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Changing the maths mindset

March 16, 2022, 9:33 GMT+1
Read in 7 minutes
  • Mastering mathematics is about more than just good SATs results, says John Canavan
Changing the maths mindset

I have been championing teaching for mastery at Cambridge Primary Education Trust (CPET) since 2015.

It was around this time that I was given the opportunity to go on a Department for Education exchange programme to Shanghai - where the concept was born - to observe maths lessons and attend lectures at a local university, before teachers from Shanghai then came to our schools in Cambridgeshire on a return visit.

The experience led me to encourage the CPET school I worked in at the time to change to the maths mastery approach, and it was rolled out Trust-wide.

There are different interpretations of what maths mastery is, but for me, there are five big ideas - drawn from research evidence – that underpin this approach.

  • Coherence - lessons are broken down into small, connected steps that gradually unfold a concept, providing access for all children. This leads to generalisation of the concept and the ability to apply it to a range of contexts.
  • Representation and structure - representations used in lessons expose the mathematical structure being taught to provide 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. New concepts must be thought about, reasoned with, and discussed with others.
  • Fluency - children need quick and efficient recall of facts and procedures, and the flexibility to move between different contexts and representations of mathematics.
  • Variation - this involves 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. It’s also about 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. This connects the mathematics and draws attention to mathematical relationships and structure.

So, how has this helped children acquire a deep, long-term, secure and adaptable understanding of the subject at our Trust? Drawing on our journey over nearly seven years, these are my key takeaways for other schools:

An inclusive, tailored approach

Before teaching for mastery, we did a range of different things, including taking children outside of the classroom to work at a slower pace, but this only increased the attainment gap. 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. This really helped lower attaining children feel part of the class, rather than being separate and working outside away from their peers. We have tailored these principles to the needs of our children.

Realistic timescales

Building from foundation up to Year 6 develops confidence and efficiency, and a by-product of that is results. This is not a year-long piece of work: it takes two, three or four years to see the impact.

You have to bring staff with you, which means taking small steps - starting with fluency for knowledge, and developing teachers’ understanding of effective use of language. This way it becomes less onerous and you can start seeing the benefit straight away. 

Changing thinking

Teaching for mastery should be seen as a continuum. In our Trust it is not happening perfectly every day in the classroom, but there has been real progression.

Through the Cambridge Maths Hub, and Fenland and East Cambridgeshire Opportunity Area, funded by the DfE, we have taken on a role to develop training in maths in other schools.

In opportunity area schools, especially, it is about changing mindsets. Primary schools are obviously measured on SATs, but we have changed the focus from preparing pupils for tests, to developing a deeper understanding of maths.

Ask questions, give ownership

I go into schools, listen to their approach to maths and ask what they are doing and how they are finding it; a mutually professional dialogue that is also a learning process for me.

Support can include lesson design, or other areas with which staff need help. Heads and senior leaders then take this knowledge into CPD sessions; training is essential to making sure mastery is happening consistently across all age phases, and that it is continually maintained.

Following on from this, leader need to constantly monitor and support pupils. As I mentioned, it takes years to bring about change. 

Provide CPD to keep staff on the journey

Looking at some schools, turnover of staff is a huge issue. We often find schools we supported a few years ago now have different teams in place, which can make it difficult to maintain forward momentum. 

At CPET, former classroom teachers are now assistant heads / maths leads. The Trust does not have a high turnover of staff, which means we have consistency, and this is due in large part to the professional development opportunities on offer. I know lots of people who have come a long way - colleagues who now lead the training themselves.

Instil 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 national picture of ‘can’t do’ maths.

Before maths mastery, children did not have a deep understanding, or knowledge of the big ideas that underpin the subject. They were procedural mathematicians. This was impacting on GCSE results and beyond, because the understanding was not there.

We want to create critical thinkers, rigorous learners, and to build deep understanding of concepts. Every school is judged by results, but there is a bigger picture to consider.

How to implement maths mastery

  • A whole-school strategy on teaching for mastery is essential, but you need to be realistic on timescales for delivery and impact.
  • A change of mindset on the approaches to teaching maths can have a deeper impact on children than one that simply seeks to prepare them for national tests.
  • An inclusive approach where every child has access to the same learning, fluency, problem-solving and reasoning, is key.
  • Give ownership and hear colleagues’ ideas. Don’t be regimented, but at the same time do not dilute the mastery approach and ensure that staff have the support they need to take the learning forward themselves.
  • Always remember that if the children are happy, if they are enjoying themselves, the learning comes.


John Canavan is assistant headteacher and Year 6 teacher at Hatton Park Primary School, part of Cambridge Primary Education Trust