An Introduction to Mastery

Jurassic Maths Hub Teaching for Mastery Statement

Principle: The intention of teaching for mastery is to give all children access to equitable classrooms; classrooms where they can all participate and be influential, and classrooms where they are encouraged and supported to develop a deep connected and sustained understanding of the mathematics being explored.

The following may indicate that a teacher is aiming to provide an environment and experiences in line with teaching for mastery:

  • All children working on the same focus with different support provided to enable all children to access the mathematics
  • Children behaving as mathematicians as part of a mathematics community, including:
    • Making decisions both independently and collaboratively
    • Working flexibly to answer questions, reflecting on the efficiency and simplicity of their chosen methods
    • Making conjectures and generalisations, applying and testing them
    • Having a go, willing to share even when unsure and understanding that this is when learning is taking place
    • Being comfortable with not getting everything ‘right’, embracing struggle
    • Talking mathematics:
      • Articulating their thinking
      • Taking responsibility for asking questions of others to clarify understanding
      • Agreeing and disagreeing and justifying their thinking
      • Responding in full sentences with the intention that everyone understands them
    • Exploring the mathematics guided by the teacher
    • Working and learning collaboratively
  • ­The use of subject-specific vocabulary by all adults and children in the school from EYFS onwards
  • The use of different representations, by both adults and children, for making sense of the mathematics (exposing structure) and demonstrating understanding
  • The use of questioning to develop understanding
  • Books show children working on the same mathematics, representing their thinking and understanding in different ways (including with diagrams, models, symbols and writing) rather than children working through many different examples. This may result in less in the books (especially for younger children) and no obvious differentiation by task.

The most effective way to find out what children understand about their mathematics will be to talk them. Children really understand a mathematical concept, idea or technique if they can:

  • Describe it in their own words;
  • Represent it in a variety of ways (e.g. using concrete materials, pictures and symbols)
  • Explain it to someone else;
  • Make up their own examples (and non-examples) of it;
  • See mathematical connections between it and other facts or ideas;
  • Recognise it in new situations and contexts;
  • Make use of it in various ways, including in new situations*

*Adapted from NCETM adapted from John Holt ‘How Children Fail’ 1964.

Four ways in which the term Mastery is being used

  1. A mastery approach; a set of principles and beliefs.
    a belief that all pupils are capable of understanding and doing mathematics, given sufficient time.
  2. A mastery curriculum
    One set of mathematical concepts and big ideas for all.
  3. A set of pedagogic practices
    that keep the class working together on the same topic, whilst at the same time addressing the need for all pupils to master the curriculum. Challenge is provided through depth rather than acceleration into new content.
  4. Achieving mastery
    knowing ‘why’ as well as knowing ‘that’ and knowing ‘how.’

A Mastery Curriculum

  • All/most pupils can and will achieve
  • Keeping the class working together so that all can master mathematics
  • Development of deep mathematical knowledge
  • Development of both factual/procedural and conceptual fluency
  • Longer time on key topics

The 5 Big Ideas can be seen in this diagram and explored further by clicking on each section.

Introduction to Mastery

Coherence (the 5 idea flows through the diagram)
Connecting new ideas to concepts that have already been understood, and ensuring that, once understood and mastered, new ideas are used again in next steps of learning, all steps being small steps

NCETM Mastery Microsite

with guidance and resources to support Teaching for Mastery

NAMA_5_five_myths of mastery

The EEF blog

by Professor Jeremy Hodgen – Chair of Mathematics Education at the UCL Institute of Education – led the evidence review underpinning the recent EEF guidance report, ‘Improving Mathematics at Key Stages 2 and 3. In this blog, he discusses the links between the guidance and mastery learning.

Fluency Mathematical Thinking Representation & Structure Variation