As U.S. public schools have grown increasingly segregated by race and income, there is a growing number of school districts and charter schools striving for greater balance among their students, according to new research released Tuesday by the Century Foundation, a left-leaning think tank.

Researchers identified 91 school districts and charter school chains serving more than 4 million students — including the District of Columbia and Chicago public school systems — that are using tools such as magnet schools, weighted lotteries and changes in school attendance zones to create more balance between white students and those of color and between low-income and more affluent children.

That is more than double the number employing such tactics in 2007, according to Halley Potter, a fellow at the Century Foundation and an author of one of two new reports.

The new methods, which rely on choices and incentives, are a far cry from the forced busing policies that were a hallmark of early desegregation efforts. In many cases, school districts are focused on integrating children of different economic backgrounds, as opposed to race, although the two are inextricably linked, Potter said.

“Part of the growth of these socioeconomic strategies is a reflection of the legal environment for racial desegregation, which just continues to get trickier,” she said. “Communities serious about tackling integration find that these tools are the best way.”

U.S. public schools are more racially segregated now than they were in the 1970s, according to the study. More than one-third of all black and Latino students attend schools that are more than 90 percent non-white, according to the Century Foundation. For white students, the image is flipped: More than one-third attend schools that are nearly all white.

Research shows that children from low-income families — a group that is proportionately more African American and Latino — perform better academically when they attend schools that are not majority-poor. Segregated, high-poverty schools tend to have fewer experienced teachers, fewer challenging courses, inferior facilities, less access to private funding and higher drop-out rates.

In Hartford, Conn., for example, black and Latino students from the city attend regional magnet schools along with white students from more affluent suburbs. In 2013, there was no gap in state reading test scores for third-­graders, meaning white, Latino and black students all scored about the same. The achievement gap also was eliminated between Latino and white students on the fifth-grade reading test. And by 10th grade, the gap between low-­income students and their more affluent peers was 5 percentage points on the reading test, compared with a statewide average of 28 points.

There is no evidence that integration gives a similar boost to the academic achievement of affluent students, Potter said. But she and other researchers argue that exposure to people of other backgrounds teaches skills that are essential to success in a globally competitive world.

“You can’t argue that going to a more diverse school is necessarily going to help middle-class kids who are already coming in as high achievers,” Potter said. “But when kids have a chance to be in a classroom with peers from different backgrounds, it promotes communication, critical thinking and the kinds of cognitive skills that are at the heart of the academic mission.”

The most common strategy used by the school districts and charter networks is to redraw school attendance boundaries in a way that captures a more diverse student population. About a quarter of the districts have created magnet schools, others have school-transfer policies that take into account family income levels, and others have school lotteries that give extra weight to income levels to promote diversity.

“One of the take-home mes­sages is the variety of different strategies that are being used,” Potter said. “When people think of integration, they only have one idea in their head of what that means — usually it’s forced changes of who goes to school where. But there isn’t a one-size-fits-all approach. It’s important to look to the examples of what other communities and leaders have done to tackle these questions.”

Integration is a priority of John B. King Jr., the acting education secretary, who created a small pilot program as education commissioner in New York State that offered grants to districts to launch programs aimed at breaking up concentrated poverty in their schools. King has said that he plans to use competitive grants to encourage diversity and will work with other agencies to encourage more integrated schools and communities. In his budget proposal Tuesday, President Obama is expected to seek money in 2017 for a competitive grant program for school districts to launch integration programs.