Maths
“Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.” – Shakuntala Devi
Maths Lead - Mrs Rebecca Bateson
Intent
The intention of the maths curriculum at St Dennis is for children to become competent mathematicians. We aim to develop children’s enjoyment of maths and provide opportunities for them to build a conceptual understanding of it, before applying their knowledge to everyday problems and challenges. We believe that if children can manipulate numbers confidently, accurately and efficiently, they will be able to develop their reasoning and problem solving skills successfully.
At St Dennis, we follow the aims of the National Curriculum, whereby we intend that children:
- Become fluent in the fundamentals of mathematics through varied and frequent practise with increasingly complex problems over time.
- Reason mathematically by following a line of enquiry, exploring relationships and generalisations, and developing an argument, justification or proof using mathematical language.
- Can solve problems by applying their mathematics to a variety of problems of increasing complexity, including breaking these down into a series of smaller steps.
We follow a mastery curriculum to promote a deep, long-term, secure and adaptable understanding of the subject. We endeavour to ensure that children develop a positive and enthusiastic attitude towards mathematics that will stay with them throughout their lives.
Implementation
At St Dennis Primary Academy, we are at the 'sustaining' phase of our 'Mastery Maths Journey' and use NCETM's '5 Big Ideas in Teaching for Mastery' to cover the main aims of the National Curriculum (fluency, reasoning and problem solving).
Our long-term plan follows that of White Rose Maths, although there is scope for class teachers to flex the curriculum to best support the needs of their class. Examples of this include spending longer on a topic where children need to consolidate their learning or require more opportunities to ‘think deeper’.
Prior to a new maths unit starting, teachers break it down to ensure that the essential small steps are being taught in order to achieve the overall learning objective. Teachers look back at the previous year group’s expectations as a starting point and assess from here before moving on to ensure critical knowledge, skills and understanding are in place.
Each small step then forms a section on a pyramid that may take different amounts of time to teach, from one lesson to three. This pyramid is displayed on learning walls, so everyone (including the children, parents and staff) know where the learning is aiming.
Individual lessons are planned from this framework in the form of slides which provide a clear progression of skills. Representations and calculations are chosen carefully in order to maximise understanding.
At St Dennis we understand the need to create a balance between the two types of mathematical practise. Type one being the rehearsal of core facts, methods and strategies and type two including the explaining, justifying and proving concepts using informal and diagrammatic methods. We teach children to know core facts each year so that they can they can focus on solving mathematical problems. As a result we have created a declarative knowledge plan of the core facts children should know by the end of each year group.
The beginning of each lesson starts with a feedback and feedforward element which may include:
Work to praise and share to address misconceptions
Excellent examples of presentation
Targeted support
Time to edit basic skills errors
This also allows for activating prior learning in readiness to build on during the lesson and enables children to make links.
The learning objective is shared with children and is phrased as 'To be able to...' (TBAT). Alongside this are key success criteria so children are clear of the steps they need to take to be successful in achieving the learning objective. These are phrased as 'I can...'.
Key vocabulary is introduced, along with sentence stems which are modelled and repeated throughout the lesson. Sentence stems are used as they include accurate mathematical vocabulary in a highly structured sentence that provides children with a way to communicate their ideas with mathematical precision and clarity.
The key representations that will be used during the lesson and how they will be used is also shared and explained.
New learning is introduced in small steps with time to practise at every stage. Teachers call this 'my turn, your turn' so they can support initial attempts, making sure children build confidence. This also ensures teachers can give feedback so children are not making too many errors. In this part of the lesson, modelling is key as worked-examples reduce cognitive load.
Scaffolding is used to develop expertise. Supports are given but they are gradually withdrawn.
A range of question types are used to check understanding.
These include:
Are you sure?
How do you know?
What do you notice?
What’s the same and what’s different?
Can you convince me?
Is there another way?
Is it always, sometimes, or never true?
Can you imagine?
I think I understand what you mean, are you saying?
There is always opportunity for independent learning and during this time there may be a representation, a worked example or success criteria on display, for children to refer back to. There is also a planned opportunity within the lesson to 'think deeper' which may move to the next step, reasoning or problem solving.
There is always opportunity to revisit the learning objective and success criteria in the 'Let's Reflect' part of the lesson.
This can be to:
- Ensure children know what they have learnt.
- Find out what children have learnt.
- Provide feedback that improves children's learning.
- Have children help each other learn.
- Develop children's ability to monitor and assess their own learning and self assess against the learning objective and success criteria.
Good presentation is important in maths because when children's calculations are systematic and orderly, they are more likely to see the connections of number and to spot errors. We have presentation guidance for maths lessons.
The Ofsted Maths Review (May 2021) states that mathematical curriculum knowledge is classified into three types, declarative, procedural and conditional.
Declarative knowledge can be prefaced with the sentence stem ‘I know that’ and consists of facts and concepts.
Procedural knowledge can be prefaced with the sentence stem ‘I know how’ and consists of a sequence of steps.
Conditional knowledge can be prefaced with ‘I know when’ and focuses on strategies to reason and problem solve.
The review states that when children use each of these types of knowledge (declarative, procedural, conditional) their knowledge of the relationships between concepts develops over time. Consequently, when looking at the pedagogical approaches that support this knowledge, we plan to provide opportunities that enable our children to practise and apply these facts, concepts, methods and strategies. Our lesson structure allows for this and further daily discrete fluency sessions are taught to ensure that all children have opportunities to do this.
For this session in Reception and Key Stage 1, we are part of the NCETM's Mastering Number Project. This 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 Key Stage 1 with fluency in calculation and a confidence and flexibility with number. Attention is given to key knowledge and understanding needed in Reception and progression through KS1 to support success in the future.
For this session in Key Stage 2 we use the White Rose Flashback 4 materials. Flashback 4 is a series of quick questions covering something from the previous lesson, last week and topics from earlier in the year – maybe even last year! This resource helps to recap and ensure essential skills are regularly revisited and retrieved to strengthen retention. In addition to this, every half term, each year group has a Key Instant Recall Fact (KIRF) to learn and these are practised during this time.
Times Tables Rock Stars is also used in Key Stage 2 to develop fluency of multiplication and division facts, and to develop speed of recall for known facts. Weekly tests on number bonds are taken by all pupils in the school ensuring children learn and retain the essential number facts so they can focus on mathematical methods. These are celebrated in assembly every week.
Assessment
Before teaching a new White Rose block of learning, children carry out last year's end of block test as a diagnostic tool. This informs teachers what children need to learn in their next maths lessons in order to move on to the new learning. A key aim for this is to develop confidence and readiness to learn. For those who are already secure, they use Nrich activities to dive deeper into the unit of learning.
Children also complete a White Rose mini test of a taught unit at a distance to see what they have remembered. Again, results of these inform subsequent teaching.
At the end of each term, children complete PUMA assessments. The outcomes of these inform future learning.
Impact
The impact of the maths curriculum is measured through the following methods:
- Analysis of end of key stage data, including attainment and progress
- In school progress and attainment data, analysing individuals and key groups
- Formative assessment by class teachers and subsequent whole class feedback
- Pupil progress meetings to establish reasons for differing rates of progress and putting in measures to address these
- Diagnostic tests on previously taught content to ensure new learning builds on strong foundations
- Summative assessments of learning at a distance through White Rose Unit Tests and end of term PUMA tests
- 'Book looks' with a key mathematical curriculum or pedagogy focus by the maths lead and senior leaders
- Pupil conferencing by maths lead and senior leaders
- Lesson observations and feedback based on the outcomes, by maths lead and senior leaders
How does maths promote British Values?
Democracy Children take into account the views of others in shared activities and vote when collecting data.
The Rule of Law Children at St Dennis follow the Golden Rules during tasks and activities, for the benefit of all.
Individual Liberty Children work within boundaries to make safe choices during practical activities and also make their own choices within data handling activities.
Tolerance of those with different faiths and beliefs We use maths to learn about different faiths and cultures e.g. looking at patterns and shapes within Islam and Hindu symbols and religious artefacts.
Mutual Respect Children work together effectively in teams, take turns and share equipment. They review the work of their classmates respectfully and work collaboratively on projects and problems, helping and advising others.
SEND Provision
For children with SEND, teachers consider what the barriers could be to achieve the learning of each lesson. Overcoming these barriers, in order that the individual can access and achieve the same learning as the rest of the class, is the primary aim.
The maths curriculum is designed to be inclusive for all learners at St Dennis Primary Academy and adaptations are made to gain full access to the learning.
Supporting your child at home
Practising fluency of mental calculation (number bonds, times tables) will be hugely helpful to your child. Addition and subtraction facts up to 20 can be practised until they be automatically recalled. Using resources to support these activities is a valuable way to embed the understanding behind these operations. Talk to your child about what they are doing and ask them to explain why. Mathematical talk will deepen their understanding and build their reasoning skills.
Practical activities, such as cooking (measuring ingredients) can be a fun and rewarding way to aid their mathematical learning without formally teaching maths. There are online games listed below which might be more appealing to some learners.
The following links provide useful activities for practising and learning about maths at home:
https://www.topmarks.co.uk/maths-games/hit-the-button
This online game provides learners with a chance to practise the recall of their number bonds, multiplication and division facts where they can test their accuracy and speed of recall.
Each child from Year 2 has a log in and password for Times Tables Rock Stars. They can earn coins through practising their multiplication and division facts in a range of fun games.
https://www.transum.org/Software/SW/Starter_of_the_day/index.htm
A different problem is given each day, to test different areas of Maths and twist your brain in different ways!
https://www.bbc.co.uk/cbeebies/shows/numberblocks
This BBC resource is based on songs, quizzes and activities to build your child’s confidence and understanding in early maths.
https://www.bbc.co.uk/bitesize/primary
Another BBC resource based on quizzes, games and activities to increase confidence and understanding in maths for all ages.