Archive for October, 2010

More Definitions

October 21, 2010

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.

Definitions

October 18, 2010

Although my focus in this post is Key Stage 3 and 4 maths in UK secondary schools, some of what I have to say may well apply to other phases and other places too.

I realise I have been remiss. Some time ago, I started this blog claiming it would contain thoughts about maths, but I have never actually defined what I mean by that! I think I’m far from alone in this – throughout the blogosphere it’s very common to talk about well-used terms and concepts without ever unpacking exactly what is being talked about. So I thought I’d devote a short entry to what I mean when I use the word “maths”.

There are two categories of activity that “maths” as I use the term falls into. Firstly, there is what some people might call functional maths – making sense of number, graphical data, statistics, money, measurement… all the skills that young people need to master in order to function in society when they leave school (or the skills that young people need to master in order to access mathematics in higher education or within their career, for that matter!) Secondly, I use the word “maths” when I’m talking about an activity which involves such skills as working systematically, looking for and explaining patterns, generalising, and proving those generalisations.

I think both of these types of activity are important – maths shouldn’t be an either/or thing; maths classrooms can involve both sorts of “maths”, and in fact one particular maths lesson might be targetting skills from both sets. I think denying children either would be wrong, and saying “these children only need functional maths because they are never going to be professional mathematicians” perpetuates a mis-understanding within society of what maths is, and what mathematicians do. We should make sure that all children have the chance to explore, conjecture, and prove, and to know that these ideas are at the heart of what mathematics is all about. So I think when I think of the word “maths”, it’s the second meaning that jumps to my mind first.

When you use the word “maths”, what do you mean by it? Have you ever come across anyone who thinks about and defines “maths” in a completely different way from you?