Mathematician Vicky Neale, senior teaching associate in the Department of Pure Mathematics and Mathematical Statistics in the University of Cambridge and director of studies at Murray Edwards College, is excited.

She’s been watching some recent breakthroughs that mathematicians around the world have been making in a huge and open collaboration on an ancient mathematical problem. Neale tells Adam Smith how she is now building the news into her work that aims to improve the ways maths is taught.

This podcast is produced and presented by Adam Smith

 

Adam Smith: I’m listening to a story about a lightbulb moment. That second when a school pupil’s eyebrows soar and her head lifts up: she’s got it. In this case, she’s found a solution to an algebra problem.

Vicky Neale

Vicky Neale ...She suddenly realised that this algebra, which she’d sort of been introduced to at school, that she sort of half understood, that she could see why these manipulations worked. We drew a little picture, we talked about it, but she also suddenly understood how that had helped her to answer a problem. She’d been trying some numerical patterns, which is really important, that’s a lot of what mathematicians do, but we were chatting about how the next stage is to try and come up with a convincing argument.

I might use the word ‘proof’, that’s sort of technical jargon, and she said, “But I’m not going to be able to do that ‘cause I can’t check all of these examples.” And I said, “That’s right, you’re going to have to come up with some other kind of justification.”

And via this algebra, by a little calculation, she was able to do that and see that it was always going to be true and for her, I could see, “Oh, this is something a bit different from what I’m used to, I’m quite excited by that, I can see how this algebra gives me the capacity to do something much more than I ever thought I was going to be able to do...”

AS: I’m Adam Smith. Welcome to Pod Academy.

Vicky spends most of her time on a project with researchers and teachers trying to improve the ways mathematics is taught. Running beneath all of this work, like an underground river, is the enterprise of mathematics itself—the questions and the problems are flowing and bouncing off rocks and pushing forwards constantly through university mathematics departments across the world. I met Vicky at the college and started by saying that it seems to me that maths is a bit like Marmite—people either love it or hate it...

VN: That’s right and I find that very sad for two reasons. One is that I think very often the people who are saying that who don’t understand why I’m so excited about maths, that’s because they don’t know what it is that I’m excited about. They have this perception that’s very different from my perception. The other is that I think sometimes people have this perception that maths is an ability either you have or you don’t have. It just sort of depends how you were born. And I start from the perspective that everybody is capable of thinking as a mathematician, is everyone going to go and get a Fields Medal in mathematics—the equivalent of a Nobel Prize? No of course not, because not everybody is going to want to spend their time, immerse themselves in it, but I strongly believe that everybody has the capacity to make progress, to understand all sorts of things. And we see in schools, extraordinary examples where successful teachers, successful departments are able to have this impact, of course it's trying to help everybody to have a positive experience so that whatever they go on to do they don't feel that maths is not relevant to them, they don’t feel that they’re unable to engage with it.

AS: One of the other funny perceptions that a lot of people have about mathematics, probably myself included, is that it’s static, that there is a set of rules, your teachers try and teach you and that there are just these rules and you’ve just got to learn it,

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