When maths practice doesn’t add up

As twitter was a-buzz with Michaela quotes, something caught my eye this morning:

Practice
I wonder if any other school adopts this view?

I have, of course, written before about the issue of practice and how I feel that many teachers are not quite aware of what it takes to fully commit maths facts and procedures to memory, or to elucidate whatever pattern has been embedded in a carefully curated session of intelligent practice. This is perhaps because most primary teachers don’t even have A-level maths, let alone a degree in the subject (or a degree that uses a lot of maths). For the purpose of making my message clear, I am going to use the terms lower and higher achievers, so don’t even think about kicking up some puerile nonsense about how I’m labeling children etc.

Anyway, perhaps you’d like to join me on a little thought exercise about your lowest and highest achievers? Do the lowest achievers really have discalculia or some other SEN? Let’s do some rough maths for LKS2, concentrating on lessons involving calculations rather than recalling shape facts for example (and it really is rough, but still interesting, since looking through the books for this purpose really exposes a stark difference).

  • Average lower achiever number of calculations performed in each lesson: 7
  • Average higher achiever number of calculations performed in each lesson: 20

We have weekly tests and the children, funnily enough, tend to do the same number of calculations under test conditions (just goes to show the power of test conditions). If we assume that perhaps another fifth of the maths timetable is used for shape, time etc, that leaves us with, roughly, 3 lessons per week where children are doing calculations. Let’s also cross off a couple of weeks for days out, plays, productions, longer assemblies etc and we’re left with 37 weeks.

The difference in the number of calculations higher and lower achiever children do is roughly 1500 a year and this is a conservative estimate because I have not taken into account the difference in amount of practice during start of the day activities, or homework, or even in the ‘maths doodling’ that children do during wet play times or at home for a laugh (yes, many of the more ambitious children in my class ask for extra times tables practice sheet so that they can ‘get a PB’ in the weekly tests).  We could spend all day quibbling over the real numbers (well, you could, I have a full time job to go to!), but I hope the main message is clear: there is a huge difference in what higher and lower achievers actually do during maths lessons. Am I confusing correlation with causation? Is it wrong to assume that sheer lack of practice is the main reason that lower achievers are lower achievers?

What causes this difference? From my observations, children at the lower achieving end of the maths spectrum tend to spend longer trying to recall (or calculate, using repeated addition, for example) individual snippets of information during a calculation, thus showing an over-reliance on working memory (also increased likelihood of getting wrong answers). They also take longer to decipher a question in the first place. Additionally, there are key personality trait differences: lower achievers tend to be more resistant to requests to focus, to stop talking, to concentrate, to stop fussing over silly things like sharing rubbers. They are more likely to mess about. They are more likely to not care about presentation or laying out calculations in a systematic way. They are more likely to just sit there and wait for an adult to show them, all over again, what to do (thus clearly have ‘learned’ that they don’t need to pay attention during the initial input or bother to ask a question). Higher achievers are the opposite: focused, determined, serious, quiet, systematic, hard-working. I have worked with some of the best mathematicians in this country and I can tell you that these adults mathematicians seem to be similar to the higher achievers in classrooms. Isn’t that a weird coincidence, don’t you think?

The paragraph above illustrates to me that the main issues are more to do with lack of maturity, good behaviour and focus that would, over the years, contribute to fewer maths facts and procedures being committed to long term memory. This is a parenting issue first, but it is also a whole-school behaviour issue that perhaps shows us how important it is to make sure that the personality traits of successful mathematicians are instilled at a very early age in order to stop the rot, those gaps in learning, from setting in. However, if you look at primary schools (especially in the younger years), group tables, carousel activities and the teacher’s love of ‘buzz’ in the classroom means that these children fly under the radar for a long time, sometimes all the way till UKS2 by which time those habits of distraction, rather than maths facts and procedures, are permanently entrenched.

So, let’s think about instilling good habits from an early age.

Who’s with me?

 

 

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7 thoughts on “When maths practice doesn’t add up

  1. When Sir Peter Williams published his review of primary maths education in 2008, he considered raising the bar for teachers to a B at GCSE maths, but decided against it as it would result in a teacher shortage. About that time, my step-daughter managed a B in GCSE Maths, and she was virtually innumerate until she got a job working in a sandwich bar that didn’t have an electronic till. It really is that bad. Sir Peter argued for more CPD, but to think that one can compensate for 13 wasted years in school with a few INSET sessions is absurd. I’ve argued that we should allow anyone with a C or better at A-level maths enter directly into a School Direct programme to qualify as a specialist primary maths teacher responsible for actually delivering maths lessons–as opposed to ‘cascading’ their supposed expertise, as Sir Peter recommended. Obviously, he was enough of a realist to understand that primary education would resist any policy that would threaten the model of children sitting in the same class with the same teacher all day.

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  2. This is a fascinating one i think. I am secondary rather than primary but for me there are 2 main questions here…….

    Do we all suffer from discalculia to a greater or lesser degree, and weaker students may require e.g. 100 times the practice to achieve even a moderate level of skill. I use to practice football a good deal but I didnt seem to have the talent therefore I never became David Beckham. I hope you get the sentiment of my question even if the technicalities are not perfectly described.

    Does the lack of attention, attention to detail and poor presentation come from a lack of basic ability to learn maths or is it the cause.

    I think it would be very odd if many of the best mathematicians did not in fact have some natural ability to begin with and this created interest and an inquisitive mathematical nature.

    For me, teaching is about helping those that do not have the natural ability achieve as best they can while enabling those with ability to become excellent mathematicians.

    I also tend to believe that the more trad methods work more effectively with those learners who have the highest levels of ability. I would tend therefore to stream classes and give the more able a trad diet of activities and the lower ability a more prog diet.

    I think for the more able you often can just tell them (often you dont even have to do that) and then get the to practice. These learners can peer assess quite readily.

    Weaker students need more attention, slower practice and more of it perhaps. Some need smaller steps and more frequent feedback.

    I think I tend to agree with much of your thesis but where we part company is perhaps at that point where you see the solution lying with the child, they need to “pull their socks up” whereas as I see it more with the teacher in helping the child to pull their socks up. There are always those with the ability but for some reason do not wish to work, and for these a different solution is necessary.

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    • I agree with almost all of what you say, but the research clearly shows that the least able pupils are most in need of a traditional approach. For instance, the use of manipulatives is associated with low achievement, which is hardly surprising since maths is inescapably an abstract representation of the real world–at least at the school level!

      One of the more interesting studies I’ve come across recently cited the sharp declines in the maths scores on OECD measures between 2003 and 2012 in all but two provinces. It cites a lack of “times table memorization, explicit teacher instruction, pencil-and-paper practice, and mastery of standard mathematical procedures …studies consistently find that students who have difficulty with mathematics by the end of their primary school years have not memorized basic number facts, making further math learning difficult and resulting in feelings of helplessness and a lack of confidence and enjoyment (Hattie and Yates 2014). A great deal of time and effort is required to commit basic number facts to long-term memory, but the ability to recall them instantly frees up working memory, making it easier to learn new concepts.”
      https://www.cdhowe.org/sites/default/files/attachments/research_papers/mixed/commentary_427.pdf

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  3. Without wishing to sound overly critical, I am slightly concerned that you seem to be presuming that the struggling children in your class don’t care. In my experience, children who fall behind care very deeply, and the negative, salient traits you describe are actually their well-honed coping mechanisms. That is why I completely agree with your conclusion.

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      • I apologise if I have caused offence. You did, however, mention children not caring, in relation to their presentation and their laying out of calculations.

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