Now that the figures which show how many students have applied for teacher training are posted on the Internet, they are pored over as a kind of inverse “Footsie” index. And, as the economy has picked up, gloomy reading they make.

On current figures (table 1), there is likely to be an appreciable shortfall in nearly every subject this year - rising to 43 per cent in maths and 61 per cent in technology - with only PE, primary and, probably, art meeting their targets. As the seriousness of the situation for the Government’s education plans has hit home, the cry has gone up: what can we do to make teaching more attractive? (Short of paying more, that is.) The Government has mounted an expensive advertising campaign. The new Commons education and employment committee made teacher recruitment the subject of its first inquiry. Anthea Millett, chief executive of the Teacher Training Agency, offered her thoughts earlier this month (TES, April 3), suggesting that teacher-training institutions were not doing enough to draw people in.

But it may be that focusing on the attractiveness of the profession is not the best way of framing the problem. It could have more to do with supply lines. Perhaps, as Anthea Millett hinted, there are simply not enough graduates to fill the available training places. At first sight this seems absurd. Degree output has doubled in the last decade, and learned articles are already appearing on the perils of “over-education”.

But consider the figures. The combined targets of table 1 show that some 20,000 graduates (in addition to about 10,500 undergraduates) are being sought for teacher training this year. In order to fill those places, more than one in 10 of all new graduates (excluding those taking teacher-training degrees) will be required.

Tough you might think, but not impossible. However, the global figure includes all those taking degrees in medicine, law, engineering and business studies, as well as the many and various courses that have emerged in modern higher education. Most of these graduates do not want, or would not be qualified, to teach school subjects.

When we look at those subjects, as in table 2, we can appreciate the enormity of the task facing teacher recruiters. It will take nearly half the new maths graduates and more than 40 per cent of language graduates to fill this year’s training places.

If a balance is sought between biology, chemistry and physics in science recruitment, this will take more than half the physics output and more than a quarter of the chemistry output. But it is not only in maths, the physical sciences and languages that the requirement is so large. Teacher-trainers will be looking for nearly a third of English and drama graduates, and about a fifth of history and geography graduates.

In fact, quite high proportions of graduates do go into teaching. This is especially true of women. English, for example, where two-thirds of the graduates are female, experiences less difficulty in meeting its targets than do maths or physics. But even where the interest is greatest it is not enough to fill the training places.

Teaching is facing a deep-seated structural problem. This is borne out by looking at teacher recruitment over time. It is clear from table 3 that science and maths have only met their targets in the years of severest economic recession, and that is also true of other subjects like languages.

It appears that recruitment has never fully come to terms with teaching becoming an all-graduate profession, serving a comprehensive education system. During the late Sixties and early Seventies when there were 60,000 applicants for 40,000 places in the colleges, teacher training tended to be treated as an alternative form of higher education, supplementing the small university system.

Yet many of those successfully completing the courses were, in effect, trapped in teaching because their certificates were not negotiable elsewhere.

Now that teachers’ certificates have become degrees, teaching finds itself competing on the open market against all the other occupations, including a burgeoning service sector.

Against this background, it is doing well to attract as many as it does. But the struggle the admissions tutors are having is evident from the few indices (becoming fewer) publicly available. Table 4 shows that when the entry qualifications of those on PGCE courses were revealed, some subjects were having to take students with poor degrees. The training courses are also having to cast their nets widely to draw in students from related subjects, but even so, many teachers have no post-A-level qualification in the subject they teach.

Given that there is a structural problem, what can be done about it? It has been suggested that the numbers of university places in the national curriculum subjects should be increased, to create larger pools from which the teachers could be drawn. But this is not easy, as the engineers found when the number of places in that field was increased above demand.

As higher education has expanded, courses have spread way beyond the disciplines - the fundamental ways of making sense of the world - that comprise the school curriculum. While there has been an explosion in media studies, design, psychology and business studies, subjects like maths, the physical sciences and languages have remained on a plateau. The situation is similar at A-level.

Since the number of applications barely reaches the places already available in maths, the physical sciences and languages there is little scope in these subjects for improving the supply of teachers by increasing the graduate pool. Something along these lines would be possible in the humanities, but here the need is less acute.

Any structural changes are most likely to have to come from the other end - and hence perhaps the emphasis on attractiveness. But recognising it as a structural problem would at least mean that easy solutions are not sought in advertising, exhortation and scapegoating.

The plain fact is that teaching is now in open competition with other graduate occupations where formerly it was not, and it needs a massive number of graduates. To ensure a continuing supply of high-quality entrants will probably require a major overhaul of the profession - what teachers are expected to do, how they are deployed and what they are paid.

There are more trained teachers of working age not teaching than are serving in our schools - which is telling us something. If only some of those had stayed, then fewer replacements would be needed; and the training institutions would not now be seeking to capture an unrealistic proportion of graduates.

Professor Alan Smithers and Dr Pamela Robinson are director and deputy-director of the centre for education and employment research at Brunel University.