A commitment that ALL pupils can and will achieve in mathematics, by providing opportunities for all pupils to develop the depth and rigour they need to make secure and sustained progress over time.

What is Teaching for Mastery?

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 of maths demonstrates a number of characteristics that underpin the approach. Some are listed below, and more can be found in the NCETM’s 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 underpin teaching for mastery in both primary and secondary schools.

The Five Big Ideas of teaching for mastery

Behind all NCETM and Maths Hubs' work in the field of teaching for mastery are the Five Big Ideas in Teaching for Mastery.

Underpinning principles

• Mathematics teaching for mastery assumes everyone can learn and enjoy mathematics.
• Mathematical learning behaviours are developed such that pupils focus and engage fully as learners who reason and seek to make connections.
• Teachers continually develop their specialist knowledge for teaching mathematics, working collaboratively to refine and improve their teaching.
• Curriculum design ensures a coherent and detailed sequence of essential content to support sustained progression over time.

Lesson design

• Lesson design links to prior learning to ensure all can access the new learning and identifies carefully sequenced steps in progression to build secure understanding.
• Examples, representations and models are carefully selected to expose the structure of mathematical concepts and emphasise connections, enabling pupils to develop a deep knowledge of mathematics.
• Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other.
• It is recognised that practice is a vital part of learning, but the practice must be designed to both reinforce pupils’ procedural fluency and develop their conceptual understanding.

In the classroom

• Pupils are taught through whole-class interactive teaching, enabling all to master the concepts necessary for the next part of the curriculum sequence.
• In a typical lesson, the teacher leads back and forth interaction, including questioning, short tasks, explanation, demonstration, and discussion, enabling pupils to think, reason and apply their knowledge to solve problems.
• Use of precise mathematical language enables all pupils to communicate their reasoning and thinking effectively.
• If a pupil fails to grasp a concept or procedure, this is identified quickly, and gaps in understanding are addressed systematically to prevent them falling behind.
• Significant time is spent developing deep understanding of the key ideas that are needed to underpin future learning.
• Key number facts are learnt to automaticity, and other key mathematical facts are learned deeply and practised regularly, to avoid cognitive overload in working memory and enable pupils to focus on new learning.

More information about teaching for mastery and how it can support primary and secondary schools can be found on the NCETM website.