Does it sometimes seem that almost every secondary head you come across is a scientist or mathematician? In these hard-nosed times of targets and delegated budgets, is the lover of spreadsheets and systems triumphing over the touchy-feely, inspirational arts specialist?

Well, up to a point. There are certainly a lot of scientists and mathematicians in top positions. A survey carried out for The TES Magazine by the Association of School and College Leaders (ASCL) found that nearly three in 10 heads or deputies had studied either maths or science.

Of the 642 members who replied, the largest group were scientists. They accounted for 17 per cent of the total, while 12 per cent were mathematicians. Modern linguists accounted for a further 10 per cent. In short, shortage subjects seem to rule.

But some humanities specialisms scored highly too. English, of course, with 13 per cent of the total - although that is slightly lower than the proportion among secondary teachers generally. But historians and geographers scored almost as many, accounting for roughly 12 and 11 per cent of heads and deputies, even though there are relatively few of them in the secondary workforce.

John Dunford, general secretary of ASCL, is a former headteacher and a mathematician. He has a straightforward explanation. “In the late 1970s and 1980s, when people now in their fifties started on their teaching career, there was an acute shortage of maths and science teachers. People like me got promoted to head of department very quickly. By the time we were in our early thirties, we’d already done five years as a head of department and were ready to apply for deputy headships; we got quick promotion. The same applies for modern linguists.”

But hasn’t there also been a shift in the qualities required for the job? Don’t governors look for different skills when appointing a head these days - less rhetoric and more numeracy?

“Of course, skill with numbers is useful once you get the job but I don’t think it’s as apparent at interview as people skills,” he says. And he suggests that heads need a wider range of personal skills now in order to act as leader of a senior management team rather than working in isolation.

Peter Jenkins, head of Ferndale Community School in Rhondda Cynon Taf, has all the personal skills required to energise and inspire staff and pupils in an isolated former mining community. The economist and statistician took only four years after qualifying as a maths teacher to become head of department in a 2,000-pupil comprehensive. He became head at Ferndale in his early forties.

Peter is well aware of how useful his facility with numbers is, especially for timetables and budgeting. “So much of it is figures-driven,” he says. And he can also fill in for the odd business or maths lesson. In seven years as a head, he has taught timetabled lessons for four of them.

Alan Smithers, director of the Centre for Education and Employment research at Buckingham University, thinks it is not just the vagaries of teacher supply that have propelled all these scientists and mathematicians to the top of the profession. There is a basic psychological dimension to it all, he believes.

“At one end of the spectrum, you have ‘people people’,” he says. “In teaching, they are clustered in English, the performing arts and - among the sciences - in biology. At the other end are those who are less people-oriented and like abstract patterns, typified by mathematicians and physicists.

“There’s no great overlap between the satisfaction provided by physics and that provided by teaching so only a small proportion of physicists are attracted to teaching. But they’re really quite well suited to running the whole show. Whereas biologists, who tend to be female, are more interested in people and in teaching in the classroom.

“You need good personal skills to be a head,” he says. “For instance, you need to be able to read non-verbal behaviour. But you also need to be able to take an overview and not be dependent on a close relationship to make things happen.”

What about all those historian and geographer heads, far more numerous than their share of the secondary teaching force (about 5 per cent) would suggest? He puts them in the middle of his psychological range, with the best able to balance people skills and love of systems. He also points out that historians who enter teaching are highly qualified and intelligent people, who have to compete to enter teacher training.

Joan McVittie, head of Woodside High School, a business and enterprise college in north London, must also be somewhere in the mid-range of Professor Smithers’ spectrum. She is a graduate in biochemistry and has taught all three sciences as separate subjects and managed to become a head of department (biology) while working part-time when her two daughters were at primary school. She thinks that numeracy, disciplined working and an emphasis on problem-solving in her science degree have helped her as a head.

She taught science for at least six periods a week in her former headship, but now restricts herself to frequent “popping in” to the classroom. Her outside roles, including membership of the governing council of the National College for School Leadership, make it impossible for her to teach timetabled lessons any more. “I do miss it,” she says.

There is no denying the loss to teaching that all these heads in shortage subjects represent, even if they are valuable role models. As John Dunford remarks, only half in jest, the shortages in maths, science and modern languages could be solved “at a stroke” by sending all the heads in those subjects back to the classroom. But, he adds, they might be reluctant to do it, especially when teaching styles have changed so much. Rather than bemoaning the diversion of rare teaching skills to admin, it might be more productive to stress these heads’ rapid career progression as a way of enticing more trainees into the profession.

As a teacher, a maths or physics graduate may not earn wealth beyond the dreams of avarice, but the promotion prospects are good. The brightest still stand a chance of finding themselves, in their forties, at the helm of a large enterprise catering for 1,000 or more members of the next generation. What could be more tempting?

The specialist one

Paul Harrison loves his subject (modern languages) and still teaches it on and off. “It’s a case of stepping into the breach,” he says. But his removal from the classroom started when early promotion whetted his ambition.

Having made head of department in his late twenties, he remembers reaching his mid thirties and thinking: “I’ve done that - where next?” “Next” was a deputy headship in another school, followed by his present post as head of Teesdale School, an 800-pupil mixed 11 to 18 comprehensive in Barnard Castle, County Durham.

Does he think his specialism has prepared him particularly well to be a head? “If you’ve got to manage a shortage subject, you need to be a bit more creative,” he says. “You may have to manage non-specialists or weaker teachers and that broadens your experience.

He also cites the usefulness of good communication skills - verbal and non-verbal - the self-reliance produced by a year as a teaching assistant in France, and the eye-opening experience of learning about other cultures and education systems, during his gap year and later school exchanges.

A perfect preparation, then. But what about managing the money? Maths and MFL skills are said to be related, he says, and he has a maths A-level anyway. Budgets hold no terrors for him - other than the balancing required.

While careful, like all heads, not to promote his subject at the expense of others, he is determined to keep languages going post-16.

He has devised a successful scheme to do it, partly through e-learning, with a neighbouring school.