Teaching for Mastery

What is it?

Mastering maths means pupils acquiring a deep, long-term, secure and adaptable understanding of the subject. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Achieving mastery means acquiring a solid enough understanding of the maths that’s been taught to enable pupils to move on to more advanced material. Teaching for mastery in maths demonstrates a number of characteristics that underpin the approach. Some are listed below, and more can be found in the NCETM’s 2016 paper ‘The Essence of Maths Teaching for Mastery’.

It rejects the idea that a large proportion of people ‘just can’t do maths’.
All pupils are encouraged by the belief that by working hard at maths they can succeed.
Pupils are taught through whole-class interactive teaching, where the focus is on all working together on the same lesson content at the same time. This ensures that all can master concepts before moving to the next part of the curriculum sequence, allowing no pupil to be left behind.
Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other.

The Five Big Ideas

The Five Big Ideas underpin teaching for mastery in both primary and secondary schools.

Coherence - Lessons are broken down in to 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
Mathematical Thinking - 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
Fluency - Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics
Variation - 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.

What is the Teaching for Mastery Programme?

The NCETM and Maths Hubs have been running the national Primary Teaching for Mastery Programme since 2015, and more recently secondary schools have also become involved with teaching for mastery. In the first year, 136 schools from all over England each nominated a teacher to begin training as a Primary Mastery Specialist. The teachers were given a year’s intensive training in the principles of teaching for mastery, underpinned by its ‘Five Big Ideas’, and in professional development leadership. In the following year, they further developed teaching for mastery in their own schools, and they shared the approach with neighbouring schools by leading Teaching for Mastery Work Groups. In each subsequent year, a new cohort of Primary Mastery Specialists has been trained, increasing the pool of specialists leading Work Groups of local schools. By summer 2020, more than 8,000 schools have participated in the Teaching for Mastery Programme. Hundreds of thousands of children are now benefitting from a changed experience of maths learning at school. The programme is open to all state-funded schools in England. Secondary Mastery Specialists are now also being trained, and hundreds of secondary schools are starting to develop teaching for mastery approaches, especially at KS3. All of the 40 Maths Hubs across England offer professional development to help teachers develop a mastery approach in their own classroom, department and school.