‘Mathematics is, in its way, the poetry of logical ideas.’ Albert Einstein
Children’s chances of success are maximised if they develop deep and lasting understanding of mathematical procedures and concepts.
At Barrow Hill Primary Academy, our aim is to raise levels of achievement in maths, and increasing appreciation of the power and wonder of maths. Mastering maths means children acquiring a deep, long-term, secure and adaptable understanding of the subject. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Achieving mastery means acquiring a solid enough understanding of the maths that’s been taught to enable children to move on to more advanced material.
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. Crucially, a sound knowledge of mathematics is vital for young people seeking employment, and securing a qualification in mathematics is a fundamental requirement for the majority of employers.
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.
In line with the National Curriculum Objectives for Mathematics, our intent is that all children:
- 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 children 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.
Central to our approach are the 5 Big Ideas which underpin mastery in mathematics.
In line with our whole school focus on oracy and vocabulary, we expect and encourage children to use mathematical language to describe, discuss, examine, explain, justify and analyse.
The essence of Maths Teaching for Mastery is that it rejects the idea that a large proportion of children ‘just can’t do maths’. At Barrow Hill Primary Academy, we have created a whole school approach that is underpinned by the belief that by working hard all children can succeed.
Children are taught in mixed ability year groups for mathematics. In each class, the teacher is responsible for the planning, teaching and assessment of all children. Highly skilled teaching assistants take responsibility for the delivery of the maths lesson for a year group of children in each class. This enables our groups to remain under 15 children and allows for mixed ability teaching whilst focusing on the conceptual journey for each year group.
Each year group has a long-term plan for the sequence of learning. This plan maps out the conceptual journey to ensure there is complete national curriculum coverage by the end of each key stage. The long term plan has evolved significantly due to gaps in learning as a result of the Covid-19 pandemic, and continually updated, high quality resources created by the NCETM. Small steps of learning are planned using Inspire Maths and the NCETM Curriculum Prioritsation document. The Professional Development Spines support teachers with their mathematical understanding and planning small steps. White Rose Maths and other sources are used to create well sequenced lessons. This has been adapted to suit the needs of our children and can be found in appendices 7.
For each conceptual journey the class teachers, alongside their supporting maths teaching assistant, produce an S plan. This method addresses a theme and aims to strip it down into smaller steps by which teachers can reflect on the strategies to move learners along the "learning journey". Once the steps have been identified teachers can focus on how best learners can master the conceptual & procedural skills and knowledge of each one in turn. Where possible links are made to previous learning. Many of these steps are planned for using the Inspire Maths Teacher Guide and NCETM prioritisation documents but knowing the journey in advance and planning for further opportunities ensures that the needs of all children are planned for and nothing is left to chance.
This planning is visible in the classroom and is a working document shared with the children.
Class teachers intervene when a child/children are having difficulty keeping up. This may be within a lesson or during timetabled ‘Keep up time’. There may also be occasions when children are pre-taught a concept prior to whole class teaching. Where appropriate ‘Keep Up’ time may also be used to pre read content to a child/ group of children. Where appropriate, Ready to Progress exemplification is used to support struggling learners. If there are children who do not require specific keep up then the time should be used to practice mental skills e.g. time tables, finish off earlier work, attempt additional challenges or explain their learning. Rapid graspers are challenged by having opportunities to deepen their learning through carefully chosen challenges/ problem solving activities.
The first few years of a child’s life are especially important for mathematics development. Research shows that early mathematical knowledge predicts later reading ability and general education and social progress(ii). Conversely, children who start behind in mathematics tend to stay behind throughout their whole educational journey(iii). The objective for those working in Early Years, then, is to ensure that all children develop firm mathematical foundations in a way that is engaging, and appropriate for their age. The materials in this section (https://www.ncetm.org.uk/resources/51439 of the website) are primarily designed to support Reception teachers (those working with 4-5 year olds), and are based on international research. The materials are organised into key concepts (not individual objectives), which underpin many early mathematics curricula. The typical progression highlights the range of experiences (some of which may be appropriate for younger children) but the activities and opportunities could be developed across the Reception provision.
There are six key areas of early mathematics learning, which collectively provide a platform for everything children will encounter as they progress through their maths learning at primary school, and beyond:
- Cardinality and Counting
- Shape and Space
You can explore these areas in further detail in a special Early Years episode of our podcast with Dr Sue Gifford and Viv Lloyd.
These areas form the fundamental mathematical basis of a CBeebies series of five-minute animated programmes called Numberblocks. The NCETM has provided support materials linked to the Numberblocks programmes. These are designed to help Early Years practitioners draw out and build on the maths embedded in the stories contained in each episode.
At Barrow Hill, the Foundation stage use the principles of mastery to ensure the children are building firm, mathematical foundations. The learning environment enables the children to see and experience maths through play and interaction with adults and other children. Early use of concrete resources such as tens frames, Numicon, counters, objects etc support children with their understanding of maths. The environment in Early Years is language rich and children are encouraged to use the environment to support their learning. In addition to the continuous play and adult led activities there is also a daily 20 minute discrete lesson for all reception children. The NCETM, White Rose Maths Hub and Inspire Maths are used to plan and prepare these lessons. This ensures the five elements of mastery are promoted in Early Years.
In 2021-2022, we have been part of the DfE Mastering Number programme organised and led by NCETM. The project aims to secure firm foundations in the development of good number sense for all children from Reception through to Year 1 and Year 2. The aim over time is that children will leave KS1 with fluency in calculation and a confidence and flexibility with number. Attention will be given to key knowledge and understanding needed in Reception classes, and progression through KS1 to support success in the future. Staff participants in the workgroup will:
- develop skills in working in a professional learning community, reflecting with other colleagues on their own practice, and refining skills through support and challenge within a community
- develop a secure understanding of how to build firm mathematical foundations with a stronger subject and pedagogical understanding for EYFS and KS1
- work to develop intentional teaching strategies focused on developing fluency in calculation and number sense for ALL children
- develop understanding and their use of appropriate manipulatives to support their teaching of mathematical structures.
Children spend 15 minutes every day following the Mastering Number programme. In EYFS, this is enhanced through the continuous provision, learning environment and interactions with children throughout the day. In Y1/2, Mastering Number is taught in addition to the daily 45 minutes mastery lesson.
From year 3 onwards, children practice their times tables every day to build fluency, accuracy and automaticity. The booklets used in school have been carefully created by the NCETM to reduce cognitive load, build on from known facts and learn times tables systematically. Each child completes a 2-minute times table challenge, ideally twice per day. The challenges are times but children may go over the time if needed; they just record their time using the class timer. This is a low threat, high challenge quiz where children aim to beat their own times and own scores. The booklets are worked through in the following order, to match the order suggested in the National Curriculum Guidance (July 2020)
Booklet A: 10 times table
Booklet B: 5 times table
Booklet C: 2 times table
Booklet D: 4 times table
Booklet E: 8 times table
Booklet F: 3 times table
Booklet G: 6 times table
Booklet H: 9 times table
Booklet I: 7 times table
Booklet J: 11 times table
Booklet K: 12 times table
Within each booklet there are 22 tests, ordered as follows:
- Tests 1 – 4: First half of the new times table
- Tests 5 – 8: Second half of the new times table
- Tests 9 – 12: All the new times table
- Tests 13 – 22: The new times table combined with previously learnt times tables.
There are two exceptions to this, the 10 times and 11 times table booklets. As these are quicker for children to learn, all the facts are introduced at once rather than split into ‘first half’ and ‘second half’ of the times table.
- Children must work through the booklets in the order provided in the table above, otherwise they will meet facts in tests 13 – 22 that they have not yet learnt.
- The NC Guidance explains that the facts it is essential to master in Year 4 to be ready to progress to Year 5 are the facts up to 9 x 9, as these facts are the ones that occur as within column calculations in formal written methods. Therefore, Booklets B – I include facts with multipliers of 2 – 9 only.
- Times tables facts with a factor of 11 and 12 are only introduced in the final 2 booklets, so that most of the time can be spent learning the most essential facts. However, all booklets should be complete so that children are secure in all times tables facts prior to the Year 4 check.
- Facts with a multiplier of 0 and 1 are not included, as these do not need to be learnt in the same was as other facts.
- The 10 times table is of course also essential for progression, and this is learnt in booklet A, and then included in tests 13 – 22 in each of the subsequent booklets.
- About 20% of the facts are expressed as division facts, to give children practice deriving division facts from learnt multiplication facts.
In addition to the Times Table Booklets, children have access to Times Table Rockstars. Practicing on the app encourages the children to respond with speed and accuracy. Children play the app both at home and school. This prepares the children well for the statutory multiplication check in Y4 and for automaticity in upper key stage two reducing cognitive load during more challenging mathematical concepts.
The impact of our mathematics curriculum is that children are fluent in the fundamentals of mathematics. They are able to solve problems by applying their mathematics to a variety of questions and have resilience when faced with more challenging and complex problems. Through pupil voice and pupil interviews, we will ensure that children are enjoying mathematics and feel they are received appropriate support and challenge. Where there are gaps in knowledge, children are given additional support to keep up with their peers.
At the end of reception, we report to parents the age related expectation levels. Children in foundation stage are assessed within the Foundation Stage Framework and their progress is tracked termly using EAZMags. At the end of Key Stage 1, children are assesses using the national SATs tests. It is reported to parents whether child has reached the expected levels of attainment.
In year 4, the national Multiplication Check is administered to determine whether children can recall their time tables fluently, which is essential for future success in mathematics and to identify children who have not yet mastered their times tables so that additional support can be provided.
Progress and attainment are monitored daily though assessment for learning strategies. Children in Key Stage 2 are assessed termly using NFER tests. At the end of Key Stage 2, national SATs tests assess if the children are meeting the national expected standard, are working towards or are working at greater depth. This information is reported to parents.
Children will develop a lifelong enjoyment of mathematics and will understand how the concepts they have been learning relate to real life.
The Maths lead will monitor for appropriate pitch and progression, monitoring will take the form of:
- Lesson observations and feedback;
- Learning walks and pupil voice conversations;
- Planning scrutiny followed by support where necessary;
- Book/work/digital media scrutiny
- Monitoring of book band progression and 1:1 reading via GoRead
- Quality of learning environments including reading areas across school
- Purchasing and organizing resources
- Keeping up to date with research and best practice
The Maths Lead conducts staff audits and along with SLT, designs appropriate Professional Development for staff in school. The Maths Leader models excellent practice leading by example and supporting colleagues in school to develop their knowledge and skills of the subject.
The Maths Lead ensures that school engages with workgroups led by the East Midlands West Maths Hub. As an NCETM Primary Mastery Specialist, the Maths Lead receives high quality PD training which is disseminated to staff and improves practice in school.