More than 100,000 secondary school pupils will be taught maths and science by teachers untrained in the subjects because of a chronic shortage of new recruits, education experts will warn today.

They predict the shortfall in expertise will discourage sixth-formers from studying the disciplines – which have been identified by the Education Secretary Michael Gove as “national strategic priorities” – at A-level.

Research by Professor John Howson of Oxford Brookes University and DataforEducation, which specialises in analysing recruitment trends, has revealed that up to 30 per cent of maths places on PGCE teacher training courses due to start in September remain unfilled, potentially leaving schools 700 recruits short next year. There is a similar problem with physics, where courses have attracted 386 fewer recruits than in 2012, while other key subject areas such as modern foreign languages and English are in a similar position.

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Chris Waterman, co-author of the research, said that every missing maths teacher meant 150 secondary school pupils would be taught the subject by a non-specialist, putting 100,000 pupils at risk of receiving their education from someone who has no specialist maths training.

Professor Howson explained that when the jobs market is improving – as it appears to be at present, albeit slowly – potential candidates often turn their backs on the teaching profession.

He said: “The Government got complacent after the recession [in 2010]. Secondary school rolls were falling so we didn’t need so many teachers; we were coming to the end of the high spot of teacher retirements and we had all those people who wanted to come into teaching because there weren’t any others jobs available. The danger, though, was that this wasn’t going to go on.

“We’ve now had successive years when public sector wages have been held down, and regular stories about the problems facing the profession. No wonder graduates in the Stem (science, technology, engineering and maths) subjects are accepting jobs elsewhere. That was always the risk.”

The way in which the top candidates are recruited has also undergone significant change in the past year, with fewer entering teacher training institutions and more being recruited directly by schools.

Professor Howson’s research is based on published recruitment figures for PGCE courses, plus data on the number of teachers recruited directly by schools from the Department for Education’s website.

It shows the number recruited in maths has fallen by 709, physics by 386, design technology by 350, chemistry by 345 and English by 343. English was one of the subjects that over-recruited last year, meaning the 343 shortfall left it just 113 teachers short of its recruitment target for 2012.

By contrast history courses have recruited 75 more candidates in 2013 than the year before, which is 170 more than 2012’s target. The number of primary school recruits has risen from 20,760 to 23,380, coinciding with a bulge in the birth rate which has meant that the sector needs extra staff.

Brian Lightman, general secretary of the Association of School and College Leaders, said: “We’re very concerned about [the shortage of maths and science recruits]. The sort of feedback we’ve got from our heads is that recruitment directly to schools has been very, very patchy across the country.”

Under the new arrangements, schools can either recruit trainees or take on salaried staff who are aiming to switch careers, but Mr Lightman said the calibre of some of those seeking to switch was “very variable”.

“We’re seeing big gaps in recruitment – particularly in the Stem subjects,” he added. “It’s a very big cause for concern considering their importance for the future of the economy and it means that some schools have got difficulties in filling places now.

“One would hope much of this would be about teething troubles that can be resolved.” A spokesman for the Department for Education said that new School Direct scheme – under which teachers train on the job – was “proving extremely popular”.

“By May, around 22,500 people had applied for 10,000 places and applications continue to rise,” he said.

“Of course it is right that headteachers are selective and choose only the brightest graduates best suited to their schools.”

Case study: If you haven’t mastered maths, doors close

Carol Vorderman chaired a report on SATs tests for the Education Secretary Michael Gove in 2011

You wouldn’t want me teaching your child PE or music as I’m pretty useless at both and by the same reasoning I guess you wouldn’t want your sons or daughters to be taught maths by their PE teachers. Or music teachers, or whoever.

Maths has to be taught in a very clear way and cannot be fudged. When taught brilliantly, maths is easy and beautiful. With maths you need a deeper understanding. Mathematics is not just any old subject, it is a language, it’s the language of commerce, industry, finance, science, engineering, the internet, communication and all technology. It’s such an important subject that a First World society cannot afford to teach it to any other standard than first class. Understanding it opens so many doors. But equally, if you don’t understand it, doors will slam shut. But the problems in teaching maths lie much deeper than just a shortage of trainees. Part of the problem is that almost all of those people going into primary school training, as shown by Professor Adrian Smith’s 2006 inquiry, gave up maths at 16.

In a report I chaired for Michael Gove, we found that of those children who achieved Level 4 in their SAT tests aged 11 – Level 4 is the government target – just over half went on to achieve their GCSE at grade C or better. Of those who failed to get Level 4, almost all of them failed. In other words, if you are on the mathematical scrapheap by the age of 11, there you are likely to remain. Secondary school is having little effect on the outcome for these children. My concern is that the potential shortage of qualified maths teachers at secondary level can only compound these problems.

But perhaps the biggest problem is our society’s attitude to maths. It is regarded as “too hard for me” or “geeky”. This is very much a British malaise. We undervalue maths at our peril.