One in four maths teachers in England is not a specialist in the subject, government-funded research suggests.
The shortage is most severe in maths
A study by the National Foundation for Educational Research into the teaching of maths and science found both had problems of staff recruitment.
Shortages of well-qualified maths and science teachers were worst in schools with low GCSE scores and those serving the poorest children, researchers said.
Ministers have said no government has done more to tackle the problem.
The study examined staffing in maths and science departments at one in four of England's maintained secondary schools.
They asked heads of department what proportion of their staff were specialists, defining them as those with a degree in the subject they taught or even those who had studied the subject as part of their initial teacher training.
Science teachers were more likely to be specialists than maths teachers, with only 8% seen as non-specialists compared to 24% of maths teachers.
Schools with the lowest GCSE attainment and those where more children received free school meals had the highest proportions of the least qualified teachers, the study found.
A total of 60% of the heads of maths departments said they had experienced either "a great deal" or "quite a lot" of difficulty in terms of staff shortages.
Problems were worst in low-performing schools and in areas where scientists and mathematicians could earn good salaries outside teaching.
The president of the Royal Society, Lord Rees, said: "This report reveals a disappointing number of teachers with a specialism in the subjects that need it most.
"If we are to halt the worrying decline of numbers of students studying maths and the sciences, physics and chemistry in particular, at A-level and beyond, then we need teachers who are both enthused and knowledgeable in the subjects that they are required to teach."
The Minister for Schools, Jacqui Smith, said there was "an historic shortage" of qualified maths and science teachers, but no government had done more to reverse it.
She said targets for recruiting new science and maths teachers were now being exceeded.
"But there is still more to do and that is why we have introduced such a strong package of incentives," she said.
"This includes golden hellos of up to £5,000, tax-free bursaries of up to £9,000, record pay and new initiatives to help people with real industry experience pursue a career in the classroom."