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.

So they modify their claim: Biden is addled and wandering, except when he is given some sort of medication, perhaps a stimulant, that reverses that effect. And here we are, with Trump and those seeking his reelection to the White House demanding that Biden submit to some sort of drug test before this week’s first presidential debate, purportedly in effort to sniff out this theoretical drug.

Experts who spoke with The Washington Post, though, confirm that no such medicine exists.

At the outset, we should recognize that this claim is generally not offered seriously. It is, instead, an effort to escape the aforementioned contradiction, a way to hold both that Biden is incapable of serving as president and yet, unquestionably at times, not demonstrating any such impairment. What’s more, the demand that Biden undergo a drug test is itself not serious. It is, instead, meant to create a condition that allows Trump and his allies to continue to claim that any strong performance from Biden is a function of medication. The result is win-win for Trump, who can blame any loss on this wonder drug.

If you haven’t been paying close attention to the debate (such as it is) over this idea, consider a snippet of conversation that aired on Fox Business on Tuesday morning.

Host Maria Bartiromo — no stranger to conspiratorial argumentation — hosted Rep. Eric Burlison (R-Mo.) where she offered an observation made by Rep. Ronny Jackson (R-Tex.).

“Jackson says Biden will have been at Camp David for a full week before the debate,” Bartiromo said, “and that they’re probably experimenting with getting doses right. Giving him medicine ahead of the debate.”

Burlison agreed that this was possible, though he offered that it might be more innocuous than medication. Perhaps, he said, Biden’s team is “jack[ing] him up on Mountain Dew.”

Jackson, you will recall, was Trump’s personal doctor while Trump was in the White House. He is not an expert on cognition or cognition-related illnesses, though he is familiar with drug prescription.

“Nothing like that exists,” Thomas Wisniewski, director of the NYU Langone Alzheimer’s Disease Research Center, told The Washington Post by phone. “There are no medications or stimulants that can reverse a dementing process transiently.”

“All of those sorts of things can perhaps make an individual more alert, but quite often that can just exacerbate their confusion, as well,” he added. “They can be more stimulated, but they are not going to be behaving in a more cogent or normal fashion as a result of being stimulated by anything. Very often it’s the reverse.”

Adam Brickman, associate professor of neuropsychology at Columbia University Irving Medical Center, concurred with that assessment.

“I’m not aware of any medications that would reverse or mask cognitive decline,” Brickman said. What’s more, he noted that “the association between energy and cognition is a very weak one. In other words, someone could have low energy but totally intact cognition and vice versa.”

Both doctors noted that such a medication would be of enormous benefit. Reversing cognitive decline, after all, would mean turning back the damage done from diseases that impair cognition in the first place. It would be akin not just to treating the pain of a broken bone but, instead, to directly healing the break itself. Sadly, no such drug for cognition exists.

Again, the argument that Biden is or could be receiving targeted treatment to improve his mental state fails multiple logical tests. Why, for example, would he not simply take this medication all the time? Why would he need to retest his dosage for a debate after giving a lengthy State of the Union address? The answer is that there is no good answer, that the intent of the allegations is simply to maintain the political argument that Biden is mentally deficient even in the face of his performing above expectations in a debate.

Not that that argument is itself well-grounded, as Brickman noted.

“It’s not possible to conclude or to determine whether someone has subtle cognitive change without doing a true clinical evaluation,” he said. “So to judge whether there’s an underlying disease or neurodegenerative condition based on public speeches or interactions that are captured by the press is irresponsible.”

Wisniewski offered a more succinct dismissal of the claims being made by Trumpworld.

“It’s spurious,” he said. “It’s nonsensical.”

In other words, if Biden fares better in the debate this week, it’s not because of a secret Camp David drug-dosing regimen that enabled the administration to mask Biden’s physical degeneration. It’s because Biden out-debated the guy who won’t accept that that’s possible.