CIRCLEVILLE, Ohio (AP) — As one group of squealing, chanting students smack a ball into the pavement in a heated game of four square, another finishes an after-school writing lesson inside Circleville Elementary School.

Later in the library, an instructor guides other students in a role-playing activity on how to handle criticism from a sassy friend.

The children already snacked on breakfast bars and apple juice. And there will be more study time before buses take them home, some to the small city down the road and others to farther parts of these Ohio hills.

This after-school enrichment is funded largely by the federal 21st Century Community Learning Centers, a $1.2 billion program serving about 1.6 million low-income students nationwide that President Donald Trump proposes eliminating. His administration says there’s “no demonstrable evidence” that such programs improve students’ performance in school.

But a 2016 report from the Education Department, issued when Barack Obama was president, credited the funding with aiding state efforts to close the achievement gap and found the program “touches students’ lives in ways that will have far-reaching academic impact.”

Fourth-grade teacher Jennifer Walters said she sees that in Circleville, the heart of a county that solidly backed Trump in November.

“It shows drastically even in the amount of homework we get returned,” Walters said.

In Concord, New Hampshire, junior Elida Ntirenganya got after-school assistance with a tough bit of math — a necessity on her planned path toward medical school — and elevated both her grade and her optimism.

“If I go in a classroom and I don’t understand what the teacher is saying, not all hope is lost,” Ntirenganya said.

Students aren’t the only beneficiaries, said Susan Farrelly, who runs the Concord programs.

“Parents can stay at work until 6 o’clock and know their students are happy, safe and learning,” Farrelly said.

The funding program was created in 1994 as part of federal education legislation and then expanded under the 2001 No Child Left Behind legislation, which was signed into law by President George W. Bush. Schools, community groups and faith-based organizations get funding through a competitive process, and the programs typically offer targeted academic intervention and other activities.

Circleville has park outings and family movie nights that get parents involved. Concord offers debate and karate classes.

In Priest River, Idaho, after-school self-defense lessons with a National Guard recruiter led 17-year-old Emily Sedbrook to think about a future in the military.

“I didn’t really know what I wanted to do, but now I’m seriously considering enlisting,” she said.

The federal funding program wasn’t perceived as effective in its early years but has evolved and included accountability markers that show it’s delivering the intended academic and socio-emotional development for students, said Heather Weiss, co-director of the nonprofit Global Family Research Project, who has researched such programs.

“This is a good public policy investment, not just because they have strong data and a lot of it that demonstrate value, but also because they’ve made this commitment to learning and continuous improvement, which means we’ve got a good chance of continuing to get those outcomes,” she said.

The Education Department overview of 2014-2015 program data showed just under half of the regular participants for whom data were reported improved their math and English grades between fall and spring. Teachers reported that two-thirds of those students showed improvement in completing homework and class participation, and over half showed behavioral improvements.

More than a quarter of the elementary students who regularly participated moved from not proficient to at least proficient on state assessments in reading, and a least one in five regulars from middle- and high-school programs improved to proficiency in state math testing.

But some say that isn’t the full picture.

A report last month from the U.S. Government Accountability Office calls for better oversight of the 21st Century program. Available research comparing participants and non-participants indicates the program is effective in improving students’ behavior more frequently than their academic outcomes, but the Education Department doesn’t have enough data to know whether the program meets goals such as increasing school attendance and lowering disciplinary problems, the report said.

A large-scale, randomized study published a decade ago found that the funding stream didn’t positively affect student achievement, and that the after-school participants were more likely than non-participant students to get into trouble in school, said David Muhlhausen, who analyzes federal social programs for the conservative Heritage Foundation.

A similar large-scale analysis of the funding’s effectiveness hasn’t been repeated more recently, and lacking that, Trump is right to cut it, Muhlhausen said.

“If you’re going to judge a program based on whether it works or not, it’s the right call,” he said.

He cautioned against taking individual programs’ successes as evidence that the funding is effective overall, but school officials focus on that local impact.

In Ohio alone, about 270 programs received six-figure, multi-year 21st Century grants over the past five years. In Circleville, the sessions serve over 160 third- through 12th-graders, many of whom struggle academically.

After-school support was a driving factor in raising the district’s graduation rate from 79 percent in 2008 to about 94 percent last year, Circleville Superintendent Jonathan Davis said.

Some of the Circleville funding is nearing the end of its grant cycle, and organizers hoped to apply again. Without a shot at 21st Century grants, continuing after-school sessions would be “virtually impossible,” Davis said.

Associated Press reporter Kathleen Ronayne in Concord, New Hampshire, contributed to this report.