Wednesday, 15 June 2011
How much mathematics do students need?
A report came out yesterday (Tuesday) showing that many UK university students are poorly prepared for the mathematical requirements of the courses that they register to study. The report was produced and published by a not terribly well known institution, ACME, the Advisory Committee on Mathematics Education, an independent body based at the Royal Society. The latest report is in three parts - an overview/summary plus two substantive papers - and it is the outcome of a two year project run by ACME on the topic, Mathematical Needs.
The findings of the report make rather dismal reading, for they show that about two-thirds of the UK students who enrol for degree courses that require some mathematics, do so without the proper mathematical foundations that they need, with the result that many universities have to run remedial maths classes to bring students up to the right level. Better late than never, I suppose, but much of this extra maths could so easily have been done in secondary schools. Employers, too, are widely dissatisfied with the mathematical knowledge and skills of those they employ, so the problem is not just about preparing for university entry.
The fact is that we live in a world where mathematical expertise (or at the very least, a basic competence) is needed in all sorts of different areas of work. Yet as the ACME report shows, UK school students are increasingly lagging behind those in other advanced and emerging economies both in terms of the share of such students who continue with mathematics beyond age 16, and in the academic levels they aspire to and achieve. This is really quite a distressing situation, given our intensely competitive world - how on earth will UK young people be able to compete for and occupy the best and most productive jobs if this critical dimension of their education is so weak? Not surprisingly, therefore, the report includes lots of advice on ways of improving mathematics curricula and teaching in order to strengthen the UK's position in this important area.
Moreover, quite aside from this strictly utilitarian and functional approach to mathematical knowledge, surely we ought also to put a bit more weight than we do on the sheer joys and delights of mathematical explorations? Curiously, it seems to be socially acceptable in the UK to be 'bad at maths', whereas it most definitely isn't so acceptable to admit to functional illiteracy. There is also a widespread perception that 'maths is a difficult subject'. Both these views seem to me complete nonsense. They are not shared by our leading competitor countries, and they create a culture that makes it far too easy for the UK to under-perform. In my view (though I do admit to being a bit biased here), maths is no harder than anything else provided that students are prepared to put in the necessary hours of effort - I've always found history much harder going than mathematics, for example.
And mathematics is full of beauty and elegance, once one advances just a little beyond the routine (and rather dull) mechanics of basic calculations. For instance, lots of interesting geometrical shapes - plane or solid - can be constructed using elementary methods known to the Ancient Greeks, many important equations are both simple and beautiful, and by moving up a dimension or two some truly amazing objects arise.
Just recently, I managed to buy from a company in California an intriguing item, a Klein bottle, depicted here. The company concerned is actually the ACME Klein Bottle Company, though its name has no relation to the organisation referred to above. It is the only company I have ever dealt with that asked me to state the dimensionality of space in my neighbourhood, showing that at least some mathematicians have a sense of humour.
As I have tried to explain (unsuccessfully) to my wife, this object really requires us to be in four-dimensional space, and what I have purchased, therefore, is merely the projection into our familiar three-dimensional space of the real thing. But isn't it lovely? As it happens, I can't think of any economic applications of this sort of object, nor indeed any applications at all, but who cares?
And wouldn't it be great if more people took the same delight in discovering a new equation, or a new geometrical result (here I probably reveal that my maths is slightly old fashioned, as little geometry seems to be taught nowadays, sadly), as they do when they discover a new writer?