Mastery maths

What is mastery maths teaching and learning?

The National Centre for Excellence in the Teaching of Mathematics (NCETM) explain the essence of mathematics teaching for mastery as follows:

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.

Behind all NCETM and Maths Hubs' work in the field of teaching for mastery are the Five Big Ideas in Teaching for Mastery, which are detailed in a diagram that can be viewed by clicking on the link at the bottom of this page. The 'Five Big Ideas' are:   


Teaching is designed to enable a coherent learning progression through the curriculum, providing access for all pupils to develop a deep and connected understanding of mathematics that they can apply in a range of contexts.

Representation and Structure

Teachers carefully select representations of mathematics to expose mathematical structure. The intention is to support pupils in ‘seeing’ the mathematics, rather than using the representation as a tool to ‘do’ the mathematics. These representations become mental images that students can use to think about mathematics, supporting them to achieve a deep understanding of mathematical structures and connections.

Mathematical Thinking

Mathematical thinking is central to how pupils learn mathematics and includes looking for patterns and relationships, making connections, conjecturing, reasoning, and generalising. Pupils should actively engage in mathematical thinking in all lessons, communicating their ideas using precise mathematical language.


Efficient, accurate recall of key number facts and procedures is essential for fluency, freeing pupils’ minds to think deeply about concepts and problems, but fluency demands more than this. It requires pupils to have the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections, and to choose appropriate methods and strategies to solve problems.


The purpose of variation is to draw closer attention to a key feature of a mathematical concept or structure through varying some elements while keeping others constant.

  • Conceptual variation involves varying how a concept is represented to draw attention to critical features. Often more than one representation is required to look at the concept from different perspectives and gain comprehensive knowledge.
  • Procedural variation considers how the student will ‘proceed’ through a learning sequence. Purposeful changes are made in order that pupils’ attention is drawn to key features of the mathematics, scaffolding students’ thinking to enable them to reason logically and make connections.