After another last minute call for help, I found myself on **Wednesday** helping out with the *Maths Extra* day that the maths department at Edinburgh were trialling for the first time.

The department usually organises a couple of revision sessions per year for local students studying Higher and Advanced Higher maths. For the past couple of years we’ve used these sessions as an opportunity for a few postgraduates to do short (15 minute) talks on their research. This widens the students’ perspective on what mathematics is, what kind of people do it (for example, women! trendy people! non-bearded people!) and why it is useful.

This year our outreach coordinator, Lois, decided that it made more sense to have the postgraduate talks on a day of their own, together with a set of interesting maths problems that the students could work on in groups. They also got a lecture from our Director of Teaching, Toby Bailey, who worked through a seemingly simple geometry problem to show how an inquisitive nature can reveal many beautiful insights.

I was involved both in giving a talk (about knots in DNA) and in helping to design some of the problems that the students worked on. My favourite problem was one that I plagiarised from the Masterclass Training Day that I was at, where I heard it given by Demi Allen, an undergraduate at St Andrews.

Imagine a very long corridor of rooms, one for each number 1,2,3,4,… To begin with all the lights are turned off.The rule is that on the nth pass down the corridor, you flick the switch of every nth room. So on the first pass, you turn every light on. On the second pass, you turn every second light off. On the third pass, you flick the switch of every 3rd room, etc. The question is which lights are still turned on at the end, and why?

It’s a really neat problem – very easy to get stuck into, and a few different layers to the answer when it comes. I encourage you all to have a think!

My knotty DNA talk seemed to go ok, but the kids were pretty quiet and didn’t ask any questions or interrupt with any remarks. I guess 15 minutes is a bit too short to really explain an aspect of your work AND make it interactive. I’m also getting bored with knots these days and would really like to work on designing some talks in other areas. Longer ones perhaps, with more of an element of discussion around them. Like whether 0.999…=1, or whether Euclidean geometry is ‘wrong’ or just a specific way of thinking. I can feel myself being influenced in these thoughts by Eric Mazur’s lecture (which I’ll discuss in Friday’s post!) – that we don’t just want to impart information but we want students to really think deeply about them too. If anyone has good ideas for discussion points in maths I’d be glad to hear them!

My next speaking opportunity will be on 26th May at Linlithgow Academy, which is hopefully enough time to design a new hour-long masterclass as well as preparing for the science festival and revising for the thesis defence. Time goes so fast these days!