Attempts to lure science and maths graduates into teaching have included scholarships and bursaries of up to pound;25,000 a year for the most highly qualified candidates.
But as the shortfall persists, universities are increasingly recruiting teachers for subjects in which they do not hold a degree, it has emerged.
Teacher trainers have warned that a significant expansion of so-called subject knowledge enhancement (SKE) programmes will be needed to meet the demand for physics, chemistry, maths and computing teachers.
SKE courses equip graduates in one subject with the ability to teach another and can also be taken by career-changers who require a refresher course.
Although such courses have been offered by universities since the 1990s, changes to the funding formula two years ago led to a reduction in the number available. But now universities are looking to expand programmes amid fears of an acute teacher shortage.
Birmingham City University, which already runs a maths enhancement course, is introducing one in physics from April and is also aiming to develop similar courses in computer science, chemistry and design and technology, according to Kevin Mattinson, head of the School of Education.
"There are many people who might not have the subject knowledge but have the potential to become good teachers," he said. "There is a growing recognition that enhancement courses are an important way to get the maths and physics teachers we need."
SKE courses can be as short as eight weeks, although they are typically taken over an academic year prior to teacher training. As well as being available to PGCE students, the courses can be taken by school-based trainees through the School Direct and school-centred initial teacher training schemes.
A spokeswoman said the Department for Education was encouraging schools to offer their own SKE courses, as well as commissioning them from universities. The DfE is also providing additional resources on the importance of subject knowledge enhancement, including online seminars.
This summer, the University of Cumbria will launch short courses in computer science, chemistry and physics, in addition to the maths SKE it ran last year. It also offers long courses in physics, chemistry and maths.
John Cawkwell, School Direct and school-centred initial teacher training lead at Cumbria, said there was an increasing awareness of the importance of enhancement courses for addressing teacher shortages in certain subjects. "Schools are finding it difficult to recruit and there is a realisation that it isn't necessary to have a degree in those subjects," he said. "We're expecting [SKEs] to grow over the next few years."
Tom Rimmer graduated in psychology but has just finished a chemistry enhancement programme at Cumbria. "Chemistry was the science I enjoyed most at college so it seemed the most relevant one for me," he said.
"I was concerned that, as I would be working with people who had chemistry degrees, I would be out of my depth, but I feel really comfortable with it now."
SKE programmes mean that teachers can be recruited in priority subjects who would not otherwise be in the classroom, according to Rob Rolfe, SKE lead tutor at the University of Wolverhampton.
"We have put more than 250 teachers into secondary maths teaching in the West Midlands who would never otherwise have done it," he said.
But Mr Rolfe added that although universities were keen to expand their enhancement courses, they were constrained by uncertainty over how many teacher training places they would be allocated in the future.
"There is a massive shortage of people teaching maths and physics. We need a structured approach to teacher supply where SKE has a big part to play in shortage subjects," he said. "It has the potential to make a real, significant difference across the country."
A spokesperson from the DfE said: "Subject knowledge enhancement courses allow more candidates to train in priority subjects, ensuring the best and brightest teachers are working in our schools."
`I was nervous that I'd be found out'
Career-changer Pascale Rollings became a maths teacher after taking a subject knowledge enhancement course at the University of Wolverhampton. She had previously worked in business and marketing, and the pharmaceutical industry.
Although Ms Rollings has an A at GCSE in maths, she did not take the subject at A-level. She now teaches at Holyhead School in Birmingham.
"When I was at school I really didn't like maths, but I thought if I did the course I could teach it alongside something else," she says. "But I really enjoyed the course and I really enjoy teaching it.
"When I first started in the classroom I was nervous that somebody would find me out and say I was not a real maths teacher. But halfway through my PGCE I realised I was OK and now it doesn't bother me."