I just glanced at an article (though I can't find it now) that said teachers in Thailand and some other country carry guns. It always seems like mass shootings happen in gun free zones, so it makes sense to me.
Of course we would need to train them which makes me think we would get the added bonus of sorting out the irresponsible teachers from the ones who are serious. As for kids getting their hands on the guns, just put them in a safe under the teacher's desk and have the teacher carry the key at all times.
To me it seems like a more reasonable preventative measure than just getting rid of all guns.