“The parametric engines are jammed! Orthogonal vector’s gone! I’m almost out of ideas!”
I have a guest post at The Aperiodical reporting on the London Mathematical Society’s birthday party last week, where Doctor Who was a recurring theme.
Technology
For many years, maths lessons have run in roughly the same way: the teacher stands at the blackboard, giving a mini-lecture on some mathematical topic or technique, introducing the idea, outlining the theory, and then running through an example or two. The students would sit patiently (or not), taking notes (or not), so that at the end of the day they will be able to tackle some exercises on the same subject as homework… or not.
As the years have rolled by, the blackboard may have been replaced by a whiteboard, and then by a smartboard, but otherwise the formula has remained by and large the same: theory in the classroom followed by exercises for homework.
The idea of “flipping” the classroom, is to reverse this process. The insight is that in the age of youtube, today’s students can perfectly well take in the lectury bit at home — with the added advantage of being able to pause, rewind, and rewatch in their own time. This leaves lesson-time free for practice, providing the teacher with more time to go around talking to students individually or in groups, meaning more opportunities to help those who are struggling or to supply extra challenges to those who need stretching.
I have no experience of this method myself — all the same it immediately appeals to me as a way in which technology may really be able to improve the teaching and learning experience, rather than just adding bells and whistles. One person who is convinced by this new approach is Colin Hegarty, an old friend of mine from university, who I’m delighted to say has returned to the world of maths after a few years in finance, and is now expertly flipping classrooms in North London.
Even if you don’t have the good fortune to be one of Mr Hegarty’s students, you can still peruse the 611 (!) videos that he and his colleague Brian Arnold have created for this purpose, all of which are freely available on Hegartymaths, or on youtube. Judging by the 800,000 odd views their videos have gathered, it’s not only their own pupils who are benefiting from these experiments in flipping.
As a sample I’m embedding one in which Colin talks through the Chinese postman problem:
I was invited to give this year’s WP Milne lecture at Leeds Festival of Science. Professor Milne was a maths teacher at Clifton College, before going on to become the head of Leeds University’s maths department. In honour of this slightly unusual career path, the annual Milne lecture is delivered to an audience of sixth form students (aged 16-18), as well as to the members of the Yorkshire Branch of the Mathematical Association.
I was delighted to be asked, both as a general honour, and in particular because I have also spent a (very) little time teaching in schools, before migrating to the university sector.
I spoke about The Maths that Makes the Modern World, and divided my talk into two halves: on the simplex algorithm for linear programming, and on Google’s Pagerank algorithm, topics also covered in my book.
On Saturday, I gave my first ever webinar, on the topic of “Some families of polyhedra”. And if you don’t know your tetrahemihexahedron from your tridiminished rhombicosidodecahedron, the good news is that the whole thing is available to see and hear here. It’s just over an hour long, but of course one advantage the recorded version has over the live one is the ability to fast forward, pause, and rewind.
It was hosted over at Mathfuture, by Maria Droujkova. My aim in the talk was to give a very brisk overview of how several different families of wonderful, complex shapes all arise from juggling a very small number of simple criteria. I’m separately uploading the slides for my presentation here [pdf]. They are quite rough and ready, without any detailed explanations, or even any pictures – I used Stella for those. But it does sketch the central story (which I also covered in this blogpost). I may spruce them up one day, if I give the same talk again.
I found the whole thing a thoroughly enjoyable experience, and the Elluminate technology worked extremely smoothly. The format allowed me to talk while sharing my whole desktop with the audience, with the optimal result of people being able to hear my voice and watch everything I was doing, without having to endure looking at my face. And we could all do it from the comfort of our living rooms! This is sort of thing the internet was intended for, isn’t it?
I’m jabbering on here, in illustrious company, in a Maths Special edition of the Guardian’s Science Weekly podcast.
I was recently also scheduled to host an online event over at Mathfuture, but regretfully postponed it. It will be rescheduled, and I’ll provide advanced warning of the new date, in case anyone wishes to come and meet me in the aether…
Simple City 