“Most of our money went toward students and closing the gap in learning loss,” Ms. Newman said.

Other districts have spent more relief funds on facility upgrades. Researchers at Georgetown University’s Edunomics Lab estimate that a quarter of the last round of relief funds would be spent on facilities.

Oregon’s Klamath County school district plans to use about 30 percent of its $16.1 million federal share on academic recovery programs and 70 percent on facilities projects. Those include buying new turf fields, replacing HVAC systems, upgrading flooring, renovating bleachers in baseball fields, constructing a gym and surfacing an elementary school parking lot.

Glen Szymoniak, the district’s superintendent, said the projects would help improve student safety and wellness. Some bleachers had “nails popping up” and boards that were cracking. Without a new turf field, some students would not have a place to play during recess, and one of the football teams would need to travel half an hour to practice. Officials chose not to spend the funds on hiring staff because the money would eventually run out.

“We would have to fire them in three or four years,” Mr. Szymoniak said. “It’s not a way to treat people.”

Officials instead tapped millions in annual state funding to hire reading specialists, add counselors and expand small group and project-based instruction, which Mr. Szymoniak said has already led to improved proficiency in math among elementary school students this year, according to early assessments. Last year, 36 percent of third graders met state grade-level expectations for English, down from 42 percent in 2019.

Wisconsin’s Cudahy School District is spending about 80 percent of its $4.7 million in relief funds on facilities upgrades and 20 percent on academic recovery, which includes professional development for staff members and employing literacy specialists. Among the district’s third graders, 29.8 percent were proficient in reading in 2022, up from 23.6 percent in 2021 and down from 35.9 percent in 2019.

Tina Owen-Moore, the district’s superintendent, said officials were worried about sustaining salaries, so they spent more on upgrading HVAC systems and remodeling classrooms to allow for social distancing.