Quaker Valley High School, in a leafy century-old borough on the Ohio River near Pittsburgh, does not look like a hothouse of teenage academic ambition and curiosity. But it is.

In 2016, one of its students, Gabriel Weiner, took and passed 20 Advanced Placement tests, the most for any boy in Pennsylvania. Last year, 29 of Quaker Valley’s students took six to 14 college-level AP tests each, often after online courses or independent study with little teacher involvement. Some of its students with learning disabilities take AP. The school does not label students as gifted, pays all AP fees and believes in saying “not yet” — rather than “no” — when a student asks to do something many educators would consider crazy.

Letting students fly free is rare in American education. There are plenty of little public schools like Quaker Valley, with fewer than 700 students. But very few — I don’t know of any others — require AP exams of all AP students and let them take so many without teachers.

Taking so much AP improves neither college admission chances nor college success, but students who do it have other reasons. Weiner took nine AP courses in class, two online and had nine more through what the school calls “self-study.” The subjects he studied on his own were European History, Comparative Politics, Physics C (Mechanics), Art History, English Language, Environmental Science, Statistics, Macroeconomics and Human Geography.

Weiner started college at Technion — Israel Institute of Technology in Haifa, Israel. It doesn’t give credit for AP. He transferred to the University of Pittsburgh, where he majors in math and economics. He said high school usually “kills the natural drive to learn” so that “being able to go at my own pace” at Quaker Valley was “much more engaging.”

I first encountered this attitude in a high school student in 1999. She was Stephanie Park of Potomac, Md. Her desire for a future in music or philosophy led her to create, with parental support, her own home school. It included many SAT achievement tests she prepared for without a teacher. She had dreaded the sciences but found she loved researching unresolved questions in libraries.

She is now associate concertmaster of the Sinfonietta de Lausanne orchestra in Switzerland. “People underestimate the power of curiosity, and the capacity a kid has to learn,” she said.

Linda Conlon, the Quaker Valley High academic specialist who handles requests for extra courses, said, “We know we can do even better, but for now, any kid who wants to take an AP course does, and we make sure that anyone we think can is strongly encouraged. . . . We are mindful of ‘too much’ and counsel kids strongly about work/life balance and careful choices.”

Quaker Valley Principal Deborah Riccobelli said, “Student voice and self-advocacy are woven into our culture and are at the heart of how we do school.”

Guillaume Shippee, who took 12 three-hour AP tests at Quaker Valley, said being free to overdo it meant “APs became an opportunity, rather than an obligation.” He prepared with a friend for two of the exams, alternating study with tennis.

Some Quaker Valley students can tap into the adolescent competitive urges that produce champion quarterbacks and spelling bee winners. “I wanted to show that I could do more than anyone else with less effort,” Weiner said.

Many of us remember classmates in college like that. By cramming and remembering earlier courses, Weiner managed passing scores in Environmental Science, Statistics and other subjects, although he almost failed Art History, for which he had to memorize 250 works.

In his first years at Quaker Valley, Weiner’s grades and attitude were unimpressive. But the chance to conquer so many tests inspired him. “The heavy load of APs confirmed what I had taken all of those exams to show — that the American education system fails high potential students by setting the bar so low.”

A New York student once described to me a typical reaction to such ambition. She asked to take AP European History as an independent study so she would have room in her schedule for Chinese. The department chair said: “What would we do if everyone wanted to do something like that?”

Good question. I will have more about academic freedom at Quaker Valley next week. Why can’t schools give it a try and see what happens?