The show is over and the screaming starts. Close your eyes and the reedy cries of teenage girls suggest the finale of a Red Hot Chili Peppers concert. That would be wrong. Instead, this is last Wednesday's performance of  Hedda Gabler at London's Almeida Theatre. Hedda, it is true, has messages for the PlayStation generation or, at least, its detractors. Born bored, as John Osborne put it, she is the pampered rebel who places her dangerous dreams at the centre of the universe. Give her an iPod, a double vodka and a slot in Heat and she would seem a modern stereotype. But Hedda is not Britney, any more than Henrik Ibsen is a natural contender for  Sugar magazine's gallery of 'lads who turn us on'.  So why the enthusiasm for fusty playwrights and Norwegian parlour tragedy? It's obvious really. The girls in the audience were a busload of Welsh pupils doing drama A-level. That makes them typical of a new breed of teenager, with  Teen Vogue in one hand and Ibsen in the other.  The demystifier of this tribe is Peaches Geldof, the 16-year-old daughter of Bob and Paula. Following a wave of pre-publicity, her one-hour documentary,  Teenage Mind, will be shown tomorrow night on Sky One. It is a film that every nervous parent should watch.  To explore what it means to be a teenager in Britain today, Peaches meets an advertising executive, a neuro-scientist, a sociologist with a nose ring, geeky tree-huggers (too uncool for her), a northern street gang (too antisocial), some chavs and rude boys, plus many of her own friends. The result, though varied, may contain too many 3,000-a-term accents for some tastes.   Then there is the precocity. At roughly the age when the new Pope was square-bashing for the Hitler Youth, Peaches has become a fully hatched opinion-former. Luciana Berger, the 23-year-old student who has been denouncing anti-semitism and rumours that she is Euan Blair's girlfriend, looks like Betty Boothroyd in comparison.  Both Peaches's youth and pedigree have prompted some media gloom. One newspaper profile hints nastily at similarities with her mother, but that is horribly unfair. Peaches is a droll observer and her film is an intelligent assessment of whether adolescence is chiefly a social construct or a hell imposed by unformed brains and unruly hormones as well as unreasonable old folk.  In addition - here's the bit for the nervous parents - she offers the sort of guidelines that adults try, often vainly, to impose by bribery, imprecation or edict. No to drugs, drink and eating disorders. Yes to pizza, homework and always telling your dad where you will be.  In Peaches's world, sketched out in her documentary and newspaper columns, teenage girls are diligent, if screwed up. ('When you reach 14, dieting is a way of life,' sighs Peaches.) They didn't think much of Pawlikowski's film,  My Summer of Love (arty lesbianism for grown-ups) but loved Thirteen (underage Hedda Gablers on substance-abusing self-destruct mission). Yes, teenage girls are the victims of a sexualised consumer society and of parents who expect them to morph seamlessly from 'peeing dolls' to adulthood.  And, yes, teenagers have sex. Peaches doesn't talk much about that (too embarrassing) but is all for sex education in teen magazines. The inference is that if your daughter is mature and well-informed enough to avoid pregnancy or a sexually transmitted disease, then what exactly is your problem? This sounds like a snapshot of teenage life recognisable   to most girls I know, though it will sound bizarre to some adults. Many prefer an Ibsen-style narrative and we are not talking dolls' houses here.  Surveygirl, the birth child of magazine polls and government statisticians, has grim prospects. She is either skeletal or designed along the lines of Andrea Dworkin. Her parents don't talk to her about sex and she may, like 22 per cent of 14-year-olds, have slept with a boy. If so, she was probably drunk on the first occasion (60 per cent are) and unlikely always, if ever, to have been protected by contraception (65 per cent aren't).  She might have been beaten by a boyfriend. Almost half of teenage girls think it's sometimes all right for boys to be violent, and 42,173 in the 15 to 17 age band got pregnant in the last recorded year, a tiny drop but astronomical still. Surveygirl's small sisters are already primed for mental illness or the depression that afflicts nine out of 10 teenage girls. An Australian study of five- to eight-year-olds found that half were thinking of dieting, which makes Peaches's 14-year-old weight-watchers sound almost menopausal.  Whether you buy the doom or go for Ms Geldof's sunnier view of adolescence, the consensus is that teenagers need some help. Whatever that package might comprise, it is barely visible in an election campaign which has failed to register their presence in 'hard-working families'.  Both Labour and the Tories are desperate to beguile the very young and old. Beyond the cradle, and before the grave, the state can barter benevolence for votes. Young teenagers, stuck in the middle with no suffrage, get little but a yobbish reputation. Yet, on the election trail outside London, the pensioners who are supposed to be terrified are pleading for more leisure centres for young people.   For months, youth services have been hanging on the government's green paper on youth, due out last year and overtaken by the election. A leaked version suggests scrapping the under-funded Connexions scheme, a sort of SureStart for teenagers, plus smart cards with discounts for activities, an administrative shake-up and not much extra money. Imaginative possibly, but hardly a revolution.  Teenagers deserve better from politicians. They need a catch-all education system geared to fine vocational training as well as university. They need compulsory school sex education with a parental opt-out only on grounds of faith. They need sports grounds and meeting places in every town and they need parents who can better decipher the people behind the hype.  Ms Geldof's message, if I have read it correctly, is that adult laments for squandered innocence are not only self-indulgent. They are also a foolish misunderstanding of how appearance changes almost nothing. Childhood is still childhood, even if it comes dressed in plunge-neck Lycra and Bad Girl eyepaint.  The other thing adults rarely see is that both studious sophisticates and girls risking their health for bad sex may actually be too unrebellious for their own good. Ninety four per cent of teenage respondents told a magazine that they want to be married by 25, and there is a growing evidence of a retreat to babies, domesticity and a dependency on male breadwinners.  Maybe these born-again traditionalists don't want to be like their mothers. Maybe they crave security in a society where freedom comes tempered with neglect.  Either way, it is worth heeding the teen gurus. Henrik Ibsen knew all about the dangers facing desperate housewives. And Peaches Geldof will be smart enough to realise that her success as a teenage visionary owes a lot to adult blindness.