Mastery in Mathematics – an update

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By Nicki Allman

Find out how to incorporate the ‘concrete, pictorial, abstract’ mastery approach into your teaching.

mastery in maths

An overview

Over the coming weeks we are delighted to bring you a brand new collection of articles looking at the latest mastery practices in the key areas of mathematics: number place and value, calculation, fractions, decimal and percentages, measurements and statistics. This first article briefly outlines the theory of mastery and explores recent updates in the field, focusing on the concrete, pictorial, abstract (CPA) approach (for a more detailed description of what mastery in maths is, please read this article).

We master concepts by following a series of steps and move from beginner to master over time. It is a journey with set points along the way.
  • There is a starting point: we learn how to do something.
  • The process or concept then becomes embedded and we can do it almost without thought (it becomes an automatic process).
  • With practice and repetition, we become very good at it.
  • Finally, we are able to explain how to do the process to another person in a coherent way. We have become a ‘master’ in the process (however, this mastery is not retained if we don’t practice the process; fluency in the process is vital).
A mastery approach in mathematics has several key points:
  • Acquisition of mathematics throughout a lifelong learning journey.
  • Embedding deep conceptual knowledge and understanding. Depth of learning not breadth.
  • Teaching of fluency in both recall and procedures used.
  • Building on prior knowledge and being able to apply it to different areas.
  • Making connections and links between areas, eg fractions, decimals and percentages.
  • A potential move away from ability setting to mixed ability teaching, whilst paying attention to the needs of the children - support in terms of adults, resources etc… are provided for those who find concepts harder, but also for those who understand the concepts more quickly.
  • Planning in small steps rather than a sprint through the content at pace. Spending more time to ensure concepts are embedded and understood before moving on.
  • Provision of high ceiling, low threshold tasks and open ended activities means that all will be able to access the lesson.
  • Talk and reasoning become vital in the maths classroom and children should be able to explain their thought processes. Vocabulary and questions extend knowledge and understanding.
  • Children are able to use a concrete, pictorial and abstract (CPA) process and move through the stages as their understanding develops.
  • A change in how mathematics is viewed is needed.
    • A potential mindset change from a “can’t do, it’s too hard” attitude, to one of “I can try, I can have a go even if I find it difficult”. Carol Dweck’s work on fixed and growth mindset is a good research point.
    • It is about building confidence and allowing children to make mistakes and see this as a learning opportunity.
    • Crucially, it is about knowing that maths is achievable for all.
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  1. Ruth Bray
    on 17 January 2018

    CPA & Questioning

    Thank you a useful article, especially the questioning section. Useful for CPD

    4out of 5