But on a tour led by the school’s principal, Pamela Price-Haynes, Mr. Carranza liked what he saw. Children who had recently immigrated to the United States from the Dominican Republic, Mexico, Senegal and Yemen were conducting a science experiment, effortlessly using the word “hypothesis.” The staff spoke proudly about the school’s winning debate team and its swim lessons, dance and chess.

Back in his chauffeured car, whisking downtown to his office at the Tweed Courthouse, Mr. Carranza sighed. Test scores can’t capture what P.S. 161 is all about, he said. He wished parents — white parents, college-educated ones — would understand how their children could thrive at a school like this. “Parents would be better served if they actually visited schools in the neighborhood,” he said, instead of simply looking up test scores or demographic numbers online.

But the city has given families the ability to opt out of attending schools like P.S. 161. Nearly 60 percent of the kindergarten families zoned for it use the city’s choice process to escape it, just as across the city white and middle-class parents choose to avoid similar schools. They can be seen across New York City in the early morning hours, walking their children, hand-in-hand, past their zoned schools.

Ultimately, Mr. Carranza said he believes parents have the right to do that. He suggested that better programming and after-school opportunities could lure middle-class families to a broader array of schools. “Parents will always do what they want to do, or need to do, for what they feel is good for their children,” Mr. Carranza said.

It is an argument similar to the one made by the Bloomberg administration, and by the mayor and Mr. Carranza’s predecessor, Ms. Fariña.

Mr. Torres, the Bronx councilman, for one, notes the gap between what Mr. Carranza has said, and what he has actually done — at least so far. “There remains a profound disconnect between the boldness of his rhetoric and the timidity of the Department of Education’s policy,” he said.

Mr. Carranza said he looked forward to hearing Mr. Torres’s ideas. “His expressed desire to not be incremental has also been expressed to me by lots of people,” he said. “People are starting to get excited and motivated to have this conversation, this discussion, and then to develop a plan.”

“I’m really optimistic,” he added. “I’m excited.”