How would you check if mask mandates worked in schools?
I can think of only one way. Contrast kids in schools with mandates and in those without. Get them all, too; the kids, I mean. Measure something useful, like serious illness or death. Not infection, because every kid is likely to get this bug. Or has already had it.
You’d have to do this carefully, because the kids would almost surely differ class by class, or at least school by school, by all kinds of things causative of infection and illness. You’d have to count very delicately.
What you wouldn’t do is come up with some weird, derived measure, something that takes you away from the decisions you need to make. Like, “If we impose a mask mandate, are fewer kids going to get sick?” And, “Is it worth the costs, which only zealots say are non-zero?”
The new CDC report is “Pediatric COVID-19 Cases in Counties With and Without School Mask Requirements — United States, July 1–September 4, 2021” by Budzyn and a slew of others.