A few exits north of Beijing Airport, it seems a village has been torn down with no particular plan in mind. Beyond a half-collapsed brick wall lies a rubble-strewn patchwork of foundations – the footprints of traditional single-storey courtyard houses – that stretches on for several hundred yards. At the far corner of the abandoned village is a surprising sight: a tidy quadrangle of red-brick buildings stands behind a wrought-iron fence, looking like the Hollywood set of a school. Against the relentless grey of suburban Beijing, the grass lawns are so green they appear lit from within.

This is Keystone Academy, whose website boasts that the school will nurture the emergence of “the Bill Gates or Mark Zuckerberg of China”, tapping in to the ambitions of the country’s new elite. Such schools are wary of journalists, so I posed as a prospective parent to take a look inside. Keystone Academy is modelled on a New England boarding school, and says it uses the same curriculum as Sidwell Friends, where Barack Obama’s daughters study. It is the brainchild of well-connected private investors, and it charges fees of up to £25,000 a year, roughly six times the per-capita income in China.

Standing in front of a conference table strewn with candy-coloured luxury bags and tablets, the head of admissions explained the benefits of Keystone’s extra-curricular activities, including a swimming programme taught by a pair of Olympic gold medallists. Fathers peered at smartphones; mothers in thick mascara, pressed jeans and rhinestone-encrusted platform Chuck Taylors snapped pictures of the PowerPoint presentation. A woman in a red leather jacket clutched my arm and earnestly told me how lucky I am not to be Chinese.

“You have other choices,” she said. “For us it is just this.”

The “us” she was referring to are wealthy Chinese passport-holders. Since 2005, UK public schools including Harrow and Dulwich College have opened satellite schools in China, but these are open only to students with a foreign passport. Chinese nationals can study an international curriculum at a private school, but only at the same time as they follow the Chinese programme.

In recent years the number of private schools catering to Chinese nationals has grown rapidly. A Chinese-owned chain offering a Canadian curriculum dominates, with more than 30 schools across the country. Schools offering British, Australian and US curriculums are also popular.

An educational arms race has developed. One school has outdoor fields shielded by a football-pitch-sized dome, intended to filter out the Beijing smog. Administrators from elite New England prep schools are installed at private Chinese academies with the kind of pomp usually reserved for the pandas the government donates to zoos overseas.

The people I met at the Keystone Academy open day are in many ways privileged. State schools are so crowded that parents will pay hundreds of dollars to secure front-row seats for their children, in the hope that teachers will notice them. For the children of migrant workers, substandard illegal schools are often the only option.

Yet wealthy Chinese still face a stark choice. They can send their kids to local schools, where young lives are consumed by days and nights memorising enough information to compete with the ten million candidates who sit each year for the gaokao, the gruelling national college entrance exam that a third of all students fail. Or they can send them to one of the new crop of schools, such as Keystone.

Despite the apparent emphasis the private schools place on encouraging free thinking, there will be many questions that students cannot answer, and that teachers won’t ask. Under law, discussion will veer around certain topics. School libraries will not stock history books that mention events that shaped the lives of parents and grandparents: Tiananmen Square, the Great Leap Forward, the famine that ensued. If topics of equality and justice arise, there will be no mention of the wealth accumulated by the families of the most powerful men in the Communist Party. Students will learn subjects such as Chinese handicrafts and dance, but this will not be enough to bind them to their national culture and heritage.

Although the population of school graduates grows each year, the number of pupils sitting the gaokao has remained steady as ever more students opt out. Few private-school students will take their gaokao, knowing that they are unlikely to pass. They will have no choice but to study abroad and return as outsiders. There will be so much they know, yet they will never be allowed to say.