“At GCSE level, for example, they cannot manipulate algebraic expressions or solve equations with confidence,” the report says. “They are too dependent on calculators to carry out the simplest of calculations. Many cannot simplify straightforward fractions for themselves and end up working with recurring decimals instead.”

The report into the sciences, which includes computing and maths and is the third largest curriculum area in FE, was based on college inspectors’ observations of more than 12,000 teaching sessions between 1993 and 1997.

Overall, the quality of teaching and learning was comparable with other subject areas with many examples of well-planned courses and lively, innovative teaching. But it found “a substantial though smaller volume of less imaginative teaching which barely addresses students’ needs.

“Many mathematics teachers employ a narrow range of teaching methods. Some GCSE mathematics and science lessons are particularly uninspiring and fail to motivate students.”

In spite of much good teaching, the report identifies “significant weaknesses” where teachers talked for too long, failed to involve students in discussion and wasted lesson time by making them copy out notes. The best teachers held question-and-answer sessions to ensure students’ understanding of theories, gave handouts of overhead transparencies, and made good use of teaching aids such as video.

In general, practical assignments and real life examples engaged students’ attention and won higher inspection grades than theoretical classes, which also tended to discriminate against less able students.

Science staff should spend more time on developing effective teaching methods and sharing good practice. “There are few opportunities in most colleges for science, mathematics and computing staff teaching in vocational areas to come together to share ideas and teaching materials,” the report notes.

The report also criticises the use of IT in mathematics lessons - fewer than 20 per cent of colleges inspected in 1996-7 used computers to promote learning in mathematics. “There are not enough computer workstations in most of the classrooms where mathematics is taught.”

Poor guidance from the college is partly to blame for the high drop-out rate from GCSE mathematics courses, particularly among adults, who should be directed onto more suitable programmes. “They become disheartened by the pace and difficulty of the course and often leave before the end.”