Eleventh-grader Diane Garcia, center, asks teacher Julia Penn a question during her math class at Capital City Public Charter School in Washington. (Evelyn Hockstein/For The Washington Post)

At Achievement Prep, the test scores of low-income African American children rival those at wealthy neighborhood schools. Over at D.C. Prep, middle school graduates routinely go on to top high schools. And at Latin American Montessori Bilingual, the combination of instructional approaches is so attractive to parents that more than 800 names filled the school’s waiting list for pre-kindergarten classes last spring.

Such high-performing public charter schools in the District are in constant demand. But their policies of limiting new enrollment to certain grades and times of the year have been causing their class sizes to dwindle to less than half of their original size by the upper grades.

The enrollment cutoffs — which leave seats at some of the city’s most successful urban schools empty — put the charters in the middle of a debate that has divided advocates across the country.

Some argue that limiting student mobility is crucial to building the kind of routines and school culture that enable success and offer students the chance at a challenging, college-preparatory education. Others say it’s not fair for publicly funded schools to have a key advantage in bolstering academic performance that neighborhood schools don’t have: the ability to limit the number of underprepared transfer students they serve while focusing on more stable students who are better able to meet the schools’ higher expectations.

With 8,500 students on waiting lists for public charter schools in the District last spring, an increase of 18 percent from the previous year, many wonder whether it makes sense to limit the number of students who can access the highest-performing schools.

Julia Penn teaches math at Capital City Public Charter School in Washington. (Evelyn Hockstein/For The Washington Post)

“At a time when we are pushing for more funding to launch new charter schools, and when so many people are on waiting lists, you want to make sure that charter schools are open to accepting all students that come to them,” said Nina Rees, president of the National Alliance for Public Charter Schools, who encouraged charter schools this summer to “backfill,” or enroll students as seats become available.

By limiting enrollment, some advocates say, charter schools can offer poor students an opportunity many wealthier children take for granted: classrooms full of motivated students and few distractions.

“I see nothing wrong with charters functioning as a poor man’s private school. I see much that’s right about that,” said Robert Pondiscio, a senior fellow at the Thomas B. Fordham Institute. But he maintains that the schools should be more transparent about their competitive advantage. “What’s not right is to say, ‘We are just the same as any other public school,’ when you are not behaving the same way as a public school.”

The Harlem-based nonprofit group Democracy Builders estimated in a report this year that New York’s charter schools leave 2,500 seats empty in grades three through eight when students transfer out — a practice that appears to raise test scores in some schools.

With charter schools becoming a larger part of the District’s public school system, enrolling 44 percent of all students, the city has begun discussing the role that the once-experimental start-ups should play now that they have matured. This fall, Jennifer Niles, deputy mayor for education, is convening a task force to look at how traditional and charter schools can work together to address citywide challenges, including how to limit the thousands of students who cycle in and out of public schools each year.

Student mobility, particularly during the school year, is associated with lower academic performance and increased risk of dropping out.

Charter schools have far more control over how and when they admit new students, choosing which grades will accept new enrollment and whether they will take students midyear. Most of the city’s neighborhood schools must admit students at any time.

Some traditional schools also put limits on enrollment, with similar goals of offering a more rigorous program or specialized curriculum. Four of the school district’s six selective high schools stop accepting new applicants after 10th or 11th grade. And the school system’s dual-language schools and programs admit students after first grade only if they can pass a Spanish proficiency test.

Enrollment practices vary at charter schools and are not always transparent, but just over 85 percent of charter schools accepted applications for all grades last year, according to the D.C. enrollment lottery Web site My School D.C. and an analysis by the D.C. Public Charter School Board.

But some school leaders said that although they accept applications for every grade, they do not necessarily enroll students in all grades. Two Rivers, a Northeast charter school with the longest waiting list in the city, does not typically enroll students in eighth grade, its terminal year. And Capital City, a popular school in Northwest, does not enroll students in 12th grade.

Officials at both schools said they are committed to replacing students who leave in earlier grades. “It can be tricky, but for us, it has felt like the right thing to do,” said Karen Dresden, Capital City’s head of school.

But by high school, in order for students to meet the school’s rigorous graduation requirements, which include a major research project, students usually need more than a year to prepare, she said. So the school concentrates on enrolling most students in ninth and 10th grades. This year, the school accepted five juniors to backfill some empty seats.

Lindsay Kelly, a spokeswoman for KIPP DC, said that KIPP schools backfill when seats become available in all grades as a matter of principle. But they do it “in the least-disruptive way possible,” she said — enrolling them only at the beginning of the school year, a common practice in charter schools.

Charter schools lost 5 percent of their students in the 2013-2014 school year, according to District-level data. At the same time, the traditional school system grew by 2 percent.

Niles, the city’s deputy mayor for education, is overseeing an effort to restructure how schools are funded by tying per-pupil payments more closely to actual enrollment. The change is meant to give all public schools an incentive to enroll — and hold on to — students throughout the year.

In New Orleans, where nearly all public schools are now charters, schools must maintain the same number of seats in each grade and fill empty seats as they become available.

“We did not want a system where a school starts with 90 kindergartners and slowly weeds everyone else out so that by fifth grade, there are only 40 kids, and they happen to be the high-performing ones,” said Neerav Kings­land, former chief executive of New Schools for New Orleans, an organization that supports charter schools.

Scott Pearson, executive director of the D.C. Public Charter School Board, has argued that if the city’s charters grow too large, there could be additional pressure to regulate the independently operated schools as if they were neighborhood schools. That would endanger the flexibility that helps fuel their success, he said, including the option to not backfill.

Achievement Prep, in Southeast, has been recognized by the charter board as one of the city’s top-tier schools each of the past four years. The school advertises test scores as much as 40 points higher than nearby schools.

The most recent results from the city’s DC CAS standardized test showed that scores rose the longer students stayed at the school and as fewer students took the test.

In spring 2014, 114 students in the fourth grade took the math test, and 66 percent scored proficient or advanced. Of the 30 eighth-graders who took the test, 97 percent were proficient or advanced. The fourth-grade scores partly reflect students who came from Septima Clark, a failing elementary school Achievement Prep took over that school year. The school does not take applications for seventh or eighth grade.

Shantelle Wright, the school’s founder and chief executive, did not respond to requests for comment. But she talked about “the burden of being high-performing” during a panel discussion held at the Fordham Institute about expanding high-performing charter schools in 2014.

“You don’t get grace,” she said. “People want you to grow but don’t want to give you room for mistakes or change or things that come with growth.”

D.C. Prep’s Edgewood middle school campus had 70 fourth-graders and 36 eighth-graders take the test in 2013-2014. Its math proficiency rate for the fourth grade was 89 percent; for the eighth grade, it was 100 percent. Amber Walker, a spokeswoman, said that D.C. Prep used to accept new seventh- and eighth-graders but stopped because it did not have enough time to prepare them for admission to college-prep high schools.

Latin American Montessori Bilingual does not accept students after pre-kindergarten, an admissions policy that the charter board flagged as “extremely restrictive,” raising concerns about “equity and access” during a review of the school’s charter last November. At the same time, board members lauded the school for its “extraordinary” success.

Executive Director Diane Cottman said that the school’s policy is based on research that shows it takes seven years to gain complete biliteracy, the goal for the school’s students. She said school leaders are thinking about accepting applications in kindergarten.

“Lottery time is never easy for us when we have to turn away so many applicants,” she said.

Ted Mellnik contributed to this report.