But I wonder about that confidence. Because the other thing girls seem to be really, really good at, besides passing exams, is making themselves and each other utterly miserable.

All summer, meeting up with friends and family, I have been hearing about girls who are unhappy at school. Or to be more precise, unhappy with themselves at school.

There is the girl who won’t take the school bus because of the other girls who taunt her every morning; the girl who sobbed on the sofa every evening last autumn because she had no friends. There is the tubby girl, desperate to lose weight, and the skinny girl unable to eat from anxiety. There are girls with headaches and stomach-aches; girls who work for hours every night to keep up; girls who have friends who go to the school toilets after every lunch and stick their fingers down their throat ...

Some of these girls are high-achievers in competitive schools, whose tough demands of themselves and the world around them seem bound to cause them grief, but their angst is nothing more than the angst of their peer group writ large. Because, more significant than the kind of school they attend, seems to be the fact that every single one of these girls is in her pre-teen or early teen years, and at the bottom end of secondary school.

I have great sympathy for how they feel because my own transfer to high school was marked by a psychological blip which manifested itself in such stomach-churning anxiety that I ended up off school and, as they say, under the doctor.

To this day I have no idea what it was about. Logic dictates that factors like being, at 10, too young for the secondary school environment must have played a part, but all that remains from that time are a few fragmented memories - an irrational terror of being sick in public, reading the whole of Arthur Ransome’s Missee Lee in the child psychologist’s waiting room, and lagging so far behind on return to school that I puzzled for weeks over the apparent presence of Satan in our French textbook: “What is that, Toto?” “Satan chien” “And what is that?” “Satan chat.”

For any child, the transition to secondary school is a major rite of passage, and however sensitive schools might be to their small fry, however carefully they organise induction days and hand out useful maps, there is nothing they can do to change the facts of this new life - big buildings, older pupils, loads of teachers, and a social web of Byzantine complexity.

When I visited a class of top junior pupils at the end of last term they were already anxious about what loomed ahead. They worried about getting lost, not being able to open lockers, not being able to make new friends and when asked to describe the school they were going to, immediately listed, after the name of the school, exactly how many primary school friends would be going there with them.

But significantly it was the boys who freely acknowledged these fears, not the girls, whose answers were altogether quieter, more dutiful and honed to please. Yet a year down the road, if any of these children are miserable at school, my hunch is that they will be girls not boys. And if that’s the case, I believe it’s explicable. These days we’ve put mere sexual equality behind us and are moving fast towards understanding that men and women are different right down to their brain chemistry and neural circuitry. We know that girls use an additional region of the brain behind the right eyebrow for processing words, and a different part of the brain from boys for processing emotions, and are altogether more intuitive and better able to read subtle facial expressions than boys, who in their turn are better at spacial analysis and mathematical problems.

Add these kinds of perceptual differences to a sea change in the school environment and the lurching moods of early adolescence and you have all the right pre-conditions for a spell of stormy weather.

Because while growing boys seem to be able to continue to look out on the world from some place inside themselves, teenage girls seem fated to gather in perceptual overload, and to come to view themselves only as they are reflected - or as they imagine themselves reflected - back through the eyes of their friends and parents, teachers and classmates.

More and more aware of the world around them, less and less sure of who they are, they all too easily become obsessed by perceived imperfections. They cleave desperately to best friends or reject them savagely, if that’s what they feel their own survival necessitates, or else turn their conflicts inwards and make themselves ill. Balance is nowhere. For the sensitive girl, everything becomes a matter of life for death, whether it’s the end-of-term maths exam, who they sit next to on the school bus or the burning question of whether gothic green or ecclesiastical purple is this week’s nail varnish of choice.

But there’s another thing, too. If you are fated to be aware of the world around you, then you are also fated to come to understand, as childhood ends, that it can be a truly cruel and terrible place.

When I think back to being 10, I can remember nothing threatening or malign about school, but I do remember the shattering impact of watching a television documentary about the Holocaust, and understanding for the first time what those pictures really meant. This summer, coming across my 12-year-old daughter in tears over the ending of the Diary of Anne Frank, I realised that some things never change.

Children transfer to secondary school just as they are undergoing these profound upheavals and if girls take this stage of life harder than boys, then schools need to be aware to this.

They also need to know what to look for, since, while disaffected boys traditionally kick up a lot of noise, miserable girls are often ashamed of how they feel, consider it yet another sign of personal failure, and try to hide it behind a mask of casual confidence.

Which brings us back to this year’s exam results, and how, while it’s great that after so many years of under-performance girls are getting into their full academic stride, we need to remember that no one has higher expectations of girls than girls themselves, and as they work to become ever cleverer - not to mention sportier, slimmer, healthier, better dressed, more ambitious, more popular, more everything - we also need to keep in mind just what these elevated public expectations might be costing them in private.