But the speed of the changes proposed by the Government’s curriculum agency has provoked angry criticism from academics and exam boards and has drawn expressions of concern from the main Opposition parties.

A leading maths professor described the ban on technical aids as “farcical” and predicted a return to the days when candidates wrote out long-divisions by hand.

Twenty-five per cent of all marks must be “non-calculator”, according to the plans drawn up by the School Curriculum and Assessment Authority for a new mathematics “core”.

The proposals, now published for consultation, also include a greater emphasis on mathematical proof in an attempt to meet the concerns of university maths departments about falling school standards. Britain’s long “tail” of mathematical under-achievement will be dramatically illustrated in next week’s Third International Maths and Science Study.

The latest measures proposed by SCAA have however been heavily criticised amid allegations that the maths A-level has effectively been re-written in just three days. SCAA has pressed on with changes even though its own consultative group on maths and science asked for additional time and the Royal Society called for a one-year extension. Now the main Opposition parties have got involved. In a letter to Education Secretary Gillian Shephard, Liberal Democrat Don Foster said that the changes could prove “unworkable and damaging”.

Labour’s education spokeswoman, Estelle Morris, said this week: “We’re certainly concerned. If there’s going to be division of this sort, it won’t do anything to improve the take-up of maths.”

Universities have complained that students no longer have the basic skills to cope with undergraduate degrees and have blamed the move away from traditional maths. This appeared to carry substantial weight with Sir Ron Dearing whose review of 16 to 19 education said that ways should be found to meet their concerns.

But even the academics who have written SCAA’s latest proposals are concerned about the speed. “It’s moving too fast for there to be proper consultation, ” said Professor Chris Robson from Leeds University, a member of the drafting committee. “It needs to be slowed down. SCAA says that because this is so important it has to be done quickly. We say it’s so important, we have got to get it right.”

Margaret Brown, professor of maths education at King’s College London said: “We’d rather stick with what we have at the moment, for at least another year rather than make these complex changes and find that we have got it all wrong.”

She described the calculator ban as nonsensical. “I can understand barring calculators that have ‘algebraic manipulators’ built in. But it’s farcical not to allow scientific calculators. Are we going to have A-level students writing out long-divisions in full?” She said the ban would make it substantially more difficult to set exam questions in pure maths.

A spokesman for the Northern Examinations and Assessment Board said: “We hope the new syllabuses could be delayed for a year in all subjects.”

The “core ” elements of all A-levels have been re-drafted so that they can form the basis of the new one-year AS-levels proposed by Sir Ron Dearing. For the most part this has involved only minor changes and students will be able to start the new syllabuses in 1988.

But maths is problematic. While SCAA wants to keep to the timetable, it also wants to address the concerns expressed by universities and it rejected proposals from its own drafting committee that no changes should be made for the present.

SCAA maintains that it could still recommend a delay after the consultation period, but that it would prefer to introduce the new exam system in one go. Assistant chief executive Tony Millns said: “We have to take account of what is manageable in schools. It is not fair to tell them they have a change now, a change next year and one the year after that.”