“I’m not ever happy when I see a low percentage of those students participating in schools that are high rigor,” he said. “It’s important for the halls of Stuyvesant, the halls of the Bronx High School of Science, to be reflective of the city itself.”

Instead, the schools that make up the upper crust of the public education universe belie the system they are part of and the city where they reside, and the disparity between the races has grown even more pronounced over the past decade.

In this city of 1.1 million public school students, about 40 percent are Hispanic, 32 percent are black, 14 percent are Asian and 14 percent white. More than two-thirds of Stuyvesant High School’s 3,247 students are Asian (up from 48 percent in 1999). At Brooklyn Technical High School, 365 of the 4,669 students, or 8 percent, are Hispanic; at the Bronx High School of Science, there are 114 blacks, 4 percent of the 2,809-student body.

The other schools in the elite group, considered a second tier, are more diverse: Brooklyn Latin School, for example, which became a specialized high school in 2007, is 23 percent Hispanic and 32 percent black (though it has 183 students, a fraction of the top three).

The portrait of test-takers from public schools is closer to the overall enrollment, but hardly a mirror: 28 percent of last year’s were black, 23 percent Hispanic, 30 percent Asian and 19 percent white.

Marcia V. Lyles, deputy chancellor for teaching and learning, acknowledged that racial diversity at the schools “is not where we would want it to be.”

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Elizabeth Sciabarra, who oversees student enrollment planning, said the city had increased its efforts to inform families about the test, with the hope that interested students of all backgrounds might start preparing earlier. But, she noted: “It is a choice. There are kids who might be wonderful candidates for this who will just not sit for the test. That transcends ethnicity; that’s across the board.”

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The test-prep institute, which includes a full-time five-week summer session and twice-a-week workshops during the school year, was a core part of the city’s strategy to diversify the ranks of the elite schools. But the intensive program has been hampered by a Supreme Court decision last year that ordered districts to remain race-neutral in efforts to diversify schools. Now the program gives preference to students based only on family income, not race.

And enrollment in the institute has fallen to 2,800 students at 10 sites this year, from 3,800 students at 17 sites in 2006. Education officials said that they reduced the number of sites to standardize the curriculum and that despite the drop in enrollment, more students were currently receiving the full test-prep regimen.

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The test itself, consisting of 45 verbal questions and 50 math questions, measuring students’ ability, for instance, to put sentences in order and discern geometrical angles, has also become a subject of criticism.

Joshua N. Feinman, an economist who graduated from Stuyvesant and is the parent of a Bronx Science junior, recently released a study challenging the validity of the test, saying it had not undergone normal predictive bias studies to see if it was skewed toward any gender or racial groups. The study revives complaints from the 1960s, when civil rights groups charged that the tests were unfair to black and Puerto Rican children and should not be the only criterion determining access to the schools.

Department of Education officials said they were confident that the test, which is manufactured by Pearson and has been used since the 1970s, was reliable.

On a recent Saturday morning, as hundreds of anxious students lined up for the test outside the stately stone-gray facade of Brooklyn Tech, parents and students attributed the racial disparities to a lack of private tutoring, subpar middle schools that do not expose students to test material, transportation problems, cultural differences and a simple lack of motivation on the part of some students.

Tiffany Gomillion, a single parent, said families like hers were at a disadvantage. Her 15-year-old son, Dalon, attends Our Lady of Miracles, a Catholic school in Canarsie, Brooklyn, but is hoping to go to a specialized school.

“He didn’t really get the preparation that he needed because it was so expensive,” said Ms. Gomillion, a nurse. “Even at home, a lot of times children’s parents are working, so they don’t really have somebody there to supervise to make sure they are doing the work and they are studying.”

Dalon, who is black, began studying for the test days before it was given. He was the last to arrive at Brooklyn Tech, a few minutes before its scheduled start, because he and his mother had trouble finding the school, which is near Fort Greene Park.

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Terrence Busby Jr., 13, who is also black, said many of his friends did not take the test because they did not know how to get to the school or have a parent available to take them. “They can’t get there or they don’t feel like they’re smart enough,” he said, suggesting that the city make the test mandatory for all eighth graders.

Ashley Wright, a black 13-year-old who has her eyes on Brooklyn Tech and Stuyvesant, said many of her black and Hispanic friends were simply not motivated to do well on the test. “I see a lot of people who have an opportunity at a good life, but they mess it up,” she said, her legs shaking in anticipation of the exam.