The joint report of the London Mathematical Society, the Institute of Mathematics and its Applications and the Royal Statistical Society refines some of the concerns about maths standards expressed earlier this year by five academics. Tackling the Mathematics Problem does not claim to have all the answers; but it does establish some of the right questions.
It is not just a matter of things not being as they used to be; more whether they are as they need to be. As Professor Geoffrey Howson, one of the original five who chaired the group of nine, put it earlier this year, the average 16-year-old knows more mathematics than he or she did 20 years ago. But what about the minority who do maths A-level? Are those who will become the mathematicians, engineers, physicists and technologists sufficiently well prepared for and by advanced-level maths? And in sufficient numbers?
Employers and universities receiving such students apparently think not. This sensible and cogent report gives a number of examples and examines some of the contributory factors, without claiming that theirs is the only view that matters.
Possibly its weakest argument is that the national curriculum is largely to blame. It may be that undergraduates are weaker in numerical and algebraic manipulation, in analytical powers and in understanding that maths involves precision, logic and proof, as these nine academics say. But none of today's university students were subject to the national curriculum which has yet to work its way up that far.
That does not totally negate their doubts about the national curriculum, however, especially if in mathematics it is simply a crystallisation of what had become accepted practice; if, say, maths GCSE - the effects of which certainly have worked their way up to undergraduate level - was father to the national curriculum rather than the other way round. Indeed, the lengthy riposte of the School Curriculum and Assessment Authority, to the effect that the revised national curriculum from this September does attempt to give greater emphasis to number for younger pupils and algebra for older ones, confirms one of the academics' points.
They have others which the curriculum review did not address. The fact that pupils can obtain a grade B at GCSE without ever doing the algebra required for A-level and the reduction in time devoted to maths are two which underline the futility of broadening the curriculum to keep open students' 16-plus options if GCSE work is thereby so diluted as to prevent advanced level study of the subject.
The report's focus on the national curriculum may also be symptomatic of the lack of trust these mathematicians have in SCAA. The inclusion of prestigious mathematical bodies in the lists of those routinely consulted by the authority apparently gives them no confidence that their views are given due weight. Hence the call for the Government to establish a committee commanding greater confidence in higher education to advise and support maths education.
Such a demand may cause the Government some concern; it should certainly worry SCAA. School maths-for-all must not be dictated from the top down in the way the academic curriculum used to be. But it cannot ignore higher education's importance either. The nine rightly say there needs to be more consensus between mathematicians, scientists and engineers and school teachers on what should be taught and how. And a forum for the more open and expert debate of these issues - in contrast to the secretive and politicised motions of SCAA committees interspersed with self-cancelling consultations - could help to achieve this. But why not simply create one rather than wait for politicians to do it for them?
Given the strategic importance of maths, our poor showing internationally and the low take up at A-level, another authoritative committee of enquiry into the five to 16 maths curriculum may indeed be timely if it reports towards the end of the five year moratorium on curriculum change. Sir Wilfred Cockcroft, chairman of the last one 14 years ago, was one of the famous five expressing concern earlier this year.
The future of mathematics beyond 16, however, is inextricably bound up with that of the three A-level system. While in some parts of France entries for the science and maths Baccalaureate have trebled in the past 10 years, our percentage of 18-year-olds taking science and maths A-levels has fallen from 38 per cent in 1965 to 9 per cent last year. In some European countries, 20 per cent of sixth-formers study calculus to A-level standard. In Britain, the figure is 7 per cent.
The Department for Education's paper last year on the supply of maths and science students was unduly complacent about this. This report does not pretend to prove all its hypotheses, but it provides a timely wake-up call.