maths mastery essay

• From the Director

Mastery in mathematics: What it is and why we should be doing it

An article from our Director, Charlie Stripp

• Published: 03/10/2014

Approaches to differentiation; defining a ‘mastery’ approach; the ‘England-China Mathematics Education Innovation Research Project’

I’ll be controversial: I think it may well be the case that one of the most common ways we use differentiation in primary school mathematics, which is intended to help challenge the ‘more able’ pupils and to help the ‘weaker’ pupils to grasp the basics, has had, and continues to have, a very negative effect on the mathematical attainment of our children at primary school and throughout their education, and that this is one of the root causes of our low position in international comparisons of achievement in mathematics education.

If my suspicion about the damage caused by current practice in differentiation in many maths lessons is correct, we should do something about it. However, I do recognise that an individual school’s interpretation of differentiation is rarely as black and white as I paint it below, and I know that many primary teachers put a great deal of thought and effort into developing differentiation models for maths teaching. For that reason, we should examine the evidence very carefully and carry out serious trials to help determine whether a different approach will improve children’s mathematical learning.

Put crudely, standard approaches to differentiation commonly used in our primary school maths lessons involve some children being identified as ‘mathematically weak’ and being taught a reduced curriculum with ‘easier’ work to do, whilst others are identified as ‘mathematically able’ and given extension tasks. This approach is used with the best of intentions: to give extra help to those who are having difficulty with maths, so they can grasp key ideas, and to challenge those who seem to grasp ideas quickly. It sounds like common sense. However, in the light of international evidence from high performing jurisdictions in the Far East, and the ‘mindset’ 1 research I referred to in my last blog , I’m beginning to wonder whether such approaches to differentiation may be very damaging in several ways.

For the children identified as ‘mathematically weak’:

• They are aware that they are being given less-demanding tasks, and this helps to fix them in a negative ‘I’m no good at maths’ mindset that will blight their mathematical futures.
• Because they are missing out on some of the curriculum, their access to the knowledge and understanding they need to make progress is restricted, so they get further and further behind, which reinforces their negative view of maths and their sense of exclusion.
• Being challenged (at a level appropriate to the individual) is a vital part of learning. With low challenge, children can get used to not thinking hard about ideas and persevering to achieve success.

For the children identified as ‘mathematically able’:

• Extension work, unless very skilfully managed, can encourage the idea that success in maths is like a race, with a constant need to rush ahead, or it can involve unfocused investigative work that contributes little to pupils’ understanding. This means extension work can often result in superficial learning. Secure progress in learning maths is based on developing procedural fluency and a deep understanding of concepts in parallel, enabling connections to be made between mathematical ideas. Without deep learning that develops both of these aspects, progress cannot be sustained.
• Being identified as ‘able’ can limit pupils’ future progress by making them unwilling to tackle maths they find demanding because they don’t want to challenge their perception of themselves as being ‘clever’ and therefore finding maths easy. A key finding from Carol Dweck’s work on mindsets 1 is that you should not praise children for being clever when they succeed at something, but instead should praise them for working hard. That way, they will learn to associate achievement with effort (which is something they can influence themselves – by working hard!), not ‘cleverness’ (a trait perceived as absolute and that they cannot change).

I’m not going to address differentiation in secondary school maths teaching directly here as I plan to make that the subject of a future article in this blog, but I do think much of what I’m saying here also applies at secondary level.

Countries at the top of the table for attainment in mathematics education employ a mastery approach to teaching mathematics. Teachers in these countries do not differentiate their maths teaching by restricting the mathematics that ‘weaker’ children experience, whilst encouraging ‘able’ children to ‘get ahead’ through extension tasks ( terms such as ‘weaker’ and ‘able’ are subjective, and imply that children’s ability in maths is fixed - I think they are very damaging and we should stop using them – many teachers already have, but many still use them ). Instead, countries employing a mastery approach expose almost all of the children to the same curriculum content at the same pace, allowing them all full access to the curriculum by focusing on developing deep understanding and secure fluency with facts and procedures, and providing differentiation by offering rapid support and intervention to address each individual pupil’s needs. An approach based on mastery principles:

• makes use of mathematical representations that expose the underlying structure of the mathematics;
• helps children to make sense of concepts and achieve fluency through carefully structured questions, exercises and problems that use conceptual and procedural variation to provide ‘intelligent practice’, which develops conceptual understanding and procedural fluency in parallel;
• blends whole class discussion and precise questioning with intelligent practice and, where necessary, individual support.

Colleagues at the NCETM and I have produced this short paper: ‘Mastery approaches to mathematics and the new National Curriculum’ , which defines what we mean by mastery, links it to the National Curriculum, and highlights its implications for the professional development of teachers. This work is supported by the Department for Education, which is keen to see how mastery teaching can raise achievement in schools. This video clip of an English year 2 primary class learning how to add fractions shows mastery teaching in action.

A major element of the NCETM’s leadership and development of mastery teaching is through the DfE-funded ‘England-China Mathematics Education Innovation Research Project’, involving more than 60 teachers from England shadowing primary mathematics teachers in Shanghai (the English teachers are in Shanghai as I write this) to observe mastery teaching in practice, followed by the Shanghai teachers coming to England to exemplify mastery teaching in our classrooms and to support the English teachers in making sense of and trying out a mastery approach to their maths teaching.

This project is being run through the NCETM’s Maths Hubs initiative. Testing out new ideas in the classroom to gather evidence of how effective they are, before advocating which should be adopted more widely, is a key role of the Maths Hubs. The English primary school teachers involved have embarked on this project with great enthusiasm. They have a strong desire to learn as much as they can about how maths is taught in Shanghai and want to use what they learn to develop their own teaching back in England to improve their pupils’ learning.

The project will help us to develop how we use the mastery approach to maths teaching in our primary schools, to improve maths education and the mathematical futures of our young people. It also provides a brilliant opportunity to develop close working relationships between the English and Chinese teachers involved, so that they can learn from each other, to the benefit of teachers and children in both England and Shanghai.

It might also lead us to start moving away from the practice of dividing primary maths classes into different tables, with harmless sounding names, but names which nevertheless don’t fool even the pupils on the ‘red’ table!

It will not be quick or straightforward to improve the learning of our lower attaining pupils, narrowing the wide gaps between pupils’ mathematical attainment that currently exist in our classrooms, but we must be committed to doing so. I believe that mastery teaching will – with time and effort – enable us to achieve this.

1. ‘Mindset’, Carol Dweck, 2006, ISBN 978-1-78033-200-0

Is there anything wrong with this page?

Subscribe to our newsletter

The NCETM is led and delivered by Tribal Education Services, with MEI as a key partner. Learn more about Tribal Education Services and what they do via the link to their website in 'About the NCETM'.

About this website

Stay connected.

All you need to know to choose your course, from foundation to bachelors or integrated masters

Ready for advanced study? Explore our Postgraduate Courses and Research Degrees

Discover our part-time online courses for study any time, anywhere

Looking to improve your skills or change career? A short course could be the key

• Research degrees
• Part-time study
• Apprenticeships
• Campus and facilities
• Fees and Finance
• Student support
• Study abroad
• Employability

Let the adventure begin. Where could you be living?

Culture, adventure, fun, sport, shopping. Derby has lots to offer, whatever you love doing

Make friends, learn a skill or share your interests with our varied clubs and societies

How to make the most of your time - on campus and beyond.

• International students
• Sport at Derby
• Union of Students

Discover how we are pushing the boundaries of innovation and research and learn about our approach

If you have a curious, independent mind then join us. Explore your options for research degrees

Explore our research case studies and discover how our research is having a real world impact

Whether you are from industry or academic, we’re always keen to collaborate on research projects

Learn more about our researchers and our research focus

Find out more about our colleges and departments

Coral reefs are dying off at an alarming rate. Our Aquatic Research Facility is carrying out work with organisations across the globe to make corals more resilient in the face of man-made afflictions.

Discover how you can benefit from working with us.

If you have an idea for a new business or are in the early stages of establishing yourself, see how we can help.

If you're ready to grow your business, see what support and funding we can offer.

Even if your business is well-established, there are still plenty of ways we can add value.

• Research and Innovation
• Talent and Recruitment
• Training and Development

Get in touch with the relevant team to find out how we can make a big difference to your business.

Mathematics Mastery: a blessing or a curse?

Mathematics Mastery was founded by Dr Helen Drury – a pioneer of teaching and learning for mastery in UK schools – back in 2012. Since then, the programme has been adopted in many schools across the country.

By Dave Benson - 6 February 2018

Dave Benson, Mathematics Education Coordinator at the University of Derby, discusses the pros and cons of the scheme.

Mastery Mathematics has been adopted as a term by the National Centre for Excellence in the Teaching of Mathematics (NCETM) since 2014. It has many roots in well-established pedagogical approaches in high-achieving East Asian countries. The NCETM has sought to define it and establish principles for teaching mathematics which help to raise standards in achievement across the primary and secondary sectors in the UK.

What is Mastery of Mathematics?

Defining Mastery Mathematics is in itself a complex business. Helen Drury, founder of the programme, explains the definition when she says:

A mathematical concept or skill has been mastered when, through exploration, clarification, practice and application over time, a person can represent it in multiple ways, has the mathematical language to be able to communicate related ideas, and can think mathematically with the concept so that they can independently apply it to a totally new problem in an unfamiliar situation.

So, ‘mastery’ of a mathematical concept would suggest that we understand it at a deep level. In this context, ‘deep’ is obviously a relative, complex and even subjective term. What is deep for one person may be shallow for another. That said, if a concept has been ‘mastered’, one would expect the learner to be able to apply their knowledge and skills effectively to solve new problems and also to demonstrate a growing ability to explain as well as justify their thinking.

Although complicated to define, many would argue Mathematics Mastery is still persuasive as an idea and potentially supportive to both primary and secondary school practitioners. For example, in the light of new-style Key Stage 2 SAT and GCSE papers, which are expected to assess pupils’ ability to use and apply skills more rigorously, an emphasis on secure understanding, confident reasoning and problem solving skills, rather than on mechanical application of mathematical procedures, certainly feels like a positive and wise aspiration. For me, despite its potentially divisive label, there is something positive and pedagogically persuasive in the intentions of the idea of ‘mastery’. Its emphasis on depth of understanding, over breadth of knowledge and procedural approaches to learning, for example, chimes with my personal philosophy for teaching and learning mathematics.

Does Mathematics Mastery work in the classroom?

For some time, however, my sense has been that we need to move on from a debate about the definition of ‘mastery’ to the much more interesting and challenging idea of classroom implementation and evaluation of experiences. Only that way can we begin to ascertain the potential benefits and shortcomings of a ‘mastery’ approach in our primary and secondary schools. With this in mind, since March 2016 I have worked with more than 100 teachers and 20 schools to explore with them ideas for implementing a ‘mastery’ approach in their classrooms. Throughout my research with these teachers, I have seen both the pros and cons to Mathematics Mastery.

The pros of Mathematics Mastery:

• Teachers feel less constrained by planning structures and are at ease with the idea of carrying more in their head with less detail in their written plans.
• Participants see the value of ‘dwelling on’ topics for longer periods as beneficial because it helps provide a more secure base for learning.
• The balance between ‘pacey’ activities to support fluency and richer exposition and tasks which demand more reasoning and problem-solving skills could be beneficial to pupils’ progress.
• Teachers have developed their own subject knowledge by engaging with a mastery approach.
• Many have experimented with grouping pupils in alternative ways. Although grouping by ability is still used, many have begun to recognise the potential benefits to learning of mixed ability groupings.
• Generally, participants report that pupils are strengthening verbal reasoning skills more obviously than developing confident written explanations of their thinking.

The cons of Mathematics Mastery:

• Losing the awe and wonder of learning mathematics.
• Providing adequate intervention.
• Dealing with differentiated learning needs.
• Managing pace of lessons and learning.
• Maintaining variety and creativity in pedagogical approaches.

The question of how to provide intervention for those pupils falling behind the expected pace of learning has persisted among teachers I have worked with. In addition, concerns surrounding headteachers’, parents’ and Ofsted’s views of the changes in approach also remain uppermost in participants’ minds. Understandably, they wonder whether the rationale for and intentions of the changes will be shared and understood, particularly with regard to differentiation and grouping of pupils. Paradoxically, they sense progress in their professional practice yet feel concerned about how they will be judged, particularly if outcomes for their pupils who do not improve.

Would I see Mastery in Mathematics as a blessing or a curse?

With its emphasis on conceptual understanding of mathematics as a complement to confident procedural skills, I would probably go more with the former than the latter. However, a reading of key figures in the history of educational thought on the learning of mathematics, would suggest that mastery is far from a new idea and that similar principles have underpinned much academic writing for more than 40 years.

The ‘Curse of Mastery’ could be the way in which it has become yet another educational initiative which seeks to control rather than liberate the potential of professional practice. With their plethora of strategies for improving outcomes in mathematics across the primary and secondary sectors, recent governments have tended to de-professionalise teachers by denying them genuine opportunities to exercise professional judgement and, instead, creating cultures of fear in which teachers feel constrained to be seen to be engaged in expected practices.

Although well-intended and, in my view, fundamentally persuasive at heart, if Mastery Mathematics becomes regarded as some kind of perfect ‘recipe’, official directive or solution for teaching mathematics, we shall once again find ourselves in a position where the potential to promote children’s learning in mathematics will be lost.

Do you agree with Mastery in Mathematics? What are your thoughts? Comment below and let us know.

For further information contact the press office at [email protected] .

About the author

Dave benson i am senior lecturer in and subject leader for mathematics education.

I joined the University of Derby ITE Team in 2003 when I assumed the role of Subject Leader for Mathematics Education. Exploring the nature of effective pedagogies in mathematics has become a passion for me.

Related categories