Guest Blog: Mastery and maths - how our guidance can help

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.

Since the EEF guidance report was published, several teachers have asked me if the guidance encourages mastery. The short answer is yes. 

The starting point for the guidance was a series of questions from teachers about the effective ways of enabling all pupils to succeed mathematically. And, of course, these questions addressed many aspects of mastery, including fluency, use of representations, and achieving deeper understanding.

Let’s look in detail at how the recommendations in the Maths guidance report relate to the National Centre for Excellence in Teaching Mathematics’ (NCETM) Five Big Ideas for mastery: coherence, representation and structure, mathematical thinking, fluency and variation.

Coherence refers to connecting new mathematical ideas to ideas that pupils have already understood. Key to this is using assessment to understand what pupils do and do not understand in order to adapt teaching and/or provide feedback for pupils. Recommendation 1 in the EEF guidance outlines evidence-based approaches for doing this. Of course, coherence is also concerned with enabling pupils to develop a rich network of mathematical ideas, which is the overarching focus of Recommendation 4.

Representation and structure emphasises how representations should be used to expose mathematical structure and develop independent understanding, which is the focus of Recommendation 2 (Use manipulatives and representations) and Recommendation 4 (Teach pupils to recognize and use mathematical structure). The evidence indicates that how manipulatives and representations are used is crucial – teachers need to have a clear mathematical rationale. It is particularly important that manipulatives are used as a temporary tool for achieving understanding rather than becoming a crutch for pupils.

Mathematical thinking is addressed throughout the recommendations, but particularly in Recommendation 4 (Teach pupils to consciously choose between mathematical strategies, and Teach pupils to recognize and use mathematical structure), Recommendation 3 (Teach pupils problem solving strategies) and Recommendation 5 (Develop pupils’ independence and motivation). It is important that teachers provide regular opportunities for pupils to develop metacognition by encouraging them to explain their thinking to themselves and others.

Fluency stresses the importance of developing quick, and efficient, recall of number and multiplication facts, and the skilled and flexible use and application of procedures. This is tackled in Recommendation 4 (Ensure that pupils develop fluent recall of facts, Teach pupils to understand procedures, and Teach pupils to consciously choose between mathematical strategies).

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The idea of variation is central to mastery and emphasises the importance of presenting mathematical ideas to pupils in different ways, using a range of examples and non-examples of concepts, as well as deliberately choosing tasks to avoid ‘mechanical repetition’. Variation is a key feature of several recommendations, notably Recommendation 3 (Teach pupils strategies for solving problems), and Recommendation 6 (Use tasks and resources to challenge and support pupils’ mathematics).

The Guidance also addresses ways of developing mastery for pupils who are struggling with mathematics in Recommendation 7 (Use structured interventions to provide additional support). It is important to consider how interventions support classroom learning, and to ensure that pupils do not miss things that they enjoy or mathematics that that they need to learn.

If you are already working on mastery, how will the guidance help? The guidance highlights teaching approaches that are supported by the strongest international evidence and which are most likely to impact positively on children’s mathematical attainment. If you’re working on mastery, don’t stop! But do look to the guidance to dig deeper into the evidence on the “best bets” for developing pupils’ mathematics. And do let us know what you think and what additional material you would find useful.