When asked about school segregation in New York City, Mayor Bill de Blasio has said that schools are segregated because neighborhoods are: “We cannot change the basic reality of housing in New York City.”

Now, as a debate about plans to integrate middle schools has engulfed one Manhattan district, a report released on Wednesday undermines that notion. It found that a full 40 percent of New York City kindergartners do not attend the nearby school to which they are assigned. That’s a vast stream of 27,000 5-year-olds funneling through the city each day.

Percentage of kindergarten students leaving their zone Note: Values for some schools in Community School District 3, on Manhattan’s West Side, may contain small errors due to changes in zone boundaries.

While parents of all races choose to send their children out of their zones, the overall pattern of their choices may make schools more segregated. It also concentrates the effects of poverty at zoned schools, the schools to which children are assigned based on where they live.

“I don’t think anyone realized that number was so big,” said Nicole Mader, the lead author of the paper, which was conducted by the Center for New York City Affairs at The New School. “If 40 percent of elementary school students aren’t going to school where they live, how can residential segregation be the only factor driving school segregation?”

The schools they pick, the study found, tend to share two main features: They had fewer poor students than the zoned schools the families were leaving, and they had higher test scores.

As students move from lower-income schools to higher-income schools, the study found, they also tend to move toward the city’s economic heart, tracking the subway lines from East New York to Crown Heights, or from Harlem to the Upper West Side. The students who leave are then replaced by children from lower-income neighborhoods.

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At Brooklyn’s Public School 287, 28 percent of the children zoned to the school are white, but no white children attend. The pattern is a familiar one in gentrifying neighborhoods. John Taggart for The New York Times

School choice has been heralded as a way for all children to get a better education, allowing them a way out of failing schools. And indeed, the study found that for many students, choice allowed them to attend higher-performing schools. But its authors found that the choice came with unintended consequences: “The schools they leave behind face ever-greater challenges as they struggle to serve the city’s neediest children.”

The study looked at ten years’ worth of data on kindergarten enrollment, starting in the fall of 2007 and running through the fall of 2016, during which time 715,000 students signed up for kindergarten. Using data from the city’s Department of Education, the authors were able to determine whether each child attended their zoned school or went someplace else, like a charter school, a gifted and talented program, or a different zoned school outside the neighborhood.

Over the course of that time, the options available to those who wanted to avoid their neighborhood school grew: There were 567 zoned elementary schools and 196 other options at the beginning of the decade, and 491 zoned schools and 457 alternatives by the end.

The study does not deny that housing segregation exists, but it found that if everyone went to their zoned school, students would be “marginally” less segregated, racially and socioeconomically, than they are today.

White students Black students

Black children were the most likely not to attend their neighborhood school, with 59 percent of them going elsewhere last year, according to the study; 39 percent of Hispanic families also did not choose their neighborhood schools. (A small portion of each of these groups lived in school districts that did not have zones.)

The groups that were the least likely to leave their zoned school were white and Asian students, the study found, which ran counter to research elsewhere in the country, which has found that white families are most likely to exercise choice. That, the study’s authors say, may be because in New York City, they are more satisfied with the schools in their neighborhoods, which tend to be higher-performing, so families have no reason to flee them.

But when white and higher-income families live in a “diverse” or gentrifying neighborhood, they are more likely to send their children to schools elsewhere. At some schools in Bedford-Stuyvesant, Harlem, Fort Greene and Crown Heights — all of which are historically black areas now in the midst of dramatic gentrification — fewer than 25 percent of children actually attend their assigned school.

“Zones provide families of means with exclusive access to the schools they like,” the study, said, “while choice allows them to flee the ones they don’t.”

Take Public School 287, the Bailey K. Ashford school, which is perched at the northern edge of Downtown Brooklyn, not far from the waterfront. Standing in front of the school, the familiar brown brick of city housing projects stretches out in three directions. But about a block behind the building, new condo and rental buildings sprout like a thicket of new money.

Children from some of those buildings are zoned to attend P.S. 287, and overall, 28 percent of the school’s zoned population is white. But no white children attend the school. While only 44 percent of students in the district are poor enough to be eligible for free lunch, all of the students who attend the school are.

Jasmine Sweeney has a daughter in the first grade at P.S. 287. They live across the street, and Ms. Sweeney said she chose the school because her niece attended. But she has not been satisfied.

“If I would have known, I would have never chosen this school,” Ms. Sweeney said after picking up her daughter on a recent Friday. “The academics——” she added, and shook her head.

The study found that the families who exercised choice tended to have more advantages than those who did not, a pattern that was true nationally as well. “We know some parents are much more effective advocates than others,” said Kevin G. Welner, the director of the National Education Policy Center, which is at the University of Colorado Boulder. “That’s tied to parental education, that’s tied to race, that’s tied to wealth, that’s tied to networks. And it’s hard, given all of that, it’s hard to avoid a rich-get-richer system.”

The education department does not dispute the effects. “School choice on its own doesn’t guarantee high-quality or diverse schools,” Will Mantell, a department spokesman, said in a statement, adding that the city was trying to improve all schools.