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For months, in two of New York City’s most politically progressive neighborhoods, parents debated what to do about their deeply segregated schools. Now, after adopting a series of initiatives last year following many spirited and emotionally charged discussions, these neighborhoods are starting to see swift changes in enrollment, according to city data released on Monday.

Several schools in districts in Manhattan and Brooklyn will be more racially and socioeconomically diverse on the first day of school this fall than they are today as a result of these new measures. And the apparent success these districts are seeing could prompt other neighborhoods to consider their own diversity initiatives.

Also, the strategies parents implemented, which included setting new enrollment rules and eliminating using academic screens to sort students for admission, could compel City Hall to take more forceful action to integrate one of the nation’s most segregated school systems.

“Part of why we did this is we felt very strongly that you couldn’t improve just one school,” said Kristen Berger, who helped create the plan for Manhattan’s District 3, which includes the Upper West Side and Harlem. “That’s not very useful. It’s really a system. We really wanted to see movement at high- and low-demand schools.”