Schools reopened. Students and teachers were, for the most part, kept safe from covid. But what about academic recovery? Did the money help kids get back on track?

Two new reports offer the same answer: Yes.

“There were many reasons to think the money wouldn’t have a very big effect on kids learning because it wasn’t targeted and there were lots of other needs,” said Sean Reardon, an education researcher at Stanford University and co-author of the first paper. “But in fact it did have a significant effect on learning.”

Yet it didn’t finish the job. Between 2019 and 2022, the average U.S. student lost about a half grade level in math and a third of a grade level in reading, according to test data from 30 states analyzed by researchers at Harvard and Stanford universities in the Education Recovery Scorecard project. Students made up about 30 percent of the loss in math and 20 percent of the loss in reading between spring 2022 and spring 2023. Some — though not all — of that can be traced to the federal funding, the researchers conclude. (Results of spring 2024 testing are not yet available.)

“Despite what is an unprecedented amount of money, kids are still far behind,” said Dan Goldhaber, an education researcher at the American Institutes for Research and the University of Washington, who co-authored the second research paper.

Why wasn’t $190 billion — the largest one-time education investment in U.S. history — enough? Among the reasons: Some of the money was spent on covid mitigation and testing, the main focus of the legislation, not academics. Not all of the money for academics was invested in the most effective strategies, because they had other priorities or perhaps were unaware of the research. Not every district got robust funding. And the losses were deep.

Fully catching kids up would require additional spending, the researchers find. The opposite is actually unfolding, with districts running out of the money already allocated. Schools are required to spend the last of the covid relief funding in the coming months, and across the country, districts are cutting staff and programs that were aimed at accelerating academic recovery.

“If the goal is having all students made whole from the pandemic, I do think that states will need to step up,” said Tom Kane, a professor of education and economics at Harvard University and co-author of the first paper, which was produced by a team of researchers from Harvard, Stanford and Dartmouth universities.

Still, the gains already recorded were big enough to pay for themselves, based on how increases in academic achievement translate into higher wages in adulthood, Kane said.

Both papers take advantage of a quirk in how the nearly $190 billion in federal covid relief funds, which came over three allotments in 2020 and 2021, were allocated to K-12 school districts. The government relied on a formula that gave more money to districts with higher portions of students living in poverty. Due to oddities in that formula, districts with similar poverty levels got different amounts. Among the districts where at least 90 percent of students are from families poor enough to qualify for free or subsidized school lunches, federal allocations ranged from less than $4,000 to more than $13,000 per student — in some cases, much more.

The differences among district allocations allowed researchers to estimate the relationship between more funding and test scores. One study examined funding from only the third allocation, by far the largest, approved in 2021; the other looked at the second and third tranches. Both studies examined the impact of the money on all districts, rich and poor.

The two teams came to the same conclusion: An additional $1,000 per student in federal funding translated into a gain of about 3 percent of a grade level of learning in math. For reading, the gains were similar in one study and a bit smaller in the other. These results are in line with what pre-pandemic studies found of earlier, more modest increases in education spending.

This implies that giving a school district an extra $8,000 per student would have been enough to make up nearly half of the average math losses. That compares to average per-pupil spending of $13,187 in 2019, before the pandemic and the surge of federal dollars.

Looking at it another way, the Harvard-Stanford team compared achievement levels between high-poverty districts with similar levels of past achievement that received larger grants and smaller grants. Students in the high-grant districts gained about a fifth of a year more in math than the low-grant districts did and almost as much in reading.

The money appears to have made a difference in the School District of Philadelphia, which received more than $1.6 billion in federal funding — more than $14,000 per student. Between spring 2022 and spring 2023, students made up on average a half grade in math — more than 80 percent of the average losses sustained in Philadelphia between 2019 and 2022.

A large share of money in Philadelphia was spent on extra learning time for students — before and after school and over the summer, and to add social services and counselors. The district also spent $325 million on facilities improvements, something meant to make old buildings safer but that did not directly impact student learning.

Superintendent Tony B. Watlington, Sr., in a statement, credited the federal funding with playing a key role in Philadelphia becoming “the fastest improving large, urban district” in the country.

Now the district is hoping that a statewide lawsuit challenging Pennsylvania’s school funding formula will result in more funding for Philadelphia to replace the lost federal dollars. For now, the schools are using reserve funds to maintain the supports put in place, said Christina Clark, a spokeswoman for the district.

“We’re working on preserving those because we’ve seen the impact it’s had on students,” she said.

The Cleveland Metropolitan School District also saw significant federal spending — nearly $427 million in the second and third allotments, or about $12,000 per student. As in Philadelphia, students also gained about a half year of learning in math between spring 2022 and spring 2023, but the losses in Cleveland were deeper, so this erased only about half of the slide since 2019. Early data from spring 2024 testing shows progress continued, though details were not available, officials said.

One of Cleveland’s key investments was a robust summer learning program, which combined engaging and fun activities with academic review. The district also upped funding to each school, and some used the extra for tutoring or other academic supports.

“We would not have been able to do some of this work at scale if we did not have this funding,” said Selena Florence, the district’s chief academic officer.

With the federal money running out, Cleveland this year cut back its summer program, which had served more than 5,000 students in the last few years, by about half. The district cut back other programs too, and eliminated the extra school-based funding.

But Florence said she is optimistic that Cleveland can continue making progress. “Having additional money is always going to help us doing the work we have to do,” she said. “The work can certainly be done without it.”

Researchers did not credit all the academic gains recorded to more federal spending. Many districts that received no money, or very little, saw large gains. These were typically wealthy districts that consistently have other advantages.

And low-income districts saw improvements beyond what the federal funding alone would have predicted, the Harvard-Stanford group found. Among districts with at least 70 percent of low-income students, between one-third and one-half of the improvement in test scores could be attributed to the federal funding. It was not clear what accounted for the rest; possibilities include deeper parental involvement, extra efforts by teachers or extra local funding.

Kane bemoaned that there is scant data to explain how districts spent their money, seeing a missed opportunity to assess which interventions were most effective. Past research has found certain initiatives — such as intense tutoring or small class sizes in the early years — produce greater academic gains than others. The federal rules required that districts spend at least 20 percent of their money addressing learning losses, but there was little guidance beyond that.

“In the absence of being able to say which interventions work, we can ask the next best thing,” he said. “Did the districts that got and received more money go faster in catching up?” The answer, they found, is yes.