To sit by our local pool in Bethesda, Maryland, at swimming-lesson time, as I do every Saturday morning, is to marvel at American ambition, positivity and derring-do. Those qualities are apparent in the enthusiasm with which my children are whooped into the water by their relentlessly upbeat instructors. They are there in the short shrift the instructors give to any whingeing. My youngest was just three when he started at the pool and liable to protest; he got a lot of warm-hearted sympathy, but no let-up. “C’mon dude, stop complaining, let’s get on with it!”

Yet my children’s experience of school in America is in some ways as indifferent as their swimming classes are good, for the country’s elementary schools seem strangely averse to teaching children much stuff. According to the OECD ’s latest international education rankings, American children are rated average at reading, below average at science, and poor at maths, at which they rank 27th out of 34 developed countries. At 15, children in Massachusetts, where education standards are higher than in most states, are so far behind their counterparts in Shanghai at maths that it would take them more than two years of regular education to catch up.

This is not for lack of investment. America spends more on educating its children than all but a handful of rich countries. Nor is it due to high levels of inequality: the proportion of American children coming from under-privileged backgrounds is about par for the OECD . A better reason, in my snapshot experience of American schooling, is a frustrating lack of intellectual ambition for children to match the sporting ambition that is so excellently drummed into them in our local swimming pool and elsewhere.

My children’s elementary school, I should say, is one of America’s better ones, and in many ways terrific. It is orderly, friendly, well-provisioned and packed with the sparky offspring of high-achieving Washington, DC , commuters. Its teachers are diligent, approachable and exude the same relentless positivity as the swimming instructors. We feel fortunate to have them. Yet the contrast with the decent London state school from which we moved our eldest children is, in some ways, dispiriting.

After two years of school in England, our six-year-old was so far ahead of his American peers that he had to be bumped up a year, where he was also ahead. This was partly because American children start regular school at five, a year later than most British children; but it was also for more substantive reasons.

Too many of my eldest son’s maths lessons consist of ingenious ways to relearn what seems obvious. I never imagined there were so many different ways to think about simple addition; but my son could add up already. He loves to read and write. But his English homework consists of exercises in arranging piles of words into groups; he considers it pointless.

At the heart of the problem is an educational ethos that prizes building self-esteem over academic attainment. This is based on a theory that self-confidence leads to all manner of other virtues, including academic achievement, because children who feel good about themselves will love learning – right?

Not entirely. There are clearly advantages to the American approach: I expect my children will be better public speakers than they would otherwise have been. But there is no compelling evidence that self-esteem is linked to actual achievement, as opposed to a woolly feeling of self-worth. In a study of eight countries, American children came top at thinking they were good at maths, but bottom at maths. For Korean children, the inverse was true: they considered themselves poorer at maths than the children of any other country, but were the best. The OECD study, similarly, found that American children believe they are good at maths and, indeed, are adept at very simple sums; but give them something halfway tricky and they struggle.

This is perverse. The self-esteem movement is drenched in the language of mutual respect; yet encouraging in children an inflated idea of their accomplishments is not respectful at all. It is delusional.

Why, you may ask, does the self-esteem culture not riddle American sports as it does American schools? The answer is that it does, in the form of an all-must-have prizes attitude; but competition mitigates the effect of that. And in my children’s swimming lesson, the most important compe­ti­tion is with the water itself. If their instructors had focused on making them feel good about swimming, instead of on making them swim, they could have drowned.