He offered a stark figure: Of 900 incoming freshman admitted to Stuyvesant, only 10 are African-American. He also said that while there are more than 600 middle schools in New York City, half of specialized students come from just 21 middle schools. He said that looking at a student’s academic record was a “much more holistic way of looking at student ‘talent’” than a single test.

"As the mayor has very, very eloquently stated, we’re not trying to penalize anybody,” Mr. Carranza said on WNYC. “This should be good news for our poor, our immigrant communities, that you’re not going to have to spend thousands of dollars on test prep for one test to get an opportunity to go to a specialized school.”

Mr. Carranza emphasized that relying on one test was out of step with admissions to other elite institutions. “If you’re applying to Harvard today, you would not be admitted based on a test score,” Mr. Carranza said. “It’s multiple measures.” (He might have chosen a different school to cite as an example: Harvard University is being sued by a group that says the school discriminates against Asian-American applicants.)

The mayor’s plan does have a basis in research. A study by Sean P. Corcoran, an associate professor of economics and education policy at New York University’s Steinhardt School, examined six strategies to diversify the specialized schools and found that taking students from every middle school was the only one that had a large effect on demographics. It also found that plan would lower the academic performance of admitted students, a key argument of those in favor of retaining the test. But a similar study, by Lazar Treschan at the Community Service Society, which included a minimum academic standard applicants must achieve, found no such diminution.

The city’s proposal also includes an academic minimum. Students must be among the top 25 percent of performers citywide. An education department spokesman said the city’s projection found that students admitted under its proposed model would have the same grades as current specialized students, and that their state test scores would be virtually unchanged.

The specialized schools carry enormous symbolic weight in the city, and a seat in one of them is seen as a glittering prize. They are among the most distinguished schools in the city, some on par with elite and expensive private schools, and they offer a real pathway out of the working class for many families.

Nonetheless, their impact is actually quite narrow. Of the more than 300,000 high school students citywide, just 16,000 attend these schools. And there are many other schools that screen students academically, like Eleanor Roosevelt High School in Manhattan, where just 16 percent of students are black or Hispanic. Sixty-four percent of the students there are white, and just 21 percent of its students are poor.

Changing admissions at schools like Eleanor Roosevelt would make more sense, argued some opponents of the plan. “Why go to Albany on three schools,” said Mr. Kim, “when you can fix those schools right now.”