Week 1 summary

That’s it for the first week of the course. We’ve covered quite a lot, We’ve looked at some examples of how probability is used in real-life settings and we’ve even spent a bit of time considering what probability actually is. We’ve looked at some of the reasons why probability can be hard to teach and learn and we’ve highlighted the essential features of what we believe is a better approach. Perhaps most importantly, we’ve given you some practical ideas to try out in your classroom by showing different ways of generating experimental data. Let’s look at a simple example of a risk calculation that becomes rather easy when carried out using ideas of expected frequencies.

Media stories have told us that a daily bacon sandwich increases the risk of getting bowel cancer by 18% this is a relative increase and I know many people don’t eat bacon anyway but to know how important it is we have to know 18% of what? It turns out that around 6% of people get bowel cancer during their life time anyway so what we’re talking about is an 18% relative increase over 6 percentage points. This is difficult! I know of no journalist who can handle this but let’s consider the expected frequencies in a hundred people.

Among a hundred non-bacon eaters we expect 6 to get bowel cancer anyway but this is increased by 18% around a 6th in bacon eaters, which brings it to 7. So a hundred people will have to eat bacon every day of their lives to get one extra case of bowel cancer. This puts things in perspective. Next week we will see how we can use a two-stage experiment to handle conditional probability. This is traditionally a hard topic but we will show how it can become remarkably straightforward. These ideas are based on empirical research, carried out and published by psychologists.

We do hope that you’ll be able to try out those ideas for yourselves - there is no substitute for trying stuff out in the classroom and seeing what works for you and your students. Use the comments to summarise your experience so far. One great thing about the course is that you come from a huge variety of backgrounds - we would love to know what you found that was new and which ideas were more familiar. Please do use the comments to let us know.