You cannot compare any training offered by the "Education Department" of a city or county to come even close to police training. You cannot be certain that monthly, or even yearly refreshers will conducted, as this it not a teacher's job! Police take their training to the field immediately and are immersed in law enforcement and emergency situations each and every day. Teachers, on the other hand hopefully will never have to use a weapon for their entire career, but if it happens 10 years from now, how much can anyone remember. I also fear that adding weapons to the school could end up with them being taken by force and used against the teacher and students. Schools today are nothing like many of us remember from schools decades ago.
Trained law enforcement from departments on a rotating basis, or off duty, may be the best option for schools.