Sadie, a 16-year-old high school junior in Harpswell, Maine, felt off-kilter in her American high school – too much memorization, not enough relevance to hands-on work in prospective careers. “I know it doesn’t have to be like this,” she says of her school days in The Smartest Kids in the World, a new documentary on international educational systems. Brittany, a junior outside Orlando, Florida, spends hours on homework but finds her curiosity unchallenged. “I kinda just wonder … what are we doing?” she muses. Jaxon, 16, from the small town of Saratoga in south-eastern Wyoming, finds himself torn between wrestling practice and sleeping two extra hours before his ACT, where one point marks the difference between free college tuition and $30,000 a year. “It’s only my life,” he shakes his head, “practically, everything in it.”

The three students are among the many, many high school students whose education is handicapped by the diffuse, disparate and often dysfunctional American education system. The US spends more than almost any other country per student, but that does not translate to results; according to the National Center on Education and the Economy (NCEE), the average student in Singapore is 3.5 years ahead of her US counterpart in math, 1.5 years ahead in reading and 2.5 in science.

They’re also among the handful who experienced something different; The Smartest Kids in the World follows four US high school students as they spend a year abroad in countries who routinely outperform the US in the basics of education – South Korea, Finland, Switzerland and the Netherlands.

The film, based on the 2013 book of the same name by Amanda Ripley, a contributor to Time magazine and the Atlantic, highlights the numerous shortcomings of the American education system by contrast, through the eager, at times overwhelmed eyes of four students so frustrated with their stagnation in school that they leave home for a year. “It’s a lot at stake,” said the film’s director, Tracy Droz Tragos, of the formative, fragile period that is late high school, as the paths ahead – university, community college, employment – crystallize.

The film outlines both models for change while observing “the tragedy in having hungry hearts and minds who really do want to learn and are being denied a decent education”, she said.

Ripley, who appears in the film, and the students’ frustration outline a host of quirks and concerns now baked into American secondary education: the prioritization of standardized test scores, which often ties to funding; the belief that hours of homework equates to learning; the one-tracking of students to universities, the top of which are insanely competitive and prohibitively expensive; the devaluation of technical schools and, in terms of salary and training, education as a profession; the expectation that under-staffed and strapped high schools act as social services; the close integration of athletics with academics, which can defuse focus.

Ripley’s book, and the film, do not attempt to make top-down or cultural arguments about these issues; both instead enlist “field agents” – American students hungry for a new, more challenging educational experience who can act as viewers’ eyes and ears on the ground in other educational models. “The students are there every single day for a lot of their waking hours,” said Droz Tragos. “They’re going to have some insight” on “what’s exciting to them, what’s useful to them, what makes sense now, and it’s not always going to be things that you can look up on your iPhone.”

The four in the film each grapple with culture shock, homesickness, expectations both thwarted and succeeded. Jaxon, from Wyoming, breezes by in a school that generally prizes athletics over academics (on in-season Fridays, enough students skip for competitions that the school is forced to shut down completely); he seeks a challenge in the Netherlands, but is so overwhelmed by his inability to keep up that he ends up leaving the program early. Simone, a 17-year-old striver from the Bronx, feels stifled and ignored in her American school; she seeks a community focused around academics in Seoul, South Korea, consistently the top PISA-test scorers in the world. Brittany, from Florida, is intrigued by the educational success but relatively lax attitude toward homework in Finland. And Sadie, who was home-schooled until high school, searches for a more hands-on educational approach in Switzerland.

Droz Tragos filmed sporadically in each country over the course of 2018 and 2019, and witnessed a “totally different” baseline from US schools in each. “It wasn’t that school was a babysitter, it wasn’t that people were afraid for their safety and that there were guns and metal detectors, it wasn’t that students were made to show hallway passes and get bathroom passes,” she said. “There’s a lot of stuff that we still do just as a weird baseline that was not a reality in any of these other places. And to see when that is lifted, what that looks like, is pretty powerful” both in the opportunities afforded to students and how disorienting other countries’ assumptions of competence and autonomy were for the Americans.

If there is one thing she could change immediately for US schools, she said, it would be that autonomy – for students to “be given some amount of freedom, to be given some amount of responsibility to come in and out of a classroom, to have lunch in a sunny park two blocks from your school”. Many US schools resemble a lockdown – students barred from using the bathroom without permission and a pass, no ability to leave the premises, punishment for attendance violations. Relative freedom of movement and scheduling is a “huge gift that changes somebody’s mentality,” said Droz Tragos, while feeling trapped “just takes all the inspiration, the curiosity, the sense of being capable” away from learning.

The Smartest Kids in the World does not offer a paean to other models; South Korea’s hagwons, extra-tutoring academies for a make-or-break test that stretch hours into the night, appear to stress Simone’s friends and make it more difficult for her to build relationships, for example. Nor does it reduce test outcomes to cultural stereotypes. The film instead observes, then summarizes, lessons from each model. South Korea demonstrates the power of valuing knowledge as a country’s most important resource, one to be cultivated and treasured; in the Netherlands, difficulty and the opportunity to fail provide opportunity for growth – with support, kids rise to the occasion. Switzerland’s vocational track, as rigorous and valued as its academic path to university, models the power of options. And Finland, where teaching schools are as difficult to get into as MIT, offers a vision in which instructor quality matters over quantity, and the autonomy afforded to students – freedom to leave campus whenever, little supervision – pays dividends in attendance and enthusiasm.

The throughline for each is trust in the students’ eagerness to not waste their time, and to be the arbiter of their own educational experience. “You can get lost in policy,” said Droz Tragos, “but if you bring it down to: what does it feel like on that first day of school? What are these kids coming in with? Big hearts, big ideas, a lot of hopes and dreams.

“The hope is in their hope,” she added.

While the film can’t provide a complete blueprint for a new model, it does offer “a starting point to say, ‘OK, some people around the world have figured out some things that we could be inspired by,’” said Droz Tragos, “‘and let’s at least commit to coming back to the table and including students at that table when we figure out what we could do differently.’”

• The Smartest Kids in the World is streaming on discovery+ from 19 August with a UK date to be announced