Flexible or modular courses, which allow trainees to fit their studies around work or family commitments, are also more likely to have vacancies, according to figures released this week.
From January, the Teacher Training Agency will pay graduates pound;150 a week to attend subject-enhancement courses in the shortage subjects.
But plans to fund up to 150 high-achieving maths, physics and chemistry students through university, due to start this term, have been put on hold.
The TTA review comes as the first figures on people starting teacher training this month showed nearly 400 more trainees are doing maths courses - an increase of 35 per cent on last year.
There will be an extra 112 physicists and chemists (total 727), and more than 200 more computer trainees (up to 763).
The number of men recruited to primary training in England has also increased by almost a quarter to 1,294, compared to 7,466 women (up 14 per cent). But Wales and Scotland have fewer men than last year training to teach the under-11s.
Three-quarters of two-year science and maths conversion courses have at least one vacancy, compared to just under half of all postgraduate maths courses and around a third of science courses.
Modular courses are also proving less popular, with 11 out of 13 maths and four out of five science programmes having at least one vacancy.
Mary Russell, secretary of the Universities Council for the Education of Teachers, said the lack of funding for students in the first year of the two-year conversion courses could be contributing to their lack of popularity.
* The number of students starting undergraduate teacher-training courses this term has increased by nearly 6 per cent since last year to 6,323 - despite roughly the same number of applications.
Just over 2,500 students have accepted places on education-related courses, such as early years, which can lead to postgraduate teacher training - up 9.5 per cent on last year.