The researchers broke the students into different groups based on how much time they had spent attending in-person school during 2020-21 — the academic year with the most variation in whether schools were open. On average, students who attended in-person school for nearly all of 2020-21 lost about 20 percent worth of a typical school year’s math learning during the study’s two-year window.

Some of those losses stemmed from the time the students had spent learning remotely during the spring of 2020, when school buildings were almost universally closed. And some of the losses stemmed from the difficulties of in-person schooling during the pandemic, as families coped with disruption and illness.

But students who stayed home for most of 2020-21 fared much worse. On average, they lost the equivalent of about 50 percent of a typical school year’s math learning during the study’s two-year window.