Mathematics
The principles outlined below are informed by advice from specialist improvement advisors and research from NCETM, EEF, NRich as well as White Rose. We have also used research from ‘Greater Depth in Primary Mathematics’ by Andrew Jeffery and ‘Teaching Walkthrus’ by Tom Sherrington.
- We teach for Mastery, which enables pupils to make sense of what they are doing through the classroom practice and organisation in place.
- We use the ‘White Rose’ schemes for learning and follow the National Curriculum, which is a mastery curriculum.
- Pupils are taught through whole-class, ‘back and forth’ interactive teaching
- Every lesson we teach incorporates opportunities and learning through fluency, reasoning and problem-solving.
- Every lesson we teach includes the opportunity to build competency through the Concrete-Pictorial-Abstract (CPA) approach, which we refer to as ‘Build it, Draw it, Write it’
- We use manipulatives as a scaffold, purposefully, with a clear rationale.
- We develop conceptual and procedural fluency through daily lessons and also through repetition and practice outside of the maths lesson.
- We put depth of learning before breadth, going slow so pupils can go ‘fast’
- We provide greater depth through carefully selected and targeted open-questions.
- We teach pupils to make connections and develop curiosity
- We use White Rose in the EYFS. Maths in the Early Years revisits and develops key concepts over the year and enables teachers to teach a mathematically rich curriculum.
Teaching for Mastery
We use the ‘White Rose’ schemes of learning to plan our maths teaching, which ensures learning progression over a lesson, sequence of lessons and over the course of a year and Key Stage. Through the mastery approach, pupils are taught through whole-class interactive teaching, with all pupils working on the same lesson content at the same time. This ensures that all can master concepts before moving on. Whole-class interactive lessons will typically include questioning, short tasks, explanation, demonstration and discussion. We refer to this as ‘ping pong’ teaching: short intervals of the above and no prolonged independent tasks.
We spend significant time ensuring pupils acquire a depth of knowledge in the key ideas required to underpin future learning. Key ideas and skills are revisited.
We teach using explicit instruction which includes clear teaching of key concepts using modelling of worked examples as well as the modelling of thought processes (metacognitive talk) and live modelling. The explicit instruction will also include deliberate vocabulary development and support connections and the revision of prior learning.
Fluency
Fluency is a vital aspect of pupil’s mathematical development. Both procedural fluency and conceptual fluency are developed in tandem as they support each other. Fluency is taught through daily lessons as part of the three key areas of the National Curriculum and also through repetition and practice outside of the maths lesson. This practice is used to reinforce procedural fluency and develop conceptual understanding and will not necessarily be recorded in pupil’s books.
Key number facts, such as multiplication and addition facts, are learnt automatically to avoid cognitive overload in the working memory.
Manipulatives and Concrete-Pictorial-Abstract (CPA)
The CPA approach allows pupils in all classes to work with manipulatives to build an understanding of the concept. Manipulatives are used purposefully with a clear rationale. They provide a scaffold which is temporary and removed once independence is achieved. Alongside concrete resources, pupils will work with pictorial representations, making links to the concrete. This allows pupils to visualise a problem, which supports reasoning and problem-solving. With the support of both concrete and pictorial representations, pupils develop their understanding of abstract methods. In class, we use the phrase ‘build it, draw it, write it’ to support children’s understanding of the CPA approach.
Deep thinking and Greater Depth
Teaching for mastery is concept based and we encourage pupils to think deeply about a concept and make connections. We aim for all pupils to develop a secure understanding of each concept taught so that they are able to connect and become with it.
We aim to develop curiosity through deliberate planning and metacognition through the modelling of our own thought process and the encouragement of metacognitive talk.
If pupils have the required knowledge and skills in a particular concept and are therefore fluent, the use of open questions are used to promote deeper thought. Teachers plan the use of such questions and consider how the questions will encourage children to pause, reflect, discuss and share their ideas.
Scaffolding and misconceptions
We plan carefully how learning will be scaffolded to ensure all pupils can learn the concept being taught. Some scaffolds will be personal to the need of the pupil and others used on a whole-class level. In addition to the use of manipulatives as a scaffold, breaking tasks in to smaller steps and planning for misconceptions are vital elements. Through this planning, we design resources which support pupils to complete each step successfully. Detailed scaffolds may include; prompts, examples, useful connections, diagrams and varies forms of duel-coding. Whole-task scaffolds may include; partially completed examples, checklists and examples of completed tasks.
Assessment and Feedback
Throughout every lesson, teachers constantly assess the learning. This is a vital aspect of lessons to ensure no pupil falls behind and all pupils who require it, are provided with a deepening task. Assessment is also vital for ensure all misconceptions are addressed swiftly. Teachers use a wide range of methods to assess, such as questions and ‘show me’ tasks.
White Rose end of unit assessments are used when required to ensure teachers have a clear picture of the learning.
Pupils are given verbal feedback on their tasks throughout each lesson. For longer written tasks, staff may provide some written feedback in exercise books, if this is useful for the pupil to develop their learning further.
Intervention and support for the lowest 20%
- We recognise that not all children make progress at the same rates. We aim to keep children with the main group within maths lessons and provide additional support within and outside of lessons to enable them to consolidate and catch up.
- Pre-teaching of new content will be used for those pupils who require this.
- Where additional support is needed, it follows the same progression and principles as the mainstream programme but with instruction that is broken down into carefully structured, small and cumulative steps to provide the important knowledge children need to consolidate. Intervention is targeted to consolidate key concept