Phillips Exeter Academy, which we recently named the most elite boarding school in America, has a reputation as a “feeder school” – a school that sends a high number of students to Ivy League universities. As I drove to the quiet town of Exeter, New Hampshire, I expected to hate it.

Before arriving on campus, I imagined the quintessential boarding-school stereotype – Vineyard Vines-wearing, silver-spoon-fed teenagers crumbling under academic pressure, bragging about their college acceptances, and sneaking off into the woods to get high.

But I spent the day as a student in “the bubble”, as students call the Exeter community, and it was nothing like I expected. I never wanted to leave.

Only 19% of applicants are admitted to Exeter every year. To apply, students submit testing scores, essays, and their middle-school principal’s recommendation. These flags represent where current students come from, and the pins show the hometowns of applicants for the Class of 2019.

I arrived on the Phillips Exeter campus at 8am the day after a Nor’easter. Heavy rains had wiped out most of the autumn foliage, and students in their LL Bean boots sleepily filed out of the dorms, headed to the first class of the day.

Melia Robinson / BI Melia Robinson / BI / BI

My day began inside McConnell Hall, an all-girls dormitory in the centre of campus, where Jeanne Olivier was assigned to show me around. Olivier, captain of the girls’ varsity crew team at the time, also served as a hall proctor, a leadership position designated to seniors who act as liaisons between students and the dorm’s faculty advisers.

Melia Robinson / BI Melia Robinson / BI / BI

A majority of the boarding students live in single rooms. As they get older, they earn nicer rooms with better views in the same building. They also get later curfews.

Faculty members must live in private apartments in the dormitories or residences next door for a minimum of 10 years. Math teacher Gwynneth Coogan lives with her family in a house behind McConnell and Cilley Halls, and often invites her students over for dinner.

These live-in teachers double as the residents’ academic advisers and mentors. They know if you stay up too late, if you make it to sports, and probably if you’re dating someone. If you want to have a guest during nightly visiting hours, you must ask permission of your and your guests’ faculty advisers; the door stays open and “three feet must be on the floor at all times”.

Melia Robinson / BI Melia Robinson / BI / BI

At 9.50 the bell tower rang, signalling the start of Assembly. Twice a week, all 1,085 students gather in the Academy Building to share in a cultural experience, often an outside speaker or performer.

Students heard from Class of 1945 grad Milton Heath Jr, recipient of the John Phillips Award. He reminisced on glee club, living in Wentworth Hall (which prompted the Wentworth residents in the balcony to echo “Wentwooooorth!”), and how Phillips Exeter prepared him for life at Harvard and Columbia Law.

Assembly ended – but not before faculty reminded us that the next week “Breaking Bad” producer and alum Stewart Lyons would speak – and students scurried off to class. I took notice of the dress code: boys wear shirts and ties, and girls wear pretty much anything appropriate. Jeans are okay.

In a 300-level social-ethics course, religion teacher Russell Weatherspoon took a seat at the round table and said: “Where do you want to start?” Within minutes, students were batting around text citations, asking open-ended questions, and leading the discussion without interference. No one raised hands.

In the 1930s, the school established a model of teaching called the Harkness Method, which places students in charge of their own learning. There is no lecturing. “This is really asking the kids to think about the material, come back, and engage with each other,” Weatherspoon says.

When Weatherspoon first sat in on a Phillips Exeter class in the 1980s, he says he’d never seen anything like it in all his years of teaching. He joined the faculty in 1987 (most faculty I met had worked there for 20-plus years) and later served as dean of residential life and of multicultural affairs.

In any class, the instructor and 12 students sit at an oval-shaped table, called the Harkness Table. Some teachers will map the conversation flow on a diagram to identify who hogs the discussion and who needs encouragement to find their voice.

“Exeter teaches you more than talking,” one student tells me. “It teaches you to listen.”

I encountered Harkness tables all over campus. They were in the Phelps Science Center, which also housed taxidermy exotic cats in every lab …

… and a breaching humpback whale in the atrium. Philips Exeter students and instructors helped extract the skeleton when it washed up on a Cape Cod beach in 2000.

A Harkness table stood in the art studios, where I found this mixed-media canvas. It was a paint-by-numbers of sorts, using jelly beans and a hot-glue gun.

A makeshift Harkness table took shape in the choir room, where a music class was underway.

At 1pm, all students and faculty converged at the dining hall. I joined an eclectic and outgoing group of students, all of whom introduced themselves to me by their name, hometown, and residence hall, as that is just as central to their identity.

Lunch is included in the tuition fee and served buffet-style, with cuisines from around the world represented. The menu changes with the seasons, and the kitchen sources one-third of ingredients locally. The individual chicken potpies and sticky-sweet honeycomb looked delicious.

The sit-down meal gave me time to get to know some students. Kevin Zhen, at the time a junior and Student Council member from Miami, Florida, receives full financial aid. Over the years, he says he’s encountered endless generosity – indicative of the school’s motto, “non sibi”, or “not for one’s self”.

When a flight home for the holidays was cancelled, a peer gave him a ride on her family’s jet. When his winter boots broke and money was tight, his financial-aid adviser bought him a fresh pair. Zhen says his school is far from “elitist”. In fact, a “goodness” campaign asks students to record one act of kindness every day.

I noticed the students often police each other on sounding snobby. The crew laid into then Student Council President Benj Cohen, from Allentown, Pennsylvania, for his Vineyard Vines and Polo Ralph Lauren ensemble. They also quickly dismissed a residence hall’s annual invite-only dinner, in which lobster fettuccine is served and white tablecloths are used, as “not the norm”.

Student Council Vice President Emily Lemmerman, who was a junior at the time, said her school is very progressive in the way it confronts the stereotypes. “We try to be ‘meta-cognitive’ about it. You know, everyone wants to go to that dinner party. What does that say about us?” she said, having attended once before. “We talk about it. And really, it revolves around free food.” Everybody laughed.

After lunch, it was back to the classroom. Instructor Becky Moore began her 200-level English course with quick games, one involving clapping hands and one challenging students to recite the alphabet as a group. No one person could say two letters in a row, and if two people talked at the same time, the group had to start over. It began, “A, B, C,” and so on, at random …

… until the students reached a standstill. Finally a small girl wearing glasses piped in. Why the lull? A student explains: “Hillary was the only one who hadn’t spoken yet, so I knew not to talk.” Moore, who’s taught here for over 24 years, says the game mentally prepares students for discussion, reminding them to attend to everybody. Then I realized I hadn’t heard one student talk over a peer all day.

Universal free period began at 3.30pm, and the Phelps Academy Centre filled with study groups and kids hungry for a snack at the mini-market.

Others attended a South Indian music and dance performance in the David Dance Studio. Phillips Exeter offers 90 student organisations, from a fair-trade club to “The Exonian” school newspaper to a North Korea human-rights-advocacy group.

The library, a nine-storey work of art designed by renowned architect Louis I Kahn in 1965, was also hopping. It provides access to 260,000 print and electronic volumes, and we hear from an anonymous alum that it’s a popular meet-up location for couples.

Late afternoon rolled around and that meant sports. Phillips Exeter requires students to participate in a physical-education programme four days a week. Luckily, students have 60 varsity and junior varsity teams in 20 different sports, as well as intramural clubs, to choose from.

Football is, of course, the hallmark of the school’s athletics programme. Its rivalry with Phillips Academy Andover, a Massachusetts boarding school also founded by the Phillips family, spans 137 years.

Over the last two decades, Coach and Director of Athletics Rob Morris has shaped the Big Red team as one of the most consistently successful football programmes in New England. He believes strongly in football’s ability to teach life lessons.

As I returned to campus from the athletic fields, exhausted and feeling enriched, I crossed over Hill Bridge, a modest arch over the Exeter River. Jumping into the cool, murky waters below is perhaps one of the most cherished senior spring traditions. They are kids, after all.