What's the answer, Professor?

Next month a Government-commissioned inquiry into the state of mathematics in Britain will report that radical measures are needed to save the subject from slipping into terminal decline in schools and universities. It will propose a £130m package of measures to establish a nationwide network of "regional maths centres" to drive up standards and to get schools, colleges, universities and employers to work together to design a new and more relevant curriculum. But academics and educationalists are up in arms over proposals in the report which they fear could damage school mathematics and herald a return to the old "sheep and goats" system of O-level and CSE. Professor Adrian Smith, principal of Queen Mary University, London, who has headed the 15-month inquiry, is demanding a big overhaul of maths lessons for 14 to 19-year-olds to halt the decline in numbers taking A-level maths, and to train the future workforce.

"It is no secret that I think GCSEs and A-levels are failing to do the job that needs to be done," says Professor Smith, who is a former professor of maths at Nottingham University. "We need to make the material much more inspirational so that people want to study maths for longer than they do now."

A national panic about the state of mathematics was sparked by the catastrophic AS level results in 2001. Almost one third of candidates for the new exam failed - putting a generation of sixth-formers off maths. Since then, the numbers putting in for A-level maths has plummeted by 20 per cent, prompting warnings of a crisis in the subject. Numbers fell by more than 13,000 between 2000 and 2002, from 67,036 to 53,940, but bounced back slightly to 55,917 this summer.

Mathematicians believe that their subject is trapped in a vicious circle. Many pupils don't enjoy school maths lessons, so few sixth-formers apply to study the subject at university, so few graduate, meaning the pool from which maths teachers can be recruited is small, so there are few qualified teachers, leading to more pupils having unhappy experiences of mathematics.

A recent report by the Department for Education and Skills confirmed this grim picture. More than 800,000 secondary school pupils are being taught maths up to GCSE by teachers who do not have an A-level in the subject. The proportion has risen to 26 per cent from 20 per cent seven years ago, despite the Government's boast that there are more better-qualified teachers in schools than ever. And schools are facing a demographic timebomb because nearly a third of maths specialists are now aged over 50.

Professor Smith argues that the teenagers of today must be targeted as the teachers of tomorrow. "You have got this decline of people doing maths post-16. The key issue would be to solve the general question of how to get kids to do maths post-16."

But the transformation of teenagers' maths lessons looks as though it will be the most controversial part of his report. Early submissions to Professor Smith's own review called for a "maths for citizens" course for those who find conventional maths too difficult. The plea - from the Mathematical Association - was that children should be taught how to use graphs, calculate speeds, and change money into foreign currencies. Professor Smith, however, would like an end to the "one-size-fits all" approach.

He is thought to favour the creation of a range of pathways - both academic and vocational - so that every student can follow a maths course to match their ability and interests. It should be possible for students to switch between pathways so that they do not restrict their choices too young. But his proposals received a stormy reception at a seminar of maths experts last autumn. Opinion is divided between those who want all students to study the same material, whatever their ability, albeit at different paces, and those who want students of different abilities to follow different courses. Roger Porkess, project leader of Mathematics in Education and Industry, an independent curriculum body, advocates a ladder of exams similar to music grades operating in maths, and opposes plans to recreate the O-level/CSE divide.

"I was really horrified by what I was hearing at the reception," he says. "The issue of different pathways is really a big one. There seemed to be a suggestion that, at 14, students would embark on totally different routes towards totally different destinations. We don't want a return to the old O-level and CSE structure where people are told they are too thick to do anything worthwhile at the age of 14."

Other maths experts would like the subject to be made optional from the age of 14. Terry Bladen, president of the National Association of Schoolmasters and Union of Women Teachers, believes it is a waste of time teaching advanced mathematical concepts to the less able when they would never need them in later life.

"I would always argue that pupils should be num-erate, with numeracy taught throughout all the key stages, but numeracy can be divorced from mathematics," he says. "How often do the majority of people need or use mathematical concepts once they have left school?"

But Tony Gardiner, a reader in mathematics at Birmingham University who has seen a draft of the report, believes that Professor Smith's proposals do not distinguish enough between the more and the less able. The plans are "an absolute disaster" for students at the top of the ability range, he thinks. "The drafts I have seen were simply awful. It is a crazy English trait to believe that a subject like maths can be sexed up by cramming it full of practic-al applications."

GCSE maths is expected to be particularly criticised in the report. The fact that 30 per cent of 16-year-olds are entered for the lowest of the exam's three tiers, where the best grade they can achieve is a D, is a "national scandal", say educationalists. With a C grade being the minimum standard needed for GCSE league table success, it is no wonder that these students feel their maths courses are pointless, they argue. The report is expected to resolve this by demanding a reform of maths courses so that every student learns basic numeracy, continues with the subject for longer and emerges with a meaningful qualification. "You need to create a variety of pathways which people can master at their own rates without it running into the criticism that one is recreating the old O-level/CSE system of sheep and goats," says Professor Smith.

His review is also expected to call for the exam system to become less age-fixated. "The assumption that everybody gets from A to B in the same time in mathematics is nonsense", said one senior figure who gave evidence to the inquiry. But the problems with mathematics do not only lie within schools. Professor Smith's report is expected to lambast universities for their failure to nurture mathematical talent or to encourage maths graduates to pursue teaching careers. The Government will be forced to face some awkward facts about the recruitment of maths teachers. The shortage of well qualified maths teachers is at critical levels, according to the review. The report is likely to demand that the Government funds new conversion courses to allow graduates whose degrees contained some maths to retrain as maths specialists. This would emulate a Teacher Training Agency scheme for training more physics specialists which pays graduates £150 a week to attend a conversion course.

Professor Smith would like more financial incentives for maths graduates to train as teachers. The Government has already introduced training bursaries and "golden hellos" and even pays off the student loans of teachers who stay in teaching for 10 years. Some senior figures would like maths teachers to receive higher pay. But DfES officials are thought to oppose differential salaries on the grounds that they would be unpopular in the staff room. However, the inquiry report may attempt to kill two birds with one stone by advocating paying maths teachers more - but only if they complete new training courses. In any case it will take a generation for the effects of any changes to be seen. British school children have a lot more maths lessons in front of them before Britain becomes a nation of maths lovers.

education@independent.co.uk