We can’t expect teachers to function as Special Weapons and Tactics squads... that’s too much to ask.
But they should be armed.
If those teachers willing are trained and told the gun is primarily for defense - it’ll work. A killer opens the door and they can defend their students by shooting the guy. That’ll work as a deterrent - it takes way the miasma of ‘gun free zone’... puts killers on notice.
Here in NJ they’re certainly paid enough; there would be no shortage of takers for the jobs. One additional bonus to that scenario would be one that isn’t brought up, but should be after Beslan (the school massacre in Russia): Protection against terrorists, since schools are comparatively soft targets.