Mathematics KS1 - KS4
At Heyford Park School we aim to provide a mathematical experience that prepares students for their next level of education, for the workplace, and the mathematical literacy and problem-solving skills needed in life. We strive to enable students to develop the confidence to learn through making mistakes and reflecting effectively on their learning. This is accomplished through teachers’ commitment to excellence in teaching, a well-designed curriculum and a supportive environment where students take pride in their work and progress. We ensure our pupils develop a deep understanding of whole number, fractions, geometry and algebra, and help embed in them a natural ability to use mathematical language. This is achieved using a wealth of methods including hands-on resources, visual modelling and abstract examples.
KS1 AND KS2 Mathematics
At Heyford Park School, our mathematics curriculum is designed to be accessible to all and will maximise the development of every child's ability and academic achievement. We deliver lessons that are creative, engaging and fun. We want children to make rich connections across mathematical concepts to develop fluency, reasoning and competence in solving increasingly complex problems. We intend our children to use their mathematical knowledge across the curriculum. As our pupils' progress, our children will have a better understanding of the world, can reason mathematically and have a sense of enjoyment and curiosity about the subject.
Children can underperform in Mathematics because they think they can’t do it or are not ‘naturally’ good at it. We want to ensure that we address these preconceptions by ensuring that all children experience challenge and success in Mathematics by developing a growth mind-set. At Heyford Park we want every child to feel like they are a maths learner and have the appropriate skills to tackle real life problems by the time they leave our school. Teaching children efficient and compact problem solving methods enables them to access further learning, increases their career options and improves their understanding of the world. We want children to feel confident, competent and happy mathematicians so they can enjoy the challenge and reward that maths offers.
How we teach Maths in Key Stage 1 and Key Stage 2?
We use the Maths Mastery approach for the teaching of maths across all primary year groups at Heyford Park.
Maths Mastery is a teaching and learning approach that aims for pupils to develop a deep understanding of maths rather than just being able to memorise key procedures or resort to rote learning. The end goal and expectation is for all pupils (with very limited exceptions) to have acquired the fundamental facts and concepts of maths for their year or key stage such that by the end of it they have achieved mastery in the maths they have been taught. At this point they are ready to move confidently on to their next stage of maths.
Mastery of a mathematical concept means a child can use their knowledge of the concept to solve unfamiliar word problems, and undertake complex reasoning, using the appropriate, technical mathematical vocabulary. Maths mastery is a not a quick fix to maths learning but a journey that the teacher and pupils go on together, with regular diagnostic assessment to check the pupils’ understanding and direct instruction that teaches to close any gaps. Mastery make use of the Concrete-Pictorial- Abstract (C-P-A) approach. In the first stages of learning a new concept, concrete resources (‘manipulatives’ such as counters, plastic cubes, bead strings) are used to model and aid understanding. This is followed by the gradual introduction of overlapping pictorial support (such as pictures, diagrams and drawings on the board or a sheet) which finally leads to a more abstract understanding where the pupil uses a more formal method written in their book or on a worksheet.
The rationale and structure of our maths lessons are shown in the diagram below:
In the primary phase at Heyford Park, we follow the White Rose Curriculum and Schemes of Learning. We use the White Rose Calculation Policies (Addition and Subtraction / Multiplication and Division) across classes, year groups and phases. This ensures a consistent and progressive approach to both formal (written methods) and also the use of concrete manipulatives (such as counters, blocks and other resources) which form an essential part of the C-P-A approach to maths mastery.
Each of our maths lessons usually begins with a learning review where skills and knowledge from previous lessons and topics are revisited to ensure knowledge is embedded. Pupil understanding may be assessed using teacher questioning and/or a ‘Show Me’ task.
New learning is then carefully guided by the teacher to ensure all learners are supported and stretched.
Independent tasks are planned using Bloom's taxonomy which supports as well as allows children to achieve greater depth, with more able children being offered rich and sophisticated problems, as well as exploratory, investigative tasks, within the lesson as appropriate. Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts. Teachers use precise questioning in class to evaluate conceptual and procedural knowledge and assess children regularly to identify those requiring intervention, so that all children keep up. Teachers base their teaching on the 5 key principles of mastery.
Testing and misconceptions
We make use of regular, low level testing as well as summative assessment to enable teachers to forensically investigate children’s misconceptions and effectively teach gaps in their learning. This enables teaching to be dynamic and diagnostic and means that the curriculum is catered to individual year group and children’s needs.
Assessment data in maths is reviewed throughout the year to inform interventions and to also ensure that provision remains well-informed to enable optimum progress and achievement. End of year data is used to measure the extent to which attainment gaps for individuals and identified groups of learners are being closed. This data is used to inform whole school and subject development priorities for the next school year.
Planning and Structure
We follow the White Rose Curriculum and Schemes of Work(Primary school maths resources | White Rose Maths (whiteroseeducation.com)) and use resources from White Rose, Deepening Understanding (Planpanion) alongside NCETM and NRICH to aid mastery and deepen pupils’ understanding.
Mathematical topics are taught in blocks, to enable the achievement of ‘mastery’ over time. This ensures that children are able to focus for longer on each specific area of Maths and develop a more secure understanding over time. This approach is also designed to enable children to progress to a greater depth of understanding. Subsequent blocks continue to consolidate previous learning so that the children continually practise key skills and are able to recognise how different aspects of Maths are linked.
Times tables and arithmetic are taught daily, by the end of year 4 children are expected to be fluent in timetables up to 12x in order to complete the statutory multiplication check. To aid children’s learning we use regular low stakes testing in class. We also make use of TimesTable Rockstars app as homework to engage children to learn their times tables in different ways.
What is the impact of our teaching?
The school has a supportive ethos and our approaches support the children in developing their collaborative and independent skills, as well as empathy and the need to recognise the achievement of others. Regular and ongoing assessment informs teaching, as well as intervention, to support and enable the success of each child.
First Encounters with Maths: The Building Blocks:
There are fundamental skills that it is important for children to develop the building blocks to future learning in maths, including that linked to calculation. These will be taught initially in EYFS/Year 1 but also revisited throughout Key Stage 1 and Key Stage S2 to ensure depth of understanding. These skills include:
- Ordinality – ‘the ordering of numbers in relation to one another’ – e.g. (1, 2, 3, 4, 5…)
- Cardinality – ‘understanding the value of different numbers’ – e.g. (7 = 17 = + 12 =
- Equality – ‘seven is the same value as four add three’ – e.g. =
- Subitising – ‘instantly recognizing the number of objects in a small group, without individually counting them’ – e.g. → five
- Conservation of number – ‘recognising that a value of objects are the same, even if they are laid out differently
- Counting on and back from any number – e.g. ‘five add three more totals eight’, ‘ten take away three totals seven’
- Using apparatus and objects to represent and communicate thinking
- Maths language – using mathematical words verbally in every-day situations – e.g. ‘climb up to the top’ / ‘climb down to the bottom’
The ability to calculate mentally forms the basis of all methods of calculation and has to be maintained and refined. A good knowledge of numbers or a ‘feel’ for numbers is the product of structured practise through progression in relevant practical maths experiences and visual representations.
By the end of Year 6:
Children will be equipped with efficient mental and written calculation methods, which they use with fluency. Decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next Step. At whatever Step in their learning, and whatever method is being used, children’s strategies must still be underpinned by a secure understanding and knowledge of number facts that can be recalled fluently.
The overarching aims are that when children leave the primary phase at Heyford Park School are that they:
- Are able to recall number facts with fluency,
- Have developed conceptual understanding through being able to visualise key ideas – such as those related to place value - through experience with practical equipment and visual representations;
- Are confident to reason using the language of ‘support’ and ‘challenge’. Make use of diagrams and informal notes to help record steps and part answers when using mental methods that generate more information than can be kept in their heads;
- Have an efficient, reliable, written method of calculation for each number operation that they can apply with confidence when undertaking calculations that they cannot carry out mentally;
- Are able to make connections between all four number operations, understanding how they relate to one another, as well as how the rules and laws of arithmetic can be applied.
KS3 AND KS4 Mathematics
At KS4 all students follow a linear GCSE course working towards either the higher or foundation tier. Those sitting the higher tier can achieve grades 9 to 4, whilst those sitting the foundation tier can achieve grades 5 to 1.
The GSCE course content is split into modules which spiral up through the grades over the two years. The exact topics and order in which modules are covered will depend on the tier a student is working towards.
GCSE HIGHER TIER
GCSE FOUNDATION TIER