More Definitions

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Following on from the variety of things we mean when we use the word “maths”, I’ve been thinking a bit of what we mean when we say someone is “good at maths”.

Of course, some of this is tied up with the previous question; if I describe someone as being “good at maths”, I presumably mean they show some aptitude in whatever set of skills I have identified as being “maths”. But I think there are also lots of other issues in play here. It depends who is identifying someone as being good at maths, and it depends where this identification happens. I’m sure there are whys and hows and whens too, but I’ll stick to those for now.

The who is interesting, because as teachers, we are often asked to make judgements about whether pupils are good at maths, and our judgements can have important consequences for a child’s maths education. In schools where setting is the norm, teachers have to make a decision about whether children are “good at maths” or not, and decide which group to put them in. This is often done through testing, so “good at maths” becomes a shorthand for “good at passing maths tests”. Children might assess how good they are at maths based on a teacher’s judgement of them. So children who are not in “Set 1” may consider that they aren’t very good at maths, and might consider that the children who are in “Set 1” are. But in the top sets I taught, there were several pupils who thought they shouldn’t be in Set 1, and that they weren’t as good at maths as others in the group, so based on children’s own assessment of who is good at maths, there are only a handful in each school! Perhaps in schools or classrooms with a culture of rewarding and recognising mathematical process and thinking, many more children identify as being “good at maths”.

I’ve already touched on where a little bit – within a school where setting is the norm, there may be lots of children who don’t consider themselves good at maths. More widely, in a society with lots of “mathsphobia”, or where being mathematical is seen as being a bit nerdy, people might shy away from maths and not recognise their own abilities to think mathematically. In many circles, I am considered by others as being “good at maths” – I have a degree in maths, I successfully taught maths in secondary schools for a while, and a large part of my job involves writing maths problems. And yet, when I’m with a group of friends who went on to do PhDs and study an area of maths intensively and in great depth, I don’t consider myself to be good at maths, because it seems that they know so much more (and more difficult) maths than me!

I think it’s vitally important that we look out for opportunities to recognise good mathematical thinking with praise, and to challenge people’s assumption that they can’t do maths. Competitive testing and setting seem to reinforce lots of children’s feeling that they are not (and can never become) good at maths. If we expand our notion of what it means to be good at maths to include generalising, modelling a problem mathematically, expressing mathematical ideas in conversation, looking for different methods, posing good questions, making connections… rather than just being good at passing maths tests, then all of a sudden, we have lots more young people willing to consider themselves good at maths.

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5 Responses to “More Definitions”

  1. Paul B Says:

    I did maths a-level many years ago. It was then split into 2 parts: pure maths (= playing with numbers for the sake of it) and applied maths (using maths to solve real-world problems).

    I was good at applied maths, but bad at pure maths?

    Why? I have a sort of mind that needs to be able to visualaise something to understand it, so I can easily imagine the forces of gravity and friction acting on a block sliding down a slope. But whilst I understand that a Fourier Transform lets me do things like convert a waveform into a frequency analysis, the maths involved make zero sense to me.

    (so, does all that make me good or bad at maths?)

    Funnily enough, I now give training, and one of my students commented last week that he found my giving of analogies to be very helpful in understanding what we were doing. Its good to know that I’m not the only one that finds a link to a real-world example to be helpful.

  2. lordhutton Says:

    Logic helps. Perhaps all children should do Sudokus

  3. Alison Says:

    Paul, I think lots of aspects of pure maths can be taught in a way that appeals to visual thinkers. It’s interesting that you judged yourself to be “bad” at pure maths – do you measure this in your performance on tests, your understanding of the topics, or something else entirely?

    Lordhutton, logical thinking is of course the cornerstone of mathematics, and one thing I do is introduce an understanding of generalisation and proof as early as possible (lower secondary for me because I do very little work with primary age students, but my colleagues get proof into primary classrooms on a regular basis). Sudoku is one way of developing logical thinking; there are others.

  4. Paul B Says:

    How do I measure my “bad at Maths?”

    Yes, my exam performance was not as good. I found it hard to put the topics into context (although I guess maybe a different teacher might have changed that), and I guess all that made me feel that it wasn’t as interesting, and I wasn’t as good at it.

    I still find it easier to learn new things that have a practical application, and more difficult ot learn *anything* parrot fashion (ie with less context)

  5. Nigel A. Gunn Says:

    Good and bad, of course, are relative to some unstated reference so mean little. I was not good at maths at school, not because of inability but because of laziness.
    I would never be good at pure maths because I need an application before I grasp the principals. I need to know what I’m going to use it for.
    A problem I frequently see is that most people seem to not have grasped an appreciation of numbers. They are unable to estimate at least an order of magnitude for the answer so they do not even know if they are in the correct ballpark.

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