Thursday 22 September 2016


I have such a privileged life, I get to visit schools all around the world and see maths teaching at its very best. I am able to spend time both researching mathematics education and reading the best contemporary evidence as well as well established and proven approaches to pedagogy and subject knowledge.
For decades, I have dedicated all of my time to working to improve education. It is the very lifeblood of a mature civilization, it has the power to transform lives and bring meaning and joy to the world. Mathematics education sits at the top of my priority list – every day, I live and breathe it. My only professional goal in life is to make education better.
So, being able to visit schools and meet with teachers, being able to see experts in practice, being able to hear the stories of success and to witness the extremely nuanced behaviours and dispositions that lead to a mathematics concept being grasped by a child, is an honour.
Over recent months, as I have travelled around England visiting primary and secondary schools, I have repeatedly heard the same word being slapped onto various activities like a brand label. Mastery.
Those who know me, know that mastery is something very dear to me. My education heroes list features Washburne and Bloom. Mastery is an approach to teaching that Aristotle deployed to great impact. It encapsulates the very best practices in terms of formative assessment and it drives teacher CPD by continually raising questions about how to communicate an idea, what impact that approach has had and how to make changes to one’s own pedagogy to improve that communication. Mastery is as old as good teaching. Washburne took great steps a century ago to formalise a model, which heavily influenced Bloom and was the driving force behind much of his life’s work. Guskey, in particular, but also Kulik and others, have tested the approach across long periods of time in a wide range of settings and culturally differing jurisdictions. Mastery, as a model for schooling, can be summed up simply: it is great teaching.
I have just been reading some research papers I wrote on mastery some years back and a piece of feedback I received at the time, which slated mastery. Interestingly, that same person, as so many others have, has jumped on a bandwagon boldly branded Mastery and is a part of a machinery propagating an obtuse and deficient approach to teaching mathematics under the banner of Mastery. This saddens me greatly.
Mastery, at its very best, is transformative for both teacher and student. I am certain, long after the fashion for the word has passed and those on the bandwagon are singing the praises of whatever is en vougue at the time, I will still be beating the mastery drum. It drives me to distraction that the word has been hijacked and misinterpreted.
As I have visited each new school of late, I have – almost without exception – been faced by the most regressive and damaging practice falsely labeled mastery.
I will speak more at MathsConf8 about mastery and why I have been such a long term supporter and will write a blog afterwards highlighting what the model really is about and why it is impactful. For now, though, here are some #MasteryFails that I have come across just in recent weeks, all told to me by subject leaders with sincerity and solemnity.

“the first term in year 7 is place value, nothing else”

Why on earth would you do this? Not only is this bonkers in terms of learning about place value, because of the loss of interconnectedness with other mathematical concepts and ideas, it is also a sure fire way to turn kids off maths. Is that really the kind of experience we want year 7 children to have of mathematics?  A term of place value? Jeez.  Don't go complaining when they yell 'maths is boring and shit!'
Place value is one of the non-negotiable fundamentals of learning mathematics and it is incredibly important that kids grip how to work with place value, but this is not the way to do it.

“we now do mastery from year 7”

No, no, no. Mastery, at its heart is about the full journey through learning a discipline. It is not possible to simply switch it on halfway through learning. Also, what is this nonsense of ‘we do mastery’? Mastery is not something one does.

“we do mastery on Tuesdays”

Fuck me.

“we have written a new mastery scheme of work from year 1 to year 6”

No. You are missing the point. In a mastery model, time is the key variable – the length of time that a teacher spends on a concept or topic varies because they are ensuring that all students attain a level of knowledge, understanding and skill. It is not possible to write down a mastery curriculum mapped out by year group because there is no "year group". There are cohorts of children (classes, usually) on a journey. The timing is fluid and the teacher’s skill is in continually working out what has been gripped and what needs to be corrected.

“we don’t do differentiation now, we do mastery instead”

This one breaks my heart. Somehow the message has reached schools that differentiation is bad. Particularly, that the brightest kids should not be accelerated. This is showing itself in some schools as really bright kids being asked to work on mundane crap for months because the whole class hasn’t yet caught up. This is not what mastery is about at all. If anything, in a mastery model, the very brightest kids have the most stretching experience. Every single concept in mathematics is infinitely extensible. In a mastery model, the brightest kids go way beyond the demands of the national curriculum and work on incredibly deep maths. Also, because human beings grip things in different ways, one of the great things about a mastery approach is that everyone has a turn at being the one who grips something early and therefore gets to work on the deep material.

“we have mastery indicator questions, which show when a child has mastered a concept”

Jesus wept. There is no such thing. There is no question that shows a child has mastered a concept. Nobody at all ever masters anything (how dull would life be if we did!). There is always more depth, always more to learn, always new connections or ways of looking at a concept. An army of ill informed consultants and advisors are reducing mastery to a bloody checklist, just like they did with AFL.

“mastery means staying on a topic for much longer”

No it doesn’t. Mastery approaches treat time as a variable. Stay on the topic for the right amount of time, not just longer for the sake of it.

“we never revisit topics – spiral curriculum is bad – the kids master each topic so don’t need to do it again”

Reading these words again, I ask myself, can any professional teacher actually be this stupid? But again and again I come up against this pronouncement.
Learning is not linear. Mathematics is a complex web of interconnected ideas and knowledge. The notion that one should never revisit areas of mathematics beggars belief. It is incredibly important that students have opportunities to revisit learning and build new understanding in the new framework they have as they learn more and more. This is not just about memory (spaced practice is good for this, by the way!), but also about the need to expose mathematics carefully over time as concepts and ideas come together to form a wider picture.

“we downloaded a mastery scheme for this year group”

No. No. No. No. No. No. No. There is no mastery scheme for this year group. Because there is no this year group. Schemes should be bespoke to each and every class. No year 7 class is the same as the next.

“we do AFL questions now and record mastery in an excel sheet”

Desperate to find a way of evidencing, schools have once again turned to reducing teaching mathematics to a series of checklists. Heartbreaking.

“mastery is a new thing that Ofsted is looking for”

No it isn’t. Mastery is ancient, steeped in extensive research and evidence.
This is quite possibly the most damaging lie: that mastery is new. The NCETM and others have perpetuated this lie. Schools hear this as a new initiative and try to implement what they think it means. This is what has led to all of this confusion and will lead to practice that ultimately lowers standards and turns students off maths.
If you have heard more #MasteryFail statements in your school or schools you know, I’d love to hear about it. Please add in the comments section below.


  1. I share your concerns. I did a 2-year PGCE to become a Specialist Maths teacher and every suggestion about improving our teaching made was either ignored or changed beyond recognition because the other teachers had been teaching longer than me, so they knew better. Or, because it didn't quite match what 'OFSTED wanted' - which they had mostly misconstrued anyway. I left the school in question and now look for temporary contracts that suit me, and where I can use my specialism. Now the same school is madly trying to implement much of the detail I had suggested because now it is dressed up as 'Mastery'. However, they still insist on planning in weekly blocks, just moving from topic to topic whether the children have mastered it or not. They really do not understand the concept at all. I am well out of it.

  2. Yes, it annoys me when this is touted as the great shiny new thing. I mean, we've been teaching maths to kids for a couple of hundred years now. It's not perfect but surely improvements come through research and investment in teachers CPD. I have a sense of throwing the baby out with the bathwater sometimes.
    I agree with most of your comments but not having a scheme of work for a year group I think is unrealistic. Children are organised into Year groups in schools and then into classes (mixed or set). It seems like the only pragmatic way to do it, if "there is no this year group", what is there?

    1. Thanks for your comment, Mark.

      I have never understood how it can be possible to have a scheme of work for a year group. Each year, new students enter a school and they have different histories and experiences to the cohort that passed through the year before. Why would it be appropriate to give them the same mathematical diet?

      I take the point that it could be difficult to have completely bespoke schemes for each class, but that is exactly what our schools do. Using Complete Maths, making a scheme takes a few seconds, so the admin burden is gone.

      This makes the task then one of diagnosing each class, identifying the secure base from which to start a mathematical journey and moving from there.

      Because mathematics is such a hierarchical subject, there is a very well define progression that can be laid out (or course, there are many possible pathways). So, what we did over the last 10 years of so was to create a map of mathematics from number sense through to calculus.

      Schools can therefore create schemes for each class, which are easy to amend as new insights into pupil knowledge come to light. That way, every class can have a mathematical journey that is mindful of what has come before.

    2. I believe we have been teaching kids mathematics for a lot longer than a couple of hundred years.

      I understand in the old days, the traditional way to teach was one to one or one to few. It is only recently that we have started to teach the masses mathematics in classes of 30 or more.

      Much of what is discussed when people talk about "teaching maths", is not about "teaching maths" it is about "teaching maths to a group of 30 or more at the same time".

      Precision of thought is the key to discussing teaching methods I feel.

  3. Thankyou for this insight. I find it helpful, particularly the part about schemes. I think this is a key problem of people trying to find a 'solution' to teacher producing off the peg pre written schemes. As long ago as the 1990s when I was maths coordinator in a failing primary, I banned the downloading of plans off the Internet on a Sunday night, for this very reason. The plans went from Internet to folder without ever passing through the brain, so this approach is nothing new. In fact it is the very essence of early years teaching, which is where I now sit.
    I've been out of primary sector for quite a while now and still don't feel with enough confidence I know what the key elements of this mastery approach actually are and in what way are they apparently 'new'. So I continue to read the discussions in order to understand more

  4. Thank you for this, it is a very useful blog, and one that all leaders in maths departments and schools in general should read. I have left teaching in the UK recently and the whole jumping on the mastery bandwagon as if it were something completely new was one of the reasons. Unfortunately there are too many snake oil salesmen going into schools and telling heads that they have the key to impressing Ofsted and it is called mastery.
    You didn't mention it but I think there is a further problem with the Shanghai maths becoming fashionable at the same time as mastery. The "no differentiation" thing is what people are getting out of the Shanghai approach, and the having learnt a concept really quickly and ticking it off as well. I haven't been to Shanghai so can't really comment, but I imagine the consultants out there selling their expertise in that are as wrong on that topic as they are on mastery.

    1. None of the maths courses I have been on have actually said that there should be no differentiation. However, what is being promoted as good practice to maths leaders is supporting lower attainers with apparatus, extending those who grasp concepts quickly through problem solving rather than moving onto the next year group's content, and not pigeonholing children into fixed ability groups. I think messages are diluted as they move down the chain and some teachers are oversimplifying this into differentiation isn't allowed.
      The reason for schemes of work is that some teachers don't have the subject knowledge to adapt to the needs of the class or aren't organised enough to make sure they cover everything, so a scheme of work at least ensures they are covering all areas of maths. It wouldn't happen in an ideal world, but in reality it is necessary.

    2. That is my interpretation Anonymous although I haven't been fortunate enough to attend any courses. I am the only teachervat my school using mixed ability maths groups though and will need to be able to justify this at some point. I am struggling though as I have to use the planning of a teacher who sticks rigidly to setting and whose idea of mastery is to give her lower sets the same work a couple of weeks later, after her top sets have got it. Her bottom set in her words haven't got anything.

  5. I was delighted when my son's school told me that they were taking a Mastery approach, as my son was good at maths and the school was struggling to stretch him. It sounded like a great way forward.

    It was the start of a process of refusing to let him move forward, keeping him stuck on work he already knew, either because the school didn't feel that he had 'mastered' it (if he got one question wrong out of boredom), or because he didn't 'need' to move forward since they were taking a mastery approach and that would somehow mean that he was stretched by doing the same work over and over again. It was heart-breaking.

    He has now left that school, but in the first 6 months of Y3 before I pulled him out, he went from confidently doing Y4 maths (at the end of Y2) to feeling that he couldn't do any maths at all, and we've had to go back and redo a year of work to rebuild his confidence.

    1. I am really saddened to read this, Deb. Unfortunately, many schools have been misinformed about how a mastery model for schooling actually works.

      There is nothing at all to stop teachers from extending kids - in fact, extending kids is an important, integral part of the mastery model. You can read more about that in my Teaching for Mastery blog.

      The national curriculum suggests that the majority of pupils will progress at the same speed (or at least on the topics). This is in line with a mastery model, but the 'majority' just means any number over 50%. Sadly, national bodies have promoted an inaccurate interpretation of the word 'majority' to mean 'all'. This has left many schools very confused about how to implement mastery - I hear from teachers all the time that they are afraid to stretch kids because a consultant has told them that they are not allowed to. This is complete nonsense, of course, but teachers are being told downright lies.

      I hope your son recovers his love of the subject and that his new school understands mastery includes extension work!

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  7. Brownell (1935) outlining the notion of “meaningful habitation” ( relating to fact fluency) - I like to think of mastery as the journey to this and beyond.

  8. I know this is an old blog, but I couldn't resist adding my two cents. The primary school in which I work has introduced a 'mastery' curriculum bought 'off the peg' for teachers to follow. In fact, we are now a MNP accredited school with textbooks and workbooks for each year group. The problem is that we don't actually attempt to teach with a mastery approach - it's the same old conveyor belt, except now we can tell whoever comes to watch that we are a 'maths mastery' school. When I questioned this, I was told that maths mastery was apparently "unrealistic" and that "we'd never cover the curriculum if we taught that way". I have recently been teaching a group of year 5 children who have struggled with maths in the past. Most are at the young end of the cohort. I have found that on average I have needed to take an extra 10-20% time compared to the other classes (though I have obviously not prescribed this in advance) and explain things in a variety of ways, but these kids have understood all of the year 5 curriculum that has been delivered, despite significant mental maths deficits that I have also sought to address at the same time. (I know that this is not an ideal approach.) In short, almost every one of these kids has unconsciously been designated by their teachers as a "weaker pupil", so - unsurprisingly - the kids have tuned out. (What's the point of thinking hard if they know that often the teacher will move on before they've understood anything?) In short, I have become an advocate of a mastery approach. Amongst many things, your blogs have influenced me on this, and I look forward to your book. However, this leaves me as an exception in my school and - as far as I can tell - an exception among primary teachers generally. Do you have any advice? While I am at this school, would I be better off just churning through the content, conveyor-belt-style, and matching the maths teaching of my colleagues, or should I persist in trying to teach with a mastery approach? You might say "find a school that matches your preferred approach", but I think that might be near impossible to do.