Researchers Jal Mehta and Sarah Fine want our high schools to achieve deeper learning — an amalgam of mastery, identity and creativity. That means whatever the course, students should be good at it, like it and add their own ideas to it.

Mehta and Fine have spent years seeking American schools that have achieved this. In their remarkable new book, “In Search of Deeper Learning: The Quest to Remake the American High School,” they focus on three small public schools that are among the most ambitious and daunting in the country, and yet welcome average kids.

Are these realistic models for remaking the schools that got most of us through our teenage years? Each of the three campuses is real, but Mehta and Fine followed the scholarly practice of giving schools and staff made-up names so sources could speak freely.

First is Dewey High, a West Coast city campus of 550 students from varying backgrounds driven not by grades or tests but by projects. In a typical humanities class, two 10th-graders proposed distributing condoms in high schools. To make their case, they wrote an informative memo and an argumentative essay, conducted filmed interviews, drafted and revised a script integrating the interviews with other sources and screened the movie during an exhibition night.

The second school is No Excuses High, designed to prepare 600 mostly low-income city kids in the Northeast for college with the most precise and demanding curriculum and teacher training system I have encountered. New teachers spend weeks learning how to present the material. In class, timers often dictate the length of each part of each lesson. Department chairs review results on interim tests and make changes when students fail to learn.

The third school is International Baccalaureate High, a Northeastern suburban school of 800 mostly middle-class students guided by the worldwide IB program. The courses focus on thinking and writing. Each student takes independently written and graded three- to five-hour final exams that, unlike the much larger but otherwise similar Advanced Placement program, rarely have multiple-choice questions.

It is not surprising that all three are charter schools. They are way too far from the mainstream to survive in traditional school systems.

They are amazing high schools. But Mehta and Fine see room for improvement. To them, Dewey is strong on creativity but weaker on mastery. No Excuses is strong on mastery but weaker on identity and creativity. They think IB is the best combination of all three elements. Each school’s choices involve trade-offs.

Mehta and Fine ask an intriguing question: Why can’t classes be more like extracurricular activities? Sports, theater, music and clubs are “not just fun and engaging, but also highly aligned with a powerful mode of learning,” they said. Students can create their own after-school enterprises. Such activities “follow the natural rhythms of their subjects, and they free students from the instrumental mind-set — is this going to be on the test?” the authors said. They found some classrooms that felt like extracurriculars. Students learned by doing and received feedback from knowledgeable classmates and adults.

At Dewey, some administrators worry that too many projects could keep struggling students from mastering literacy. At No Excuses, they worry that having too much control doesn’t prepare students for college’s freer environments.

Students at No Excuses have an impressively high passing rate on AP exams. That’s a significant accomplishment given that the school is nonselective, meaning it doesn’t make students pass tests or clear other hurdles before enrolling, and because so many students come from impoverished families. But several find it too tough and transfer to regular campuses.

The Dewey and No Excuses staffs admire the rigor and writing at IB High, but prefer to stick with what has worked for them. Mehta and Fine said they would want IB High to change its reliance on IB rules so students have more choices, key to the authors’ vision of deep learning.

All three schools are moving in unpredictable directions, to be expected in schools that value innovation. Can they achieve deep learning? Will it work? Next week, I will explain why I think it won’t, and also why I could be wrong.