07 OCTOBER 2016

# David Spiegelhalter

Most of my career has been concerned with medical statistics, working out new methods and applying them to clinical trials, monitoring health services, and so on. But some years ago I got the chance to change direction into a post funded by a philanthropist specifically to try and improve the way that statistics, and particularly risk, was discussed in society. So now I am Winton Professor for the Public Understanding of Risk, which has given me a chance to get involved in a huge range of fascinating projects, from presentations to school audiences, numerous science and literary festivals, appearing in TV programmes about chance and uncertainty (Tails You Win, and Climate Change by Numbers, writing popular science books (The Norm Chronicles and Sex by Numbers), and doing a lot of radio and TV on issues that come up in the news. And possibly my greatest achievement – coming 7th in an episode of Winter Wipeout.

What first interested you in mathematics?

I used to line my toy cars up as a kid, collect car numbers, and sort stamps. I was good at maths at school, although it was never a hobby -  I just liked doing it, although was never so keen on applied. I then did maths at Oxford, and particularly enjoyed the pure, but to be honest by the second year it got very difficult and I hit my mathematical ceiling. Then I turned to probability and statistics, and eventually found an area that I found satisfying and fascinating.

I still like basic pure maths puzzles, although I am not very good at them, but now find that probability and stats are endlessly rewarding.

Why is probability important?

Probability is a riveting subject, but not easy. In our book we say that we are often asked why people find probability and statistics unintuitive and difficult – we say that after decades of working in this area, we have finally decided that it is because probability and statistics really are unintuitive and difficult. Probability is unlike other areas of mathematics in that there is no ‘ruler’ underlying the basic measures: there are protractors to measure angles, rulers for distances, clocks for time, and so on, but there is no ‘probability-meter’. It might be considered a ‘virtual’ quantity - in fact I find it easier to think that it does not exist at all, but is simply a neat construct that allows us to handle situations where the outcome is uncertain.

But probability is still vitally important, as the way that ‘chance’ (or whatever you want to call essential unpredictability) works is neither intuitive nor straightforward. By getting a hold on chance we can make predictions (at least rough ones). But also, if we make the rather big step of assuming that events are influenced by some chance process, probability allows us to interpret data using the tools of statistical inference. But that’s a different story.

How does Teaching Probability help teachers and learners?

The main idea is very simple. Rather than immediately introduce probability as some magical quantity that obeys a set of ‘rules’, it arises as the end of a process rooted in experimentation. By carrying out experiments, and pooling the results, learners can see how empirical frequencies of outcomes settle down, so that it is intuitive to think of what we might ‘expect’ to see on further repetitions of the experiments. Then the idea of expectation, based on ideas of symmetry and long-run frequency, leads into ‘expected frequency’, which then leads naturally into the laws of probability.

Whenever I need to solve a probability problem, I always transform it into a problem of expected frequencies - eg ‘if I did this 100 times, what would I expect to happen?’. And if I find it useful, I think that teachers and learners will too.

We also had fun working through a huge range of GCSE-level questions showing how to solve them in multiple ways. And there are so many good games and tricks with probability, that we wanted to provide a very wide range of enrichment activities. We hope teachers and learners will fund these useful, and it will help increase the popularity of probability in the classroom!