At Public School 8 in Brooklyn Heights, the auditorium’s stage is crowded with music stands that were stored there when the music room had to be turned into a first-grade classroom.

The prekindergarten program was cut because of lack of space. And with the school operating far above capacity, 50 families who live within its zone — which also includes Dumbo and much of another Brooklyn neighborhood, Vinegar Hill — were placed on a waiting list for kindergarten last spring.

To the city, the solution for the overcrowding at P.S. 8 seemed obvious: move those two neighborhoods from P.S. 8’s zone and into that of P.S. 307, which is nearby and has room to spare. The proposal, however, has drawn intense opposition, and not only from the families who would be rezoned from the predominantly white P.S. 8 to the mostly black P.S. 307. Some residents of the housing project served by P.S. 307 also oppose the rezoning, worried about how an influx of wealthy, mostly white families could change their school.

For all its diversity, New York City, by some measures, has one of the most segregated school systems in the country, in part because many elementary schools are effectively closed off to children who live outside their zones. And although the Brooklyn rezoning is mainly a response to crowding, it is becoming a real-life study in the challenges of integrating just one of the city’s schools.