It might depend on the school district, but my family has worked for 3 different ones across a couple states, and they would not get paid monthly or anything over the summer. First check for them would come in September even, and we start school in mid to late August around here.
IIRC they would get a larger sum at the end of the school year to hold them over til the fall. I vaguely recall my step mom talking about how every year there would be a teacher who budgets poorly and forgets the first paycheck isn’t until September.