Here’s a story we like to tell ourselves. Once upon a time, we were sexist, but then feminism happened and now we’re not sexist anymore. But boys and girls carry on being different because they are different. Male brains are systematising and female brains are empathising, says Simon Baron-Cohen. Boys like blue and girls like pink, say the toy aisles. Men have a “drive for status”, and women have “openness directed towards feelings and aesthetics rather than ideas,” says that bloody Google engineer in his ten-page evo-psych anti-diversity manifesto. And if we are going to live happily ever after, we just have to learn to accept it.

Here are some other stories. “I think boys are cleverer than girls… because they get into president easily don’t they?” “I would describe a girl as being pretty, lipstick, dresses, lovehearts. If a woman has a child, the men have to go to work and earn some money.” “Men are better at being in charge.” “Men are better because they’re stronger and they’ve got more jobs.” All these are things said by year three pupils at Lanesend primary school in the Isle of Wight, both girls and boys, who by the age of seven have thoroughly imbibed the idea that their sex is their fate. All of them are about to take part in an experiment designed to unpick that belief.

That experiment is actually a BBC 2 documentary called No More Boys and Girls: Can Our Kids Go Gender Free? Presenter Dr Javid Abdelmoneim finds that the boys are more likely to overestimate their abilities; the girls, to underestimate theirs. Girls are underscoring on confidence; boys, on empathy. Abdelmoneim isn’t buying that this is all down to hormones or different physiques. At seven, boys and girls are evenly matched for strength, and will be until the testosterone surge of puberty has boys building muscle mass. There are no fixed differences in their developing brains. Genitals aside, they’re simply kids. He wants to see whether teaching the kids differently will lead to them thinking differently.

First, the classroom environment has to change so sex is no longer the first division. Signs are put up affirming that boys and girls are sensitive, girls and boys are strong. The “girls’ cupboard” and “boys’ cupboard” where the children put their coats are repainted as one big gender-neutral wardrobe. Stereotyped books are swapped out for ones about adventurous girls and kind boys. The children have their career expectations shaken up by meeting a male ballet dancer, a female mechanic. And their likeable teacher, Mr Andre, has to change too: he’s trained out of his habitual reference to the girls as “love” and the boys as “mate”, and introduced to a lottery system to break his habit of picking boys first.

It’s the smallness of these things that’s really telling of the hugeness of the problem. Individually, they seem so trivial as to barely seem worth fixing, and so ingrained that trying to fix them takes constant vigilance (Mr Andre’s slips into “love” and “mate” are recorded on a wall chart). No wonder sexism seems to be one of those things that everyone’s against but no one sees as their problem to fix. The head, for example, speaks regretfully of “quite biased views about what boys are expected to do and what girls are expected to do.” But somehow this has never translated into the kind of interventions Abdelmoneim is trying.

Does it work? That’s the cliffhanger for episode two, but the first part suggests some pretty dramatic results. When the children take part in a test-your-strength contest, the difference between expectation and performance lead to tears: a girl who happily cries “I didn’t think I could do it!” about her maximum score, and a boy who predicted himself a 10 but throws himself down on the ground in an angry tantrum when he fails to get a single point. How much stronger might girls be if they didn’t absorb the myth of their own weakness and opt out of physical activity early? How much more resilient would boys be if they weren’t holding themselves up to an unrealistic standard?

We won’t know the answer to that unless adults are able to stop telling the same dull old gender stories to children. In one scene, the documentary reenacts the famous Baby X experiments, showing how adults direct infant play down strictly sex-stereotyped lines, pressing dolls on the baby in pink, and robots and shape sorters on the one in blue. But given the opportunity to be themselves first rather than their sex, the children of Laneseed seem to thrive. In fact, the only reform they chafe at are gender neutral toilets. (“The girls were like, ‘Oh they [the boys] come out with their bits dangling out and they don’t wash their hands,’” Abdelmoneim told the Mail.)

Watching No More Boys and Girls is a strange experience, validating and dispiriting at the same time. Yes, you see the evidence of sexism in action that’s usually hidden in plain sight. You also see that there’s so much of it, it’s hard to know where to begin in countering it. Maybe we should start like this: stop insulting children by pretending their understanding of gender is hardwired at birth, and take some adult responsibility for the world we’ve put them in.

No More Boys And Girls: Can Our Kids Go Gender Free? starts on BBC2 at 9pm on Wednesday.