It is an everyday tale of setting up a new school: there is hope, there are dreams, there is misbehaviour and exhaustion. And there is an unexpected romance between the headteacher and the fly-on-the-wall documentary maker who was capturing his every educational move.

Approaching the Elephant, which will be available on Netflix later this month, tells the story of the rise and fall of Teddy McArdle, a progressive school in small-town New Jersey.

For Alex Khost, the school’s headteacher, seeing himself on screen was “extremely exposing”. “It’s like standing in a room and being the only person naked,” he said.

Khost, a website designer, decided to set up a school not long after his son was born. He remembered a book his father had given him when he was a teenager, about Summerhill, the Suffolk school where the rules are famously decided by democratic vote.

“I didn’t want my son going to conventional schooling,” Khost said. “I started looking around for alternatives, and realised there weren’t any. And I decided to set one up.”

Enter Amanda Wilder, an aspiring documentary maker. “I always had an interest in progressive education,” she said. She, too, was influenced by Summerhill: her father had taken her to visit the school when she was 10 years old.

At a conference on alternative education, Wilder listened to Khost talk about his plans for a radical new school, to be named Teddy McArdle, after a character in a J D Salinger short story.

“I thought it would be really exciting to capture it from the literal first day of its existing,” she said. “It’s almost beyond education. It was the idea of starting a community - the beginning of society.”

In the spirit of the new democracy, Khost held a vote on whether or not to admit the cameras. The school community agreed unanimously. “We certainly realised that we were taking a risk,” he said. “But I just thought, go with your gut instinct. What’s the worst that can come of it?”

The film focuses primarily on three members of the school community: Khost, seven-year-old Lucy and Giovanni, a rebellious 11-year-old. Giovanni provides much of the film’s tension: he persistently breaks the rules, and the decision on whether or not to expel him is eventually put to a whole-school vote.

But, primarily, the school’s story is Khost’s story. He had decided not to pay himself a salary and so had to take a night job to pay the bills. Unable to afford childcare, he brought his one-year-old son into school every day. “A lot of people call me idealistic,” he said. “Either idealistic or naive. But I don’t really mind that that was captured on film. I hope it will help other people.”

By the end of two years of filming, the school had failed and was forced to close. But there was nonetheless a happy ending for Khost: he and Wilder are now in a relationship. Khost argues that being observed all day, every day by one’s potential partner is in fact an ideal starting point for a relationship. “We certainly knew each other very well,” he said.