Late last year, Drumduan Upper School received its first government inspection. In an era of merciless performance targets and obsessive testing, any school administrator would naturally feel apprehensive. Drumduan’s head teacher, Krzysztof Zajaczkowski, a working-class son of Polish immigrants who has an instinctive distrust of authority, expected to be shut down. He had not forgotten his last school inspection, 10 years earlier, which he compares to a visit from the Gestapo, and he worried that Drumduan’s radical ideals – no exams, no tests, no hierarchies, no sitting at desks whenever possible – would count against the school.

That is not what happened: the inspectors sat in the classes and watched the students. And if you watch the students at Drumduan, you soon notice they are confident, articulate, highly motivated and respectful. These are, in fact, the words used by the inspectors in their subsequent report. You might even believe the students at Drumduan wanted to be there. The inspectors clearly felt so, but it was when they had retired to an office to confer that Krzysztof, a master of the spontaneous gesture, delivered the coup de grace. He sang to them.

Music is something of a hallmark at Drumduan, where children participate in regular workshops – often on instruments like a wheelie bin – and start each day singing in four-part harmonies. “We were rehearsing in another room, and I said: ‘This song is terrific, we have to show these inspectors,’” Krzysztof recalls. “So we burst into their office – they were a bit alarmed – and I said: ‘I’m sorry, we’ve just got to sing this song to you.’” The song was “Media Vita”, a medieval score of haunting beauty that reduced the inspectors to tears, according to Krzysztof. Bowled over by their praise – he is a man whose emotions are close to the surface – Krzysztof asked if he could give them a hug, probably a first for all of them.

I first heard about Drumduan from the actor Tilda Swinton, who cofounded the school in 2013 with Ian Sutherland McCook, a fellow parent at the Moray Steiner School, where their children were in the same class. The two sought to persuade the trustees there to take on the project of creating an upper school, as students at Moray Steiner must graduate at 14. When that failed, they decided to go it alone.

On our terms: joint founders Ian Sutherland McCook and Tilda Swinton with head teacher Krzysztof Zajaczkowski on the site of the proposed new buildings of Drumduan Upper School. Photograph: Murdo MacLeod for the Observer

“There’s no grading, no testing at all,” Tilda had explained to me earlier. “My children are now 17, and they will go through this school without any tests at any time, so it’s incredibly art-based, practical learning. For example, they learn their science by building a Canadian canoe, or making a knife, or caramelising onions. And they’re all happy 17-year-olds. I can’t believe it – happy and inspired.”

It was this image of “happy and inspired students,” so foreign to the popular conception of school, that brought me to Drumduan. I wanted to see for myself this miracle of happy, boat-building, onion-caramelising teenagers. Tilda suggested I join them on a school trip to the tiny island of Colonsay (population: 120) where, deprived of their mobile phones, the students would be at the mercy of their own initiative. Some activities were planned, including a day studying the island’s protected black bee colony, but the week was left relatively unstructured. Tilda felt it was important for children to have the freedom to be bored. As the only award I ever won at school was for my services as secretary to the beekeeping club, I felt uniquely qualified to join the expedition.

First, though, a visit to the school. It was raining the day I arrived at the £7,500-a-year Drumduan and Krzysztof was in the small staff room battling a cold. He is a genial, square-jawed man of 57, with a passing resemblance to Richard Burton (minus the sonorous voice). He is kind, attentive and a terrific storyteller. In short order I learn that he worked briefly as a roadie for the Sex Pistols, that he narrowly escaped capture after sabotaging GM crops near Inverness and that as a child at a Catholic boys’ school he was soundly lashed for slipping the host out of his mouth during Mass. He’d been told it was a special host, made of Jewish matzo, and wanted to take a closer look. It’s the kind of curiosity that, as a teacher, Krzysztof tends to reward, not punish.

A day later I get to see him in the classroom, interacting with the students. They call him Krzysztof or Krzys (“Chris”), not Mr Zajaczkowski or Sir and there’s an easy interaction that makes the lesson seem more like a conversation than a monologue. When Arran, a pale, quick-witted redhead who likes the German noise band Rammstein, talks about “statism” in a class discussion, Krzysztof confesses the word is new to him. (Arran is happy to clarify: “It’s anarchism’s word for someone who opposes them, basically,” he explains, before apologising for losing the class along the way).

‘They’re all happy 17-year-olds’: songs around a campfire on Colonsay. Photograph: Murdo MacLeod for the Observer

Krzysztof’s aptitude for teaching was as much a surprise to him as to everyone else, given his poor track record as a schoolboy. In the 1980s, he found a job with the Youth Training Scheme and decided to stick with it. Today he lives in a static caravan in the woods.

We take a tour of the school building, little more than a rented back room of the Moray Arts Centre in Findhorn, the famous alternative community on the northeast coast of Scotland. The digs are temporary while Tilda and fellow trustee Ian Sutherland McCook raise money to build a permanent structure, though securing funds for bursaries is their first priority. The classes move seamlessly from indoors to out, the day interspersed with frequent changes of pace. A day later, in a brief interlude between a music workshop and an English lesson I am startled to see the students assemble in formation on an adjoining field to hurl a fusillade of javelins through the air, before quickly dispersing back to the classroom. (Competitive sports are generally frowned upon within the Steiner system, but exceptions are made for those associated with the ancient Olympics.)

Through the windows Krzysztof points to a pair of handsome canoes sitting outside, and fetches a paddle for my inspection. “They were made out of slabs of local Douglas fir, with no machines and no vices, just clamps on desks,” he says. To Krzysztof the boat is a paragon of interdisciplinary education. As he puts it: “You’ve got mathematics, geometry, physics of buoyancy, the chemistry of epoxy resins, the art and aesthetic of colour and shape, the process of collaboration and the physical, outdoor experience of it all.” Of course, you’ve also got a boat.

But there is no A-level exam in boat making, and the question of how these students will make it to university should they wish to go – as, for example, Arran does – is never fully resolved. The students’ work is documented in books that they write and design “to their own best intellectual and artistic standard,” and there’s some suggestion that these can take the place of exam results, but in an education system so heavily predicated on grades, it seems a big ask. There are precedents, however. The Acorn School in Gloucestershire is run along near-identical lines. This year, its students were offered places at universities in Bath, Exeter, Manchester and Bristol. The school claims that no Acorn student applying for university has ever failed to secure a place.

Life class: students sketching on Colonsay. Photograph: Murdo MacLeod for the Observer

Drumduan parents are obviously a highly self-selecting group. Sharon McAlister says she’s not worried by the absence of exams. Her youngest son, Angus, a sparky and genial 15-year-old (“You shouldn’t ask a boy his age,” he jests), spent seven years in the state system, where he was bullied and unhappy, before transferring to Drumduan in 2013. “It’s that wonderful thing of being able to celebrate a burgeoning individualism that you don’t get in a state school,” McAlister tells me. Tilda refers to this as “each chain on each moving bicycle” in contrast to the widespread practice of teaching children as if they’re all on the same bike. “I didn’t have a particularly toxic education, but my chain was not on my bicycle,” says Tilda. “I managed to coast down a few hills and got off and walked the rest of the way.”

Walking her four cocker spaniels across the sweeping expanse of beach near her home in Nairn, she says: “Whenever we have a bit of a distilling of what it is we want these years to be for these young people we end up saying the same thing, which is: ‘Know thyself, number one.’” Her own children are Xavier and Honor, 17-year-old twins. Xavier has his mother’s quietude, Honor her exuberance. They will be in the first class to graduate from Drumduan in 2016. “I said to these two at the beginning of the school: ‘You’ve got three years – just try it all on for size,’” she says. “Honor’s school project is interpretative dance – she’s never done dance in her life.” She grins. “It’s going to be really interesting.”

Earlier this year Tilda helped students secure work placements that covered the gamut from a sporran maker in Forres to a hotshot tailor in London. Xavier, who wants to be a commercial pilot, worked at Inverness airport and flight school. “I would have loved to have done that at that age – go away and be a person,” Tilda says, before calling out to Xavier that perhaps he might want to show me his cockpit. His cockpit? It is a simulacrum of the real thing, incorporating Xavier’s computer and iPad, and a riot of buttons and dials that have been installed mostly for effect, beneath a Darth Vader poster that reads: “Your Empire Needs You.” Given the late hour, we decide to fly from Inverness to Colonsay and Xavier sets the co-ordinates on his flight-simulation programme. A real person, somewhere, gives instructions from a simulated control tower, there is some pilot-to-tower banter, and suddenly we are airborne, looking down on virtual clouds and fields and the ragged, digital coastline. Tilda points to Jura, where George Orwell wrote 1984, and we examine the view as Xavier manoeuvres the plane across the restless ocean.

“It’s quite a gray day, unfortunately,” he says.

Right on song: singing in the youth hostel. Photograph: Murdo MacLeod for the Observer

“It’s like the end of the world,” I tell Tilda, as we sail into Scalasaig harbour on Colonsay. “Or the centre of the world,” she replies, watching the low rocky coast slide towards us, the gorse aglow with yellow flower, its strange pineapple scent fragrant on the air. But there is something else, too, and it has to do with the rare sense of communion within the school.

In the backpackers lodge, perched on a bluff, it is easy to feel I am in the right place with the right people at the right time. I get used to the novelty of watching Tilda sweeping the floor (“I’ve always had this joke with Krzysztof that we’re building the temple and all we do is light the candles and sweep up,” she jokes), and corralling the students. Then there’s the impromptu musical performances, arm-wrestling matches, games of Chinese whispers, morning bowls of porridge and the long walks along the cliffs listening to the students’ freewheeling chatter. They talk of the SNP, vegetarianism, Spider-Man, haggis, whether the ugly sisters were “fit” (“Definitely,” says Angus), why you should never break-dance in a kilt (“Unless you’ve got nothing to hide,” says Cosmo), and, most often, the thrill of Parkour, a sport that seems to unite them all.

“We’re just doing a little chillaxing,” Tilda says one evening as everyone sits around eating wild garlic and nettle soup, the ingredients foraged earlier that day. Chillaxing is, in its way, the purpose of the trip – an opportunity for the students to find a measure of stillness. “We wanted Colonsay and Oronsay to be a settling of all that has happened, a distilling and digesting of the events and the hard work of the year,” Krzysztof explains.

This is the reason for the ban on new technologies and the emphasis on old – the group games, the sing-a-longs, the campfires. Tilda has brought a poem called “Happiness”, by the Gaelic-speaking poet, Meg Bateman. It describes two old friends, crofters “who after a brief murmured greeting, will stand wordlessly together, side by side, not facing each other, and look out on the land, whose ways and memories unite them.” The poem’s sentiment speaks to a hope and expectation that here, away from the mainland, the students will discover the power of silence, not in place of tumult and noise, but as a balance to it.

Of course for teenagers who have learned to make longbows, knives and canoes, a rocky, mossy, grassy island like this is paradise. There is a lot of room to run wild, and they do. Watching the lean, feral boys somersaulting off the dunes one evening, I imagine William Golding, somewhere, rubbing his hands in delight. But he based Lord of the Flies on Marlborough College, his alma mater, where children were bred and bullied to become the repressed defenders of Empire. The students of Drumduan are not they. On their first night in the backpackers’ lodge, overlooked by a giant bison’s head, they drink tea and sing “Media Vita”, while Tilda butters doorstop sandwiches for the next day. At night we listen to the corncrakes in the dark.

Ride the wave: playing in the surf during the school trip to the Hebridean Island of Colonsay. Photograph: Murdo MacLeod for the Observer

We get to see the island’s famous bees on a rare, sunny day, with the island shimmering in the morning light. Andrew Abrahams is a local hero, having succeeded after many years in securing the Scottish government’s backing to have Colonsay and Oronsay declared a sanctuary for his beloved black bee, genetically pure and free of the Varroa mite. When the students hear him talk about the bee’s sad plight, the subsequent debate among them is lucid, smart and illuminating. They dissect capitalism and market economics; they talk about the challenge – and necessity – of creating altruistic societies, and occasionally they come up with a really great idea. Like creating a super bee, which Eliot, the impish daredevil of the group, is sure must already be under way in America. Tilda leans over later, and says: “Don’t you think the world would be a better place if we had a government of teenagers like these?”

Drumduan is still a very small school, just 17 students, so it doesn’t take long to develop an easy familiarity with everyone – which must also be characteristic of attending the school. (Students are encouraged to develop social lives outside.)

I’d suggested to Arran one afternoon that the conundrum with model enterprises like Drumduan was finding a way to grow them without diluting them, to which he shrugged and said, “Why grow them?” Abrahams had told us how bee colonies divide and separate when they get too big, the catalyst for swarms. “I don’t think these things can work worldwide,” Arran says.

I left the island before Drumduan’s final adventure, a crossing of the causeway, from Colonsay to Oronsay, the entire group getting soaked because they’d arrived too late and hit the incoming tide as it swept in. “Lesson number one, time and tide wait for no man,” Tilda tells me later.

Golden time: Tilda Swinton and students collect honey from Andrew Abrahams’s bee hives. Photograph: Murdo MacLeod for the Observer

For eight hours they walk the island in the company of RSPB wardens, yet another lesson in the delicate equilibrium of the planet, and then Krzysztof sets them all a novel challenge: go and find a place, alone, no more than five paces in diameter, and stay there for an hour. An island on an island. Later, I call Angus in Forres, and ask: “How did you manage?” It was boring at first, he replies. “But you had to adjust to a different setting. You had to look at it in a different way.”

Imagine teenagers, taking an hour to be with themselves, no modern distractions, just the beat of their heart, the tick of their brain, the sweep of the sea. The students are asked not to talk about how they spend the hour, but I’m curious, and ask Angus to describe his time. He says he found a space on the sand, and set himself down to watch the waves. “At first, I thought, What am I doing here, but as I sat there, I started to think about lots of different things, like life, relationships, dreams that I’d had, family – I felt homesick at one point, I welled up a little bit, it was quite emotional.” When it was time to return to the group, he found it hard to believe that an hour could be so brief.

Tilda leads pupils through a coastal cave on Colonsay. Photograph: Murdo MacLeod for the Observer

Rudolf Steiner, the Austrian founder of the Steiner schools movement, wrote: “To be free is to be capable of thinking one’s own thoughts – not the thoughts merely of the body, or of society, but thoughts generated by one’s deepest, most original, most essential and spiritual self, one’s individuality.”

We live in an age when people talk endlessly about individuality, but I wasn’t sure I’d ever seen it as clearly delineated as in the contrast between the students of Drumduan with those of more typical schools, like the one where Angus had been enrolled for so long. I remembered his mother’s observation that the pupils there, even on the coldest day, would remove their coats “two miles before getting to school” because someone had determined it wasn’t cool. “There’s so much of a horrible clique to what happens in mainstream education, whereas it’s a safe space at Drumduan to say, ‘I’m into this sport,’ or whatever, and it doesn’t matter that nobody else is doing it.”

I was sad to leave Colonsay before everyone else, sad not to hear the corncrakes at night, or to be able to see Honor arm-wrestle with her mum again. As I board the CalMac ferry back to the mainland, I remember a conversation I’d had with Tilda a few days earlier. We were waiting to board the outbound ferry, licking the grease off our fingers from the battered haddock we’d bought at the Scrumptious Fish & Chip Shop. Eliot had wandered over to ask, hopefully, if there were any dangerous cliffs on the island. Tilda glowered at him, mock disapprovingly, but we were all in a holiday mode, and giddy with the sense of possibility. I turned to her and said: “Departures are wonderful.” She didn’t miss a beat. “As long as you’re going the right way,” she replied.