August 1963. Little Stevie Wonder (as he was then) had the No 1 spot on the US Billboard Top Tunes chart with his song Fingertips Part II. The second spot belonged to Allan Sherman, a singer-songwriter who remains almost unknown outside America.

Sherman was an enormously talented parodist who rose to fame on the back of his first album, My Son, the Folk Singer, a collection of humorous songs about Jewish life in America.

It was his 1963 hit Hello Muddah, Hello Fadduh that made Sherman a national hero. Americans from all walks of life could relate to his song about a boy’s first experience of summer camp. Set to the melody of Ponchielli’s Dance of the Hours, it begins:

Hello Muddah, Hello Fadduh

Here I am at Camp Granada;

Camp is very entertaining,

And they say we’ll have

some fun if it stops raining.

The boy goes on to list the calamities that have befallen his friends until suddenly in the final verse it stops raining: “Playing baseball, gee that’s better. / Muddah, Fadduh, kindly disregard this letter!”

The fascination that the ritual of summer camp holds in US culture does not translate easily across the Atlantic. But believe me when I say that over the past month more than 11m children and adults have packed their flip-flops and headed to the hills.

At Camps Runamuck, Itchabite and Half-Blood they have been performing the sacred burnt-marshmallow ceremony. In some of the pushier places they are no doubt polishing their Mandarin, too. By contrast, only a few thousand hardy souls can be found at their British equivalent.

US summer camp may look like a shorter version of boarding school, but one would lump the two together only in the way that tomatoes are technically fruit. Summer camp is many things but it is not school.

It is more of a process than a particular place, one that’s designed to instil confidence and resilience. This is why summer camps live on in the part of the American imagination that helps to form its collective identity. Like baseball caps and air-conditioning, summer camps belong to the part that unites rather than divides.

Take a handful of movie cult classics and chances are at least one of them will be set in a summer camp: Friday the 13th, Race For Your Life Charlie Brown, The Parent Trap, American Pie 2, Addams Family Values, Meatballs, Moonrise Kingdom.

Summer camp alumni include just about every American you have ever heard of, including President George W Bush (Camp Longhorn in Texas), Bob Dylan (Herzl Camp in Wisconsin), Bill Clinton (music camp in Arkansas) and Robert Downey Jr (acting camp in New York).

Even I, Little Miss Prissy Pants living in Los Angeles, went away to camp as a child where I learnt kayaking, Kumbaya and how to fall off a horse. Particularly the falling bit.

There are two reasons why summer camp works particularly well as an American institution. The first is the obvious one: the idea that all US citizens are bound to one another and to the flag by a social contract.

The notion that the governing and the governed can form a state that serves the will of the people has its origins in antiquity. All democracies require this theoretical exchange between effort and power. In America its violent founding required the exchange to become real as citizens laid down their arms and worked to create a new country.

Learning the value of teamwork and community was built into the ethos of summer camps from their beginning, in 1861, when William Frederick Gunn and his wife, Abigail, took a group of schoolboys for a two-week stay in the wilderness.

By the 1890s, when the first charitable summer camps were coming into existence, there was no question in anybody’s mind that the teaching of civic virtue was as important as children having fun.

William George, a New York philanthropist, went so far as to claim that his children’s camps were recreating “our glorious republic in miniature — our Junior Republic”. By the mid-1920s the belief that summer camp was an indispensable tool for forming good citizens was so widespread that Charles W Eliot, a former president of Harvard, reportedly declared that it was “the most important step in education that America has given the world”.

The other influence behind the popularity of American summer camps is more subtle, however. It concerns the oldest social contract of all, the one that formed in the first settled communities 9,000 years ago, when neither king nor assembly held sway. Its basis is trust rather than power.

In Catalhoyuk, Turkey, the largest and oldest Neolithic settlement in the world, archeologists discovered that the inhabitants expressed this trust through their children, sending their offspring to be brought up in non-related households. Separated but not exiled from their parents, the children learnt to understand the different ties that bound them — familial, clan and community — and the expectations that came with each.

In modern times the deep-seated trust that Americans have in their compatriots is often mistaken for simple-minded patriotism. But it is faith in their shared values that enables them to stand unflinching in the crosswinds of different cultures and ethnicities.

All those fireside councils, capture-the-flag contests and sporting challenges really do work some sort of magic on young minds, as does the tradition of training the older children to become camp counsellors to the younger ones. Summer camp performs a service that goes far beyond depriving children of their PlayStations for a few weeks.

As for me, I haven’t been near a canoe or a kayak since I was 12. I would sing Kumbaya now only if national security were at stake. But I do have a treasured photograph that has moved with me from house to house and country to country.

It shows a girl in pigtails performing a simple circus trick. Her arms outstretched, she stands erect on a moving horse.