At Crayford Temple Grove, mathematics is understood to be an essential life skill which enables children to understand and access the world around them. We want our students to leave our school as confident mathematicians who value the subject and understand its importance in their school life and beyond. Our global curriculum lends itself to this world view of mathematics and allows our students to see how the subject is used in the local community, nationally and globally.
We foster a love of maths through embedding a mastery approach, where mathematical content is taught in depth through creative means, allowing children to flourish as confident mathematicians. We use a range of creative approaches and resources, particularly manipulatives and representations, to engage our pupils and allow them to visualise mathematical structures.
‘Mastery of mathematics is not a fixed state but a continuum. At each stage of learning, pupils should acquire and demonstrate sufficient grasp of the mathematics relevant to their year group, so that their learning is sustainable over time and can be built upon in subsequent years. This requires development of depth through looking at concepts in detail using a variety of representations and contexts and committing key facts, such as number bonds and times tables, to memory.’ - NCETM
Our mastery approach[i] ensures that every child can succeed in maths. Maths teaching for mastery ‘rejects the idea that a large proportion of people ‘just can’t do maths’ NCTEM. We recognise that mathematical knowledge needs to be taught as declarative, procedural, and conditional to ensure it is committed to long-term memory. We focus on teaching core concepts in depth, particularly in EYFS and KS1, to ensure they are embedded into long-term memory before introducing new material. When introduced, new material is delivered in small steps and builds upon core concepts. This approach ensures less ‘re-teaching’ as pupils progress through their schooling. All pupils are taught together, so nobody gets left behind.
‘A mathematical concept or skill has been mastered when, through exploration, clarification, practice and application over time, a person can represent it in multiple ways, has the mathematical language to be able to communicate related ideas, and can think mathematically with the concept so that they can independently apply it to a totally new problem in an unfamiliar situation.’ – Helen Drury 2014
We have adopted the ‘five big ideas for teaching mastery’ from the NCETM which have been drawn from research which underpins teaching for mastery:
Lessons are broken down into small, connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.
Representation and Structure
Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation.
If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student, thought about, reasoned with, and discussed with others.
Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics.
Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.
The Five Big Ideas were first published by the NCETM in 2017.
In Early Years, mathematics is taught and learnt through play and practical experiences. Teachers provide daily input through carpet sessions and focus groups, which are developed as the year progresses. Much of the teaching is based on the NCETM’s mastering number approach to secure knowledge of number before moving onto other concepts such as addition, subtraction, and shape. Through the provision, children can apply what they have learnt to real life experiences.
We use concrete pictorial and an abstract approach in early maths to ensure children have a strong understanding and foundation of number and calculation methods. At CTG, we understand that in order to master maths, children need to be confident using a resource before they can understand pictorial and abstract calculation strategies. We have chosen to focus on using a tailored group of resources to ensure children have the time to practise using these until they cannot get them wrong. Using multilink, cubes, rekenreks, and dienes are a focus in our early maths. These concrete resources are used to support learners though the school and in interventions to support the progress of children who need more targeted support.
Mastering number 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. – NCETM
At CTG, we have short daily sessions to embed the mastering number programme for EYFS and KS1. In EYFS, sessions may take longer to ensure the concept of number has been secured.
Structure and implementation
The mastery approach, as well as the White Rose Maths scheme, are used to support our intent for mathematics. The White Rose Maths scheme provides a ‘vast bank of clear, practical’ resources which can support children in securing mastery and beyond. Our teachers are encouraged to use the scheme as a supportive measure to develop their understanding of the subject and are discouraged from rigidly following every sequence of lessons.
‘In line with our mastery approach to the teaching and learning of mathematics, our schemes are split into blocks that allow plenty of time for thorough study of every topic. Teachers of course know their children and the experiences they have had best. We encourage teachers to use this knowledge to make the schemes work for them, adding extra time where necessary for topics that need most attention and adapting other learning accordingly.’ – White Rose Maths
This is because every child and class are different and our teachers need to prioritise the concepts which are not yet embedded into long term memory, and work at the children’s level, only providing greater depth questions which focus on the concept being taught once mastery has been achieved, although rehearsing and explaining the concept to others always takes place first.
Key skills and concepts are built upon sequentially each year by using our maths progression of skills map. This is then supported by the materials from the NCETM, which provide a coherent teaching sequence. The teacher guides available highlight the key teaching points, common misconceptions, key questions, links to prior learning, highlight where connections are and how the learning progresses.
To support planning, teachers then take materials from the blocks available in the White Rose Maths scheme.
This is then supported by regular, low stakes assessments, demonstrating a low-threat, high-challenge model which builds children’s self-esteem. These can be seen at the beginning of each maths lesson for years 2-6 for example, where we adapt White Rose’s flashback four to recap key learning taught the previous day, week, term, and year.
All pupils complete the available end of block assessments and teachers use these to inform future planning.
We use the S planning model to teach maths as a cohesive journey, rather than following a specific set of individual lessons produced by a scheme. The approach is flexible and allows teachers to consider: the teaching activities, representations, possible misconceptions, oracy, metacognition, feedback, and what might need to be in place, i.e., scaffolds for different groups of learners. This ensures that teachers are not influenced by the coverage, but by the depth at which pupils are learning. We focus on the needs of each individual student as opposed to where they should be at a particular point in the year.
Mathematical language and dialogue is a key aspect of our maths teaching and can be seen in lessons daily. Key vocabulary and question stems are visible in the classroom environment and give pupils the confidence to discuss their learning.
Stem sentences are available in each of the NCETM’s teacher guides. The stem sentences are repeated and used in different contexts to develop fluency.
Reasoning and Problem Solving
Research by Nunes (2009) identified the ability to reason mathematically as the most important factor in a pupil’s success in mathematics. It is therefore crucial that opportunities to develop mathematical reasoning skills are integrated fully into the curriculum. Such skills support deep and sustainable learning and enable pupils to make connections in mathematics. – NCETM
Through the supporting materials, teachers have access to a range of reasoning questions and to ensure our pupils can articulate their reasoning, we use the show it, draw it, explain it, prove it model. This allows pupils to think deeply about their responses and confidently articulate their reasoning.
Times Tables Rock Stars
Times Tables Rock Stars is a carefully sequenced programme of daily times tables practice.
Each week concentrates on a different times table, with a consolidation week for rehearsing the tables that have recently been practised every third week.
We celebrate participation in the programme weekly and expect pupils to complete a minimum of four sessions per week.
To support the programme and ensure our pupils have a deep knowledge of multiplication, we use the CPA approach (Concrete-Pictorial-Abstract) and encourage opportunities to apply their multiplication knowledge to real-life experiences.
‘Although learning tables by rote is by far the best method for speed and efficiency, accurately reciting the times tables doesn’t mean children ‘know’ them. Children who claim to know all their tables only have a superficial understanding of them.’ - Dabell 2017
Our approach ensures pupils at CTG do not just have a ‘superficial’ understanding of multiplication, but a deep knowledge to access the maths curriculum.
[i] The essential idea behind mastery is that all children need a deep understanding of the mathematics they are learning so that:
- future mathematical learning is built on solid foundations which do not need to be re-taught;
- there is no need for separate catch-up programmes due to some children falling behind;
- children who, under other teaching approaches, can often fall a long way behind, are better able to keep up with their peers, so that gaps in attainment are narrowed whilst the attainment of all is raised.
 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.