Teaching for mastery: Changing mindsets in maths

Written by: John Canavan | Published:
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Using the teaching for mastery approach in maths has led to deep, long-term, secure and adaptable understanding of the subject. Assistant headteacher John Canavan explains


For those who may be unfamiliar with the concept, or just embarking on a journey around it, maths mastery is a teaching and learning approach that aims for pupils to develop deep understanding of maths rather than being able to memorise key procedures or resort to rote learning.

The phrase “teaching for mastery” describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths.

As stated by the National Centre for Excellence in the Teaching of Mathematics (NCETM), “achieving mastery means acquiring a solid understanding of the maths that has been taught to enable pupils to move on to more advanced material”. There are five big ideas, drawn from research evidence, which underpin teaching for mastery:

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 to give a deep conceptual understanding: the aim of this principle being that pupils can ultimately 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 child – 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: 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. Also 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.

I have been championing teaching for mastery at Cambridge Primary Education Trust (CPET) since 2015. I was given the opportunity to go on a Department for Education (DfE) exchange programme to Shanghai, where the concept was born, observed maths lessons and attended lectures at a local university.

Teachers from Shanghai then came to our schools in Cambridgeshire. I encouraged the CPET school I worked in at the time to change to the maths mastery approach, and it was rolled out trust-wide.

So what has changed and how has this helped children to acquire a deep, long-term, secure and adaptable understanding of the subject? My overall reflection is that changing mindsets to the teaching of maths can have a deeper impact on children than an approach that simply seeks to prepare them for national tests.

Drawing on our journey over the past six years, these are my key takeaways for other school and subject leaders.


1, An inclusive, tailored approach for children

Before teaching for mastery we did a range of different things, including taking some children outside the classroom to work at a slower pace, but our approach was clearly not working for all pupils.

We want everyone to learn together and so everyone now has access to the same learning, fluency, problem-solving and reasoning, and we also looked carefully at our use of language. This has really helped lower attaining children to feel part of the class rather than being separate and working away from their peers. We have tailored these principles to the needs of our children.


2, A whole-school strategy, with realistic timescales

A whole-school strategy on teaching for mastery is essential. Building from Foundation up to year 6 develops confidence and efficiency. A by-product of this is that results will come, but you need to be realistic about timescales. This is not a year-long piece of work: it takes two, three or four years to see the impact. You also have to bring staff with you – a little every now and then that allows people to see the potential of mastery. Take small steps, starting with fluency for knowledge and developing teachers’ understanding of effective use of language. This way it becomes less onerous and you see the benefit straight away. For us, we have seen an impact on attainment and progress, but it was not a quick-fix.


3, Recognise that this is about changing thinking

Teaching for mastery should be seen as a continuum. In our trust it is not happening every day in the classroom perfectly, but there has been real progression. Through the Cambridge Maths Hub and Fenland and East Cambridgeshire Opportunity Area, funded by the DfE, colleagues and I have taken on a role to develop training on maths in other schools. In Opportunity Area schools especially it is about changing mindsets. Primary schools are obviously measured on SATs, but it is about how we replace the emphasis on preparing pupils for tests by developing a deeper understanding through the teaching of maths, and at which point.


4, Ask questions and give ownership

I will go into schools to find out about their approach to maths, ask what they are doing and how they are finding mastery; a mutually professional dialogue which is also a learning process for me. Support can include lesson design, or other areas they feel they need help with (all this has been delivered via Zoom during the pandemic).

It takes years to bring about change. I will have conversations with the head and senior leaders. They then take this knowledge into CPD sessions ensuring teachers are assured about expectations. Senior leaders need to make sure mastery is happening consistently across all age phases and is continually maintained. Then they need to continually support teachers.

Give ownership and hear colleagues’ ideas – you cannot be regimented but you need to be realistic in terms of not diluting the mastery approach.


5, Provide CPD to keep staff on the journey

Looking at other schools with which myself and colleagues have worked, turnover of staff can be a huge issue. You can find that schools we supported a few years ago now have different teams in place, meaning mastery approaches may have gone backwards.

CPET does not have a high turnover of staff, so we have that consistency, and one of the reasons for that is the professional development opportunities and the support that staff have to take that learning forward; classroom teachers have gone on to become assistant heads and maths leads.

Retention of NQTs and early career teachers (ECTs) has been a big thing too. I know lots of people who have come a long way here, colleagues who now lead the training themselves.


6, Instil a passion, make learning fun

I have always had a passion for maths. I love to see children grow, develop and foster a love for the subject, and we have always sought to counter the stereotype of “I can’t do” maths. Before maths mastery, children did not have a deep understanding, the knowledge and the big ideas behind it, and were procedural mathematicians. This was impacting on GCSE results and beyond because the understanding was not there. We wanted to create critical thinkers, rigorous learners, and build deep understanding of concepts.

Every school is judged by results of course. You always need to respond to the children in the building, you cannot shirk that, but there is a bigger picture. Let’s remember that if the children are happy, if they are enjoying themselves, the learning will come.

  • John Canavan is assistant headteacher and year 6 teacher at Hatton Park Primary School in Longstanton, Cambridgeshire, part of Cambridge Primary Education Trust.


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