In another class, a fiendishly difficult math problem was being worked out. When the class ended without the problem being brought to a satisfactory conclusion, the students groaned as if a movie had been interrupted at the climactic moment. The instructor assured them that “we’ll pick it up right here” the next time the class met.

The Bard High School Early College model has been around long enough and has given a first-rate education to enough students to warrant significant expansion and close study to determine just how far this promising innovation might be able to fly. (A second school, Bard High School Early College Queens, opened in 2008.)

Dr. Botstein would like to see 150 such schools created across the country, which would reach roughly 100,000 students.

President Obama mentioned the Bard school last summer in a speech in which he suggested that more attention should be paid to such “innovative approaches” to education. An application for a grant that would help cover a national expansion of the program has been filed with the United States Department of Education.

When you look at the variety of public schools that have worked well in the U.S. — in cities big and small, and in suburban and rural areas — you wonder why anyone thought it was a good idea to throw a stultifying blanket of standardization over the education of millions of kids of different aptitudes, interests and levels of maturity.

The idea should always have been to develop a flexible system of public education that would allow all — or nearly all — children to thrive. One of the things Bard has shown is that kids from wildly different backgrounds — including large numbers of immigrant children — can thrive in an educational environment that is much more intellectually demanding than your typical high school.

In this tough economic period, a program in which students come out of high school with up to 60 college credits already in their grasp can only be welcome. But the students I talked with were not fixated on the costs they would avoid in their college years. They were focused on the challenging work of the present moment.

As I watched a small group of history students enthusiastically participating in a discussion of events in the post-World War II period, I thought of a comment that a student in the biology lab, Claire Fishman, had made to me earlier: “When I get to college, I’m going to be really well prepared.”