I would take this a step beyond that. Not only should teachers and administrators be permitted arms on the job, but schools should hire *disabled veterans* as security officers.
The reason I believe this is the way to go is because it was done back in the late 1970s. A high school had student cliques that were showing signs of racial animosity, so the principal hired a disabled Vietnam Veteran (hearing aids) to keep the peace.
This quickly ended the student clique problem, but then it turned out the security guy was soon intercepting adults who were coming onto the open campus to make trouble—a previously unknown problem.
Within a few years, he had an additional three disabled veterans working for him, though he was the only one armed. And they kept very busy stopping all kinds of mischief, at sporting events, preventing car break ins and bicycle thefts in the parking lot, and pinpointing any illegal drug use. And students quickly learned “no fighting” on school property, because these four men did not mess around.
Last but not least as decorated combat vets, they were naturals as role models.
That's quite a story, and the same could work for many schools, but God help us, school administrations today are mostly led by union goons of the left that do not want what is best for the students at the schools... they just want money, lots of it, with little to nothing required of them.