I was helping out in the class of a friend, and she asked me to have a word with Susie, sitting at the back of the class. It’s a long time ago now, and I can’t begin to recall what the problem was, but I do know our conversation went pretty much like this:
Susie: Can you help me please? I can’t do this one.
Alan: Let’s have a look at it. What’s the problem?
S: I can’t do any of it.
A: OK. Well, how do you think you might start?
S: (Pause, then) Well, I suppose I could ….
A: That seems a good idea.
S: But what do I do next?
A: What do you think you could try?
S: (Pause, then) Well, I might do ….
S: But what then?
A: Well –
S (Pause, then huge, radiant, smile): Oh, I see! It’s OK! I’ve got it now! Thank you so much!
Now I’d no wish to destroy Susie’s conviction that I’m the greatest maths teacher that ever lived, but I’d not said one insightful word about the problem. I’d not even needed to look at it – all I’d needed to do was lend an ear and a little encouragement. Any teacher, or any parent, could have done the same.
And the message? Well, an obvious one is that Susie got far more satisfaction from solving the problem herself than if I’d said “First you do this, then you do that, …”. But the bigger one for teachers and pupils is that seeing maths as a subject that has to be done at a hundred miles an hour does nobody any favours. The biggest factor in Susie’s success was being able to think her own way through the question without pressure and in her own time.
It was Denise Gaskins in her blog Let’s Play Math ( http://letsplaymath.net/about/ ) who reminded me about Susie. Denise posted a famous clip of a couple of primary pupils tackling a problem about fractions, and if you’ve got 6½ minutes to spare you can see the video at https://www.youtube.com/watch?v=Q-yichde66s
It’s a very similar message – that by giving the girl and boy the time to tackle the problem (and the resources to do so practically) followed by the opportunity to talk about it at their own pace you get a depth of learning that goes far beyond giving them a batch of mechanical rules.
Here’s what Denise had to say: http://letsplaymath.net/2014/08/13/fractions-15-110-180-1/