Maths – National Curriculum Aims
Purpose of study
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 and most forms of employment. 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.
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 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 nonroutine 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.
The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.
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.
The programmes of study for mathematics are set out year-by-year for key stages 1 and 2. Schools are, however, only required to teach the relevant programme of study by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage, if appropriate. All schools are also required to set out their school curriculum for mathematics on a year-by-year basis and make this information available online.
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.
The 2014 National Curriculum for Maths aims to ensure that all children:
- Become fluent in the fundamentals of Mathematics
- Are able to reason mathematically
- Can solve problems by applying their Mathematics
At Coleridge Primary School, these skills are embedded within Maths lessons and developed consistently over time. We are committed to ensuring that children are able to recognise the importance of Maths in the wider world and that they are also able to use their mathematical skills and knowledge confidently in their lives in a range of different contexts. We want all children to enjoy Mathematics and to experience success in the subject, with the ability to reason mathematically. We are committed to developing children’s curiosity about the subject, as well as an appreciation of the beauty and power of Mathematics. At Coleridge, we want to continuously adapt, study and improve our teaching to ensure that our children receive a world class education, that creates deeper thinkers who have a strong number sense in order to deal with a range of problems, puzzles and reasoning to expand their knowledge.
The content and principles underpinning the 2014 Mathematics curriculum and the Maths curriculum at Coleridge Primary School reflect those found in high-performing education systems internationally, particularly those of east and south-east Asian countries such as Singapore, Japan, South Korea and China. These principles and features characterise this approach and convey how our curriculum is implemented:
- Teachers reinforce an expectation that all children are capable of achieving high standards in Mathematics.
- The large majority of children progress through the curriculum content at their age-related level.
Whole class together – we teach mathematics to whole classes and do not label children. Lessons are planned based on formative assessment of what students already know and we include all children in learning mathematical concepts. Therefore, children are taught in mixed ability groups and are supported in moving along at the same pace. Children are then further supported through concrete resources or consolidation tasks whilst quick graspers move onto more challenging problem solving and reasoning. At the planning stage, teachers consider the scaffolding that may be required for children struggling to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly. Staff have been heavily supported in planning in small steps using the White Rose planning and NCETM materials to create S plans to ensure small steps of progression are made. Differentiation is achieved by emphasising deep knowledge and through individual support and intervention. Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons and resources to foster deep conceptual and procedural knowledge.
Longer but deeper – in order to ensure all children have a secure and deep understanding of the content taught, our plans have been adjusted to allow longer on topics and we move more slowly through the curriculum. We use the White Rose Hub small steps planning and the NCETM spine materials to support this progression within each maths lesson. Teachers adapt each lesson to meet the needs of their children and add extra questioning / tasks which will allow children to learn the content more deeply. The learning will focus on one key conceptual idea and connections are made across mathematical topics. To outsiders it may appear that the pace of the lesson is slower, but progress and understanding is enhanced.
Questioning – Questions will probe pupil understanding throughout, taking some children’s learning deeper. Responses are expected in full sentences, using precise mathematical vocabulary, talk frames and sentence stems. Teachers use questioning throughout every lesson to check understanding – a variety of questions are used, but you will hear the same ones being repeated: How do you know? Can you prove it? Are you sure? Can you represent it another way? What’s the value? What’s the same/different about? Can you explain that? What does your partner think? Can you imagine? Listen out for more common questions you hear.
Rapid intervention – in mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together pupils need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. Ideally this would happen on the same day but this is not always possible so it may be the following morning but will be before new learning is introduced.
Discussion and feedback – pupils have opportunities to talk to their partners and explain/clarify their thinking. They use APE sheets and sentence stems and talk frames on the board to support them in their discussion.
Recording the learning – not just pages of similar calculations – Maths books are used across the school. In books you will see a range of activities including those requiring written explanations of the children’s understanding. Often orange pen will be used to show a child needs further explanation or blue pen will be used to show a misconception.
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. Students can underperform in Mathematics because they think they can’t do it or are not naturally gifted in mathematics. Our curriculum aims to show children there are a range of ways they can be successful to facilitate their love of mathematics learning. We ensure that all children experience challenge and success in mathematics by developing a growth mindset and by not grouping children into sets. Regular formative assessment through AfL, as well as interventions, enables all children to be successful.
At Coleridge Primary School we aim to equip all pupils with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning.
We started our journey to improve the teaching and learning of mathematics for every child in September 2018. There are several elements which have influenced improvements in attainment and progress in mathematics for our children. Mathematics is led by Mrs J. Shaw who is a maths mastery specialist and is working to support other schools and is travelling to Shanghai to further our research into the mastery approach. This document sets out our approach and the reasons behind our approach to maths at Coleridge.
The three aims of the NC should be addressed every day (not just in the maths lesson):
Fluency – Reasoning – Problem Solving.
- Whole class together – we teach mathematics to whole classes and do not label children. Lessons are planned based on formative assessment of what students already know and we include all children in learning mathematical concepts. Therefore children are taught in mixed ability groups and are supported in moving along at the same pace. Children are then further supported through concrete resources or consolidation tasks whilst quick graspers move onto more challenging problem solving and reasoning. At the planning stage, teachers consider the scaffolding that may be required for children struggling to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly. Staff have been heavily supported in planning in small steps using the White Rose planning support tools and S plans to ensure small steps of progression are made. Teachers follow a six part lesson structure which is as follows:
Most lessons will incorporate concrete resources at the beginning of each session and these are available to the children in all lessons in the ‘Brain Boxes’ on their tables which contain a range of resources which they may need for their lesson.
- Longer but deeper – in order to ensure children have a secure and deep understanding of the content taught, our plans have been adjusted to allow longer on topics and we move more slowly through the curriculum. We use the White Rose Hub small steps planning and the NCETM spine materials to support this progression within each maths lesson. Teachers adapt each lesson to meet the needs of their children and add extra questioning / tasks which will allow children to learn the content more deeply. The learning will focus on one key conceptual idea and connections are made across mathematical topics. To outsiders it may appear that the pace of the lesson is slower, but progress and understanding is enhanced.
- Questions will probe pupil understanding throughout, taking some children’s learning deeper. Responses are expected in full sentences, using precise mathematical vocabulary, talk frames and sentence stems. Teachers use questioning throughout every lesson to check understanding – a variety of questions are used, but you will hear the same ones being repeated: How do you know? Can you prove it? Are you sure? Can you represent it another way? What’s the value? What’s the same/different about? Can you explain that? What does your partner think? Can you imagine? Listen out for more common questions you hear.
- Rapid intervention – in mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together pupils need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. Ideally this would happen on the same day but this is not always possible so it may be the following morning but will be before new learning is introduced.
- Discussion and feedback – pupils have opportunities to talk to their partners and explain/clarify their thinking. They use APE sheets and sentence stems and talk frames on the board to support them in their discussion.
- Recording the learning – not just pages of similar calculations – Maths books are used across the school. In books you will see a range of activities including those requiring written explanations of the children’s understanding. Often orange pen will be used to show a child needs further explanation or blue pen will be used to show a misconception.
- Marking – A next step is given daily to ensure that children either consolidate their learning or a challenge is given to move their learning forward. Children respond to these next steps in green pen in reflection time.
- Maths Mash Ups – As we are teaching in longer blocks, we wanted to ensure children still have consolidation of key skills to ensure they were embedded over time. This rapid recall and practise of these fluency skills are vital so that we can address gaps in learning and ensure that key objectives are embedded.
- Maths Mash Ups incorporate 4 main strands: Addressing key skills, mental maths strategies, arithmetic and
Pre-learning. The Key skills that are addressed are: Calendar Maths, Statistics, Number, Fractions, Decimals and Percentages (Year Group dependent), Geometry, Measure and Time. Within these key skills there are non-negotiables. For example in Year 6 Roman Numerals are a non-negotiable as this has been determined as a particular area of weakness. There are done 10-15 minutes daily and are in segments of 2-3 minutes. They are fun engaging sessions and children are encouraged to all participate and pace is kept at all times.
- Maths Mash Ups are a vital part of our Maths Mastery approach to teaching. They are used to ensure key objectives are covered continuously to make sure they are retained; this means gaps in learning are addressed throughout any block of learning.
- ‘Number Talks’ can also be included to practise mental strategies explicitly which enables children to recall on a range of strategies when answering arithmetic questions and when solving problems. During ‘Number Talks’ arithmetic can also be practised during these sessions: giving children the opportunity to practise basic skills they have learnt in fluency sessions. Because of this constant practise of skills, children will become more fluent and should be able to recall answers quickly. Children are asked to discuss one strategy for the question with their partner and then are asked in silence to generate as many strategies as they can. After giving children the appropriate amount of time, these strategies should be discussed as a class.
- Maths Mash Ups should occur daily for 10-15 minutes. They should cover several blocks and should be broken down into short segments; each segment should take approximately 2-3 minutes.
- Children use a range of resources to help them improve their multiplication knowledge as this is the basis of much of their learning for their further education and life skills. Using TT Rockstars, maths frame and mash ups children are continuously supported with their knowledge of times tables. Children in Y3 and 4 are given weekly intervention using flash cards to further their knowledge and this is tracked weekly.
- Number facts are supported particularly in Year 1 and 2 using addition fact cards.
- Practising – not drill and practice but practice characterised by variation – years 1-6 use White Rose Hub small step planning and Maths No Problem textbooks to provide children with carefully chosen questions and are essential in assessing how the children have understood the concept taught. You will also see another level of differentiation within these books as some children rapidly grasp the concepts and therefore complete the pages quickly and move onto questions or activities where their understanding can be developed to a greater depth. Some children will work very hard in the lesson to complete the pages independently, some children will need additional support to complete the pages and some children will sometimes be provided with different tasks and questions appropriate to their understanding of a concept.
- SEND pupils – may be supported by additional adults, different resources, differentiated activities. They will also complete additional activities outside of the mathematics lesson if necessary.
- Children in EYFS explore mathematical concepts through active exploration and their everyday play based learning. Children are taught key concepts and application of number using a hands on practical approach. EYFS practitioners provide opportunities for children to manipulate a variety of objects which supports their understanding of quantity and number. The CPA approach is used when teaching children key mathematical skills. Practitioners allow children time for exploration and the use of concrete objects helps to support children’s mathematical understanding. Maths in the early years provides children with a solid foundation that will enable them to develop skills as they progress through their schooling and ensures children are ready for the Nation Curriculum.
NB: We do not label our children. We have high expectations of all children and strongly believe that all children are equally able in mathematics. Some may take longer to grasp concepts and may need careful scaffolding or extra time/support (guided groups, same day catch-up, additional homework, pre-teaching, intervention group, specific parental support).
At Coleridge we understand the importance of knowledge organisers and how they can support children’s understanding and learning.
They are also an excellent assessment tool which can help identify gaps in learning and inform planning, teaching and intervention. As we have developed our own curriculum, class teachers have also developed knowledge organisers to work alongside our curriculum. Children will be encouraged to refer to knowledge organisers throughout sessions to help support and enhance their learning.
Knowledge organisers can be a valuable tool for both children, staff and parents. Class teachers are the ones who write the knowledge organiser, to set out their expectations of what pupils should learn about a topic – and to clarify their own thinking around what is important.
School leaders, headteachers and subject leaders then may look at a series of knowledge organisers to check for progression and continuity both within and across curriculum subjects and to ensure standards and expectations for learning are being implemented, and if not, what CPD is required.
Pupils will review, revise and quiz themselves using their knowledge organisers. Knowledge organisers are a really clear and easy to understand way for parents to be more aware of what their children are learning and thus to support them.
Some of the benefits of knowledge organisers
- A knowledge organiser makes the teacher think hard about what will be taught.
- Knowledge organisers are an endless source of meaningful homework activities.
- Knowledge organisers are an excellent tool for inclusion.
- Knowledge organisers create opportunities for spaced retrieval practice.
- Ahead of a summative assessment at the end of a topic you can inform pupils that some of the questions will refer to previous learning; pupils can then refer to the knowledge organiser to access and practice those topics.
- Used appropriately, knowledge organisers can increase retention of facts
At Coleridge, we have several non-negiotiables that need to be included in a knowledge organiser, they are:
- Key vocabulary (linked to Progression of language)
- Key places and people
- Useful diagrams (as required for the topic)
- Key dates for a subject like history (e.g. when the two World Wars were)
- Key themes
- Important quotes
- Stem sentences for a subject like Science or Maths
We use knowledge organisers throughout school, however, in EYFS they look different to other phases of school due to the away the curriculum is structure. In EYFS, we use a holistic approach to knowledge organisers and have a topic knowledge organiser, whereas, in KS1 and KS2 our knowledge organisers are subject specific.
If you would like any information about our knowledge organisers then please contact us at email@example.com
he New Times Tables Tests Explained
All Y4 children will have their multiplication skills formally tested in the summer term of Year 4 from 2021.The Multiplication Tables Check (MTC) was officially announced by the Department for Education (DfE) in September 2017. It will be administered for children in Year 4, starting in the 2021-2022 due to impact of the current pandemic.
Times tables test / multiplication tables check Primary-school children are expected to know all their times tables up to 12×12. Under the current National Curriculum, children are supposed to know their times tables by the end of Year 4, but they are not formally tested on them other than through multiplication questions in the Year 6 maths SATs.The DfE says that the check is part of a new focus on mastering numeracy, giving children the skills and knowledge they need for secondary school and beyond. The purpose of the MTC is to determine whether Y4 pupils can recall their multiplication tables fluently. The times tables test will be introduced in English schools only. It will be taken by children in Year 4, in the summer term (during a three-week period in June; schools will decide which day to administer the check).In June 2019 the multiplication check will be voluntary (schools will be able to decide whether to administer it or not). In June 2020 it will become compulsory. Children with special educational needs will be provided for when taking the MTC.
How will the children be tested?
- Children will be tested using an on-screen check (on a computer or a tablet), where they will have to answer multiplication questions against the clock.
- The test will last no longer than 5 minutes and is similar to other tests already used by primary schools. Their answers will be marked instantly.
- Children will have 6 seconds to answer each question in a series of 25.
- Questions will be selected from the 121 number facts that make up the multiplication tables from 2 to 12, with a particular focus on the 6, 7, 8, 9 and 12 times tables as they are considered to be the most challenging. Each question will only appear once in any 25-question series, and children won’t be asked to answer reversals of a question as part of the check (so if they’ve already answered 3 x 4 they won’t be asked about 4 x 3).
- Once the child has inputted their answer on the computer / device they are using, there will be a three-second pause before the next question appears.
How can you help your children at home?
- Encouraging your children to practice using TT Rockstars at home!
- Practising times tables in order or in a song.
- Asking your child multiplication questions out of order – such as ‘What’s 11×12? What’s 5×6?’ · Using arrays to help your child memorise times tables – you can use fun objects like Smarties or Lego bricks to make it more entertaining.
- Use the practice books given to your child.
Jessica Shaw – China Exchange November 2019
At the beginning of November, after being selected as part of the DFE’s England-China exchange, I spent two weeks in Shanghai analysing and experiencing mathematics teaching at first hand. I was given the opportunity to spend time in two schools. A local Shanghai school which used government implemented text-books and scheme of work and an international which had devised its own textbooks around the accelerated progress of their children. We were welcomed into both schools and were immersed in their culture of learning and their continuous use of TRG discussions to analyse and improve the teaching of mathematics. This is a culture of learning and open door classrooms which has been developed over the last 10 years and is by no means a quick fix to rapidly improve the teaching of mathematics in the UK. I will discuss below some of the findings which were pertinent over the two weeks I spent in Shanghai.
All local schools in Shanghai follow the government implemented Shanghai textbooks which is given to teachers alongside ppts and a teacher guide. Children are given a practice book and text book which teachers use in most lessons. Because these lessons are so carefully structured, teachers are able to use these as a basis for their lesson and develop further challenge or support as is appropriate for their class. During our observations, many teachers would add real-life contexts and more complex problems to challenge their children. These textbooks always start at a low starting point and build to much more demanding content. One key concept is always introduced and maintained within each lesson so that teachers are not pressured to include too much: meaning children can concentrate on one key focus. There is a clear progression of skills throughout the textbooks so that teachers know exactly what has been taught before and where the learning is being taken. Because the same textbooks and ppts are used continuously over time, these lessons are stored and annotated and developed by each teacher so that they can be analysed and improved over time. I found it surprising that many teachers, who were part of the exchange, commented on identical lessons to the ones we had observed with small alterations or additions. We commented that going from school to school in the UK you may see a completely different topic or scheme of work in place and new lessons being created each year. Perhaps this is something to consider in creating a cohesive and progressive curriculum for the children in our communities.
TRG and lesson anaylsis
Throughout our specialist training, we have been coached and have facilitated TRG lesson analysis of which I can see the huge benefits for a more open and analytical study of lesson design around mathematics. However, to see this first hand showed me how a culture of shared learning and open-door policy can really vastly improve the teaching of mathematics. The Chinese teachers were so used to being observed and even filmed, that in one observation with 50 students there was 30 observers – some of whom were even hanging in the window, that they were not perturbed by this as they are continuously using the observations as a way to continuously design and improve lessons over time. After each lesson, a discussion was had around the session, where the teacher described the lesson focus; any potential misconceptions; the teaching process and any additions and alterations they had made with their reasoning behind their choices. After this analysis, each observer would comment on something they had noticed about the mathematics within the session. Because these teachers will often watch the same lesson multiple times over their years in the profession, they are continuously ensuring that they are learning from one another and that their lessons are improved by a shared discussion of children’s learning and the improvements on lesson design. In one seminar, we took part in a lesson which looked at the use of the number line using fractions. In this study, two planning sessions took place, the lesson was taught twice and then the lesson was analysed and reviewed. This shows the real dedication to improvements of key structures and models that will support the children in their understanding of mathematics.
Each lesson was precisely timed to 38 minutes and this was stuck to with rigour. Each lesson would end and start with music and would begin with the Chinese ‘eye exercises.’ This happens in all schools and children are focused and ready to learn at the beginning of each session. The lesson progress quickly from a low starting point to very challenging content. Chinese maths teacher in primary only teach this subject and teach around 2-4 lessons per day. After this session, children are asked to complete independent work and homework in order to consolidate the learning done in class. Therefore, when the teachers are not in class they are marking books, adapting planning or observing as part of a TRG.
Observations showed that all lessons began with a key lesson focus. Often lessons would begin with a real-life focus, especially in KS1, to ensure that children were engaged and that purpose was given to their learning. Most lessons involved a practical group activity which included rich mathematical talk. This was something I didn’t expect to see and was surprised how active and fast paced the sessions were. Children were asked to share their ideas by standing up and sharing it with the class if they were chosen after their hand was raised. The teachers always knew the answers they wanted and instead of praising answers that were incorrect they would move onto someone with the correct answer. This is something which is rather different in English schools and an interesting point to consider. Do we over-praise children when they give an answer which irrelevant or incorrect? Often key learning points and generalisations would be placed on the right-side of the board. These would be repeated by a child, then to their partner and then as a whole class. Any equations or jottings would be placed on the left of the board. At the end of each session, children would be asked what t had learnt and would use these generalisations to summarise what they had learnt. Most lessons included a reasoning question to consolidate and challenge learners and these would come in the form of true or false and multiple choice questioning. The visualiser was used in all lessons and was so important in children being able to share their ideas and for the teachers to address any misconceptions; it was also a great tool to show a variety of possibilities in problem solving.
Something that really struck me during my time in Shanghai was the quick recall of number facts throughout our observations. Children were never held back by their ability to calculate mentally which meant that as the content became harder they were able to handle it with ease. The below table shows how Chinese children learn their multiplication facts. When I asked the maths lead why children knew their multiplication facts so well, he noted that often children start school and have already learnt these facts. Chinese children understand commutativity and number facts in such a deep way that they only need to learn 45 facts to know their tables instead of our 144 facts. The language is also much easier for them to learn. Instead of saying, ‘one times one is one’ the children will simply say ‘one, one, one.’ In Chinese, 22 (twenty-two) is said, ‘two tens and two,’ meaning place value is something that is far easier for the children to understand. In geometry, quadrilaterals are called quadrangles meaning children can more easily link them with triangles and their properties.
Although a culture of learning and the importance of education it clearly instilled into the people China, this should not be something that deters us from learning from the Shanghai teachers and their teaching of mathematics. The continuous analysis and development of mathematics that has taken place over the past 10 years is something that should be admired and I feel very privileged to have witnessed this first-hand. I know that the importance of number sense and our children’s knowledge of key facts should be paramount in ensuring that children can develop their understanding of mathematics. The culture of learning from one another and sharing best practices to analyse and carefully craft lessons is so important in moving the teaching of mathematics forward. Finally, small steps are so important to ensure all children are kept together, but this must build to a challenging point where children are able apply their knowledge to different real-life contexts. Their carefully crafted lesson design and the children’s secure understanding of key facts means that the children of China are receiving an in depth understanding from the teaching of mathematics.