Whatever the supposed appeal of the job, many potential teachers are probably discouraged from joining the profession by the poor wages, particularly in the middle years of a career in the classroom.
"I have a strong hunch that money is actually an important issue," said Anthea Millett, chief executive of the agency, addressing a seminar at this week's annual conference of the Association for Science Education.
"If it's not an important issue on day one of a teacher's career, it becomes important in the second or third years when teachers look round and see their friends buying better clothes and a better car, when they see that their own salary is not moving them forward in the way they would wish," she said.
Her analysis contrasts with the repeated assertions by government ministers that pay levels are not significant in motivating teachers.
She stopped short of demanding a major salary rise. But others at the conference were not so reticent. Speaking earlier in the week in the Save British Science lecture, Professor Alan Smithers from Brunel University said that science specialists should be given higher salaries and periods of study leave as an incentive to join the profession.
Ms Millett also attacked the bad press given to teachers in recent years. Her own agency has been notably more emollient than either the Department for Education and Employment or the Office for Standards in Education.
"The negative publicity is something we have to turn round in the coming years," she said. "If we want people to enter teaching, we have to talk it up as a profession. If we don't, people won't want to join."
Speaking alongside Ms Millett, representatives from the Royal Society of Chemistry, the Institute of Physics and the Institute of Biology expressed concern at the failure to recruit high-quality specialists.
The IOP's Patrick Fullick, who works at the education department at the University of Southampton, said he has recruited only 12 chemists and 13 physicists this year, in comparison with 26 biologists. This is a shortage of 11 scientists against Southampton's official recruitment target. The problem, he said, is compounded by the shortage of good schools willing to offer training placements for these students.
The shortage of skilled physics and chemistry teachers is a long-standing problem. Apart from the years of economic recession, universitie s have consistently under-recruited on teacher-training courses by 30 to 40 per cent.
After a drastic shortfall last year, recruitment is showing signs of improvement - but only because the target for next autumn's training courses has been revised downwards from 4,000 science trainees to 3,300. This, in turn, is tied up with the Government's attempt to cap the number of early retiring teachers. Maths and science teachers are notably older than the average, and continued levels of early retirement could substantially embarrass the Government in these shortage subjects.
The TTA agrees there is a problem recruiting scientists, but John Howson, the agency's chief professional adviser for teacher supply, says that some other subjects are doing even worse. The 1996 intake of science trainees was 20 per cent short. But technology was 27 per cent short and a third of maths places were unfilled.
To counter the problem, the agency is about to launch a series of advertisements in science magazines intended to appeal to maths and science specialists. The Astronomer General, Martin Rees, and the writer Doris Lessing will be among those who feature, explaining the importance of the teaching profession to the development of their own scientific knowledge.