But in visits to two schools, highly-rated comprehensives with flourishing sixth forms and lively teachers, I didn't meet a single sixth-former prepared to train as a secondary maths or science teacher, and only two willing to contemplate life as any kind of teacher in a secondary school. Such anecdotal experience reflects the statistical reality: the chronic shortage of young people willing to train in subjects like maths, science, modern languages, music and religious education.
Like two of her best friends at Saffron Walden, Sarah Ramsey, 17, the daughter of an Essex farmer, exudes the kind of sincerity that should quicken the heart of any jaded headteacher. She is hoping to read English at Cambridge (her A-levels are English literature, history and German), so she needs to get good grades - two As and a B, she hopes. She decided to teach after five weeks' work experience in her former secondary school. "I taught English and drama and I thoroughly enjoyed it. It was that which confirmed that I would like to teach," she says.
The other teacher hopefuls - all female - were set on primary teaching, reflecting the statistics which show there is no problem attracting young women into a career as primary teachers. The pupils I met agreed secondary teaching was off-putting because of pupils' lack of respect for teachers.
By contrast, primary teaching is viewed as rewarding, the children biddable and eager to learn. "You see them progress," says Suzanne Walker, 17. "You see them from when they come in not knowing anything, to when they are leaving, having been taught by you." Her friend Suzanne Cox, 16, agrees. "You can see by their faces that they appreciate things," she says. "I would like to teach children to enjoy education rather than see it as a chore that has to be endured."
The daughter of teachers, Suzanne Walker has always wanted to follow them. "I have done loads of work experience in primary schools which I have really, really enjoyed," she says. She is hoping to get C grades at A-level (her subjects are art, French and geography) and she is looking to Homerton College in Cambridge for her education degree.
Neither Suzanne Walker nor Suzanne Cox are bothered by the scrutiny teaching methods in primary schools are currently undergoing. Nor are they affected by the barrage of criticism from politicians, newspapers and the Chief Inspector of Schools.
And Suzanne Walker knows teachers are swamped with paperwork because she sees what her parents bring home. But it hasn't put her off. Her criticisms of their job pressures are mildly felt: "They're not in the classroom as much as they should be. All that bureaucracy isn't really needed."
Often teachers claim to have been inspired by a particularly good member of staff - but only one of the three from Saffron Walden destined for teaching cites an inspired individual as her mentor. Sarah Ramsey had an outstanding English teacher at her previous school who, she says, was very clever at her subject and instilled enthusiasm. "She was brilliant where discipline was concerned," says Sarah. "And the class loved her as well."
She believes the poor image which teachers suffer should be seen as a challenge for new recruits to do better. "It makes you want to make even more effort to be the best teacher possible," she says.
Several hundred miles westwards, in the countryside outside Bristol in another sun-dappled school - Backwell comprehensive in Avon - another couple of sixth-formers talk about why they want to teach. "I've always been attracted to infants rather than secondary," says Louise Evans, 17, the daughter of a policeman, who is taking religious studies, communications studies and English at A-level and hopes to achieve B or C grades. "I like working with children. It's rewarding."
Seventeen-year-old Harriet Crosse is studying English, theatre studies and religious studies. She is not certain she wants to teach, but is toying with the idea of secondary. "I enjoy all my subjects and I'm quite sociable, " she says. "I like talking to people and I'm quite dominant in group situations. "
As one of OFSTED's "good and improving" schools, Backwell is among the top 20 best performing comprehensives in England and Wales. It is extremely sought after, and one can see why - the proportion pf pupils achieving grades A to C at GCSE was 74.4 per cent last year. Louise and Harriet are heart-warmingly enthusiastic about their teachers - "they are brilliant," says Louise.
They think society does not appreciate teachers enough and that they're underpaid - although all the potential recruits I spoke to believe money is not as important as finding something they really want to do.
Some students who have set their faces against teaching cite money as a problem. Katherine Beadle, 17, another daughter of teachers and a pupil at Saffron Walden who is hoping for As at A-level, has decided teachers don't earn enough respect or enough money. "My impression is that they're always moaning and they're always stressed," she says.
For Sophie Wakelin, 18, also on course to achieve A grades at A-level, the main issue is respect. "Teachers just don't have that from the public," she says. "I think I've been incredibly lucky because I've only had two teachers here I would class as bad and the others have been not average but excellent. And I think for the work they do, the respect they get is minimal."
David Crossan echoes her feelings. The 17-year-old, who is also the offspring of teachers (his father is a member of staff at Saffron Walden), says their status doesn't match their heavy responsibilities. "If students do well, it's because everything's too easy, but if they do badly it's all the teachers' fault. It's not perceived by the general public as being such a highly-respected profession as it was." The Government likes to condemn, he thinks. And the media is always happy to give space to knocking copy and splash headlines.
As a highly-academic student studying four A-levels - English, French, maths and further maths - David is the kind of recruit schools are crying out for. But he has decided he would rather be a sports journalist - a football writer to be precise. Isn't that a waste? That's what everyone keeps telling him, he sighs. He's not too worried about money. It's just that football is his passion. He had a week's work experience at the Independent, "which was very good. I even managed to get a few things squeezed into the paper."
David is thinking of trying for PPE at Oxford (he is hoping for three As and a B) rather than maths, which he thinks becomes too theoretical as it becomes harder. "It's not something I really want to get into," he says firmly. Students see maths as difficult. Ditto science and modern languages. Most fashionable A-levels are psychology and theatre studies.
Cambridge economics graduate Stephen Munday is director of sixth form at Saffron Walden. He admits he entered teaching by default - nauseated by his colleagues' headlong rush to the City on the fat salaries of the 1980s, he embarked on a PGCE, still not certain he would end up as a teacher. He says he enjoys it and believes it has value - and he's wedded to his six weeks' annual summer holiday.
What advice does he give to his sixth-formers? "I tell them to do a subject they like at university and that they're going to do well at," he explains. "I tell people who want to be accountants to go and do a degree in history because what employers want is someone who's done well at a decent university."
He is not surprised his sixth-formers are so concerned with money. "They're reflections of our age," he says. "They're being told that money is everything really."
At Backwell School, Michael Perrin, head of sixth form, is sanguine about the numbers going into teaching. Out of 140-odd students in Year 13 last year, more than 100 went into higher education and out of those, six chose an education degree. There will be others who choose to teach once they have graduated.
Things were much worse in the late 1980s, he says, when applications for teacher training dried up completely. And it is not easy to go into teaching nowadays, - although the latest figures published by the University and Colleges Admissions Service suggest that it is relatively simple to get on to BEd courses. "Entry grades have risen," he says. "There was a time when to do a BEd one might need a couple of Ds or a couple of Es. Those requirements have started to rise. Unless an applicant can show they have a genuine interest in teaching and experience of children, they won't get in." That should be good news for us all.