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