Kristal Hansley, 18, was quick to reply when asked to describe her Brooklyn high school: During one year, she said, she had 14 math teachers and sat for months in a biology class where there was no teacher at all — although she was able to get credit for the class anyway.

A fellow student, Ali Muhsin, 16, elaborated: “There are times when you don’t want to walk between classes. … There have been three killings around the school in one month.”

The eyes of their questioners, Sienna White, 16, and Lauren Reilly, 18, high school students from the small city of Cody, Wyo., widened. There, driving drunk after a “kegger” — a term for a beer party they had to define for the Brooklyn students — is the biggest killer of teenagers.

The four students, along with two of their teachers, were brought together by a New York lawyer, Philip Howard, who is the founder of Common Good, a group that says it aims to “restore rationality and common sense to the law.”

Mr. Howard had gathered the group together in the living room of his apartment overlooking Gramercy Park at a moment when a national debate over the reauthorization of the No Child Left Behind Act is ramping up, and as local factions are battling over restructuring the New York City public schools.

After Sienna and Lauren admired the wood and brass trim in the elevator — there’s only one elevator in the whole town of Cody, in the hospital, and it only goes up three stories, according to one of the Western visitors — and Kristal, a classical pianist, examined Mr. Howard’s baby grand piano, the little group set out to tackle issues that have flummoxed education experts and politicians for decades.

First, one of the Common Good staffers present led an ice-breaker in which it was learned that Kristal works at Starbucks, that Ali has nine brothers and sisters, that Lauren has lived in Cody her entire life, and that Sienna’s politics are staunchly liberal. Mr. Howard, the author of the book “The Death of Common Sense,” who has advised both Vice President Gore and Governor Jeb Bush, disclosed that in his younger days he once held a summer job picking tobacco.

The students then described their schools.

Ali and Kristal said their middle school is plagued with indifferent teachers, truant students, and stubborn administrators, with violence looming in the streets outside. In the Cody school, Sienna and Lauren said cliques, not gangs, reign, standardized testing constricts the creativity of teachers, and indifferent, disillusioned teachers and administrators are a problem just as rife as in Brooklyn.

The teachers, Deborah White, a 19-year-veteran from Cody, and Zachary Jones, in his second year with Teach for America since graduating from Yale, led off a discussion on what to do about it.

“Get rid of tenure, have merit pay, and pay teachers enough,” were Ms. White’s solutions. She said paying teachers for their accomplishments would weed out those who were just sticking around to see their salaries rise automatically year after year.

Mr. Jones, who teaches in Brooklyn, respectfully disagreed. He said he worried that taking away teacher tenure would leave teachers unable to protest when they saw principals and administrators abusing their power, something he said he and his fellow Teach for America corps members are concerned could happen more frequently under Mayor Bloomberg’s plan to give principals more power.

“Unless you can guarantee their competency and good intentions,” he said, “you risk losing a good teacher.”

Ms. White reassured him. She said most teachers outlive administrators anyway, and learn that what happens above and around them in the school bureaucracy often has little to do with the reality in their classrooms.

After a meal of pizza and brownies was served, while Kristal serenaded the group on the baby grand, Ms. White made the point that schools can only do so much when parents aren’t involved. She described a struggling student of hers whose father is in jail and whose mother is a crystal meth addict.

“You’re talking about kids as a product, but when you don’t have the same materials going in … it’s hard,” she said.

Yet the experience of Ali, a recently arrived Yemeni immigrant who plans on going to business school, and Kristal, the first in her family to be accepted into college, seemed to contradict her theory.

“I just take care of myself,” Ali, who helps to run his family’s deli in his free time, said. “My parents don’t know anything about my school.”

Kristal’s guardian is her invalid grandmother.

“I’m on my own,” she said.

Teachers are the key, the students said. Not just any teachers, they added: They learn the most from the ones that enjoy being around children — a subtle trait they said they could detect instantly, but that administrators don’t always pick up on.

“You can tell,” Sienna said.

The view of the park had been obscured in the darkness and the lights of skyscrapers twinkled in the distance by the end of the evening. The four students agreed that they, and their schools, had much more in common than they expected, and Mr. Howard concluded the discussion.

“I don’t know what the lessons are,” he said with a shrug. “People matter, leaders matter, and teachers have to care.”