Despite billions of federal dollars spent to help compensate for pandemic-related learning loss, progress in reading and math stalled over the past school year for elementary and middle school students, according to a new national study released Tuesday.

The hope was that, until now, students were learning at an accelerated clip, but that didn’t happen during the last academic year, according to NWEA, a research organization that analyzed the results of its widely used student assessment tests taken this spring from about 3.5 million public school students. students in third through eighth grade.

In fact, students in most grades showed slower than average growth in math and reading, compared to students before the pandemic. That means learning gaps created during the pandemic aren’t closing — if anything, the gaps may be widening.

“We’re actually seeing signs of a rebound,” said Karyn Lewis, lead researcher on the study.

On average, students need the equivalent of an additional 4.5 months of instruction in math, and an additional four months in reading to catch up to the typical pre-pandemic student. That is in addition to the regular classroom time. Older students, who generally learn more slowly and face more difficult material, are the furthest behind.

National tests last year showed that students in most states and across nearly every demographic group experienced troubling setbacks, especially in math, because of the pandemic, according to the National Assessment of Educational Progress, a gold standard federal exam. And last month, national maths and reading test results for 13-year-olds hit their lowest level in decades.

Students who don’t achieve may be less likely to go to college and, research has shown, could gain $70,000 less during their lifetimes.

The question for educators and federal officials is how to deal with the four-month gap. Few academic interventions—standard instruction, summer school, smaller class sizes—are powerful enough on their own. And the latest round of federal Covid relief funding — a record $122 billion to help schools recover from the pandemic — must be spent or committed by September 2024.

Recovery plans varied greatly across thousands of school districts in the United States, with little national accounting of how the money was spent. Many districts were juggling competing priorities — including raising teacher pay, addressing student mental health and repairing long-neglected buildings.

The Biden administration required districts to spend at least 20 percent of their aid on academic recovery, an amount some experts criticized as too low.

“The recovery has been undersized from the start,” said Tom Kane, a Harvard economist. “We’ve seen examples of programs that have made a difference for students, but none have been at the scale or intensity needed.”

Research indicates that high-dose tutoring—which pairs a trained tutor with one to four students, at least three times a week, for a full year—can produce gains. equivalent to about four months of learning.

But it is expensive and difficult to scale. A federal investigation in December found that only 37 percent of public schools reported an offer such teaching.

Summer school, a popular option offered by many districts, may be giving way worth a little over a month of progress, according to research. This means that the average student would need to attend several sessions of summer school, or layer it with other interventions, to achieve.

Nationally, black and Hispanic students were more likely to have attended schools that remained remote for longer and often recorded greater losses compared to white and Asian students.

They now have more ground to make up, and, like white and Asian students, their learning has not accelerated.

“What we’re seeing here is a lack of intent,” said Denise Forte, chief executive at the Education Trust, an advocacy group focused on students of color and students from low-income backgrounds.

Although federal aid money was supposed to be focused on the students most affected by the pandemic, she said, “we clearly don’t see that. There was a real lack of accountability from states to know if those dollars were being spent that way.”

Even with one year of federal aid left, it may be difficult for some districts to pivot, said Phyllis W. Jordan, the associate director at FutureEd, a nonpartisan research group at Georgetown University that recently conducted the analysis. federal aid dollars in California and found that hundreds of school districts had already spent all or most of their money.

Dr. Kane, the Harvard economist, suggested that some states and school districts may need to turn to less popular choices — how to extend the school calendar. Another possible stop: an optional fifth year of high school.

“If we don’t make the necessary changes,” Dr. Kane said, “we’re going to add students with the bill.”

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