Why this post is wrong and dangerous – response to Mastery Overload

Here, Debra Kidd writes about her concerns with respect to the idea of a mastery curriculum.

I should begin by noting that I agree entirely with the sentiment of wanting children to love and enjoy mathematics.  Also, I sympathise with the mistake being made in this post, because I made it myself.  In fact, almost every newly minted, naive maths teacher I know has made the same mistake.  Those with more experience tend to fit into two categories: they feel guilty because they don’t understand why following the vision isn’t working, or it was explained to them why following the vision won’t work, and the inordinate complexity of mathematics teaching is still unravelling before them.

If you want to reach for the moon, you don’t point your rocket at it and fire; if you do, you miss.  Instead you have to point it somewhere else, compensating for a staggering range of complex variables, but in the end you reach the vision of landing on the moon.

Why is it wrong?

First, the post represents a misunderstanding of what mastery teaching is.  This isn’t wholly unreasonable; as noted both by Mark McCourt and me at the last La Salle mathematics conference, ‘mastery curriculum’ is a term that is being interpreted in a few different ways.  Still though, the definition as suggested in the blog post, that mastery is all about ceaseless repetition of the same content and prep for exams, is so grossly far from any fundamental intention of the ‘mastery curriculum’ concept as to be, simply, wrong.

It goes on to suggest repeated practice of basic arithmetic is a bad thing.  The post notes that when asked what they did enjoy about maths in the past:

…they start to talk about investigations and inquiries they’ve done in the past. Lessons where “you had to work out codes and clues and find out things for yourself – it makes you think”. And they mention lessons where “we had to pull together as a team to figure it out – working in a group to get the answers”

I recall with any clarity only one maths lesson from primary school.  We were asked to investigate something about the relationship between the perimeter of shapes and the number of squares they were made up of.  I started finding so many patterns I wanted to keep exploring that it was not only my most enjoyable lesson, I was truly dismayed when the teacher said I had to stop!

So why is it wrong to pursue this?  Here’s where it gets very tricky, and deeply nuanced…

It’s not wrong, per se.  It’s wrong if you think ‘ergo this is better than practice.’  It’s wrong if you think ‘this is how kids should learn things.’

Running an investigation because you want children in school to experience a mathematical investigation is almost certainly a good thing, and probably something we should be taking pains to do more often.  Running an investigation with the intention that children learn a new piece of mathematical knowledge is almost universally doomed to fail.  There are several reasons why, but let me just articulate one of them in the hope that it’s enough for now: if you are investigating something in a lesson, then (at best!) you arrive at the conclusion – that thing that the teacher wanted you to learn – only at the very end of the lesson.  This means that you spent most of the lesson *not* thinking about the thing you were supposed to be learning.  If you instead were taught that thing explicitly right at the start, then you can go on to spend the entire lesson thinking about it.  More time thinking about the idea, greater initial storage strength (the whole ‘memory is the residue of thought’ thing.)

There are so many shades of complexity to the above paragraph that I am omitting; but suffice it to say that ‘investigation good, explicit instruction and practice bad’ is in error to the point of absurdity.

Next up, the novice-expert continuum.  It was mentioned that the group in question were a top set.  Higher achievers notoriously tire of simple drill practices much more quickly than others, and they do generally need less of it (though, typically still more than they *think* they need.)  They are also more able to take on and learn from more complex forms of unguided instruction.

Furthermore, there are boring ways to practice, and there are fun ways to practice.  Just look to all the incredible work Bruno Reddy did on Times Table Rockstars for examples of fun ways, and I’ll say no more.

Why is it dangerous?

The ideas expressed in the post are not new, they are in fact very common.  A similar view was expressed by Conrad Wolfram only a few months ago in this article.  This notion has actually been kicking around for decades now, as noted by Professor Askey – apparent veteran of the US ‘math wars’ – when he said the following back in 1997:

“Mathematics is like a stool; it sits on three legs. In the New Math period the only leg used was the structure of mathematics. The feeling was that if you understood the structure of mathematics, then you could compute and solve problems. That turned out to be false for all except a small group. Then we got ‘Back to Basics’, which was founded on computation. However, the level was too low, and good problems and structure were both ignored. This failed badly. Then NCTM tried Agenda for Action and later the Standards. Both of these were built on the idea that if you could solve problems, then you could do mathematics. You can, but at too low a level. All three are needed—problems, technique, and structure. I fail to see why this obvious fact is not appreciated, but it does not seem to be. The New Math failed for good reasons, and the New New Math will fail for good but different reasons. Maybe then we can start to try to do this right.”

The assertion from the post that ‘We need more Mystery than Mastery’ is an intellectually deficient idea.  Although it was no doubt intended as a pun on some earlier commentary in the post as to the distinction between ‘master’ and ‘mistress,’ and a not uncommon response by the author might be to suggest that it was only meant as some light-hearted fun, it’s only once you’ve seen what ideas of that ilk do both to maths teachers and to their poor suffering pupils that you can grasp the danger in treating it as such.  Mathematics education is so curiously complex that while we’ve been uncovering more and more of its nature for more than half a century now, we still haven’t yet pieced it all together into a structure that works.  I agree with the sentiment that asks:

What is the point in taking children on a learning journey in which they feel like passengers trapped in a repetitive hell?

Obviously this is not a vision of mathematics education to which we wish to aspire, but the ideas expressed in the post are dangerous precisely because they risk once again moving us away from achieving that vision.  They are dangerous because they take the name of ‘mastery curriculum’ and then slander it, twisting its intent (probably through ignorance, not deliberate slander.)  I’m all in favour of Mill’s notion of free speech as a means to ensure we don’t stifle truth.  Where previous articles such as Wolfram’s have equally missed the mark in their ideas, however, it is this defamation of a named concept that meant I felt the need to respond now in particular, equally in the spirit of Mill’s freedom of speech.

Debra’s post isn’t the real danger, though. It’s the ecosystem of thought that surrounds it, the idea professed by others with the heft of academic credential behind them, or capital investment, who would also repeat the now decades-faded echo that any and all ‘drill’ must equate to ‘kill’.  How could they be wrong?


About Kris Boulton

Teach First 2011 maths teacher, focussed on curriculum design.
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5 Responses to Why this post is wrong and dangerous – response to Mastery Overload

  1. teachwell says:

    I was discussing the nonsense that is discovery learning with others only the other day. Why would we want to send children back into an educational stone age when there is so much still out there to discover.

    All the things we teach in schools is so that they know what is already out there and can move on. It never seems to occur to progressives that it took some humans a lifetime to come up with some of these concepts and we don’t have several ourselves!!

    Besides all this stuff about applying mathematics only works if they have a solid grasp of it – otherwise it is pointless – I’d rather children spent their time learning moving from concrete to abstract than on made up word problems.

    Here’s the worst lie of all – that children don’t enjoy repetition or learning skills at a deeper level. There are plenty of ways to make the challenging learning a bit more fun for the younger ones – getting them to write out the 5 times table in the playground in chalk and then playing a game where they have to jump on each square and say the times tables. Mixing it up comes after. Although of course we can’t have competitive games because it upsets them…

    Mastery is something that is to be welcomed. The constant flitting back and forth between units was an annoyance at best and did not help children learn. Informally I have been doing much of what the mastery curriculum suggests. If they don’t understand place value, then there is a limit to which they can use the operations, similarly without addition and subtraction, multiplication and division are harder to grasp. No point in going near fractions if they don’t understand division or have a basic understanding of times tables.

    It’s about time that we stopped allowing a few students who did not enjoy trad methods to have the whole education system run for them. The fun brigade are full of hot air.

  2. Pingback: Is drill practice boring and pointless? | …to the real.

  3. Brian says:

    As the traditional vs progressive discussion cools, I feel that there are people out ther who feel that they have a duty to educate the rest of humanity. These people (or type as one famous blogger likes to call them) will often start with the patronising approach……….I quite understand why you make this mistake as I actually made this mistake myself, before I knew better.

    As it is here.

    They will then go on to give you all of their opinions about the world, or education within the world as if they were facts. These facts would be obvious to anyone with even a minimal amount of intelligence.

    As it is here.

    When somone presents a different opinion (opinion) they then take on the task of re-education with all of the panache of the Fast Show’s Billy Bleach, the misguided individual who would offer advice on any subject he had an opinion on.

    As it is here.

    Examples are extreme and quotes can be out of context but this matters not because the person “just knows”, a bit like the person standing on the street corner directing the traffic because they need to.

    Debra seems to recount her personal experiences of talking with kids and in the post above I can see the blogger expresses similar sentiments regarding drill and practice ad nauseam.

    I recently interviewed a student from Asia who attended school Mon-Fri, Sat am and Sun Pm. Daily hours were 6.30 am to 9.30 pm after which they had to complete 3 hours homework each day. Sat pm and Sun am were spent catching up if they got behind. Time was spent practicing maths and science problems over and over and over and over. This is not an approach most in the UK would welcome for their own kids, but neither would they wish the classroom to be a free for all where kids do as the wish in an effort to have fun and pick up a bit of knowledge along the way by accident.

    I believe this is what Debra Kidd was talking about. The need to balance mastery with mystery. I don’t believe Debra is suggesting that kids are encouraged to invent differential calculus by running around at various speeds and accelerations and noting relationships between distances, speeds and times.

    I see teaching as a profession. No two teachers have the same presage variables or intervening factors. I see teaching as a complex dynamic process.

    Everyone is welcome to their opinion, this is a free country (mostly) after all, but I have to say the suggestion that Debra Kidd’s post was “dangerous” did make me laugh outloud.

    ps…..it wasn’t long ago that if one mentioned having fun with an engaging task such as History meets the Mr Men, one might have been reminded of Daniael Willingham, biscuits and undergrounds. All of sudden, “rock Stars Timetables” is an “incredible piece of work”. How quickly times change, Dan Willingham eat your heart out.

    • Kris Boulton says:

      I think you misunderstood the theory underpinning Willingham’s ‘biscuits and undergrounds’ example.

      The anecdote was supposed to elucidate how one can engage kids in a ‘fun task,’ but if what they spend their time thinking about isn’t what you want them to learn, then they will fail to learn.

      In Reddy’s TTRS, kids spend 100% of the time thinking about times tables, and their progress in memorising times table facts. The reason TTRS for Year 7 pupils is hailed as an incredible piece of work is precisely because it succeeds in creating a ‘fun and engaging’ task while ensuring all of the children’s time is spent thinking about that which is to be learnt.

      By contrast, the reason the Mr Men activity for A Level students was ridiculed is, I expect, in part because it failed on this count (hence the Willingham comparison to which you alluded) and also because it rather patronises people who are two years away from very serious academic study at university.

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