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In their brave search for depth in American high schools, scholars Jal Mehta and Sarah Fine suffered many disappointments.

In one 10th-grade class reading Shakespeare’s “Romeo and Juliet,” the students were asked to draw swords next to lines about hate and hearts next to lines about love. Only three of the 18 students appeared to be marking anything. “C’mon, you guys. . . . Okay, I’ll give you a freebie,” the teacher said. He read another line and ordered them to “draw a heart there.”

At another school, Mehta and Fine found a science course in which ninth-graders had spent three class periods sewing stuffed-toy versions of endangered animals. The plan was to sell the toys to raise money for advocacy organizations of their choice. When asked what they learned about science or extinction during those periods, the students had little to say.

Such time-wasting might not be so surprising if these had been visits to random schools, but the researchers were looking only at top public schools with reputations for rigor and 21st-century learning. Undeterred, they spent 750 hours observing classes, interviewed more than 300 people and produced the best book on high school dynamics I have ever read.

Much of it is depressing, as these examples show. But Mehta, of the Harvard Graduate School of Education, and Fine, of the High Tech High Graduate School of Education and the University of California at San Diego, managed to find a few high schools that have come close to the mastery, identity and creativity the researchers define as depth. Interestingly, those are not schools that admit only the best students.

This column is about the frequent mishaps Mehta and Fine exposed in their 446-page book, “In Search of Deeper Learning: The Quest to Remake the American High School.” I will do a second column about the three high schools that yielded the best evidence of how to teach students deeply, and a third about what chances other schools have to make similarly radical improvements.

I have two problems with the book that, fortunately, did not get in the way of its convincing detail. Like most such work by scholars, “In Search of Deeper Learning” does not identify the schools it describes. That makes it easier for them to get the most revealing and disturbing information, but journalists like me would prefer to know what these places are so we can check the facts. I also have much less faith than Mehta and Fine do that average high school students will ever be mature enough or average teachers skilled enough to achieve the depth the authors crave.

Nonetheless, their classroom observations are startling. “In an English class,” they said, “a teacher might ask students about themes or symbols they noticed while reading. But once students began to respond, teachers would appropriate the early shoots of what students were trying to say (often only a few words) and incorporate them into their own longer comments. We seldom heard students speak more than a sentence or two at a time.”

They noted a 1997 study of 224 lessons across nine high schools by Martin Nystrand and Adam Gamoran that found free discussions in ninth-grade English classrooms averaged less than 15 seconds a day.

At the 30 schools throughout the country that Mehta and Fine studied, dramatic differences existed between lessons for top students and for grade-level (often euphemistically called “college prep”) students. They once discovered, while comparing notes at lunch, that the deep and lively history lesson one of them had seen that morning in a selective class, and a very dull and simple lesson on the same topic the other had observed in an average class, had been delivered by the same teacher.

“Students told us over and over that they couldn’t see the point of what they were doing,” the authors said. “They came to school mainly to see their friends and participate in extracurriculars, or to get to college.”

As I will show next week, such conversations led them to look much more closely at extracurriculars, often shrugged off as playtime. The authors came to a very different conclusion.