Fewer than half of maths teachers have a degree in the subject, despite a multi-million pound recruitment drive.

Tory shadow schools secretary Michael Gove said: “We simply can’t compete with other countries when we don’t have the scientists and mathematicians in teaching to train the next generation of innovators.”

The National Foundation for Educational Research surveyed more than 14,000 teachers in nearly 330 secondary schools in England.

It found there had been an overall 10 per cent rise in the proportion with degrees in their specialist subjects.

But only 43 per cent had a degree in the subject they taught and 38 per cent had no relevant post A-level qualification. Science subjects tended to have the highest proportion of teachers with relevant degrees.

But some had no post A-level qualification in the subject, including 10 per cent of those teaching physics.

The survey also found that grammar and smaller schools in wealthier areas had a higher proportion of staff with qualifications beyond A-level than those with deprived pupil intakes.

Lib Dem shadow schools secretary David Laws said: “It’s no wonder that many young people from deprived backgrounds struggle to do well.”

Schools Minister Jim Knight insisted that the Government’s “revolution” in teachers’ pay and conditions meant mass staff shortages were over. He said: “Shortages only remain in a few areas where all sectors are struggling to find qualified staff.”

The Government plans to make teaching a masters-level profession for staff entering their first job.

The Association of Teachers and Lecturers’ Dr Mary Bousted said: “Teachers also need a good understanding of learning, assessment and individual pupil needs, and the teaching skills to offer the best learning experiences for all their pupils.”