The Bonillas and Rozende felt lucky to have children in Greenwich. But historically speaking, researchers haven’t been so sure that it is beneficial to enroll low-income children in wealthier schools. A lot of sociological data, dating to the definitive Coleman Report of 1966, which studied the outcomes of 570,000 students, show that a child’s success in school, more than anything, was determined by her parents’ wealth and education level. So in the decades after the report was issued, attention was lavished on various reforms and integrating schools according to race, not economics.

New research, however, suggests that economic integration may be the answer. Recently, Heather Schwartz, a policy researcher at the RAND Corporation, began studying the public-school system of Montgomery County, Md. The county, a suburb of Washington, has one of the most affluent populations in America and an innovative housing authority that allows low-income citizens to rent homes alongside wealthier neighbors at steeply discounted prices. The renters are randomly assigned to different parts of the county; some Montgomery County schools have many poor students, others have almost none. In 2009, Schwartz concluded that students from poor families did much better in predominantly wealthy schools than in predominantly poor ones. On average, the poorer children in wealthier schools cut their achievement gap in half compared with their peers in poorer schools.

The same thing is happening at Greenwich High. Around 13 percent of the school’s students receive free or discounted lunches, a commonly used proxy for low income. And more than three-quarters of those students scored at or above proficiency on the most recent statewide 10th-grade performance tests. At nearby Stamford High School, where nearly 47 percent of students are on the lunch program, almost half the students failed to meet proficiency levels.

Schwartz still isn’t exactly sure why poor kids do so much better when they are surrounded by wealthier ones, but the stability of wealthier districts probably plays a role. (“High-poverty schools are often lurching from crisis to crisis,” she told me.) As such, there is now a small but fast-growing effort to integrate schools on economic lines. Richard Kahlenberg, a senior fellow at the Century Foundation, says that 80 school districts, serving four million students — or roughly 10 percent of all students in the country — have some kind of economic-integration policy. (That’s up from a single district in the late ’90s.) The remarkable thing about economic integration, Kahlenberg says, is that it seems to improve outcomes for the poor without diminishing educational attainment among the rich. Christopher Winters, headmaster of Greenwich High School, says that the greater diversity of the population makes for a better educational experience for all students. The low-income population has nearly doubled in the past seven years at Greenwich High, and no parent, he said, has complained.