To be reviewed – July 2015
“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 in most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, and a sense of enjoyment and curiosity about the subject.” The National Curriculum, 2013
“Good mathematics teaching is lively, engaging and involves a carefully planned blend of approaches that direct children’s learning. Children are challenged to think. […] The pitch and pace of the work is sensitive to the rate at which the children learn while ensuring that expectations are kept high and progress is made by all children.”
Primary Framework for Mathematics, 2006
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 have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
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. The programmes of study are organised in a distinct sequence and structured into separate domains. Pupils should make 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 school’s aims for all pupils to have equality of opportunity:
- To develop a sound understanding of basic mathematical concepts through practical and investigational work
- To acquire appropriate and necessary mathematical skills and to apply them confidently and accurately
- To enjoy mathematics, be successful and have a positive attitude to the subject
- To be able to demonstrate their skills and knowledge and talk about their work using appropriate mathematical language
- To develop thinking skills and logically apply their mathematical knowledge to solve problems
- To use mathematics as part of their everyday life in school and at home.
- To ensure that all pupils follow a broad and balanced mathematics programme based on the requirements of the 2013 National Curriculum
- To ensure that all pupils are provided with interesting and challenging rich tasks that enable them to achieve standards commensurate with their abilities and potential
- To ensure that pupils can work individually, collaboratively in groups and within the whole class
- To allow pupils to develop as independent learners, able to make decisions about their own work
Principles of Teaching and Learning
Mathematics means knowing about numbers and number operations. More than this, it requires an ability and inclination to solve numerical problems, including those involving money or measures. It also demands familiarity with the ways in which numerical information is gathered by counting and measuring, and is presented in graphs, charts and tables.
Numerate pupils should:
- Have a sense of the size of a number
- Know by heart tables, doubles and halves
- Figure out answers mentally
- Calculate mentally and with pencil and paper
- Make sense of problems
- Have strategies for checking
- Explain methods and reasoning
- Suggest suitable units for measuring
- Make sensible estimates
- Make predictions
- Describe properties of shape, position and movement
Differentiation and Additional Education Needs
During lessons pupils may work in groups on tasks linked to the learning objectives of the lesson. Differentiation is used to cater for all abilities between the most and least capable in a class.
Teaching is organised to enable pupils of all abilities access to the learning. Pupils with AEN may be supported within the class by Teaching Assistants. Groups of pupils will sometimes move outside the classroom to carry out practical work, to use ICT or to work with support staff.
All pupils, including those with AEN, are set targets in mathematics that are regularly reviewed, monitored and reset. The most able mathematicians are provided with appropriate materials to ensure that they broaden, deepen and apply their knowledge.
Breadth and Balance
The curriculum will include a full range of mathematical activities covering all aspects of the subject including number, measurement, geometry, statistics, ratio & proportion and algebra. Using and applying mathematics will be integrated throughout lessons include practical, investigational, problem-solving and oral activities. Every lesson will include reasoning allowing children to explain their understanding.
Our three key principles are:
- Regular lessons every day
- An emphasis on mental calculation
- A clear focus on direct, instructional teaching and interactive oral work with the whole class and groups
- The following principles should be borne in mind:
- The phases within lessons should introduce, develop and review the learning focus while maintaining a sharp beginning, coherence across the session and a clear conclusion.
- Children should know what they are learning and why, along with the extent of the progress they are making.
- Children should have the opportunity to enquire, question and explore to build knowledge and understanding.
- Planning needs to be adapted to meet the needs of children’s learning in response to assessment and on going review.
Lessons will have clear learning objectives that are communicated to the children.
They will involve different elements:
- Demonstration – showing how to
- Explanation – giving examples
- Questioning –challenging understanding
- Discussion & evaluation – thinking about methods and errors
- Direction – taking care, setting out neatly
The aim is to secure good progress within a class as a whole. Within the Foundation Stage mathematical development is through teacher directed and child initiated tasks. ICT will be used to enhance the teaching and learning of numeracy where appropriate. Display is to consolidate understanding and support strategies for the children.
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.
Key Stage 1
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 (e.g. 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 3-4
The principal focus of mathematics teaching in lower Key Stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 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 – Years 5-6
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 four operations, including long multiplication and division, and in working with fractions, decimals and percentages.
Pupils should read, spell and pronounce mathematical vocabulary correctly.
The mathematical curriculum offers pupils opportunities to use and apply their mathematical skills and knowledge to solve problems and puzzles. Mathematics will often be presented in everyday situations that are relevant to primary pupils.
Cross Curricular Skills and Links
The programmes of study are organised in a distinct sequence and structured into separate domains. Pupils should make 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.
Information and communication technology (ICT)
Calculators should not be used as a substitute for good written and mental arithmetic. They should therefore only be introduced near the end of Key Stage 2 to support pupils’ conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure. In both primary and secondary schools, teachers should use their judgement about when ICT tools should be used.
The National Curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.
Continuity and Progression
Each teacher will keep a record of the achievements of his/her pupils. The record will indicate the progress made by the whole class against the end of year group expectations.
Assessment, Recording and Reporting
Teachers are expected to make regular assessments of pupils’ progress and record them systematically.
This may involve:
- Informal testing of mental recall and mental calculation, given orally.
- Half-termly assessment tasks linked to key objectives.
- Evaluation of group progress against termly plans
- Assessment and recording of each pupil’s progress against National Curriculum levels three times a year (December, March, June).
Teaching materials are chosen to reflect the cultural and ethnic diversity of our society. We try to avoid stereotyping through gender or race. Pupils’ performance is monitored to ensure that no group of pupils is disadvantaged. In lessons the full participation of both girls and boys is encouraged and care is taken to ensure that the emphasis on whole class teaching does not disadvantage any gender group.
Health and Safety
In line with the school’s Health and Safety Policy, pupils are instructed in the safe use of all equipment. In particular, extra care should be taken when using heavy weights with balances on the floor. Care needs to be taken when younger children are using small apparatus such as counting objects. Pupils working outside the classroom will work in pairs or groups.
The Role of the Subject Leader
The Subject Leader will:
- Take the lead in policy development and oversee the production of schemes or work designed to ensure progression and continuity in Mathematics throughout the school.
- Support colleagues in their development of detailed short term plans and the implementation of the scheme of work and in assessment and record-keeping.
- Monitor the delivery of the Mathematics Curriculum and advise the Headteacher on action needed.
- Take responsibility for the purchase and organisation of central resources for Mathematics.
- Keep up-to-date with developments in Mathematics and disseminate information to colleagues as appropriate.
An annual review of resources is overseen by the Subject Leader for Mathematics.
This policy will be reviewed by the Numeracy Subject Leader July 2015.
Policy Reviewed by: Mrs E Rye July 2014
Share and agreed with staff July 2013 and 2014.