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David Levin, who co-founded KIPP nearly 15 years ago and is now the superintendent of the KIPP schools in New York, said he would fully cooperate with the union, but had no details of how and when contract negotiations would begin. He pointed out that KIPP Academy, a Bronx middle school, has had a union since its inception, because it grew out of an existing public school.

As for complaints about overwork, Mr. Levin said: “Just because the school is available to kids at all times, that doesn’t mean that each and every staff member has to be available at all times. We’ve been able to successfully work that out.”

Ms. Bonifacio said that 15 of the 22 teachers at KIPP Amp had signed cards saying they wanted a union; charter schools in New York generally must grant union recognition once workers show majority support.

Last summer, rival groups of educators circulated competing educational manifestos. One, which included some former leaders of Teach for America, espoused a get-tough policy based partly on pressing teachers and administrators to dramatically improve student achievement. Another faction argued that schools alone could not close America’s racial acheivement gap and urged new investments in school-based social programs to help poor students learn. Mr. Duncan was the only big city superintendent to sign both manifestoes.

In the hearing, Mr. Duncan warmly endorsed Teach for America and its founder, Wendy Kopp, as well as the larger movement of social entrepreneurs seeking to improve public education through tactics like founding charter schools and seeking to end teacher tenure. He called himself a “big supporter” of charter schools. But he warned that only thoroughly qualified educators should be allowed to open charter schools, which receive public money but enjoy less governmental oversight than traditional public schools.

For as long as anyone can remember, introductory physics at the Massachusetts Institute of Technology was taught in a vast windowless amphitheater known by its number, 26-100.

Squeezed into the rows of hard, folding wooden seats, as many as 300 freshmen anxiously took notes while the professor covered multiple blackboards with mathematical formulas and explained the principles of Newtonian mechanics and electromagnetism.

But now, with physicists across the country pushing for universities to do a better job of teaching science, M.I.T. has made a striking change.

The physics department has replaced the traditional large introductory lecture with smaller classes that emphasize hands-on, interactive, collaborative learning. Last fall, after years of experimentation and debate and resistance from students, who initially petitioned against it, the department made the change permanent. Already, attendance is up and the failure rate has dropped by more than 50 percent.

“We’re not questioning your heart,” he told his players. “But there are teams that play with heart and sometimes lose. We don’t want to do that. We need to play with heart, and we need to execute and make smart decisions.”

With that, they gathered in a huddle for their signature chant, each with a hand raised toward the middle.

Goodman said, “One, two, three. ...”

“Hard work,” they yelled.

Goodman: “Four, five, six. ...”

“Together,” they yelled.

And they were soon out in the crisp January night for the bus ride home, still No. 1 in the nation.

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