What are we trying to achieve by teaching maths?
We want all pupils to:
End of Key Stage Expectations
The following expectations apply to most pupils at our school. We make reasonable adjustments in our expectations of pupils with Special Educational Needs or Disability, and for pupils who have only just begun education in England and whose first language is not English. Likewise, if pupils show exceptional talent in maths, we may expect more of them than their peers. Any adjustments in our expectations are agreed with senior leaders and are they are continually monitored to ensure they are serving the individual pupil's needs.
F1 and F2
Early Learning Goal: Number
- Have a deep understanding of number to 10, including the composition of each number;
- Subitise (recognise quantities without counting) up to 5;
- Automatically recall number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.
Early Learning Goal: Numerical Patterns
- Verbally count beyond 20, recognising the pattern of the counting system;
- Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;
- Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.
KEY STAGE 1
Year 1 and Year 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 involves working with numerals, words and the four operations, including with practical resources [for example, concrete objects and measuring tools]. At this stage, pupils develop their ability to recognize, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching also involves 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 know the number bonds to 20 and are precise in using and understanding place value, when working with numbers up to 100. An emphasis on practice at this early stage aids fluency. Pupils read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.
KEY STAGE 2
Lower KS2 - Year 3 and Year 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 ensures that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching also ensures 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 ensures that they can use measuring instruments with accuracy and make connections between measure and number. By the end of year 4, pupils have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Pupils read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.
Upper KS2 - Year 5 and Year 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 develops the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. At this stage, pupils 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 consolidate and extend knowledge developed in number. Teaching also ensures that pupils classify shapes with increasingly complex geometric properties and they learn the vocabulary they need to describe them. By the end of year 6, pupils are fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils read, spell and pronounce mathematical vocabulary correctly.
How do we organize the maths curriculum?
Progression from year to year
We want all children to make progress in their maths knowledge, understanding and skills, from term to term and from year to year. Lessons are generally pitched at a level that is appropriate to the children's age. Minor adjustments include recapping content that has been (should have been) previously taught or accelerating learning by introducing content earlier than anticipated. The order in which content is usually taught and learnt is outlined on a 'progression map'. Medway teachers refer to a progression map when planning and include a 'prior learning' section on their medium term planning, as an aide memoire. Knowing what pupils of a given age are supposed to learn, helps teachers evaluate pupils' progress. Teachers at our school also use this information to evaluate the efficacy of their teaching.
NCETM, White Rose and Lancashire County Council have produced detailed progression maps that are valued documents at Medway. Below is a simplified version of a progression map.
Whole School Long Term Plan
The whole school long term plan (LTP) is an overview of what we teach in each term of each year. Teachers have ensured that all aspects of the National Curriculum are included. To see what is planned in more detail, please refer to teachers' medium term plans (MTPs) on the class pages. The LTP and MTPs are our school's 'maths scheme of work'. We don't follow a commercial scheme, though we are mindful of schemes of work devised by reputable agencies such as NCETM and White Rose and teachers are free to use any of the great ideas they find. The rationale for not following a commercial scheme is that we want our maths curriculum to be delivered by teachers who have developed their own expert subject knowledge and are agile in their thinking; we want the curriculum to be responsive to pupils' ability and interests; we want it to be relevant to topics we are teaching.
Cross Curricular Maths
Maths is used within a variety of other subjects. When it is used, its usefulness is made explicit to children. Teachers are aware that some children, if not all, find the application of their maths knowledge, understanding and skills is what makes it meaningful to them. It provides an added motivation for learning more maths, which can only be a good thing.
Teachers spent time reflecting on the cross curricular maths opportunities they provided in 2020-2021 and year groups each produced a document to show what was offered. This is now a 'working document' which means the teachers' own copies will be updated from time to time.
How do we deliver the curriculum we have planned?
Whole Class Teaching or Ability Sets?
We have no hard and fast rule about this at our school. In principle, we agree that every child should have the opportunity to learn alongside children who are their own age, no matter what ability. However, we know there can be circumstances when teaching and learning is more effective by creating ability sets, either for a whole cohort of children (year group) or part of it. For example, there might be a separate set for pupils who need to work in a more supported way to reach the expected standard for their age. What's important to know is we think setting doesn't have to be for the whole academic year or for every maths lesson in a week. Setting for part of the year can support some pupils to 'catch up'. Also, individual children can progress into another set/the main class or vice versa.
It is not unusual, at Medway, for pupils identified as working well below the expectations for their age group to be taught maths separately to the main classes/sets, in 'intervention groups' (same/similar age). This is to ensure they are not overwhelmed by whole class/set teaching and their needs are not neglected. Teachers and HLTAs plan to ensure progress takes place at a reasonable pace.
- Didactic - We show children how to solve a problem and they follow a given method to practise solving several similar examples.
- Deductive - We ask children to work through several examples and ask them whilst working or afterwards to figure out the pattern or rule.
- Inductive - Children are given a problem to solve and we ask them to use their pre-existing knowledge, understanding and skill to figure out how to approach and solve it.
- Calculation Methods - Children are gradually introduced to different methods of calculation that allow them to work with increasingly larger or decimal numbers. Children are given chance to practice using new methods, but we don't ask them to complete long, repetitive tasks if it's clear they have grasped new learning. More efficient methods are ultimately desirable, but not at the expense of understanding and accuracy.
- Concrete, Pictorial and Abstract - We use these interchangeably so children can identify and use the relationships between real objects or situations, visual representations that may be real or abstract and mathematical forms of recording, including using various symbols.
- Maths vocabulary acquisition - We use a wide variety of maths vocabulary and expect children to understand and use it too, when they are making suggestions, explaining, describing, hypothesizing, generalizing or categorizing.
- Oracy - The ability to talk out loud about maths helps children to express their knowledge and it consolidates and deepens their understanding. Since Medway children often need support to speak in English, maths is also a vehicle for the use and development of high standards of oracy that impact the curriculum in general.
- Collaboration - Children are encouraged to work together in most lessons, for at least part of each lesson. We believe collaboration supports all learners: more able learners have the challenge of explaining to or guiding others, middle ability learners aren't as shy about asking questions to clarify their understanding and less able learners have maths modelled for them by pupils their age (showing that it is possible).
- Individual work - In the adult world, maths is often used alone, rather than in collaboration with others, therefore we also provide opportunities for fostering independence and self-reliance in solving problems. We encourage individuals to recognize what they are capable of and how they might approach a problem confidently on their own. They are allowed to recall and choose methods of calculation or equipment that suit them. We encourage and teach ways of checking answers.
Tests - We use tests to check fluency of recall of maths facts. It's recognized that speed of calculation can be an advantage to children when they are faced with multi-step problems.
- Marking/teacher feedback - At least once each week, teachers help children to understand their progress and standard of work in relation to expectations. This can be through commenting verbally and/or through marking work. Teachers' ongoing assessment of attainment and progress relates to outcomes within each lesson, from one lesson to the next and across a maths topic. It can include maths used in a different context/subject. Teachers set specific targets, when necessary.
- Peer and self assessment - When children are sufficiently mature and able to mark their own or another child's work, they are given some opportunities to do so. This is to allow them to become more reflective about their progress.
- Developing metacognition - We make broad steps in their learning explicit to children. We encourage reflection on what they used to know compared with now. At a more focused level, we help children to retrace their steps through a problem to identify an error in thinking or presentation.
Examples of Tasks and Pupils' Work
What happens to ensure standards of teaching are always improving?
Quality of Teaching
Our staff ranges from newly qualified teachers to teachers with more than 30 years experience. The majority of maths lessons observed by senior leaders are at least good with some outstanding practice evident too. Teachers plan interesting lessons and pupils' engage with them fully. Professional discussions with teachers show that their subject knowledge is very good. Willingness to develop maths practice ensures maths continues to thrive and remains high profile. Teachers' expectations of pupils is in line with national expectations. The standard of work produced by pupils is very good.
Teachers' Professional Development
The subject leader supports all new members of staff and teachers new to a year group by meeting with them informally early in the autumn term and following this up in the spring term with a professional discussion, a lesson observation, work scrutiny and pupil interviews. Teachers who join our school are often newly qualified/early career teachers. These teachers usually have lots of input from the headteacher who has a 'hands on' approach to ensuring they make good progress from the start. Liaison with their mentors throughout the year/s also ensures these teachers are adequately supported.
The subject leader identifies courses that are in line with school priorities and/or the professional development needs of teachers and teaching assistants. Most school staff have been on at least one externally organized course. The subject leader also keeps up to date with national priorities by attending network meetings.
Twice a year, there are maths 'Curriculum In Action' (CIA) meetings. The headteacher, deputy, maths subject leader, plus another senior teacher, meet with teachers from each year group. The teachers use this opportunity to present pupils' maths work and to discuss pupils' outcomes, resulting from their planning and implementation of the maths curriculum. Suggestions may be made about ways to improve pupils outcomes and any support needed is identified. This is as much an accountability meeting as it is a professional development meeting. The quality of teaching and pupils' learning are evaluated and scores are given.
In addition, the subject leader instigates and supports new initiatives through a variety of development and monitoring activities - action research, PPT presentations, informal meetings, informal work scrutiny, learning walks and observations. For example: maths habitus (2020-2021); cross curricular maths (2020-2021); use of inductive methods (2020-2021); additive reasoning (2021-2022); quality of teaching and learning in maths intervention groups (2021-2022).
Local universities are reliant on Medway to provide placements for student teachers. Each year, staff host around a dozen students. Some of these are developing a maths specialism and conduct short research projects that Medway staff support. The maths subject leader provides demonstration lessons and advice to all of them.
What are the outcomes for our children and what do we think about that?
Based on 2019 data (due to covid this is the most recent official data)
Expected standard or above: 76.8% (national 76%)
Greater depth standard: 24% (national 27%)
Progress score: 1.2 (average)
Scaled score: 105 (national 104)
Reading, Writing and Maths combined: 66% (national 65%)
It is usual for pupils to make a significant amount of progress during KS2 at our school. As pupils become more proficient in speaking English, they are able to rapidly build on the foundations of maths knowledge and calculation skills begun in EYFS and KS1.. We are pleased that data showing pupils' progress in maths from KS1-2 improved between 2017-2018. Though there was nothing exceptional about 2019 progress data, it was a larger than usual cohort due to new arrivals and overall attainment of the 2019 cohort was not significantly below national data.
Expected standard or above: 55% (national 76%)
Greater depth standard: 26% (national 22%)
Our KS1 data reflects the significant proportion of pupils who, mainly due to EAL, fall short of meeting the expected standard in maths. The data also shows the opportunity to excel in maths is always present for any pupils who are able. Whereas attainment of the 'expected standard' is significantly below the national average 2017-2019 and is in the lowest 20% of all school, the percentage of pupils attaining greater depth in maths is slightly higher than the national average.
Overall GLD: 67%
EYFS data likewise shows the impact of pupils starting school with limited spoken English. Maths attainment was significantly below national data for 2017 and 2018 and, though there was a rise in 2019, it was not significant in relation to national data.
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