Instead of having an armed police officer physically present at every school, how about just parking a police vehicle in the parking lot of the school so it looks like there is an officer on the premises?
This ploy has worked for reducing speed on roads by parking an empty police vehicle with a dummy in it beside the road, and motorists would see that car and slow down immediately.
A real officer could be moved randomly from school to school, and an attacker would not know if there was one in the school or not.
Ray Stephins
Vancouver