Mathematics is a creative and highly inter-connected 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 across the curriculum.
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.
In Early Years, Mathematics involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measure.
Pupils are taught to:
- Count reliably with numbers from 1 to 20
- Place numbers 1 to 20 in order and say which number is one more or one less than a given number
- Add and subtract two single-digit numbers and count on or back to find the answer using quantities and objects
- Solve problems, including doubling, halving and sharing
Shape, space and measure
- Use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems
- Recognise, create and describe patterns
- Explore characteristics of everyday objects and shapes
- Use mathematical language to describe them.
Key Stage 1
The National Curriculum (2014) states that:
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 four 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
The National Curriculum (2014) states that:
The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four 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
The National Curriculum (2014) states that:
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 four operations, including long multiplication and division, and in working with fractions, decimals and percentages.
At Enfield, in order to make Maths lively, hands-on and interactive subject, we employ a variety of teaching methods including the concrete, pictorial and abstract approach to mastery maths. Children study mathematics daily covering a broad and balanced mathematical curriculum including elements of number, calculation, geometry, measures and statistics. Due to the interconnected nature of mathematics, at Enfield we aim to teach maths in a cross curricular manner as well as discretely to teach the practical application of mathematical skills. We focus not only on the mathematical methods, but also on mathematical vocabulary and the use of Maths Mastery to broaden and deepen mathematical understanding.
We aim for each child to be confident in each yearly objective and develop their ability to use this knowledge to develop a greater depth of understanding to solve varied fluency problems as well as problem-solving and reasoning questions. We follow the White Rose Scheme of Learning for Maths, including mixed year group schemes, and supplement this using a wide range of textbooks and online resources throughout the school to ensure a curriculum that is specific to each child’s learning needs.
Children are also given access, encompassed within maths lessons, to daily arithmetic sessions, which focus on ‘The Big Five’ (addition, subtraction, multiplication, division and fractions) to build fluency and precision in these areas and to think about numbers in different ways.
From the 2019/20 academic year onwards, schools in England will be required to administer an online multiplication tables check (MTC) to year 4 pupils. The purpose of the MTC is to determine whether pupils can recall their times tables fluently, which is essential for future success in mathematics. It will help schools to identify pupils who have not yet mastered their times tables, so that additional support can be provided. To support the children with their multiplication practice we use ‘Numbots’ and ‘Times Table Rockstars’ as an online and fun learning platform which also offer resources to be used in the classroom.
At our school, we are developing a mastery approach to the teaching and learning of mathematics
- Long term plans and medium term plans are provided by White Rose and these guide the teaching of mathematical concepts
- Lessons reflect the school’s calculation policy, securing and supporting conceptual understanding though, concrete, pictorial and abstract approach at whatever stage of learning.
- Concrete resources and adult support are used to aid children in mastering maths
- Children are provided with daily opportunities to practise written arithmetic and rapid recall of number facts
- Regular opportunities are provided for children to work in pairs and small groups to verbalise their thinking and explain, allowing them to ‘master concepts’
- Deeper learning opportunities, where the children reason and problem solve both verbally and in writing, are evident throughout school and allow the children to apply their skills in a variety of contexts including real life and cross-curricular ones.
- Lessons include a balance of fluency, reasoning and problem solving within each maths
- Where appropriate, bar-modelling and visual representations are used to help children to visually solve calculations and problem solving problems
- Evidence of practical reasoning activities should be recorded through the use of photographs and included in the children’s books.
- Working walls in each classroom support children in maths they practise and use.
- Post-tests in KS1 should be used at the end of a unit of learning in an appropriate style
- In KS2 teachers use Pre and Post testing to identify children’s starting points and misconceptions that need addressing
- Planning addresses misconceptions and helps children overcome progress through providing feedback, allowing time for children to respond to this feedback and improve their work in order to make progress.
- A growth mind-set has been established for both staff and children where learning from mistakes is supported and celebrated.
- Subject knowledge is supported and developed by the maths leader.
- Children from Enfield will become fluent in the fundamentals of mathematics. Through varied and frequent practice with increasingly complex problems over time, pupils will have the conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- Children are happy learners within mathematics. They experience a wide-ranging number of learning challenges in the subject and know appropriate responses to them
- Children of all abilities and backgrounds achieve well in mathematics, reflected in outstanding progress that reveals a clear learning journey.
- Children talk enthusiastically about their learning in mathematics and are eager to further their learning in the next stages of their education.
- There is a proven track record of test success that reflects the impact of deep learning. Children from Enfield achieve higher than the expected standard nationally and show mastery of many mathematical concepts.
- Clear outcomes focus and guide all mathematical development plans and drive improvement.
- Children will be able to reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, developing an argument, justification or proof using mathematical language.
- Children will solve problems by applying their mathematics in a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering to seek solutions.
- Learning in Mathematics will ensure children understand how mathematics is essential to everyday life, critical to Science, technology and engineering, and necessary for financial literacy and most forms of employment.