I feel it should be an option, but just an option. I can't personally think of many teachers I know that would want to be armed up at school, there are some though. There are also some cops who shouldn't be, like that guy in Broward Co. who didn't go in.
I have two main concerns with having teachers armed. First, what are the training requirements going to be? Will they be run through something equal to the local PD's academy firearms training with ROE, legal concerns, hours on the range, stress inoculation, sims, and annual re-training and quals? Or is it going to be what I suspect would be more realistic, a basic week or two class with a range day at the end?
Second, what will they be instructed to do when my squad and I, as patrol officers, make entry? Are they to defend their classroom only or are the armed teachers going to be allowed to go hunting? I've met some teachers who were (likely still are) badasses before they were teachers. Most I've met aren't cops or in the military for a reason. There is a mindset difference there.
First concern to be addressed is the arming therein. Like with the potential for college students to be armed, in my case, they need to first have a CHL in their possession. And, that's it. Why? Because it takes someone with an understanding of the hostilities of the world around them to go out and spend the money to get a CHL. To put it in perspective, there's an additional $60 fee in Louisiana for the license if the applying party hasn't resided in the state for 15-years. My total was $295 after the CHL fee, the class, and the digital fingerprinting. I have met very few applicants who were ignorant of the point of obtaining one. Now, does that mean the training class that I ran through was enough? No, not necessarily. But, what is. The point of the class was to cover the laws one is expected to abide by. The point wasn't to train an individual in, what I believe, amounts to combat with an armed assailant. You must take it upon yourself to train for that scenario and the handling of a firearm that is required therein.
The second point is something I've also thought about. Albeit, as a student, so bear with me. If I was to engage an armed individual, I would want to get that word out as quickly as possible. A plan that I've had for awhile is to immediately get on the phone with emergency services with statements on who I was, to shortly explain that the original gunman was downed, and to explain where it had taken place. I would inform them that, until first responding law enforcement entered the building, I would hold security in case there were other hostiles in the area.
Now, at that point, there are some grey areas. I, and the teachers, would be relying on the dispatcher to get that information to officers just like you. Those points are vital to you guys. The bad guy is dead, he's been killed by a CHL holder and the CHL holder is holding post inside waiting for the cavalry to arrive. And, if it was me, I'd be thinking:
"For the love of fuck, don't shoot me, guys." It's a risk. It's a risk for me to defend other people that way and it's a risk for you to have to encounter me after the fact. And it's the same for an educator in the same scenario. But, in my mind, I need to get that information out to you guys. What if there are a pair of active shooters? One is down now and here's the location, so go get the other guy first. At least, that's what I'm thinking is a properly conducted scenario. Send SWAT after the other asshole and send some regular uniforms for my location. Information has to be used properly because it's the most important asset to everyone involved.
Should they, or I, go after the other guy or the lone gunman across campus? My first thought is that this isn't a Liam Neeson movie series, but if it's in the first minutes, and you know the first responders just got the call? I wouldn't go bounding across the campus with my sidearm drawn. I may go, as quickly as possible, to the location to see if I can assist in subduing the asshole. But, that's me speaking from the position of doing the right thing. I'd like to think I'd do that weaponless. I'm not law enforcement and I'm not military (former or otherwise). It cuts me to the core of my soul to see the body counts of mass shootings and there wasn't anybody there who had the heart and sack to take on the shooter. It just seems like the right thing to do.
You're looking for a doctrine that has civilian and law enforcement cohesion in mind, WAVandal. I don't think it will ever get anywhere close to being as good as it is between two patrolmen. Us holding down our own mental forts, in a manner of speaking, is as good as it will get, I think. I don't want to get shot, by the police, after having taken down a gunman. You don't want to get shot by a nervous civilian and you don't want to walk into an ambush, due to a clear-call to your dispatcher, from an assailant. It's all about trust.
All in all, I don't think there's a clear cut answer aside from that. Situational awareness and trust may be as good as it gets.