Major TES survey reveals that four-fifths of heads want governors' role clarified.
Applications from graduates to train as secondary maths teachers are more than 15 per cent down on last year's figures.
The Graduate Teacher Training Registry says that by the end of August there had been 1,765 applications for postgraduate certificate in education maths courses, compared to 2,084 in 1995.
The figures also show serious shortfalls in secondary science - particularly physics, where applications fell by more than a quarter.
Overall, there were almost 500 fewer people applying for any sort of postgraduate secondary teacher training than in August, 1995.
"The situation is obviously pretty dire. It shows no sign of improving to the point that we really need," said Mary Russell, of the Universities Council for the Education of Teachers.
Applications for primary teacher training were up 3 per cent, with an increase in the number of men applying - 93 more than this time last year.This will please teacher-training experts and primary heads concerned about the minimal male role model in many schools.
Women accounted for more than half of the 20,029 applications for secondary teacher training, with 80 more applying for courses than a year ago. Applications from men dropped by 545 to 8,751.
The statistics show decreases across the secondary sector in applications for teacher training in music, classics, the sciences, maths, business studies, CDT and home economics.
In maths, institutions have so far accepted just two-thirds of those graduates applying for places.
Geology was the hardest hit of the sciences, with a 40 per cent drop in applications. Less than a third have been accepted. Physics had a 26 per cent decrease, chemistry a 10 per cent drop and biology, 8 per cent. Two-thirds of the applicants to each subject have been accepted.
Subjects enjoying increased applications were art (up 26 per cent), drama, history, RE (13 per cent), French, modern languages, economics, PE and computing, which rose by 135 per cent.
Applications for secondary English teacher training remained stable at 2,783.
Ministers have asked the Teacher Training Agency to recruit 50 per cent more secondary teachers and 34 per cent more primary teachers between 1995-96 and 2000-01.