A third of the lessons in England's secondary schools are being taught by people who do not have degrees in the subject they are teaching, an official survey indicates.
Some specialists are in particularly short supply
And almost a fifth of lessons are taught by people with no qualification in the subject beyond A-level.
The Curriculum and Staffing Survey does show an increase of 12 percentage points since 1996 in the overall proportion of full-time teachers who are graduates.
But maths, science subjects and modern languages increasingly are taught by people who have not specialised in the subjects.
The figures show that the proportion of lessons taught by full-time teachers with a degree in the subject they were teaching rose from 42% in 1996 to 50%.
A further 15% of lessons were taught by people with a bachelor of education degree in the specialist subject.
The survey published by the Department for Education and Skills is based on responses from 209 secondary schools - a quarter of those asked to take part - in November last year.
The department says the sample was "stratified" to represent different types of schools such as grammars and comprehensives.
However, the published data do not show that breakdown, so it is not possible to say for example whether there are more specialists in, say, the grammar schools.
Also there is no breakdown of the data within schools.
Anecdotally, school managers focus their resources on the exam years.
So concerns have been raised that lessons in the early years of secondary school in particular - Years 7 to 13 - are more likely to be taught by non-specialists.
The published figures do not show whether this is the case or not.
The leader of the National Union of Teachers, Doug McAvoy, said: "This survey hides more than it reveals. It is a classic example of spin concealing the facts.
"All the evidence is that teacher shortages continue particularly in the core subjects of maths, science and foreign languages. Head teachers are still having to adopt coping strategies to provide a full curriculum."
The survey used to appear every four years but the last one came out in 1996.
Professor John Howson of Oxford Brookes University, who closely follows trends in teacher recruitment, said there was less information in it than in any previous survey of its kind.
The percentages in the survey were meaningless because the numbers underpinning them had not been released.
The Department for Education and Skills stressed that most of the teachers with no more than an A-level in the subject they were teaching were likely to be qualified teachers and graduates in other subjects.
For example, those teaching maths are likely to have a degree in physics or ICT and might teach just one or two maths periods per week - although the survey did not ask this.
"There are also specialists instructors in the classroom. For instance, a computer expert, music or sports coach. These people play a very valuable role in schools and it is absurd to suggest they shouldn't," a spokesperson said.
"Or you might have a teacher from France who has a degree in Spanish. Would you stop them also teaching French?"
'Best generation of teachers'
The Education Secretary, Charles Clarke, said: "Ofsted says we have the best generation of teachers ever and the best generation of newly qualified teachers ever," Mr Clarke said.
"Our pupils can expect top quality teaching in the classroom with further improvement on the way. Change takes time to filter through and I am confident we are on the right track."
In maths, between 1992 and 1998 graduate recruits to maths teaching courses had fallen by 34%, but from 1998 to September 2002 had risen by 50%, he said.
"Maths recruitment is a priority for me and it takes time to turn round but we are getting there."
His Conservative shadow, Damian Green, accused him of complacency, however.
"Tens of thousands of secondary school pupils are being taught by staff not trained in the subject that they are teaching," he said.
"This contributes to the damning statistic that 30,000 pupils leave school every year without a GCSE."
The head teacher of Haydon School in Pinner, north-west London, Peter Woods, typifies the problems schools are having recruiting and retaining staff - even though it is a good school with above-average results.
"Our biggest problem areas are in mathematics and the physical sciences," he said.
"If we advertise for a physics teacher in the national press we will get one or no replies. They simply do not exist."
Two years ago he had had "serious difficulties" with getting mathematics staff.
"This term we're fully staffed. Having said that, we have recruited from overseas - they, in the main, are not trained in this country.
"Some of them are very good indeed but I'm not sure it's due to the efforts government has made."
The figures also show the changing age profile of the profession.
Between 1996 and 2002, the proportion of teachers aged under 30 rose from 16% to 20%.
Those in their 30s was static on 24%. Those in their 40s fell from 43% to 29%.
And those aged 50 or over went from 17% to 27%. A third of chemistry and physics teachers were more than 50 years old.
The general secretary of the Secondary Heads Association, John Dunford, said the increase in mathematics, science and French lessons taught by teachers with no qualification beyond A-level reflected the difficulty faced by head teachers in recruiting well-qualified teachers.
"I am also very concerned at the fall in the proportion of well-qualified teachers in mathematics and science in the under-30 age range," he said.