The school — along with six others in New York City — is part of a new Education Department initiative aimed at maintaining a racial and socioeconomic balance at schools in fast-gentrifying neighborhoods. For the first time the department is allowing a group of principals to set aside a percentage of seats for low-income families, English-language learners or students engaged with the child welfare system as a means of creating greater diversity within their schools. The continuing segregation of American schools — and the accompanying achievement gap between white, middle-class students and poorer minority children — has become an urgent matter of debate among educators and at all levels of government. Last week, President Obama lent his weight to the issue when he included in his budget a $120 million grant program for school integration aimed at de-concentrating poverty. Principals at these schools say they know that middle-class families often bring with them higher test scores, making the schools look better on paper. But several added that chasing test scores was not what had drawn them into education. Administrators at the seven pilot schools say they are all motivated by their belief that classrooms that are racially and economically diverse are good for students, according to recent research, maybe even making them brighter. Emily Cowan, a freelance artist and social worker, said she was willing to even sacrifice her own kindergartner’s slot next year to “preserve that diversity,” though it would mean sending her son to a different school next year.