#MasteryFail: Common misconceptions about maths mastery

An expert in maths education laments the lack of understanding that surrounds mastery approaches in schools

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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 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 civilisation, 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 on to 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 else is en vogue 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 labelled 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 advisers 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. 

Mark McCourt is the CEO of La Salle Education. He tweets at @EmathsUK. On Saturday 1 October, he will be speaking at the National Mathematics Teacher Conference in Kettering.

This article was originally published on Mark McCourt's blog, which can be found here.

You can read more about maths mastery in the cover feature of the 30 September issue of TES.

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