As support among local advocates and officials builds for policies to help desegregate New York City schools, two Manhattan moms say mixing students of different ability levels is a key part of the equation.

Robin Broshi and Shino Tanikawa, both members of the District 2 Community Education Council, point to the middle schools in their district, which includes lower Manhattan, Chinatown and the Upper East Side. Most middle schools there are unzoned and supposed to be open to everyone. But with a highly selective application process, many of the schools end up divided academically — and by race and class.

Broshi and Tanikawa are determined to change that, but first they’ll have to convince their peers that academically integrated schools work for everyone — even students who are already high-achievers.

“My feeling is most parents will support a racially diverse school and they might even support a socioeconomically diverse school, but they still might have a problem understanding that an academically diverse school is also good for their kids,” Tanikawa said.

Their effort is rooted in an understanding of how race and class impact student achievement, and how using test scores and report cards in admissions decisions can shut vulnerable students out.

“If you look at test scores and you say, ‘We want to create academically screened schools that also reflect all the other diversities,’ you’re not really going to be able to do that,” Broshi said. “The whole reason we’re in this situation is because there’s an academic component.”

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The kind of academic mixing that Broshi and Tanikawa propose is something similar to the city’s “educational option” high schools. Also known as “ed-opt,” these schools were designed to enroll students from across the educational spectrum. The city Department of Education has said it’s not interested in adding screened programs at the high school level, and has increased the number of ed-opt seats by 14 percent since 2015.

Broshi and Tanikawa aren’t yet advocating for specific changes to the middle school admissions process; they hope those details will grow out of community conversations that are just getting started. One forum the educational council organized last spring, which featured researchers talking about their work on integration, attracted a crowd of parents.

Still, Tanikawa knows it will take more than that to convince wary peers. If necessary, she’s ready to visit every PTA in the sprawling district to make her case.

“The only way to do it is to go to where the parents are, not to ask them to come to where we are,” Tanikawa said.

She is likely to face fierce resistance.

In 2013, when the city Department of Education opened a new middle school on the Upper East Side and proposed that only half the student body be screened, about 500 people wrote to the department calling for full academic screening instead.

“Without a screen … there is no ability to control what kind of kids will enroll,” one commenter wrote. “Half of the students will get in purely on luck, and these students will impede the success of the school.”

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The question of how mixing students affects an overall student body has yielded a significant amount of research, much of which supports a different conclusion: As with integrating students of different races and economic backgrounds, mixing students with different academic abilities can benefit all.

One meta-analysis of four decades of research showed that academic mixing had positive effects for struggling students — and no effect, positive or negative, for average and high-achieving students.

Other studies have found more advantages.

One study of a Long Island high school found that graduation rates among all students shot up when the district stopped using different academic “tracks” with separate curricula for high- and low-performing students. Instead, all students were taught under a program that was previously only taught to top students.

Certain mixed-class models are especially promising, said Richard Kahlenberg, a senior fellow at the Century Foundation, a think tank that studies inequality.

He recommends approaches such as “embedded honors,” where students are taught the same lessons in the same classroom, but assigned varying levels of work. Cooperative learning, where small groups of students at different achievement levels help each other, can also work, he said. A review of almost 400 studies found that cooperative learning can boost higher-level thinking and promote the generation of new ideas, Kahlenberg writes in his book “All Together Now.”

But de-tracking is not easy to get right. In cases where the gap between top-performers and struggling students is too big, there may be no benefits for either.

Other research has shown that struggling students can, in fact, have a negative effect on peers. In one study, economists looked at the impact of the arrival of hurricane evacuees on Houston schools. The result: low-achieving evacuees brought down the average performance of high-achieving Houston students. On the other hand, the arrival of high-performing evacuees had a positive effect.

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Michael Petrilli, president of the Thomas B. Fordham Institute and author of “The Diverse Schools Dilemma,” said it’s “reasonable” for parents to ask how their children will do in an academically mixed classroom.

Regardless of a school’s student body, he says, educational success depends largely on the quality of teaching and leadership.

“If the school can do a reasonable job to provide some accommodations for your child, and you get to have this experience of integration, then that’s great,” Petrilli said. “But there are tradeoffs. And I guess in the best case scenario, parents should be able to make a decision about those tradeoffs.”

For Tanikawa, the tradeoffs, if there are any, are well worth it if academic mixing leads to greater integration by race and class. The benefits of diverse schools — better graduation rates in high school and college, and even higher incomes later in life — have been thoroughly documented.

In the classroom, students from different backgrounds bring new experiences and ideas, which stimulates more engaging classroom discussions, improves critical thinking and may even boost creativity, according to one 2016 report from the Century Foundation. It prepares students to work in multicultural environments and can lead to more civic participation later in life.

“I know there’s a lot more to schools than academic achievement,” Tanikawa said. “I want parents to start thinking about what else makes a good education.”