I was thinking about this a couple days ago. It seems to me that stationing one or two police at schools would be more effective than this idea if we're interested in taking an active defense approach to stopping school shootings or minimizing their harm, though I hasten to add that they're a tiny fraction of total homicide and probably don't deserve this kind of attention.

My thinking is that uniformed officials with the weight of authority behind them would probably have a more salient deterrent effect than whatever armed schoolteachers would imply, and also that forging non-confrontational links between police forces and civilians would have substantial positive externalities. Though this latter would depend greatly on style; a scare-'em-straight approach might backfire, and I'm almost sure that using cops purely as glorified security guards would. Arming and training teachers might put shooters down faster, but I can't see much deterrence or any substantial externalities, and it would be an expensive program.

Though on the other hand I don't see many negative externalities either; last time I looked at data on shootings (accident and murder inclusive) attending trained and licensed bearers of firearms, the rates turned out to be quite low.