Poor standards of numeracy are as much a problem for Britain’s sixth-formers as they are for younger pupils in primary and secondary schools, according to a major survey by government inspectors.

In a four-year analysis due out in the spring, inspectors from the Further Education Funding Council found widespread failings in algebra and number work among the 3.25 million students in further education and sixth-form colleges.

Worse still, colleges are in a weak position to tackle the problem, says the FEFC. It found that few have mechanisms to set academic targets and monitor progress - a weakness which will fuel the gathering debate on academic standards in further education.

Only a small number of colleges attained the top grade 1 ranking for maths, science and computing, and inspectors uncovered wide and apparently inexplicable variations in expenditure and achievement across the sector.

The survey was undertaken as part of an FEFC report on the three subjects that will be published in March.

The weakness in maths was described as “a major cause for concern” by Professor David Reynolds, the head of the Government’s numeracy task force.

His group is responsible for devising a national “numeracy strategy” and is due to publish its preliminary report next week.

Speaking at last week’s annual meeting of the Association for Science Education, senior inspector Denis McEnhill outlined the main flaws highlighted by the survey, although he insisted that these occur alongside much good teaching. It found: * The biggest problem is student drop-out.

* Significant variations in teaching time are not based on curricular needs. GCSE courses range from 3.15 to 6 hours, A-level from 2 to 6 hours a week.

* Few colleges have all the characteristics of a well-run institution. These include: sound strategic planning; effective quality assurance; strong leadership; good communications; good teamwork.

* A common failure to set targets and monitor progress.

* A low proportion, 7 per cent, gaining the top grade 1 (although 69 per cent gained grades 1 or 2 and only 3 per cent were ranked 5).

* A large number of students enter for inappropriate GCSE re-takes in maths. Many fail and some find their grades decline. Other types of course might be more appropriate as “stepping stones”.

* Distance and open-learning provision is under-developed.

* The most common classroom weaknesses were: not involving students in decisions; not allowing for different ability levels; narrow range of teaching methods; in maths a failure to develop numerical and algebraic skills; a failure to use information technology to promote learning.

* Maths students have inadequate opportunities to tackle practical problems. There were particularly wide variations in standards of maths on vocational courses.

* A number of students fail to get the specialist support they need.