So the Arthur Kill team had the home-turf advantage, plus passion, not to mention direct personal experience — of the four debaters, three are currently special students at the New School, as are many of the two dozen inmates who were on hand to watch. Then there’s the advantage of general life experience, on the outside and in.

Image CHALLENGERS The New School team, from left, Johanna Goosens, Skanda Kadirgamar, Nick Olson and Santiago Posas, conferring. Credit... Brian Harkin for The New York Times

“I’m kind of used to public speaking,” Andrew Cooper, 43, said.

In his dark green uniform and wire-rimmed glasses, Mr. Cooper had the look of a graduate student working some night shift to play the bills. He said that he had done some teaching while in prison, and that he occasionally spoke to at-risk youth about the consequences of “bad choices.” Fifteen years ago, while a student at Medgar Evers College in Brooklyn, he made a bad choice and joined a robbery on Long Island. “I was a fair student,” Mr. Cooper said. “But I went for the quick fix.”

He and his teammates displayed a consistently confident, Obama-inspired style: some measured, almost soothing oratory; some strategic finger-pointing; some appeals to reason. Statistics poured out at a steady rate, about the country’s high recidivism problem and the links between higher education in prisons and lower recidivism rates. Higher education, Mr. Cooper argued, represents “the last bastion of civility and the last hope for inmates to slip the bonds of incarceration and become tax-paying, productive, caring members of society.”

The New Schoolers could not quite bring themselves, as one of them, Santiago Posas, put it, to make some “Republican we-can’t-coddle-criminals argument.” Instead, they went nuclear, debate-style, rejecting the education system altogether: Even if higher education in prisons is ethical, Mr. Posas argued, that premise “does not address the basis for true equality within our society that is structured by complex and hierarchal racist, classist and gendered norms that produce the prison-industrial complex.”

Why import into prisons the same flawed educational system that landed inmates there in the first place? The undergraduates spoke of “the dominant discourse” and “hegemony”; there was talk of “the revolutionary praxis” and, of course, Foucault.