NEW YORK — Tausifa Haque, a 17-year-old daughter of Bangladeshi immigrants, walks in the morning from her family’s apartment in the Bronx to the subway and rides south to Brooklyn, a journey of 1 1/2 hours.

There she joins a river of teenagers who pour into Brooklyn Technical High School, who are Bengali and Tibetan, Egyptian and Chinese, Sinhalese and Russian, Dominican and Puerto Rican, West Indian and African American. The cavernous eight-story building holds about 5,850 students, one of the largest and most academically rigorous high schools in the country.

Her father drives a cab; her mother is a lunchroom attendant. This school is a repository of her dreams and theirs. “This is my great chance,” Tausifa said. “It’s my way out.”

Brooklyn Tech is also subject to persistent criticism and demands for far-reaching reform, along with other test-screened public high schools across the nation.

Liberal politicians, school leaders and organizers argue such schools are bastions of elitism and, because of low enrollment of Black and Latino students, functionally racist and segregated. Sixty-three percent of the city’s public school students are Black and Latino, yet they account for 15% of Brooklyn Tech’s population.

For Asian students, the percentages are flipped: They make up 61% of Brooklyn Tech, although they account for 18% of the public school population.

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Some critics imply the presence of so many South and East Asian students, along with the white students, accentuates this injustice.

But several dozen interviews with Asian and Black students at Brooklyn Tech paint a more complicated portrait. These students speak of personal journeys and struggles far removed from the assumptions that dominate the raging battles over the future of their schools.

Fully 63% of Brooklyn Tech’s students are classified as economically disadvantaged. Census data shows Asians have the lowest median income in the city, and a majority speak a language other than English at home.

Brooklyn Tech, which sits in the haute brownstone neighborhood of Fort Greene, is regarded as a diamond in the city’s educational crown.

The school boasts many advantages, as most students are well aware. Nearly all balked, however, at describing it as segregated, not least because the descriptor “Asian” encompasses disparate ethnicities, cultures, languages and skin colors.

Tausifa looks at the multihued sea of students pouring through the doors of Brooklyn Tech. She expressed puzzlement that a school where three-quarters of the students are nonwhite could be described as segregated. “I have classes with students of all demographics and skin colors, and friends who speak different languages,” she said. “To call this segregation does not make sense.”

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The debate over an entrance exam

Critics of specialized high schools argue these institutions are out of step with the zeitgeist and educational practice. Better to cast aside standardized tests and seek heterogenous classes in neighborhood high schools, they argue, than to cloister top students. Some studies, they say, show struggling students gain from the presence of talented outliers. And the entrance exam has fueled the growth of a private and inequitable tutoring industry.

Those who champion specialized high schools point to alumni who became top scientists. With few exceptions, these were the children of working-class and immigrant families. The best students, they argue, should press as far ahead as brains and curiosity might take them.

The mayor and school officials preside over a system of 1.1 million schoolchildren, they add, in which only half are proficient in math and 24% of Black students fail to graduate. As Americans struggle to stay competitive with other nations in science, technology and mathematics, why obsess about the anti-egalitarian sins of a handful of high-performing schools that hold 6% of high school students?

That said, the dwindling number of Black and Latino students at these high schools is a great concern and a mystery. Bill de Blasio, when he was mayor of New York, suggested the heart of the problem lay with a biased entrance exam.

That does not reckon with history. Decades ago, when crime and socioeconomic conditions were far graver than they are today, Black and Latino teenagers passed the examination in great numbers. In 1981, nearly two-thirds of Brooklyn Tech’s students were Black and Latino, and that percentage hovered at 50% for another decade.

Black and Latino students account for 10% of the students at Bronx High School of Science; that percentage was more than twice as high in the 1970s and ’80s.

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To understand this decline involves a trek back through decades of policy choices, as city officials, pushed by an anti-tracking movement, rolled back accelerated and honors programs and tried to reform gifted programs, particularly in nonwhite districts.

Black alumni of Brooklyn Tech argue this progressive-minded movement handicapped precisely those Black and Latino students most likely to pass the test. Some poor, majority Black and Latino districts now lack a gifted and talented program.

Citywide, elementary school gifted classes enroll about 16,000 students and are 75% white and Asian.

Getting in and staying in

A visitor steps inside Brooklyn Tech and finds the honor roll list for last year’s senior class, the surnames offering variations on an old story: There is a Dong and a Doogan, a Goyer and a Huynh, a Subah and a Wai.

The specialized high schools serve as a homing beacon for immigrant and working-class teenagers. The 1950s and 1960s saw the arrival of Holocaust survivors and West Indian families. Later waves rolled in from Asia and West Africa.

Hasiba Haq, 28, lives in Kensington, a low-slung Brooklyn neighborhood known as Little Bangladesh. Her parents grew up on an island in the Bay of Bengal. Her father worked as a taxi driver when she was a student. She attended middle school in well-to-do Park Slope.

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By the time she turned 11, her family and neighbors talked of the high school examination. Her parents enrolled her in a tutoring center, a rigorous boot camp with teenage Asian teachers drawn from the specialized high schools. The sticker price was $4,000. Her parents bargained hard but still paid a small fortune.

“It was every weekend and classes over the summer,” said Haq, now 28 and a producer at TED Talks. “Everyone in the community knew it was your turn to take the test.

“It was more difficult than college,” said Haq, a Fordham University graduate. “It was a hustle-and-grind culture.”

Folk wisdom has it that South Asians dominate the test, but reality is messier. Many students in her tutoring classes fell short, and parent and child cried together. Some students dropped out.

More than 23,500 teenagers took the specialized high school test last year. Roughly 41% were Black and Latino, and 34% were Asian.

The examination can be problematic, as it requires knowledge of algebra, which is not offered to many middle school students. Haq was lucky enough to get offered that course. Tausifa, the teenager from the Bronx, was not. Had her parents not paid for tutoring classes, she would have been at sea in that portion of the test.

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Some of Tausifa’s middle school classmates had no chance. “One Black classmate, really smart, did not even realize there was a test,” she said. “There were uneven advantages.”

Being a Black student at Brooklyn Tech

Diane Nunez, who is Black, and her son, Ricardo, 15, share a goal: to maximize his education and get into a top college. When Ricardo was in seventh grade, Nunez received a guidance counselor’s email intended for another family. It mentioned a city-run tutoring course for the high school test. “I thought, ‘Wait a minute. Ricardo is smart enough for this,’” she said. “Why isn’t he getting offered this?”

Nunez dug into her savings and enrolled Ricardo in a private tutoring agency favored by Asian parents. Ricardo understood the lost weekends of study it would entail. That was the most challenging academics I’d ever done,” Ricardo said. “But I knew where I wanted to end up.”

Once at Brooklyn Tech, he joined the Black student union. “I don’t feel like a minority,” he said. “We resist being pitted against each other at this school.”

Rachel Germany, a social studies teacher at Brooklyn Tech who is Black, serves as adviser to the Black student union. She is moved by the struggles of all her students. “I appreciate the diversity and love these kids. Having said that, the dearth of Black and Latinx students in a public high school feels palpable and strange,” she said, using the gender-neutral word to describe people of Latin American descent.

City officials have long sought to arrest the decline in Black and Latino students at specialized high schools. In the mid-1990s, a chancellor started a tutoring program, to much applause. Officials today could not say what became of that.

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The Department of Education runs another tutoring initiative, known as the Dream Program, a pale shadow of the rigor of the tutoring academies.

Still, tutoring is no replacement for identifying gifted students and placing them in accelerated classes.

“The most clear failure has been establishing an accessible pipeline” for Black and Latino students, Jumaane Williams, a Brooklyn Tech alumnus and the city’s public advocate, wrote in The Daily News. “In the past gifted and talented programs in middle schools have been a reliable pathway.”

Students and teachers spoke of other approaches. Establish variable passing scores so economically disadvantaged, Latino or Black districts face somewhat lower bars than a wealthy, majority-white district. Offer the exam to all eighth graders and improve tutoring.

“We’re really trying to have this nuanced conversation about race and class and opportunity,” Haq said. “We haven’t found the words for it yet.”