Origins

I’ve loved the recent questions and interest in my mastery books on Twitter. In this blog – extracted from the introduction to How To Teach Mathematics For Mastery – I share some of the key themes in my primary and secondary writing.

I begin by explaining that, “This book is grounded in two things: a belief that every child can enjoy and succeed in mathematics – regardless of background – and a dedication to transform mathematics education.

I began teaching secondary mathematics in 2002. I taught in comprehensive schools in England – in rural Oxfordshire and inner-city London. After several years, I found myself becoming frustrated at the many barriers standing in the way of student achievement.

Teachers, myself included, were increasingly overwhelmed by the daily challenges of bureaucracy, lack of staff and an unmanageable workload. Professional development, when time allowed for it, was generic and patchy.

In short, teachers were unable to thrive. It didn’t matter how talented, dedicated or hard-working we were. The essence of great mathematics teaching was getting lost. Why? Because mathematics teaching was playing second fiddle to a multitude of other demands.

Unsurprisingly, these challenges were reflected in classroom attitudes and attainment. Students were often disengaged. They struggled to push beyond a surface-level understanding of mathematical ideas. Mathematics was seen as too hard, too boring or irrelevant to everyday life.

International league tables such as the Programme for International Student Assessment (PISA) told the same story. The United Kingdom was trailing behind a whole host of countries in mathematics. What on earth had gone wrong in such a well-resourced nation, full of well-intentioned people working in education?

Teachers in the UK work in a high-stakes environment where exam results are paramount. But the pressure to ensure students perform well on paper – alongside all the other challenges – comes at a price. Time and resources are invested in playing catch-up instead of planning for the long term. The ‘system’ has trapped schools in a false economy.

As my years in the classroom progressed, I realised I had a deep motivation to change things. Not just for one class, one year group, or even one school. I wanted to help bring about change on a national scale.

Teachers wanted to do the best job they possibly could. Students were capable of achieving significantly more. But a step change was needed. In my role as Director of Mathematics at the education charity, Ark, I began to research how to best support teachers in mathematics. How could we improve mathematics teaching across a range of different school contexts and enable more students to achieve their goal?

Specifically, I was interested in what could be done here and now to provide support and raise standards. While the growing issues of workload, school funding and policy changes were beyond my reach, I was convinced that positive change was still possible.

I was struck by the level of success seen in high-performing jurisdictions such as Shanghai and Singapore. What did they do differently that enabled their students to achieve their goal in such great numbers?

I was faced with questions: are the teachers in Shanghai and Singapore simply better? Are the children simply more ‘able’? The answer to both questions is a resounding no.

It can’t be denied that certain cultural differences support the high levels of achievement in these nations. Parental engagement and societal value placed on education – and specifically mathematics education – do go a long way.

But that’s certainly not all there is to it – and to claim otherwise is nothing but a convenient excuse to maintain the status quo.

What I discovered in my research wasn’t dramatic or revolutionary. These countries weren’t hiding a mysterious ‘silver bullet’ that could magically fix a broken education system. They weren’t doing anything that couldn’t be done – at least in part – in countries across the world.

So what were these countries doing differently that led to their sustained success in mathematics? Now, answering this could take up an entire book in itself, but there were three core elements that excited me most:

• Teachers have ongoing access to high-quality professional development throughout their career, with an emphasis on mathematics-specific pedagogy. Time is carefully allocated for training, engaging in research, collaborative planning and knowledge sharing – and the value of this activity is widely understood.
• Teachers have high expectations for every single learner, rooted in a belief that anyone can become an excellent mathematician. Teachers reinforce this attitude to build confidence and resilience.
• The curriculum is designed to promote mathematical thinking and time is given to ensure every learner truly understands the mathematical concepts taught. Mathematical discussion, multiple representations and problem solving play a central role in lessons that have been carefully crafted. Misconceptions are rapidly addressed to ensure all learners progress at the same pace.

As part of my research, I also began considering the purpose of mathematics education. The vast majority of people – teachers, parents, politicians, and yes, even students – agree it’s important. But it’s not always clear why it’s important.

Do we want learners to be able to reproduce standard techniques, such as solving simultaneous equations? Do we want learners to know when it is appropriate to use one technique rather than another? Do we want learners to appreciate how ideas and techniques are connected? Do we want learners to be able to solve unfamiliar problems?

Without clarity concerning the underlying purpose of mathematics education, how can we agree on which classroom practices best enable us to achieve our goal?

In high-performing jurisdictions, the purpose of mathematics education is clear and centrally communicated. This lends structure and continuity to how it’s taught across the country.

My research has led me to argue that the ultimate aim of mathematics education in to enable learners to solve new problems in unfamiliar contexts. …

To achieve this aim, everything we do in mathematics education should support students in developing a deep structural understanding of mathematical ideas and how they fit together. Students need to build fluency in applying mathematical techniques and develop skills to communicate mathematical ideas.

It should also go without saying that students must be exposed to rich mathematical content that enables them to problem-solve on a regular basis. Crucially, this rich content should be accessible to all students – not just the students who have been labelled as ‘gifted’ or ‘more able’.

Eventually, my research evolved into the development of an approach to the teaching and learning of mathematics: Mathematics Mastery. This is a structured, whole-school programme of mathematics-specific professional development, integrated with a complete curriculum framework and classroom resources. The programme was launched in schools in England and Northern Ireland in 2012. Five years in, the programme runs in around 500 primary and secondary schools around the country.

In launching this programme, I set out to bring together schools that share my ethos concerning how and why mathematics should be taught. I wanted to find teachers who believed that mathematics was for everyone. Teachers who believed that deepening understanding was a better use of time than accelerating through the curriculum. Teachers who believed that the ultimate aim of mathematics education was to be able to solve new problems in unfamilar contexts.

‘Mastery’ was coined as an umbrella name for the set of principles and effective classroom practice underpinning our approach. While an hour’s lesson might be sufficient for someone to say they have learned something, mastery is a much longer-term investment. Mastery, at it’s heart, is about the entire journey of learning a discipline – in this case, the discipline of mathematics. In the last few years, the term ‘mastery’ has taken hold across the country as a standard of mathematics education to aspire to.

It remains to be seen whether giving this approach a name – ‘mastery’ – is of benefit or not. Perhaps it doesn’t matter. In this book, I have sought to look beyond the name and simply focus on what it means to put the underlying principles into practice. I set out to transform mathematics education in the UK and this remains my aim. I am humbled, excited and highly motivated by the number of teachers, school leaders and educationalists across the country who share this goal and are making a positive difference to the lives of young people.

As mentioned already, the journey to mastery is a long one. We are still refining and evolving our approach every day. But the importance of recognising incremental shifts in attitude and standards cannot be underestimated. Over time, these gradual changes morph into something much more significant.

Gradually, classroom by classroom, a transformation in mathematics education is taking place. Thousands of students are benefiting from increased understanding, enjoyment, resilience and achievement in mathematics.

No teacher has ever said this was easy. It took investment, dedication and perseverance to make this transformation happen, often in the face of huge pressure and resistance.

If a national transformation in mathematics education is going to take hold, we must aim for more students to reach- and exceed – our national standards. However, this is only viable if we invest in developing our teachers over the long term, and if we refocus our efforts on building a deep foundation of mathematical understanding among learners.

The evidence is clear. The leading countries in mathematics education have shown what is possible. The single most powerful thing we can do now is aim high.”

Content taken from the introduction to my book, “How To Teach Mathematics For Mastery”, published by Oxford University Press.