A new range of 60-hour maths programmes, to be run by the three main examination boards, are the first to bridge the divide between academic and vocational study. They offer “bolt-on” mathematics for any student, whether in school, college or the workplace.

The initiative has already been warmly welcomed by maths educators, including traditionalists, who are concerned that most adults have no opportunity to study the subject.

Lack of mathematical knowledge has frequently been cited as a factor in the under-performance of the British workforce.

Students in schools and colleges are already studying pilot versions of the qualification, provisionally titled “Free Standing Maths Units”.

The Qualifications and Curriculum Authority, which devised the scheme, has described the maths involved as “rigorous”. Ranging from foundation (GCSE equivalent) to advanced levels, it provides intensive coverage of the mathematics relevant to a range of other fields - calculus for science students, for example, or statistics for geographers.

“There’s a huge public demand for maths, and these units provide the sort of maths that people need in an accessible, bite-sized chunk,” said Professor Alison Wolf from London University’s Institute of Education, who has backed the qualification from the start.

“This is a way of broadening the post-16 curriculum without trying to turn everybody into four and five A-level people, and it’s desperately overdue. ”

The courses will be roughly the size of one sixth of a single A-level module or a single GNVQ unit. But students cannot build up the units to create either of thesequalifications.

Dr John Marks, director of the Educational Research Trust and a well-known critic of Britain’s vocational qualification system, welcomed the units:

“There’s a big need for them. There seems to be a great gap in the system for teaching mathematics from 16 to 19,” he said.

But Professor Alan Smithers, of Liverpool University’s centre for education and employment, was doubtful about the value of the courses. He believes a more appropriate alternative might be to develop already recognised maths qualifications such as the AS-levels.

He suggested the units were developed with the long-term demise of A-levels in mind.

“The A-levels and GNVQs would dissolve into modules and you would now have these maths units. Students could accumulate modules appropriate to where they want to go. It would be open to the QCA to specify these maths units as a way of all students continuing with maths post-16,” he said.

But Dr Jack Abramsky, one of the QCA’s principal subject officer for maths, said: “The aim is to provide real, in-depth study which students can apply to other courses of study.

“There are many very bright GCSE students who don’t do any more maths for the rest of their lives. That’s a shame and a waste of talent. Now there is an opportunity to do a little maths beyond GCSE.”

HOW IT ADDS UP

* The new maths programme will be generally available from September 2000.

* Units will be of a similar size to the new modules being developed for A and AS-level maths courses - also due out in 2000.

* Units will not “add up” to make an A-level, but “add on” to other courses, such as business studies or art and design.

* 45 of the 60 hours are expected to be teacher directed - and will require good liaison between subject departments.

* Students will have to produce a portfolio of work and successfully complete a written exam to gain a unit qualification.

* A foundation level unit would equate to a GCSE pass at grades D to G, with an intermediate reflecting an A* to C grade pass.

* Advanced units would take candidates beyond the top end of GCSE and into A-level standard.

* Units could support science, social science, business, engineering, teacher training and foundation courses.