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A true understanding of these ideas will probably come about only after discussion with other teachers and by exploring how the ideas are reflected in day-to-day maths teaching, but here's a flavour of what lies behind them:

Coherence

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.

Fluency

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.

Variation

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.

The Five Big Ideas were first published by the NCETM in 2017.

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The fundamental characteristics that underpin teaching for mastery in all school and college phases

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An Introduction to the Five Big Ideas at Secondary

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In an introduction to our series on the Five Big Ideas at secondary, we explore the principles that underpin teaching for mastery.

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Autumn 2024 - Raising standards and improving attainment

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Autumn 2024 - Raising standards and improving attainment

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Maths Subject Leader Day - 12.11.24.pptx (2)

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Summer 2025 - Thinking strategically to the year ahead

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Summer 2025 - Thinking strategically to the year ahead

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Maths Subject Leader Day - 11.06.2025.pptx

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Autumn 2022 - EYFS and the key principles

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Autumn 2022 - EYFS and the key principles

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Subitising

Cardinality and conservation

Composition

Unitising

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_North Schools - Subject Leader Day - 05.12.23

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Spring 2024 - Using manipulatives in KS2

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Spring 2024 - Using manipulatives in KS2

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Hyperlinked to videos so you can use these with staff.

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North Schools - Subject Leader Day - 02.02.24

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Summer 2024 - Subject leadership and Ofsted Framework

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Summer 2024 - Subject leadership and Ofsted Framework

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Copy of South Schools - Subject Leader Day - 14.06.24

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Maths Vocabulary Policy - ST BENETS VERSION (2) (2)

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At a small, rural primary school, pupils in mixed-age classes benefit from teaching for mastery approaches

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Making mastery work in KS2 mixed-age classes

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How a new two-year rolling programme strengthens curriculum coherence and deepens content coverage for all pupils

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Oracy in the classroom - part 1 (secondary focus)

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Oracy in the classroom - part 1 (secondary focus)

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In Part 1 of our discussion with Kathleen McBride from Voice 21 and Jane Hawkins from the NCETM's Secondary Team and Jurassic Maths Hub, we discuss the definition of oracy, its significance for students' mathematical development, behaviour and overall well-being, and the role of Research and Innovation Work Groups (RIWGs) in exploring oracy's impact in classrooms. We also take a look at Voice 21's Oracy Framework for schools and teachers.

A transcript (PDF) of this episode is available to download.

Show notes

Taking part in the discussion:

Kathleen McBride, Senior Learning and Innovation Lead, Voice 21

Jane Hawkins, Assistant Director for Secondary, NCETM and Assistant Maths Hub Lead, Jurassic Maths Hub

Julia Thomson, Communications Manager, NCETM.

Episode chapters

00:06 Welcome and introductions

03:03 Definition, importance and research

08:58 Oracy challenges and misconceptions

13:01 Oracy Research and Innovation Work Groups

14:21 Oracy's impact on learning

15:54 Purposeful talk

17:07 The Oracy Framework

19:54 Oracy in the maths classroom

28:33 Reflecting on teaching practice

30:15 Conclusion.

Useful links

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Exploring the transformative potential of oracy in the maths classroom

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Oracy in the classroom - different types of talk 

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Oracy in the classroom - different types of talk 

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//www.ncetm.org.uk/podcasts/we-need-to-talk-exploring-the-oracy-commission-report/

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Exploring the transformative potential of oracy in the maths classroom

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Maths and SEND (Twilight by Angles Maths Hub)

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Maths and SEND (Twilight by Angles Maths Hub)

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Autumn 2025 - Pre-recorded before Face to Face Visit

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Autumn 2025 - Pre-recorded before Face to Face Visit