The Government was this week urged to address the "crisis" facing maths teaching by introducing new cash incentives for staff who want to teach the subject.
Professor David Burghes, acting director of the new pound;15 million national centre for excellence in maths teaching, said non-maths graduates should be paid to attend training courses so they can teach it to GCSE.
His call comes after a report for the Government painted a damning picture of how shortages of specialist maths and science teachers are affecting English secondaries.
One in four secondary maths lessons is being taken by teachers of other subjects, while more than a quarter of 11 to 16 schools have no physics specialists, it said.
The problems are worst in inner-city schools and those at the bottom of league tables, which were most likely to be staffed by non-specialist maths teachers, said the National Foundation for Educational Research report.
Across England, pupils in lower sets for maths were less likely to be taught by a teacher who had post-16 maths qualifications, it said.
And one in eight A-level physics lessons was being taught by teachers who themselves only had an A-level in the subject.
Jacqui Smith, the schools minister, said no government had done more to address the "historic" shortage of maths and science teachers.
Incentives already on offer include tax-free bursaries of pound;9,000 and pound;5,000 "golden hellos" for maths and science trainees. But Professor Burghes said the report confirmed that the subject was facing a "crisis".
He said: "The Government has tried to do things, but it's not enough."
He said: "There would be quite a lot of people who would have been quite happy to convert to maths, but their subject knowledge is not strong enough. We need to give them more support."
Ms Smith said that the number of trainee maths teachers had increased by 76 per cent from 1998 to 20045. Over the same period, the number of science trainees had risen by 28 per cent, while recruitment of physics trainees had more than doubled since 2000.
Asked whether teachers could be paid to go on in-service training courses in maths, a Department for Education and Skills spokesman said: "This would probably be a decision for the individual school to take through their professional development funds."