It was a group of older pupils from my son's school, boys and girls, and their subject was swimming costumes, and in particular which parts of their costumes pinched which bits of themselves where, and which other bits of themselves were left to float, loose and vulnerable, in the water.
So free, friendly and anatomically frank was this conversation that I elbowed myself up to look with awe at these relaxed young teenagers.
At their age, I thought, lying back, just about the only contact I had with the opposite sex was the daily jeer, down from the top of our high-school bus, on to the scarlet-faced public-schoolboys below.
For years after I left this school I didn't have a good word to say for single-sex schools, which I felt did nothing to prepare their pupils for the wide blue yonder. But later, confounded by the evidence, I had to accept that perhaps the best thing any mother could do for her daughter was to send her to an all-girls school. Not only did such schools reign supreme in the exam leagues, but it was becoming increasingly clear that co-educational schools let their girls down badly.
At this time, such sentiments - now regularly debated, as they have been again this summer - were pretty new, but I knew more about them than most, since I was The TES's "gender reporter", and spent my working week sifting through the mounting evidence of the inequalities that riddled schools.
Boys dominated the playgrounds, the computers, the Bunsen burners, and teachers' time and attention; men dominated the headships and pay scales. A majority of all teachers, men and women, said science classes mattered less for girls than boys, while girls were less likely than boys to get the remedial help they needed.
Then there was the "30 per cent rule", by which, in matters of sexual equality, one third mysteriously came to equal a half. This applied not only to the boys' public schools, which opened up a third of their places to girls and declared themselves "fully co-educational", but also to the classroom teachers who, when asked to try their damnedest to devote equal time to both sexes, always felt their goal had been reached when they managed to give girls 30 per cent of their attention.
One particular survey from that time, of daily life in nine London comprehensives, sticks in my mind to this day. Girls reported a constant level of harassment. They listed 80 words, many foul, which the boys called out after them. They described erasers being shoved down their blouses and pencils being thrust up through the holes in their science lab stools. And if a girl dared to answer a question in class? "Well," said one girl, "they (the boys) put their pens down, you know, time for a break. If she carries on, they fold their arms, lean back in their chairs and, sort of, look deliberately bored." What struck me most was the tone of shrugging resignation that permeated the remarks of the girls interviewed. That's how life is, they seemed to say; we don't like it, but it isn't going to change, is it?
Happily, 10 years down the road many things have changed, not least in general awareness of the issues, and teachers and pupils alike are now a hundred times more likely to try and stamp on sexism whenever it rears its ugly head.
Other things, though, seem to stay exactly the same and maybe will forever. Now that I'm rearing children of both sexes, I'm discovering that boys, even the gentlest of souls, have quite a different type of energy from girls. They push, shove and shout; and in pursuit of something they want - a rugby try, an idea, the last chocolate biscuit - they barge ahead, seemingly oblivious to anything around them. I'd bet my last dollar that boys still dominate most playgrounds, still shout more in class, and still tie up the majority of any teacher's attention.
Yet I haven't sent my daughters to an all-girls school simply because, when it came to the crunch, I couldn't get past the feeling that, since life is co-educational, schools should be, too. It feels, quite simply, normal.
I know my girls would flourish in a single-sex school. They'd have more friends to choose from, see more women in positions of authority, and never be shouldered aside from a Bunsen burner, or made to wonder if their sporting achievements were somehow second-best. But I don't want them to grow up thinking of half the human race as aliens, or believing that the only way they can make anything of their lives is to be shielded from nasty, rude, distracting boys. Neither do I think it's necessary.
Yes, many girls' schools do splendidly. But, along with Professor Alan Smithers, whose report backing co-education sparked such controversy this summer, I believe this has much more to do with the fact that they're excellent schools, attracting gold-card pupils, than with the simple absence of boys.
And that, of course, is another thing. Boys. Because if you want girls' schools, you have to accept that boys' schools come in the same package. And while the arguments for girls' schools are persuasive, I for one find it much harder to find any good reason for perpetuating all-male institutions.
One of the stories I remember from my days on the gender beat was about how some new science modules, designed to rouse girls' interest in physics, turned out to catch the boys' imaginations just as much. It seems that what improves things for girls, the researchers reported, actually improves things for everybody. Or, as Hillary Clinton put it in Beijing last week, women's rights are human rights.
Or, as the frank and fearless friends at my local swimming pool might have said, more blankly, if I'd asked: "Boys' schools? Girls' schools? What's the point of that?"