How white is too white? At the Academy of Arts and Letters, a small K-8 school in Brooklyn founded in 2006 to educate a community of “diverse individuals,” that question is being put to the test.

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.

In New York, Mayor Bill de Blasio and Carmen Fariña, the schools chancellor, have disappointed school diversity advocates by failing to make integration a priority. The set-asides plan, approved by Ms. Fariña in November, was the first attempt at addressing the issue across multiple schools.