“It’s all a matter of introduction and exposure,” said Stefan Davenport, director of dining services at Friends Seminary. “Freshly prepared is night and day with frozen.”

At Friends, all the food is made fresh, of course, and more and more of it is locally sourced. Rather than a slab of sketchy beef on a white bun with deep-fried French fries, students are given grass-fed beef burgers on whole-wheat buns, with roasted potato wedges and fresh fruit for dessert. Vegetables are seasonal. The turkey is roasted in-house, as is the roast beef. All of it is nitrate-free, and the cafeteria itself is a certified green restaurant.

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“The student body buys into us supporting local agriculture,” Mr. Davenport said.

Mystery meat is unheard of at the Calhoun School. A pig, killed in Vermont and wrapped in plastic, arrived on Thursday at the school, where students will cut it up in biology class, make head cheese, prosciutto and bacon, among other delicacies, in cooking class, and then eat them.

Lunch on Thursday included whole-wheat penne with pesto, two kinds of squash and a sandwich of tangy chicken salad on ciabatta bread. Students quickly devoured three kinds of apples. “I haven’t gone out to eat all year,” said Carner Round, a sophomore.

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Nine years ago, Dorothy Hamilton, founder and C.E.O. of the French Culinary Institute and a Calhoun parent, suggested that the school hire Chef Bobo, a student of the Institute who wanted to focus his career on feeding healthy food to kids. Now a fixture at the school, Chef Bobo teaches a cooking class, runs a cooking club and blogs his recipes. Next year, he will teach a class in the politics of food.

“A lot of administrators think ‘It’s 30 minutes a day, what difference does it make?’ ” said the chef, known more conventionally as Robert Surles. “The theory here is that it’s part of the learning experience.”

Chef Bobo has consulted with at least a dozen other private schools, and three of his chefs — he has seven at Calhoun, all professionally trained — have gone on to other schools to run their food programs. “I hate to lose my chefs,” he said, “but I love to lose them to other schools.”

Professionally trained chefs and free-range, cage-free organic chicken eggs are not cheap. But neither is private school tuition, and some of the costs are offset by not paying overhead to institutional food providers, school heads and food consultants said.

“Zero-waste zones” are another popular goal, and where there is room, campus gardens and greenhouses are used to fill out the menu. At the Lawrenceville School near Princeton, N.J., Gary Giberson, director of dining and a founder of Sustainable Fare, a food-service company, has eliminated trays and reorganized the food staff so that cooks no longer spend their time scraping the students’ plates. Instead, they prepare entrees like seared pork loin pizzaiola and turkey-and-ricotta piadina with arugula. They are also composting 400 pounds of food waste a day on campus.

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Of course the finest chefs in the world sometimes cannot compete with the teenage desire for freedom. Most private high schools have a take-it-or-leave-it lunch policy — the tuition is the same, regardless — and during one recent noon hour students from Sacred Heart and Nightingale-Bamford could be found at Yura, a cafe on 92nd and Madison. A few blocks east, other private school students and quite a few from Hunter College High School, the prestigious public school, were in the line at the Shake Shack.