Maths prodigies should sit their GCSEs and A-levels at the same time as their classmates and not be “trained” to take exams early or fast-tracked to university, a leading maths teacher has warned.

Geoff Smith, chairman of the British and International Maths Olympiads, and vice-chairman of the United Kingdom Mathematics Trust, said that accelerating children through the exam system was “a disaster” and “a mistake”.

“If you’ve got a smart kid, it’s very easy to accelerate the child through the public examination system,” Dr Smith told TES. “These things don’t require social skills. They don’t require you to be an adult. But this is a disaster. If they’ve run out of school mathematics when they’re 10 years old, then the temptation is to send them to university. Most people who do this look back on it as a mistake.”

Instead, Dr Smith suggested that talented maths pupils should be given extended, complex problems to solve, building on the knowledge they had gained at school.

He said: “Unusually bright people find the school mathematics syllabus undemanding. But there’s so much worthwhile mathematics to keep them happy and busy while their bodies turn into adults. School maths barely scratches the surface.”

Sue Pope, of the Association of Teachers of Mathematics, suggested that schools should “enrich” students’ understanding of maths instead of “hothousing them” for tests at a young age.

She said: “By rushing them through, their understanding of mathematics may end up somewhat fragile. It’s relatively easy for children with good memories to be trained to pass exams, without necessarily understanding the maths they are doing.”

The number of pupils taking GCSEs early fell by 39 per cent last year. This shift followed the introduction of new government league tables, which do not allow schools to register the grades pupils achieve during exam resits.

In maths, early entries were down by 77 per cent, from 170,357 to 39,292. However, the number of pupils gaining at least a C grade rose from 57.6 per cent to 62.4 per cent.

Calm contemplation

Dr Smith made his suggestions to TES after the recent release of the film X Plus Y, which tells the story of a contestant in the International Mathematical Olympiad who finds maths problems significantly easier than human relationships.

The film reinforces the assumption that maths is not a subject that requires highly developed social skills from its practitioners - an assumption that Dr Smith said was based in fact.

“A lack of soft social skills is no disbarment to doing mathematics,” he said. “It’s not subtle social interactions, it’s thinking skills. My profession is full of people who are content to sit and think for a long period of time.”

As an example, he cited Fermat’s last theorem. This was successfully proved in 1995 by mathematician Andrew Wiles, who had spent seven years contemplating the problem.

“Someone with a short attention span shouldn’t enter this profession,” Dr Smith said. “Someone who isn’t obsessive shouldn’t go into pure mathematics.”

Tim Rowland, chair of the Joint Mathematical Council of the UK, admitted there was some truth to the old joke that an extrovert mathematician was the one who talked to your shoelaces rather than his own.

But he added: “Talking with one’s colleagues is an essential part of developing thinking. Most mathematicians would talk about working in teams, in the same way that scientists and engineers do.

“And maths students learn alongside other people: if they’re taking an exam early, they need to learn and be entered with other students of equal capability.”

Friendly competition

Dame Celia Hoyles, pictured, professor of mathematics at the UCL Institute of Education and a former government chief adviser for the subject, agrees that children should sit exams with their peers.

She says that pupils with a natural aptitude for the subject should be given alternative enrichment activities to enhance their ability, but adds that extracurricular maths activities, such as Olympiads, do not necessarily suit everyone.

In fact, she says, many Olympiad veterans go on to become lawyers and doctors, rather than research mathematicians.

Despite this, Dame Celia insists that maths is a social activity: the lone genius proving theorems in an ivory tower is largely a myth, she argues.