In the fall of 2015, the New York City Department of Education announced plans to redraw District 3’s attendance zones with the goal of making schools like P.S. 199 more economically integrated. The proposed changes would move several elementary school students from Public School 191—a neighboring, high-poverty, majority-minority school—into P.S. 199.

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Parents at the wealthy school were outraged, and the city’s first attempt to integrate the two schools failed amid the backlash. After contentious debates and heated protests, the city dropped the plan, stating it would need more time to devise a new approach that “reached consensus.”

The city resurrected its proposal the next year, and although the rezoning plan is still fraught with conflict, it somehow muscled its way through the dissension to reach a final vote last fall. District 3’s Community Education Council—a locally elected parent group that votes on zoning policies—had long been in favor of new zoning lines and approved the city’s plan on a 9-to-1 vote.

But parents who are opposed to the plan have continued to fight. Some are placing political pressure, threatening to campaign against any official who supports the new zones. Others have warned of enrolling their children in private school. Some have even hinted at taking legal action. Overall, the battles roiling P.S. 199 and P.S. 191’s elementary school campuses have proved that when it comes to school integration, change is no easy task.

One would think Americans are ready for school integration, though. In a new study released by me and my colleague, Ulrich Boser, we found that most Americans—more than 60 percent—report that school segregation is an important issue for them, and nearly 70 percent of Americans agree that more should be done to integrate low- and high-poverty schools.

These findings were a bit startling at first glance. After all, if most Americans are in favor of school integration, why aren’t diverse, integrated classrooms spreading across the country?

Historically, school integration has met intense resistance. But at least in principle, the general public seems to endorse it, and our poll may have tapped into the country’s sympathy for people living in poverty.

In fact, one 2012 poll found that 52 percent of Americans believe “helping the poor and needy is a top priority.” Another poll found that reducing poverty is “very” or “extremely” important to most Americans.

National support for school integration may also be due to the country’s increased attention on income inequality. More than three-quarters of adult Americans, for instance, believe “the rich just get richer while the poor get poorer.” Nearly 90 percent of Americans also believe they are “falling backward” in their finances. And a majority believe “the next generation has it even worse.”

Seeking to disrupt trends of economic inequality, Americans could be keen on helping children with low incomes have a fair shot at entering the middle class, and they see education as the best way to get there. But if there’s anything the desegregation battles in New York City prove, it’s that integration can leave both a sweet and bitter taste in Americans’ mouth. Americans might support integration in theory, but many have different reactions when it reaches their own backyards.

Research shows that reporting favorable views of integration can demonstrate a “superficial tolerance” of integration. But sending one’s own child to an integrating school is a much greater challenge: It requires a person to acknowledge—and maybe uproot—deep-seated stereotypes about families with low incomes and education.

Poverty is also racialized in the United States, and words like “low-income” in America can trigger other words like “black” and “brown.” Children of color, as young as five, are more likely to be perceived as violent and disruptive, which can stoke fears about integrating schools on both economic and racial lines.

But it may not be student diversity, per se, that is distressing to parents as is the thought of losing certain privileges. For affluent parents, they may feel territorial over the high-flying success of their school. And property values, neighborhood identity, and a sense of safety feel as though they are at stake.

“A school belongs to the neighborhood it resides,” said one parent at PS 199.

“It’s not that I don’t want my children to go to school in a mixed school … But at the same time we want the best for our children. We want the best for our property value,” said another.

And it’s not just wealthy parents who are afraid. Through our focus group sessions with diverse parents in the Baltimore and Washington, D.C., metro areas, we found that low-income parents were wary of integration, and they drew on their own life experiences as supporting evidence.

For instance, low-income white parents spoke of being looked down upon by the “rich kids.” As one parent put it: “They don’t want us there, so why should we go there?” They pictured affluent families throwing lavish birthday parties, showering the higher-income kids with fancy cars and expensive gifts, making their own children feel insecure.

Despite whatever frustrations may be brewing among high- and low-income parents, District 3’s rezoning plan will take full effect this fall. In the Upper West Side of Manhattan, children who used to live in two separate worlds will now read, write, learn, and play together.

Fortunately, it’s not the only plan to mark a real shift in school diversity for New York City. The New York City Department of Education recently unveiled its citywide plan for integration, pledging to increase diversity across their entire public schooling system.

These changes are promising. Despite rapidly changing demographics in this country, school diversity has barely kept pace, and research shows that all students perform better academically and socially when they learn in diverse classrooms.

Many Americans do believe the time is ripe for change, but it remains to be seen whether all Americans will embrace this change when it arrives in their own communities.

But evidence of the flaw in Trump’s plan was right in front of him. The charter school he was speaking at—the Cleveland Arts and Social Sciences Academy—is not doing well. The state of Ohio gives the school a grade of D for its students’ test performance.

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School choice is not a new concept. For decades, states have been trying to encourage competition among different school models. That has led to an explosion in the number of charter schools, which are publicly funded but operate outside of the control of local school districts. The trouble is, researchers have found that these schools have mixed effects. In some cases charters improve test scores, while in others students do significantly worse than they would in neighborhood schools. Some districts have also tried giving students vouchers to go to private schools—which Trump has also called for—and have had similarly mixed results.

Many public school advocates argue that even the best charter schools can cause problems, because they drain money from other schools. That raises a big question about Trump’s plan, which would redirect $20 billion in federal funds to let students choose different schools. If that comes from the Department of Education budget, as some analysts expect, it would likely come from the two big buckets of federal money that go to K-12 schools now: $15.5 billion in Title 1 funds for schools with low-income populations and $12 billion for special education. Using that money for vouchers could mean decimating before- and after-school programs, tutoring in reading and math, and other supports for students facing the most serious academic challenges. The plan would also encourage states to dig money out of their own education spending for school choice.

Though his plan is misguided, the education crisis Trump points to is real—and really serious. There’s a huge and growing gap between the academic achievement levels of rich and poor kids. Today, students from wealthy families outscore their low-income counterparts by nearly 400 points on the SATs and are far more likely to graduate from high school.

One of the most successful ways to help low-income kids do better is to reduce income segregation, which has grown by 40% since 1990. That has a serious impact: One eye-popping study found that students from lower-income, less-educated families who attend school with wealthier peers are 68% more likely to attend a four-year college than those who go to an income-segregated school with peers from similar backgrounds.

The study’s author, Gregory Palardy of the University of California at Riverside, said segregation is the single biggest way that U.S. schools shortchange low-income students. Schools serving poor children tend to get less funding, hire less-skilled teachers, and offer fewer advanced courses than their counterparts in wealthier areas. And, Palardy said, poor kids simply have a harder time succeeding when their peers are all facing similar disadvantages. He said lower-income kids are far more likely to succeed if they go to school with more affluent peers who know a lot about college and expect, as a matter of course, that they’ll continue their education beyond high school.

“They rub off on you and your view of the world,” he said.

One of the arguments behind school choice is that it would reduce segregation by letting parents send their kids to schools that are more diverse than their neighborhoods. But studies have found that the proliferation of charter schools has led to greater economic—as well as racial—segregation. There are essentially two sets of charter schools. One enrolls predominantly privileged white students—often pulling them from more diverse neighborhood schools—while another serves mainly poor black and Latino communities.

The importance of integration hasn’t gone unnoticed in education policy circles. Across the country, some school districts are working to reduce economic segregation, and earlier this year President Obama proposed a $120 million grant program to support these efforts. But all these plans depend on higher-income parents’ voluntarily participation, which isn’t always easy to achieve.

Dr. Catherine Cushinberry, executive director of the national organization Parents for Public Schools (PPS), said that richer, white parents may want to keep their children out of poorer, more heavily minority schools because they mistakenly worry that these schools won’t be good for their kids. But, she said, it’s often possible to convince them that a more diverse school has advantages. That’s part of PPS’s mission.

“The source of our beginning, really, is in Jackson, Mississippi in the early ’90s,” Cushinberry said. “It was around this notion of white flight. We’re still dealing with similar issues as we did in 1991.”

Today, PPS supports parent activists in school systems from the Deep South to San Francisco, where rapid gentrification is raising new questions about school segregation. In addition to encouraging school integration, the organization works to get parents involved in improving the schools.

One recent, hopeful story comes from Oktibbeha County, Mississippi. Two low-income, mostly African-American high schools were closed, and the students moved to the more affluent Starkville High. Fearing that wealthier white families would pull their kids from the school, members of PPS Starkville worked with the state legislature, Mississippi State University, and other local groups to help smooth the transition. They found ways to get new funding for computers, books, buses and equipment, and to open new programs—including a pre-K. In the end there was no white flight. A number of white students actually left private schools for the new, more integrated district.

As far as Trump’s plan to increase school choice goes, Cushinberry said there just aren’t enough details available yet for her to comment. But, she said, in the wake of the election, she’s been thinking about how Americans can work together across social divisions.

“Certainly one way to unify communities is around bringing together strong, quality schools,” she said.