This policy outlines the teaching and learning of mathematics at Hanwell Fields Community School.
The policy is based upon the aims of the curriculum for mathematics and the Early Years, “Development Matters” document.
Our teaching approach is based upon the mastery model, using the rich and high-quality textbook Power Maths from Year 1, so children gain a solid and deep understanding of mathematical concepts - recognizing the power of thinking not just doing, which in turn will allow all to see patterns and make connections.
We are committed to delivering mathematics in innovative ways that link to real-life experiences, where possible, to prepare our children for their next phase.
Aims of the National Curriculum
All pupils shall:
- 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 which will support them to develop an argument, justification or proof using mathematical language.
- 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.
Hanwell Fields Community School is based upon a fundamental belief that all children can achieve confidence and competence in mathematics, building fluency, a deep conceptual and procedural understanding through prolonged and varied practice.
Small, sequenced steps that are supported by a range of concrete and pictorial representations build and deepen conceptual and procedural knowledge.
Children working at mastery can: recall rapidly and accurately mathematical facts; make connections between concepts; use a variety of representations to demonstrate understanding and articulate fully in discussion “how” they have calculated rich and sophisticated problems.
We believe that knowledge is not fixed and explicitly embed a growth-mindset approach into all our children do – through hard work, practice and a willingness to see mistakes as part of their journey - they can succeed. Mathematics is taught in mixed-ability groupings which we believe necessitates vital discussion: the use of accurate and specific mathematical language to explain what is known; validate an idea or reason, develops in our children a deep understanding that underpins all future learning.
Within lessons, reflection time is built in; this allows opportunities for children to make links and focus. Where possible, working in mixed-abilty pairs or small-groups, children are encouraged to explain what they know using complete sentences and key mathematical language to discuss and express concepts precisely - this is empowering when clarifying understanding and can highlight any possible misconceptions. Maths talk is integral to the structure of teaching at Hanwell.
Maths in the curriculum
In addition to discrete mathematics lessons, our children recognize that “Maths is all around us,” and with the help of Morris – our maths detective – children experience mathematics in a range of learning throughout the day.
Targeted pre-teach sessions every Friday afternoon are used throughout the school to introduce or consolidate key mathematical vocabulary and enable revision of key concepts to take place with identified children. We believe these sessions allow all children to access the following week’s learning and send home guidance that informs parents of the upcoming learning, so they might support their child – in any way they can.
Hanwell is committed to the mastery approach to mathematics and scaffolds are used to allow all children to access the learning at their level. Targeted interventions and precision teaching of key facts, support children developing fluency and recall. All children work on the curriculum that best fits their stage of development (P scales, banded curriculum or National Curriculum) and SEND Toolkit on Classroom Monitor, allows teachers to measure progress and attainment. Mathematics specific vocabulary is pre-taught to ensure all children are able to access the mathematics curriculum
Lessons are typically an hour long and begin with a fluency activity that aids mental recall. Children are taught through whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time. This ensures that all can master concepts and deepen their understanding as far as they can, before moving to the next part of the curriculum sequence - allowing no pupil to be left behind. Textbooks are an excellent resource used to support high-quality teaching and allow children to see the concept in multiple representations. In addition to this, maths resources such as: Numicon, Diennes, multi-link cubes and bead strings are available on every table in every lesson - support developing understanding.
If a pupil fails to grasp a concept or procedure, this is identified quickly through live marking and Booster same-day interventions take place using manipulatives to support, ensuring sustained progress - children are then ready to move forward with the whole class in the next lesson.
Times Tables are taught in an extra explicit session designed to develop automaticity which avoids cognitive overload in the working memory and enables pupils to focus on new concepts. (see our document Times Tables at Hanwell Fields for more information).
Children are not required to demonstrate use of calculators in formal tests, where the emphasis is upon effective written and mental methods of calculation, but calculators can and are used to support conceptual understanding and enable the exploration of more complex number problems.
Speaking and Listening
The National Curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum. At Hanwell we recognize the quality and variety of vocabulary that pupils hear and speak are key factors in developing mathematical understanding and enabling children to have confidence presenting justifications, argument or proof. Speaking frames are used to introduce and consolidate key mathematical vocabulary in complete sentences which links to reading and comprehension skills; it is an expectation that all children use specific mathematical language at all times and support is given to those who find this challenging.
We assist children in making their thinking clear to themselves as well as others, using discussion to probe and remedy any misconceptions.
Early Years (EYFS) experiences of Mathematics at Hanwell Fields
A child’s early experiences with Number, Shape, Space and Measure are vitally important to their development as successful and independent learners. The Early-Years (EYFS) team work hard to ensure that children have access to an engaging and encouraging learning environment for children’s early encounters which focuses upon building confidence in their ability to understand and use mathematics.
We follow the Development Matters Framework and both ‘Number’ and ‘Shape, Space and Measure’ are specific areas of learning in which support children’s learning, understanding and development of key concepts. EYFS teachers and practitioners incorporate children’s interests into both their learning environment and planned activities and the ‘Characteristics of Effective Learning’ are observed and linked to what the children are observed doing independently and alongside enabling adults. ‘Thinking Critically’ is a characteristic most often linked to Mathematics, where children are seen to be making links, finding new ways to do things, solving problems, changing strategies as needed, making predictions and developing ideas of grouping sequencing, cause and effect.
Through a combination of child-led, child-initiated and adult-led activities, mathematics is taught on a daily basis, ensuring that it is fun, interactive and most importantly, linked to children’s current interests and fascinations. Within the EYFS we use the Concrete – Pictorial –Abstract process of learning when introducing new concepts. This approach develops children’s understanding at a deeper level and can be used both at home and within the EYFS setting. Young children are happy engaging with construction toys and making marks on paper, but cannot always solve the problem of 5 + 2 = 7 without a play-based introduction to this as a concept using concrete and pictorial resources. Children begin learning about number by playing with real objects and resources, e.g. shells, pebbles, toy figurines or cut out pictures. They build confidence with the basic idea of adding together or taking away alongside adults engaged in play before moving to the second stage of drawing pictures that represent their objects and fascinations. Much later in a child’s mathematical development you will begin to see them including numbers in their drawings.
Children need to be exposed to different representations of mathematical concepts in order to embed their understanding of them. Children are given opportunities to reason and develop their skills around number, recognising patterns and relationships.
Short Home learning tasks and Weekly Updates are designed to give every child a wealth of opportunities to help you understand the processes taking place at school throughout the week. Counting aloud as you walk up the stairs or peg the washing out, will help children master the skill of counting in the right order, so they can later use that knowledge to support their problem solving. At Hanwell, planning for mathematics involves providing children with ‘real-life’ opportunities to solve practical problems in different ways.
A child’s inquisitive nature and natural curiosity help greatly with observing their approach to exploring ‘Shape, Space and Measure,’ where lots of discoveries and questions start outside in the outside learning environment, in the sand or water tray, through filling and emptying containers and through messy play opportunities.
Teaching and learning - Planning
In Year 1 – 6, teachers use Power Maths as a framework based upon the CPA approach (concrete, pictorial and abstract).
Within a lesson there are periods of independent practice using practice books and/or mathematics books, and it is identified on the plan who the teacher or TA may need to support and by what means e.g. number lines, small group work. Children are encouraged to “Discover” – show how they are able to solve a mathematical concept; “Share” listen to the range of representations that may be used and “Think Together” apply their developing understanding – scaffolded until they have grasped the concept.
Role of the TA
Use of teaching assistant support is planned in every lesson to ensure they effectively support, develop and assess understanding in every part of the lesson. Our TAs Next Step mark throughout the lesson alongside the teacher to indicate where they have moved children on, developing skills further. TAs share observations made throughout the lesson to directly impact upon progression.
We have a calculation policy drawn up in collaboration with all staff, to reflect progression in the range of strategies taught, whilst giving flexibility to model the four operations in a variety of ways - this ensures consistency throughout the school.
Click Here to View our Calculation Policy
Differentiation and Support (Provision for G&T, SENd, EAL, PP)
While the National Curriculum suggests children move through the programmes of study at a similar rate, we recognize that children sometimes need work that is ,“other and different” to support and/or challenge – their mathematics “stage” not “age.” This is done in a variety of ways:
- The use of a greater variety of concrete items to support consolidation
- Real-life planned links to support abstract concepts
- The use of problem-solving activities to further develop reasoning
- Timely support and intervention, systematically checking understanding throughout every lesson to embed conceptual development
- Small differentiated tasks to suit learning needs of all
- Effective AFL throughout every lesson, picking up misconceptions and moving others to deepen understanding with a range of tasks
- Marking and verbal feedback throughout every lesson
- Booster sessions delivered by class teachers to address misconceptions on a daily basis
- SEND Toolkit that ensures children are given work and challenged at the right level for them. This banded toolkit is aligned to Classroom Monitor (our tracking system) and allows teachers to show progress with SEND pupils and closely match the objectives to the level of understanding for key children.
The purpose of marking is to ensure that all children receive constructive verbal and non-verbal feedback, including next steps, to challenge and consolidate learning further. Our marking policy is shared with children, and as they progress up the school, they become increasingly able to respond independently.
We recognize the importance of marking and verbal feedback and use a range of strategies to ensure progression in every lesson:
- Teaching staff use green pen (Green for Growth) to show where adult intervention has impacted upon learning; children’s work is marked throughout the lesson to address misconceptions and/or move children on in the lesson to further deepen understanding.
- Pink pen is used to indicate “Tickled Pink,” individualized feedback that indicates a pupil has shown a depth of understanding, reasoning or persevered.
- Next step marking is used for children to respond to (in the morning at 8.50) either to consolidate concepts, address misconceptions or give children opportunities to show reasoning. They respond in blue pen and their responses are marked with a pink tick when met.
- Peer marking is used for children to assess within a lesson and discuss alternate strategies and methods, “proving” their understanding to others this would be completed using a blue pen.
(indicates Only Upper school)
Assessment for Learning (AFL)
Formative - throughout the lesson AFL is a continuous process whereby teachers and teaching assistants review through mini-plenaries, targeted differentiated questioning, marking, verbal feedback and pupil’s self-assessment.
Summative - Hanwell Fields uses PUMA Assessment termly to assess children’s understanding on particular concepts and Classroom Monitor allows teachers to indicate concepts met in order to gauge progression and attainment. Data from assessments is analysed and is fed into the next term’s learning. Particular concepts may be revised for “morning work” and/or key children identified that have specific gaps.
At the end of each unit - Power Maths uses low-stakes "End of unit checks," mini-tests that enable children to reflect on their own understanding - "Power checks" of that concept and a game "Power play" to consolidate and demonstrate the depth of understanding.
- A link to the how we teach Times Tables is available on the school’s website – with hyperlinks to websites for support. Click Here
- Weekly in our Newsletter a section “Mathematics All Around us” shows a particular year group and how they are linking mathematics in to all they do.
- EYFS - run parent workshops showcasing how mathematics is taught in the Early Years Unit and gives advice to parents.
- Family Maths
Each week children undertake a times tables test in school(for examples click here). These tests are marked by the teacher and children will bring the tests home in order for parents to see progress made and/or support needed.
Children will receive 1 piece of maths homework linked to that week’s learning. Parents are encouraged to support their child in completing this as independently as possible.
Download Copy Here