At Dane Bank Primary School, we follow a “teaching for depth” approach to Mathematics, which is sometimes termed mastery. This approach enables all children to master the mathematics curriculum and draws inspiration from a range of sources such as White Rose Maths and NCETM. It draws heavily upon research conducted by the EEF (Education Endowment Fund) and their recommendations.
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.
At Dane Bank Primary School, these three elements are embedded within Maths lessons and are developed over time. Maths is a rich and interconnected subject and our aim is to support children to move fluently between different concepts and different representations of Mathematical ideas, through both procedural and conceptual variation. Programmes of study are carefully designed to enable children to make these rich connections across mathematical ideas and to develop fluency, reasoning and their confidence to solve increasingly sophisticated problems.
Our approach aims to provide all children with full access to a creative and engaging curriculum, enabling them to develop their independence, confidence and competence. Concepts are taught through manageable small steps, based around the NCETM curriculum prioritisation material and the White Rose Maths schemes, which build on skills children have learnt. We use mistakes and misconceptions as an essential part of learning and enable children to acquire maths skills that can be recalled quickly and transferred and applied in different contexts.
Our expectation is that the majority of pupils move through the programmes of study at broadly the same pace. Decisions about when to progress will always be based on the security and depth of the pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly work on further challenge within the learning block rather than be accelerated through new content. Those who are not sufficiently fluent with each mathematical concept will consolidate their understanding through additional practise before moving on.
Underpinning our pedagogy, is the belief that all children can learn Mathematics and that high quality Mathematics education provides a foundation for understanding the wider world and a tool for life.
In Early Years, the Maths Curriculum is led by books, following recommendations by the EEF around Early Maths. Maths teaching in Nursery focuses on covering the Mathematics milestones from the 30-50 and 40-60 months band of the Development Matters document – giving particular focus to recognising, ordering, subitising numbers up to 5 and recognising basic 2D shapes. Maths teaching in Reception follows the NCETM Mastering Number programme with some areas supplemented by the White Rose Maths materials. Maths provision includes short adult-led sessions, group activities and games that support the development of early number strategies. Alongside this, children are given opportunities to follow their own interests through play which should encourage them to foster a lifelong love of Maths. The Learning Trajectories are used as a formative assessment tool to support teachers in identifying gaps in learning and planning next steps.
In KS1 and KS2 the children have a 1 hour Maths lesson each day. In addition, in KS1 they continue the NCETM Mastering Number programme that starts in Reception 4 x weekly, 15 minutes per session. In KS2, they have daily Maths Mastery sessions base don the guidance for teaching Primary Maths published by the DfE and exemplified by the NCETM “Ready to Progress Criteria” in addition to their hour-long Maths lesson.
The NCETM Mastering Number programme used in Reception and KS1 aims to secure firm foundations in the development of good number sense for all children. 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. The consistency of these materials helps to bridge the transition from EYFS to KS1.
In KS2 the sessions are based on the 2020 DFE “Ready to Progress Criteria” and supported with the NCETM exemplification materials. The guidance identifies the most important conceptual knowledge and understanding that pupils need as they progress from Year 3 to Year 6. These important concepts are referred to as ready-to-progress (RTP) criteria and provide a coherent, linked framework to support pupils’ mastery of the primary Mathematics curriculum. This element of our Maths curriculum aims to develop children’s mathematical fluency and ability to make mathematical connections which can be used within the main Maths curriculum lessons and beyond.
Children are supported to develop their early number fluency through the “NumBots” app which provides a fun and engaging way in which children can participate in spaced practice to develop their early number fluency both in school and at home. Following on from this, children are encouraged to learn Times Tables from Years 2 – 6. Times Tables Rockstars is used to provide children with an engaging and interactive online resource, that they access both in school and at home, to practise and learn. Children who have learnt specific times tables are able to achieve bronze, silver, gold or Olympic badges. We also run frequent inter-class and school competitions and an annual Trust-wide competition.
The school’s Calculation Policy details the approach and learning progression in the main operations of addition, subtraction, multiplication and division, and also includes examples of how a CPA approach can be used to support pupils’ learning in each area. We believe that all students, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking the concrete-pictorial-abstract approach.
Concrete – students should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.
Pictorial – students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
Abstract – with the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.
Our Maths lesson structure
Lessons are carefully designed around teaching one small step within a teaching point and they are a balance of explicit instruction, collaboration and dialogue. Our aim is to unpick the small idea the lesson is based around using procedural and conceptual variation so that all children have a deep understanding before they move on to the next small step. Each lesson phase promotes the means to achieve at greater depth, with children who show a deeper level of understanding than their peers being offered rich and sophisticated problems, as well as exploratory, investigative tasks within the lesson as appropriate. In line with the school’s work around metacognition and retrieval, each part of the lesson allows children to develop these skills.
A typical daily lesson would take approximately one hour and would contain the following elements:
- Links to learning– Making links to what has already been taught. Bridging back to develop retrieval strength.
- Guided Practice– the main idea or skill within the small step to be mastered is introduced using metacognitive talk and a range of explaining and modelling techniques. The teacher will model efficient methods, drawing out misconceptions and making use of varied manipulatives and representations. Some mini tasks will then be set based on the modelled knowledge or skill and the teacher will circulate checking for success and engaging in individual feedback conversations and gathering information to inform whole-class feedback. The class and teacher will engage in a “my turn, your turn” process with each mini task building on the one before. It is an opportunity for staff to model ideas and to explore the small steps in sufficient depth so that every child in the class understands the concept sufficiently to be able to tackle independent work successfully. They may be using mathematical equipment, such as cubes, counters or dienes, they may be discussing pictorial representations or they may be engaged in solving reasoning problems collaboratively. The teacher will guide the class through the learning slowly to ensure that all children have opportunities to gain a deep understanding of the concept.
- Independent practice –Children will work in this part of the lesson by themselves, without the aid of an adult. It is an opportunity to practise what has been taught and also an opportunity to make formative assessments and judge whether to move on in the next session. Teachers will typically plan questions for the children to work on, focusing on procedural and conceptual variation to ensure children demonstrate both fluency and also a greater depth of understanding. A teacher may notice that children are persisting with errors or that the same error is occurring multiple times, if this happens, they will stop the whole class and use this as a teaching opportunity to draw attention to these misconceptions. If only a few children show misconceptions they will be directed to work as part of the guided group.
- Guided group – Whilst the majority of the class undertake independent practice, the teacher and teaching assistant will have identified some children during the guided practice phase of the lesson who may need some more guided practice to ensure they have a deep understanding of the concept. This is a flexible group responding to formative assessment and the teacher will use a variety of scaffolds to support this group, slowly fading them so they can transition to independent practice.
- Challenge – Children who have demonstrated a deeper understanding than their peers may be working on questions which require different types of reasoning, more complex steps with increased variation or are a conflation of different areas of maths. This will not involve moving on or a higher number range.
There are times when this structure does not suit the learning which takes place. It might be at the start of a unit where the teacher chooses to use manipulatives for the whole session, the children might be engaged in an activity outside or they may be playing games to support their Maths learning.
Mastering Number – Reception, Year 1 and Year 2
As an additional element to their daily Maths curriculum lessons, our children in Reception, Year 1 and Year 2 also participate in a 15 minute Mastering Number session 4 days a week. The Mastering Number materials have been developed by the National Centre for Excellence in the Teaching of Mathematics (NCETM) and runs alongside the main Maths curriculum. The sessions aim 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.
Maths Mastery – Year 3, Year 4, Year 5, Year 6
In addition to their daily Maths curriculum lessons, our children in Year 3, 4, 5 & 6 also participate in a daily 15 minute Maths Mastery sessions based on the Ready to Progress Criteria produced by the DFE and exemplified by the NCETM. The Ready to Progress criteria identifies the most important conceptual knowledge and understanding that pupils need as they progress through school. The criteria are divided into Number and Place Value, Number Facts, Addition and Subtraction, Multiplication and Division, Fractions, and Geometry. These provide a coherent, linked framework to support pupils’ mastery of the primary mathematics curriculum. By focusing on these core concepts of maths and ensuring mastery, children should be able to more easily access the rest of the National Curriculum that is not exemplified in this criteria and become fluent and confident Mathematicians.