this approach the majority of pupils access age-related objectives at their own stage of learning.
- Children with additional needs are included in whole class lessons and teachers provide scaffolding and relevant support as necessary. For those children who are working outside of the year group curriculum, individual learning activities are provided to ensure their progress.
- Children who have shown their understanding at a deep level within the unit, will have opportunities to apply these skills in a greater depth activity. This should be challenging and ensure that children are using more than just one skill to be able to answer the mathematical problems.
- Resources are readily available to assist demonstration of securing a conceptual understanding of the different skills appropriate for each year group.
- A love of maths is encouraged throughout school via links with others subjects, LifeSavers and applying an ever growing range of skills with growing independence.
- In addition to daily mathematics lessons, all classes deliver a Maths Meeting at least 3 times a week. These are an opportunity to consolidate prior learning ahead of a new concept, expose pupils to new mathematics ahead of formal teaching and allow opportunities for teachers to formatively assess knowledge and understanding. This also promotes retrieval practice and develops long-term memory.
Leadership, Assessment and Feedback
Regular and ongoing assessment informs teaching, as well as intervention, to support and enable the success of each child
- Assessment informs the teaching and learning sequence, and children work on the objectives they are assessed as being at, with fluid boosting available within a ‘keep up not catch up’ culture.
- Feedback is given on children’s learning in line with our feedback policy. Formative assessment within every lesson helps teachers to identify the children who need more support to achieve the intended outcome and who are ready for greater stretch and challenge through planned questioning or additional activities.
- In order to support teacher judgments, children may be assessed using current and reliable tests in line with the national curriculum for maths and Mathematics Mastery assessments. Gap analysis of any tests that the children complete is undertaken and fed into future planning.
- Summative assessments are completed at the end of the academic year and reported to parents in the end of year report.
- The maths leader has a clear role and overall responsibility for the progress of all children in maths throughout school. Working with SLT, key data is analysed and regular feedback is provided, to inform on progress and future actions.
We develop children’s mathematical thinking by good questioning. We provide children opportunities to:
- Explore, wonder, question and conjecture.
- Compare, classify, sort,
- Experiment, play with possibilities, vary an aspect and see what happens,
- Make theories and predictions and act purposefully to see what happens, generalise.
What will this look like?
By the end of KS2 we aim for children to be fluent in the fundamentals of mathematics with a conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. They should have the skills to solve problems by applying their mathematics to a variety of situations with increasing sophistication, including in unfamiliar contexts and to model real-life scenarios. Children will be able to reason mathematically by following a line of enquiry and develop and present a justification, argument or proof using mathematical language.
Maths Programme of Study: KS1 & KS2
By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study.
In EYFS, children follow the Early Years Outcomes to develop their mathematical skills and understanding and in reception they follow Maths Mastery.
Key stage 1 – years 1 and 2
The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the 4 operations, including with practical resources [for example, concrete objects and measuring tools].
At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.
By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.
Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.
Lower key stage 2 – years 3 and 4
The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.
At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number.
By the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.
Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word-reading knowledge and their knowledge of spelling.
Upper key stage 2 – years 5 and 6
The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.
At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them.
By the end of year 6, pupils should be fluent in written methods for all 4 operations, including long multiplication and division, and in working with fractions, decimals and percentages.
Pupils should read, spell and pronounce mathematical vocabulary correctly.