The Ideas Exchange provides an opportunity for each participant to put forward, in five minutes, an idea for subsequent discussion with sympathetic colleagues. It was suggested that this might be something which one had tried and wished to share, an idea that one was planning to implement and wanted advice on, or a mad suggestion that, with refinement and suggestions from others, might just turn into something workable. This was the second such Ideas Exchange weekend - my report on the first was published in MSOR Connections (and one of the best pieces of news from the CETL-MSOR Conference is that Connections will continue). That they work so well is due to the openness and friendliness of the participants: it's a delight to spend time with people so committed to teaching mathematics effectively.
There is a lot I could write about from both events (and much that I have still to digest). But this post will focus one of my "ideas" - not actually mine at all, in fact.
At my University's teaching and learning conference one speaker mentioned a proposal that every degree course should have a compulsory final year module on "how new technology will change this subject" or something similar. (I didn't catch the name of the person to whom this proposal was attributed.) Should maths degrees contain such a module?
My first reaction was that it would be hard to make a case to colleagues for dropping their favourite courses in Complex Analysis or the Analytical Algebraic Topology of Locally Euclidean Parametrization of Infinitely Differentiable Riemannian Manifolds or whatever. These courses obviously give students skills and techniques which are immediately valuable to a wide range of employers in a way which thinking about possibly applications of technology and mathematics could not possibly match.
But should our maths graduates be thinking more about how technology will change mathematics? I think there is a case. For one thing, new technology such as apps on mobile devices are making like better in many small (and some big) ways. I'd like our maths graduates to be among the leaders in this field, but I'm not sure that our teaching particularly promotes this kind of creative thinking. I'm also struck that, despite many university mathematicians' preference for chalk and blackboards, IT is changing maths in ways which we don't articulate to our students. At BMC last year Sir Timothy Gowers noted that Wikipedia is an invaluable tool for mathematicians, greatly facilitating the practice of our subject. In his recent LMS Popular Lecture Sir Timothy talked about the emergence of computers as research assistants. He, Terence Tao and many others use blogs as a tool for mathematical collaboration, and Gowers's Polymath project is perhaps shows how mathematics will be done by humans in the years before the field is taken over by creative computer research mathematicians.
It certainly seems to me that my childhood view of mathematics as an individual activity, which was perhaps only rarely a reality (Andrew Wiles?), is no longer tenable: technology is making mathematics an increasingly collaborative venture. And we should perhaps be making more of this in our undergraduate teaching.