Low attendance can create a feedback loop: older students with some degree of autonomy may be disinclined to show up when they know that their friends will be absent. Or parents may take their kids out once the school reaches some imagined threshold of positive cases. (I have felt this gravitational pull more than once at morning drop-off—if so many kids aren’t here, maybe mine shouldn’t be, either.) A principal in Brooklyn, whom I will call D., leads a school that enrolls about seven hundred students; lately, he has felt an urgent need to track each of them. It’s “a delicate dance,” D. said. “You have to be able to do it without hounding families who are already stressed.”…

At the moment, it is not necessarily clear who is coming to school. The new guidelines mean that more students at home are eligible to be marked present for checking in with a teacher via video or uploading classwork to Google Classroom. When I asked if the D.O.E. has an estimate of what percentage of students are physically in school every day, as opposed to marked present, a spokesperson responded, “We post our daily attendance figures online.”

The general uncertainty has parallels with the earliest days of remote learning, back in the spring of 2020. Castellano said, “At first it was, ‘If they do an assignment, you count them as present.’ Then it became, ‘If you have any interaction with them, then it counts as present.’ Then it became, ‘If you have a conversation with their parent and they say that their child will do the assignments, then it counts as present.’ ” She went on, “It becomes a philosophical question: What does it mean to be ‘present’?”