Kindergarten students eagerly raise their hands to answer her questions at Powell Elementary School in 2011. A new study shows thousands of children enrolled in and left charter and public schools. (Marvin Joseph/The Washington Post)

Thousands of students move in and out of the District’s traditional and charter schools during the middle of the academic year, according to a new report scheduled for release Tuesday, a significant level of student transfer that raises broad questions about how the city’s public education is delivered and funded.

The report, from the Office of the State Superintendent of Education, analyzes the movement of students in pre-kindergarten through 12th grade during the 2011-12 school year.

More than 6,200 students left traditional and charter schools between October 2011 and June 2012 and didn’t re-enroll in any D.C. public school, according to the report. Officials said they don’t know where those children went: They might have dropped out, moved to another jurisdiction, entered a private school or started home schooling.

Another 4,600 students entered city schools, also from points unknown. Most of them enrolled in traditional schools, which saw a net gain of 338 children over the course of the year. Fewer enrolled in charters during the year, which posted a net loss of nearly 2,000 students. The numbers exclude adult students and students with disabilities who use public funds to attend private schools.

“This almost looks like our admissions are rolling,” said Jeffrey Noel, OSSE’s director of data management, who helped produce the report based on a citywide database that records student enrollments and withdrawals. “Do we have education programs that are designed for this amount of monthly exit and entrance?”

The report shows that students shuttle from charter to traditional schools and, on a much larger scale, enter and sometimes leave city schools entirely. The level of churn noted in the report highlights the system’s complex funding concerns and quirks, which critics say send millions more in taxpayer dollars to both charter and traditional schools than either should get.

Charter schools are funded based on the number of students enrolled each year on Oct. 5. The per-pupil payment could range from about $9,000 to about $44,000, depending on the child’s grade level and special needs.

A charter’s funding remains the same no matter how many students it gains or loses after Oct. 5. Even though charters lost nearly 2,000 students during the 2011-12 school year, the schools continued receiving tax dollars as if those students never left.

The traditional school system is funded based on enrollment projections that officials publish each spring for the following fall. Those projections are routinely higher than actual Oct. 5 enrollment, which means the school system regularly receives millions of dollars more than it would if it received funding only for students enrolled on that date.

Officials have long argued that they use the additional funds to accommodate students who enter midyear. In the 2011-12 school year, the school system projected about 2,000 more students than it officially enrolled. The OSSE study shows that while thousands of students did enter the school system during that year, thousands more exited — and the system saw a net increase of fewer than 400 students.

D.C. Chancellor Kaya Henderson said internal school system numbers show a larger increase in students. She said OSSE’s report identifies key questions about funding and student movement that she and other leaders — whom the mayor has tasked with developing a comprehensive plan for the future of D.C. education — should discuss.

“This identifies some important areas that we need to dig deeper into,” Henderson said. “It begins a conversation that to date has just been driven on anecdotes and provides some supporting data.”

Federal officials don’t collect comparable mobility data nationwide, but the proportion of students entering and exiting D.C. public education is about 50 percent higher than in Fairfax County. Studies have found that students who move between schools frequently are more likely to struggle and drop out than students with more stable academic careers.

“The level of mobility in this city is far higher than I think any of us imagined,” said Scott Pearson, executive director of the D.C. Public Charter School Board. “We need to understand better who those students are and why they’re moving.”

Pearson said the report “bursts a number of myths about charters,” including the perception that charters push out large numbers of difficult students midyear, sending them into the traditional school system, which is required to take them. In 2011-12, 561 students — less than 2 percent of total charter enrollment — moved to traditional schools between October and June.

Still, that’s more than the 44 students who moved from the traditional school system into a charter school in the middle of the year.

OSSE’s report does not show how student movement varies by grade level or by school; it also doesn’t say how many students are moving from one traditional school to another, or from one charter to another. Officials said they have not completed that analysis.