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Mastering maths

This approach recognises the value of developing the power to think, understand and reason rather than just ‘do’ using a set of given rules. The fundamental belief is that every child can achieve number fluency, confidence and understanding step by step.

Children are all taught the same concept in their year and the expectation is that all children can succeed. Some children may need extra strengthening teaching whilst others are encouraged to deepen their understanding.

Maths mastery recognises the value of making a whole-class journey of a concept which is broken down into small steps of learning, one by one.

  • Coherence: 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.
  • 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.

In this way children are building secure foundations which they can build upon and make connections to other areas of maths ensuring deep mathematical understanding and confident mathematicians.

How will maths lessons work?

Each lesson has a progression, with a central flow that draws the main learning into focus. There are different elements, informed by research into best practice in maths teaching, that bring the lessons to life:

Retrieval practice starter

Children will have the opportunity to ‘warm up’ for their maths lesson using a mix of mental maths skills and retrieval practice from previous areas of learning. This content may be fluency or knowledge from a previous year group or phase, or from prior content that could link. For example, negative numbers prior to teaching co-ordinates. This aims to:

  • Revise previously taught content.
  • Practice content that supports new teaching for the coming lesson.
  • Activate prior knowledge which links with new content in order to create rich mathematical links.

Discover – ‘I do’

The core content of each lesson will be introduced by the teacher and explored using a variety of representations and structures. Within the principles of mastery, the children develop mathematical thinking and reasoning by being given the opportunity to explore.

This could include a range of concrete resources and visual representations to identify the essence of a concept. What do you notice? What stays the same? What changes?

Children will be given the opportunity to develop their understanding of a concept following the CPA approach to represent the same question in a variety of ways, rather than looking at a variety of questions in an abstract manner. Teachers will be able to summarise the key learning point from the maths lesson using a sentence stem which can be used throughout the lesson and is referred to as part of the learning wall. In this part of a lesson, children will:

  • Have the opportunity to discover the learning for themselves – exploration.
  • At some point, from someone, receive a crystal-clear explanation – partner work and generalisation.
  • Develop their understanding through a range of representations – concrete and pictorial.
  • Have the chance to develop the skills of a good mathematician – including both procedural and conceptual fluency.
  • Discover a key sentence stem which summarises a key fact for the lesson to assist in their conceptual understanding.

Think together – ‘we do’

The class shares their ideas and compares different ways to solve examples and problems, explaining their reasoning with hands-on resources and drawings to make their ideas clear. Children can develop their understanding of the concept with input from the teacher. This is a journey through the concept, digging deeper and deeper so that each child builds on secure foundations while being challenged to apply their understanding in different ways and with increasing independence.

Partner talk supports children in developing a deep understanding of a concept. This section of the lesson reduces the scaffolding and allows children to focus on a concept through a variation. In this part of a lesson, children will:

  • Have the chance to practice the new content in a range of contexts with a partner for support.
  • Master the new content before the next lesson.
  • Reduce the amount of scaffolding used to support children.
  • Share their learning with their partner and the class, guided by discussion with the teacher.

During the think together tasks, the teacher has the first opportunity for instant intervention. Children identified through the discover task and the early think together tasks can have additional teaching on a 1-2-1 or small group basis.

During the intelligent practice part of the lesson, teachers have an opportunity for early intervention. Teachers and/or teaching assistants will ‘live mark’ to identify errors and misconceptions as early as possible. This early intervention could be through additional scaffolding of a problem, 1-2-1 re-teaching or small guided groups being formed and supported by an adult. Some children may have errors to correct where they have miscalculated as opposed to misunderstanding a concept.

Intelligent practice – ‘you do’

Now children practice individually or in small groups, rehearsing and developing their skills to build fluency, understanding of the concept, and confidence. The children develop fluency with a concept through deliberate practice.

Practice that is deliberate and planned with thought to procedural variation further aims to reveal the underlying principles of a concept. When well planned, this can support teachers in identifying misconceptions and providing efficient and effective intervention. It is important that children are provided with sufficient time (no less than 20 minutes) to tackle their intelligent practice challenges.

  • In this part of a lesson, children will:
  • Independently apply their learning in both familiar and unfamiliar problems;
  • Extend their knowledge and understanding by tackling more difficult, abstract problems;
  • Creatively develop their methods and problems;
  • Explore and reason about mathematical statements and their own further lines of enquiry.

Reflect challenge (plenary)

Finally, children are prompted to reflect on their learning by tackling a carefully selected problem to solve to check the children’s understanding of a concept. This provides children with a task in a different way. For example, explaining to a different person or identifying errors.

Children will be encouraged to work together with work partners to apply their learning from the lesson to challenge and they will be challenged further by being encouraged to find a different way to solve the challenge, and explore which method they preferred and why. In this part of a lesson, children will:

  • Reflect on their success, confidence and understanding of the content of the lesson.
  • Identify and define key words.
  • Explain how to answer a problem to a partner.
  • Summarise the key content in a simple stem sentence.
  • Participate in creating a record of their learning on the working wall in order to support following lessons.

Maths meetings - ‘keep up, not catch up’

Maths meetings will be held before the follow up lesson. They aim to support children to ‘keep up’ and secure previous content before building new learning. This could be through pre-teaching of a new concept or securing knowledge from a previous lesson.

Further information

Teaching for Mastery - a useful webpage from the National Centre for Excellence in the Teaching of Mathematics.

The Education Endowment Foundation's Teaching and Learning Toolkit on Mastery Learning.