Yet Mr. Newsom, well aware of Tulare County’s conservative politics, has refrained from confronting Outside Creek. His spokesman would say only this: “School officials should use guidance from federal, state and local public officials in deciding how best to serve students.”

Karen Elliott, the county’s public health director, has stressed that it is best for parents to keep their children home. Three-quarters of Outside Creek’s parents have decided to do just that, with their children taking independent study courses devised by Mr. Bravo’s staff.

The situation in Outside Creek is exceptionally rare not only for California, but also nationwide. Every state has ordered or recommended school closures. While some religious schools initially dragged their feet, the overwhelming majority of the nation’s schools are now shuttered. Even in states that strongly advised schools to close without a formal mandate, like Kentucky and South Dakota, state education departments said on Tuesday that they were unaware of any open public schools.

Outside Creek, the oldest school in Tulare County (it opened during the Civil War), consists of two small buildings surrounded by rows of walnut trees. College pennants hang in the cafeteria, each signifying where a graduate landed. Just about everyone associated with the school proudly calls themselves Swamp Rats, a name inspired by a former football coach who told his players they needed to be as tough as those creatures. The moniker stuck, and the school even voted to change its mascot from the Eagles.

“It’s more than just a school,” said one Swamp Rat parent, Sylvia Gomez. Mrs. Gomez said that while her family is “one of the lucky ones” with a home computer, she decided against keeping her daughter home. “I send her because education is more important than anything in the world.”

Ben Orozco, a dispatcher at a trucking company, said his wife’s family had sent generations of their children to Outside Creek. He said the area was used to hardship and bad breaks. “At the end of the day, I feel like we have a higher percentage to get in an accident and die than get the coronavirus,” he said before he dropped off his 10-year-old daughter, Belynda. “If we decide to keep our kid in school,” he added, “that’s our decision as a parent, nobody else’s.”

Swamp Rat parents have also asked why Outside Creek Elementary should close when day care centers, which are exempt from the state’s shelter-in-place orders, are still open all over town. “There’s day cares open with more children,” said one parent, Marylu Cuevas, who would have continued sending her children to school if not for the fact that a hospice care worker lives with them.