Klein’s successor, Cathleen Black, made it clear that she planned to continue the bold policies that he started implementing after his appointment by Mayor Bloomberg in 2002. (Black has since resigned.) While it may still be too early to evaluate Klein’s legacy, some statistics certainly suggest meaningful progress. When Klein started, for instance, less than 50 percent of New York’s incoming high-school freshmen were graduating in four years. That number is now 63 percent. Since 2006, according to an analysis of state testing data by the city's Department of Education (which used 2010's recalibrated proficiency levels to compare 2006's testing data to 2010's), the city’s elementary and middle schools have seen a 22-point increase in the percentage of students at or above grade level in math (to 54 percent) and a 6-point increase in English (to 42 percent).

At the center of Klein’s vision was the notion that New York should not aspire to have a great school system but a system of great schools run by talented and empowered educators. To help reach this goal, Klein created an academy to train principals in the new skills the job would require and dispatched its graduates to the city’s most difficult neighborhoods with a mandate for change and the authority and autonomy to try to effect it. “I think one of our core accomplishments is that we transformed the principal from an agent of the bureaucracy to the C.E.O. of his or her school,” Klein told me.

I thought about this notion a lot over the course of the months I spent with González at 223. It’s an incongruous metaphor to apply to someone whose office overlooks one of the largest, most dangerous housing projects in New York. Still, González has shown the kind of entrepreneurial thinking that, were he a C.E.O., would attract attention: he joined the board of the Randall’s Island Sports Foundation in part to gain access to its playing fields, hired a part-time grant writer to raise money for the school, brought in a number of nonprofits to support the school’s extracurricular activities and even rented out space in his building to underwrite 223’s two-week summer-school program.

In certain respects, 223 is a monument to Klein’s success: empower the right principals to run their own schools and watch them bloom. Thanks to Klein, González has been able to avoid having teachers foisted on him on the basis of seniority. He has been able to create his own curriculums, micromanage his students’ days (within the narrow confines of the teachers’ union contract, anyway) and spend his annual budget of $4 million on the personnel, programs and materials he deems most likely to help his kids.

And yet even as school reform made it possible for González to succeed, as the movement rolls inexorably forward, it also seems in many ways set up to make him fail. The grading system imposed by Klein that has bestowed three consecutive A’s on González is based in part on how well 223 does on state tests. But the school's relative success on these tests and other measures also disqualifies him from additional state resources earmarked for failing schools. The ever-growing number of charter schools, often privately subsidized and rarely bound by union rules, that Klein unleashed on the city skims off the neighborhood’s more ambitious, motivated families. And every year, as failing schools are shut down around González, a steady stream of children with poor intellectual habits and little family support continues to arrive at 223. González wouldn’t want it any other way — he takes pride in his school’s duty to educate all comers — but the endless flow of underperforming students drags down test scores, demoralizes teachers and makes the already daunting challenge of transforming 223 into a successful school, not just a relatively successful one, that much more difficult.

The school day at 223 begins at 7:50 a.m. This is 10 minutes before the United Federation of Teachers officially permits New York City public schools to start, which means that every year a majority of 223’s teachers has to vote to approve the earlier opening bell. The early start is a way to create more time for after-school programs, especially academic tutoring, before it gets dark and the streets surrounding the school become more threatening. “The research says it’s better to start your school day later,” González says, referring to studies showing that adolescents often need to get more sleep in order to be at their best. “But those researchers don’t live in my neighborhood.”

M.S. 223 is in the heart of School District 7, which is part of the poorest Congressional district in the nation. More than 90 percent of its students live in one of five housing projects, most prominently the Patterson Houses, a sprawling complex of 15 towers across the street from the school. About 70 percent of its students are Hispanic, predominantly Puerto Rican and Dominican. The remainder are black, either African-American or recent immigrants from West African countries like Senegal. Roughly 11 percent of the school’s students are ELLs, or English-language learners. (Another 60 to 70 percent of its students are former ELLs.) About 17 percent have learning disabilities.