How do you inspire young people to pursue mathematics? Martin Ince looks at UK efforts
What is the problem with mathematics in British universities? Ask anyone and you will get the same reply: "Schools." Mathematics research in universities is lively. Andrew Wiles, the Cambridge mathematician who famously cracked Fermat's last theorem, is the first British mathematician to achieve name recognition since Alan Turing more than 50 years ago. Mathematicians are in demand for jobs everywhere, from the City to heavy industry. High-level maths that once seemed incapable of application is being used in vital tasks such as ensuring internet security. On the world stage, the Norwegian government will next year award the first Abel Prize, billed as the mathematicians' answer to the Nobel.
But insiders are sure that there is something amiss with the subject at a basic level. Charles Goldie of Sussex University, who chairs the Heads of Departments of Mathematical Sciences, points out that at school, mathematics is the most popular A level after English. But this popularity does not translate into maths undergraduates, whose numbers have not grown in line with the university expansion of recent years. Part of the problem, Goldie says, is that universities offer subjects that were not an option at school. But the fall-off is critical because university mathematics is the essential source of the large number of teachers needed to keep school maths healthy.
"If university maths departments fall over because there are not enough students, the problem feeds back on itself, into schools and also into science and engineering subjects that depend on mathematics," Goldie says. He points out that in discussions with the Teacher Training Agency, it emerged that about 40 per cent of maths graduates needed to become teachers to keep school mathematics healthy. But most graduates decide that areas such as financial services are more enticing, at least as a first career. The TTA and other bodies have responded by creating "mid-life initiatives" for potential maths teachers who want to enter the profession later - Goldie says this is helpful but not a real solution.
He believes that "too many schools now have nobody competent teaching mathematics - and the children all notice it". The Qualifications and Curriculum Authority is now consulting on a simpler structure for sixth-form maths that would reduce choice but give universities more idea of what an incoming student knows. Schools that have taken steps to enhance their maths - such as Roedean, with which Sussex has been working - have succeeded in increasing numbers and quality of students, Goldie says, but these are exceptional cases.
There is no doubt that poor school mathematics has affected university entrance, but Goldie, himself a statistician, is unhappy with the available data on the subject. He has been surveying admissions figures for the past four years. These show that some departments, such as the one at Warwick University, are expanding from a base that was already substantial. Other Russell Group universities are having trouble finding students with good A levels, while some old universities are "losing numbers quite dangerously". He adds that many post-1992 universities have given up maths in its own right and teach it mainly as a service for other departments.
Goldie also questioned maths departments about the threats they face and found "plans for savage cuts" because of the dearth of students. The research assessment exercise, he points out, offers vice-chancellors a template for closure by chopping the subject into three units of assessment. "Applied mathematics goes to engineering; the management school takes statistics; and pure maths closes." The question, he says, is how to maintain maths at a high intellectual level in a department whose emphasis is elsewhere.
Peter Cooper, executive secretary of the London Mathematical Society, says that these issues will be on the agenda later this month at a meeting with Sir Howard Newby, chief executive of the Higher Education Funding Council for England. According to Cooper, the question is partly about market forces. "At the moment, student demand drives the system, not employers' demands or the national need for mathematicians," he says. "We [the LMS and the Institute of Mathematics and its Applications] will be asking for more focus on the outcome of mathematical education."
The sector also has more immediate issues. Mathematics is in a low band for funding council cash per student despite the high cost of the computing equipment it needs. There are demands for it to be funded at a level closer to that for laboratory-based sciences.
Goldie and other mathematicians cite several unique aspects of maths as a subject for students. One is the extreme marks, high and low, that students can get. "Some sail through with irritatingly little effort, while others just can't do it," Goldie says. Chris Robson, a professor at the University of Leeds, says that it is not unknown for a student to produce a better proof in an exam than Robson would have thought of himself. At the other extreme, some students never learn to cope with maths, whereas in other subjects even a poor student will pick up the rudiments. Goldie says: "This is not surprising because of the high level of abstraction in mathematics. Some students just can't do it."
However, he warns: "We are now taking in students and awarding them maths degrees without making them mathematicians." He also expresses dismay that there is now more rote learning in university maths, adding that it is not only the expected subjects such as physics and engineering that suffer from problems in mathematics. The biological sciences are using more large databases, and understanding suffers if biologists do not know enough maths. Goldie is also alarmed at ideas for low-maths courses in subjects such as physics, fearing that their graduates could end up being unattractive to employers. "I sympathise with the predicament of some departments," he says, "but I hope they would not be cynical enough to produce graduates with too few skills to be acceptable to a graduate school."
One response to the problems now afflicting the interface between school and university mathematics is the formation of the Advisory Committee on Mathematics Education, hosted by the Royal Society and chaired by Sir Chris Llewellyn Smith, former provost of University College London. Teacher supply and school mathematics are among its first concerns. Robson, a member of the Acme executive, says: "You can argue that maths has to deal with the students who come to it, even if they know less than they used to. But a degree has to have international credibility and cannot be downgraded. Today's maths degrees are not what they were, but they are different rather than worse." Most maths degrees now take four years. "The reason for the change from three years is not that I and my colleagues want to work harder," Robson says. "But we do want to turn out students at an appropriate level, and we are starting at a different level from the one we used to see."
Robson thinks that graduates from today's four-year degrees can make excellent professional mathematicians, in academic life and in industry. "The students who read maths are good but also very self-selecting, and there is always a problem finding enough. Anyone reasonable will get in."
Like Goldie and others, he stresses that career worries are not one of the problems for university maths. "Some of our graduates become professional mathematicians, while many others use the degree mainly to develop their thinking skills and make little use of the theory later. But people with maths qualifications are everywhere. Statisticians especially are all over the place. When the Quality Assurance Agency asked us to tell them the major employers of our graduates so it could talk to them, we could not. There are just too many."