Elementary and middle-school students have made up significant ground since pandemic school closings in 2020 — but they are nowhere close to being fully caught up, according to the first detailed national study of how much U.S. students are recovering.

Overall in math, a subject where learning loss has been greatest, students have made up about a third of what they lost. In reading, they have made up a quarter, according to the new analysis of standardized test score data led by researchers at Stanford and Harvard.

The findings suggest that the United States has averted a dire outcome — stagnating at pandemic lows — but that many students are not on pace to catch up before the expiration of a $122 billion federal aid package in September. That money — the single largest federal investment in public education in the country’s history — has paid for extra help, like tutoring and summer school, at schools nationwide.

Even with the federal funds, the gains were larger than researchers expected, based on prior research on extra money for schools. Recovery was not a given, judging from past unexpected school closures, like for natural disasters or teachers’ strikes.

Still, the gap between students from rich and poor communities — already huge before the pandemic — has widened.

“One of the big and surprising findings is there actually has been a substantial recovery,” said Sean F. Reardon, a professor of poverty and inequality in education at Stanford, who conducted the new analysis with Thomas J. Kane, an economist at Harvard; Erin Fahle, executive director of the Educational Opportunity Project at Stanford; and Douglas O. Staiger, an economist at Dartmouth.

“But it’s an unevenly felt recovery,” Professor Reardon said, “so the worry there is that means inequality is getting baked in.”

Some children may never catch up and could enter adulthood without the full set of skills they need to succeed in the work force and life.

The students most at risk are those in poor districts, whose test scores fell further during the pandemic. Though the new data shows that they have begun to catch up, they had much more to make up than their peers from higher-income families, who are already closer to a recovery.

The result: Students in poor communities are at a greater disadvantage today than they were five years ago.

Yet there is significant variation. Some wealthy districts have barely improved. Some poorer districts have made remarkable recoveries, offering lessons for what has worked. In places like Durham, N.C.; Birmingham, Ala.; and Delano, Calif., students are now about fully caught up.

The data does not include any progress students may be making this school year, which will be measured in state tests this spring.

But the study suggests that many students will still need significant support, just as federal aid is running out.

“We seemed to have lost the urgency in this crisis,” said Karyn Lewis, who has studied pandemic learning declines for NWEA, a research and student assessment group. “It is problematic for the average kid. It is catastrophic for the kids who were hardest hit.”

Why Inequality Has Widened

The analysis looked at test score data for third- through eighth-grade students in 30 states — representing about 60 percent of the U.S. public school population in those grades. It examined pandemic declines from 2019 to 2022, and measured recovery as of spring 2023. It offers the first national comparison of recovery at a school district level. (It did not include high school students.)

Test scores fell most in poor districts. School closures, though not the only driver of pandemic losses, were a major factor: Schools in poor communities stayed remote for longer in the 2020-21 school year, and students suffered bigger declines when they did.

But once schools reopened, the pace of recovery was similar across districts, the analysis shows. Both the richest and poorest districts managed to teach more than in a usual school year — about 17 percent more in math, and 8 percent more in reading — as schools raced to help students recover.

Yet because poor districts had lost more ground, their progress was not nearly enough to outpace wealthier districts, widening the gulf between them. The typical rich district is about a fifth of a grade level behind where it was in 2019. The typical poor district: nearly half a grade.

Another factor is widened inequality within districts.

When looking at data available in 15 states, researchers found that in a given district — poor or rich — children across backgrounds lost similar ground, but students from richer families recovered faster.

One possible explanation: Even within districts, individual schools have become increasingly segregated by income and race in recent years, said Ann Owens, a sociologist at the University of Southern California. When this happens, she has found, achievement gaps grow, largely because students from wealthier families benefit from a concentration of resources.

Schools made up mostly of high-income families attract more experienced teachers. High-earning parents are more likely to invest in tutors or enrichment outside of school.

Even when schools offered interventions to help students catch up, lower-income families might have been less able to rearrange schedules or transportation to ensure their children attended. (This is one reason experts advise scheduling tutoring during the school day, not after.)

Racial gaps in student scores have also grown, with white students pulling further ahead.

Black students, on average, are now recovering at a faster pace than white or Hispanic students, the analysis suggests — but because they lost more ground than white students, they remain further behind. The gap between white and Hispanic students has also grown, and Hispanic students appear to have had a relatively weak recovery overall. The analysis did not include Asian students, who represent 5 percent of public school students.

Where Students Are and Are Not Recovering

Another factor in recovery: where students live.

Take Massachusetts, which has some of the nation’s best math and reading scores, but wide inequality. The recovery there was led by wealthier districts. Test scores for students in poor districts have shown little improvement, and in some cases, kept falling, leaving Massachusetts with one of the largest increases in the achievement gap. (Officials in Massachusetts hope that an increase in state funding for K-12 schools last year, as part of a plan to direct more money to poor districts, will help close gaps.)

In states like Kentucky and Tennessee that have traditionally had more middling test scores, but with less inequality, poor students have recovered remarkably well.

In just one of the states included in the analysis, Oregon, test scores in both math and reading have continued to decline.

Oregon officials pointed to investments they hope will show results in the future, including permanent funding for early literacy. “We are definitely not satisfied with where we are,” said Charlene Williams, director of the Oregon Department of Education. She added, “We need every minute of instruction we can get.”

Across the country, richer districts overall saw gains. But some have made little to no recovery, including Forsyth County on the outskirts of Atlanta; Rochester, Mich., in suburban Detroit; and Lake Oswego, Ore., near Portland.

And some poorer districts did better than expected, including large urban districts like Chicago, Nashville and Philadelphia, which saw big drops during the pandemic, but have had above-average recoveries.

In the years before the pandemic, big-city school districts often outpaced the nation in learning gains, even as they served larger shares of poor students and more students learning English as a second language.

“We have had to be more innovative,” said Raymond Hart, executive director for the Council of the Great City Schools, which represents 78 large urban school districts.

Bright Spots: What Has Worked?

When it comes to success, no one strategy appeared to lead the way.

In interviews in a sample of districts with outsize recovery, educators described multiple approaches. Some focused on spending more federal dollars on academics — and less, for instance, on renovating school buildings. Some prioritized adding instruction time — via intensive tutoring, summer school or other sessions — which research shows can produce significant gains. Many experimented, coming up with new strategies to help students, including their mental health.

“I stopped looking for these silver bullets,” said Alberto M. Carvalho, the superintendent in Los Angeles, which has seen above-average recovery compared with the rest of California, including strong recoveries for Black and Hispanic children. “More often than not, it is the compound effect of good strategies.”

The $122 billion federal aid package has helped fund this effort, especially in poor communities. The poorest districts received about $6,200 per student in aid, compared with $1,350 for the most affluent districts.

But the law required only 20 percent of the money be spent on learning loss, with no mandate to invest in the most effective strategies and little national accounting of how the money was spent. That has made it hard to evaluate the impact of federal dollars nationally.

One strategy some districts used was spending much more than 20 percent of their funds on academic recovery.

For example, Weakley County, Tenn., a lower-income and mostly white rural district, allocated more than three-fourths. (Tennessee gave districts incentives to spend at least half of their federal dollars on academics.) Today, Weakley County’s math and reading scores are fully recovered.

Its main focus was a tutoring program — students who are behind meet with experienced tutors in groups of three, twice a week. The district also hired instructional coaches, social workers and educational assistants who teach small groups in classrooms. “If you ask a teacher and say, ‘In a perfect world, if I have $30,000, what would you like me to buy?’ every teacher would say, ‘Another person in this classroom to help,’” said Betsi Foster, assistant director of schools.

Other districts focused on adding more hours of school, including Birmingham, Ala., a majority Black district where most students qualify for free or reduced price lunch.

The superintendent, Mark Sullivan, said he first wanted to make school year-round, a dramatic solution that found little support among families and teachers. So he offered a compromise: The district would hold extra instructional sessions available to all students during fall, winter and spring breaks, in addition to summer school.

Mr. Sullivan said some parents initially balked, but have come to love the program, in part because it provides child care during school breaks. More than a quarter of students typically participate.

Combined with other tactics, like hiring local college students as tutors, Birmingham made up for its pandemic losses in math.

The pandemic also spurred educators to innovate.

Among other strategies, Durham, N.C., a racially and economically diverse district that is now fully recovered, asked its most effective teachers to teach summer school and paid $40 an hour, up from the usual $25 rate.

It is one example of setting high expectations, which the superintendent, Pascal Mubenga, said was integral to recovery. “We did not just give that opportunity to any person; we recruited the best,” he said.

In the Delano Union school district, which serves mostly poor Hispanic students in central California, employees began making daily visits to the homes of students who were frequently absent — a ballooning national problem since the pandemic. The district’s absenteeism rate has fallen under 10 percent, from 29 percent.

The district focused on student well-being as a prerequisite for academics. For example, teachers now ask students to write down how they are feeling each week, a simple and free strategy that has helped uncover obstacles to learning — a fight with a friend, money problems at home.

“If a child is not mentally OK, no matter how good my lesson is, my students will not learn,” said Maria Ceja, who teaches fourth grade.

What Now?

Despite the successes, the pace of national recovery has been “too little,” said Margaret Spellings, a former secretary of education under George W. Bush. “We’re slowly recovering, but not fast enough.”

Congress has shown little appetite to add more funding, and many districts will soon end or cut back programs.

In a statement on Wednesday, the Biden administration did not push for more federal dollars, and instead renewed its call for states to take a greater role, both in financing programs and tracking the number of students receiving intensive tutoring or summer school.

Professor Kane, one of the researchers, advised schools to notify the parents of all children who are behind, in time to sign up for summer school. Despite setbacks on standardized tests, report card grades have remained stable, and polling indicates most parents believe their children are on track.

And what if students never catch up?

While test scores are just one measure, lower achievement in eighth grade has real impact in adulthood. It is associated with lower lifetime earnings, as well as a higher risk of unemployment and incarceration, research has shown.

At this rate, the United States will have a less skilled work force in the future, leading to lower economic output, said Eric Hanushek, an education economist at the Hoover Institution.

The highest-achieving students are likely to be least affected, said Marguerite Roza, director of the Edunomics Lab at Georgetown University — perhaps fewer will study advanced math and science and enter rigorous professions like engineering.

Students in the vast middle — some who may otherwise have become nurses or electricians, for example — could lose opportunities to establish middle-class lives. Community college enrollment is down from 2019.

And the lowest-achieving students may further disengage from school, making it harder to graduate from high school and hold down even low-wage jobs.

As the pandemic generation enters adulthood, they may face a lifetime of lost opportunities.