Students Osagie Atkinson, left, and Mitchell Shapiro, both 15-year-old sophomores at Washington Latin Public Charter School in Northwest Washington, go over a math problem in the school library between classes in October. The school has a mission of including diverse families, but it has served a lower share of low-income families over time as its performance and reputation have climbed. (Allison Shelley/For The Washington Post)

It was still dark at 7 a.m., when a yellow bus pulled up in a strip-mall parking lot outside a ­Rent-A-Center in Southeast Washington. A dozen teenagers climbed on board for a 10-mile ride to one of the city’s highest-performing public schools.

Three decades after cities across the country dismantled mandatory busing programs designed to desegregate public schools, Washington Latin Public Charter School dispatches buses across the city to neighborhoods with public housing and others with million-dollar homes. By 8 a.m., the students, dressed in polos and khakis, converge in a refurbished brick school, where the sign in the hallway offers a Latin welcome: “Salvete.”

Charter schools, which enroll students through a citywide lottery, have the potential to create schools that are far more diverse than traditional neighborhood schools, which, by virtue of their attendance boundaries, sort families by race and class.

Despite the promise of becoming social mixing grounds, the District’s charter schools are slightly more racially segregated than the city’s traditional public schools.

Seventy-six percent of the city’s public charter schools served exclusively, or almost exclusively, Latino or African American students in the 2014-2015 school year, compared with about 63 percent of the city’s traditional schools, according to enrollment data from the Office of the State Superintendent of Education.

Most charters — and the philanthropists who support them — have focused on serving students with the greatest needs in neighborhoods of concentrated poverty. Washington Latin represents a smaller, but growing, number of charter schools with a broader mission to serve children from all parts of the city.

“We see charter schools as an opportunity to bring kids together from different backgrounds and give low-income students what may be the best chance at academic success,” said Halley Potter, a fellow at the Century Foundation who helped found the National Coalition of Diverse Charter Schools, a new network that includes Washington Latin and a few other District schools.

Students listen to teacher Carl Lyon (not pictured) during a sophomore advisory period at Washington Latin Public Charter School in Northwest Washington. (Allison Shelley/For The Washington Post)

Dakota Campfield, 11, a sixth-grader, waits on the bus just before 7 a.m. in a parking lot in the Anacostia neighborhood of the District. (Allison Shelley/For The Washington Post)

Research during the past ­half-century has shown that integration can be an effective tool for school reform. Low-income students tend to do better in socioeconomically varied schools, where there are higher levels of parent engagement and advocacy and where a majority of students are college-bound. Studies also show that more experienced and effective teachers tend to be concentrated in more affluent and racially diverse schools.

But when charter schools took root in the 1990s, the U.S. Supreme Court was dismantling mandatory desegregation orders, and federal efforts to break down barriers by race and class were transitioning to an era of school accountability based on student results. Many charter schools opened in urban centers that had been abandoned by white and middle-class residents.

By 2010, a national study by the Civil Rights Project at UCLA found that 70 percent of black charter school students attended “intensely segregated” schools, where at least 90 percent of students are black or Latino, twice the rate in traditional public schools. The report called charter schools a political success and a “civil rights failure.”

Some charter schools, such as KIPP DC, have been successful working in racially isolated schools in poor neighborhoods, developing specialized teaching strategies and support for students who come to school years behind. A recent analysis of standardized test performance and student academic growth by the D.C. Public Charter School Board shows that the city’s charter students performed better overall in more diverse schools, but there were some exceptions: African American students’ growth in reading actually declined as the percentage of white students increased. Scott Pearson, executive director of the D.C. Public Charter School Board, said the report shows diverse and non-diverse charter schools can be successful.

Many parents and advocates see more holistic benefits to integrated schools, including broader exposure and better preparation for college life and beyond.

Kenneth Wright drops his son off to take the bus to Washington Latin from Anacostia in the mornings. “As my son gets older, the world will become more diverse for him,” he said. “The earlier he can experience that, the better he can adjust and develop the skills to navigate that type of environment.”

Median income has grown exponentially in many D.C. neighborhoods in the past decade, and the portion of white children ages 3 through 17 enrolled in schools has grown from 14 percent to 18 percent since 2000, census data show.

But the public schools remain largely segregated. African American students comprised 67 percent of students in traditional schools and 76 percent of those in charter schools last year. White students, who made up 12 percent of traditional school students and 5 percent of those in charter schools, were concentrated in a relatively small number of schools: at 10 traditional schools and two charter schools, more than half of students were white.

By a measure of socioeconomic diversity, charter and traditional schools served about the same share of students who are considered “at risk,” a designation that includes those from families that receive welfare or food stamps, who are in foster care or are homeless, or who are performing at least a year behind in high school.

But those students were spread more evenly across charter schools. The portion of at-risk students was less than 10 percent at about 15 traditional schools in affluent neighborhoods and greater than 75 percent at more than two dozen schools, mostly in poor neighborhoods east of the Anacostia River. Among charter schools, just four schools had at-risk populations below 10 percent and three had at-risk populations above 75 percent.

Charter schools that serve the greatest mix of students tend to be in central parts of the city, in proximity to gentrified neighborhoods such as Columbia Heights and Brookland. They are in high demand, with an influx of higher-income families who are looking for alternatives to lower-performing, segregated neighborhood schools.

Washington Latin first opened in a church near National Cathedral, making it the only charter school in the affluent neighborhoods west of Rock Creek Park.

The school’s mission is to make a challenging classical education accessible to students from all areas of the city.

Nearly 10 years later, the school is located several miles east in a former traditional public school in Petworth. Aided by busing, it has one of the most geographically diverse student bodies in the city, with students traveling an average of 4.7 miles to the middle school and 3.3 miles to the upper school. It’s also racially mixed. The combined enrollment for its middle and upper campuses is 46 percent black, 39 percent white, 10 percent Hispanic and 4 percent Asian.

The school takes a philosophical approach to what it means to be diverse. Socratic seminars, in which students are expected to participate and raise questions, encourage a diversity of ideas. And through the study of classical philosophers such as Aristotle and Plato, students grapple with universal questions, such as “How do I decide what I believe is true?” and “How can I become a good person?”

“One of the most satisfying things is teaching this class and realizing that these questions matter to every kid,” said Bill Clausen, chair of the Humanities Department.

Teachers and coaches also facilitate conversations about the very real differences students experience based on race and class. In one class about the history of Washington, D.C., students sometimes talk about their own lives when they look at data that shows how the average annual family income in Upper Northwest is about $200,000 higher than in Southeast.

Randy Yearby Jr., left, 17, a senior, and Robbie Pearson, 15, a sophomore, wait for the bus just before 7 a.m. in a parking lot in Anacostia. (Allison Shelley/For The Washington Post)

College banners hang in the classroom of teacher Chrys Latham, as she leads a senior advisory period at Washington Latin Public Charter School. (Allison Shelley/For The Washington Post)

Martha Cutts, head of school, said diversity, including socioeconomic diversity, is an “essential characteristic” of Washington Latin, but she said it has become more difficult to meet diversity goals.

A citywide enrollment lottery can open the door to integration, but it’s a rough tool to control for it, experts say. Choice systems tend to benefit people with the most information, often parents with higher education and higher incomes.

As Washington Latin’s academic reputation has grown, so has interest, particularly among wealthier families. Last year, there were 1,600 applications for 119 available seats (including 46 seats offered to siblings of current students).

Washington Latin’s middle school has one of the lowest at-risk populations of any school in the city, with just 4 percent of students eligible, and it’s one of two charter schools with white enrollment above 50 percent.

Cutts said she would like to see a lottery preference for children from low-income families, similar to preferences used in some other cities.

Brooklyn Prospect Charter School in New York, a diverse school with a long wait list, maintains economic diversity by aggressively targeting recruitment and also by setting aside a specific number of seats in the lottery for students who live in poverty.

“It takes constant and thoughtful stewardship, planning, and tactics,” said Daniel Kikuji Rubenstein, co-founder and executive director of the school.

This year, Washington Latin added the new bus line to Anacostia to encourage more students from that part of the city.

Randy Yearby Jr., 17, rides that new bus. He said he went to an all-black school in Prince George’s County before he moved to the District and enrolled in Latin. He recalled going to a “popsicle social” before the first day of school and walking up to a group of kids.

One was white, another Asian, a third was a girl from Palestine. They started talking about their childhoods. “I left that conversation feeling like I had traveled across the world,” he said.

Students arrive for class at Washington Latin Public Charter School in Northwest Washington on Oct. 23. (Allison Shelley/For The Washington Post)