statement, “The lives of all of our students mean more to me than anything else, especially since three of them are actually mine.”

In New Rochelle, N.Y., the school superintendent, Jonathan P. Raymond, wrote in a Dec. 31 letter that a week of remote learning would allow the district to await a shipment of rapid tests from the state, and sign up more students for in-school surveillance testing.

Some schools announcing their decision to temporarily close cited the closing of other districts — adding to an uneasy sense of falling dominoes. When the superintendent in Mt. Vernon, N.Y., announced a two-week period of remote learning, he pointed to the closure of some schools in Maryland, where, on Dec. 17, Prince George’s County became the first major district to announce an extended shift to virtual teaching.

While Omicron is more contagious than previous iterations of the virus, early indications are that it is also less severe. Dr. Allen, from Harvard, said the existing recommendations from the Centers for Disease Control and Prevention still allowed schools to operate safely, especially because children were at such low risk of serious complications from Covid-19. Those measures include vaccination, masking, handwashing, the use of portable air filters and cracking windows.

authorized Pfizer-BioNTech’s vaccine boosters for 12- to 15-year-olds, but child and teenage vaccination rates have been disappointing in many places.

The C.D.C. also recommends a strategy called test to stay, in which close contacts of positive virus cases are given frequent rapid tests; only those who test positive must stay home.

But many schools still lack the number of rapid antigen tests they need.

Dr. Allen acknowledged that rapid tests were in short supply.

“We’ve been calling for rapid testing for a year and a half,” he said. “I find it stunning that the country has so failed to prioritize kids.”

Still, many parents said that despite the difficulties of closures, they trusted their children’s schools to make the right call.

Lorenzo Spencer, whose son is a freshman at Cass Technical High School in Detroit, said he was not surprised by the district’s announcement of a three-day closure — without remote learning — to test its 8,000 employees.

“There’s no playbook for what we’re going through,” Mr. Spencer said. “As long as they’re doing what they can do to stay safe, I’m all for it.”

Reporting was contributed by Giulia Heyward, Patricia Mazzei, Tariro Mzezewa, Eliza Shapiro and Mitch Smith.

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