Allowing teachers to be armed won't solve the problem of mass killers, and may lead to more problems. It also gives schools a false sense of security. I doubt teachers are going to be walking around the classroom with gun in hand. If you are the first classroom hit by the killer, it won't do any good to be armed. These killers have been using shotguns or semi-automatic rifles. Abandoning your class and going out into the hallway is not a good idea. Yes, if you are not the first class, and have advanced warning, you might prevail and save lives, but lives will still be lost. There are some politicians that like it, since it is the cheapest way they think to provide security. Again, there is a greater probability of gun violence involving students arguing with teachers, accidents, and so forth, than a mass shooting.
It wont solve the problem is correct. On the other hand will likely deter a lot of people from going into a school and shooting it up. I know if I was to walk into a school and knew that a teacher in that school might be carrying. I wouldn't take that chance. These shooters are cowards. Another aspect is to train these teachers that are willing to carry in the school.
Another system that could be put into place is a advanced warning system that alerts authorities that there is an immediate emergency going on in the school. Im not talking about fire alarms. Im talking about something along the lines of what banks have put into place. Each classroom should be equipped with such devices. These are just measures to help when a situation has occurred. Its not going to stop someone from acting out. We need our society to wake up and get off their butts to make a significant change in the minds of the youth.
I doubt any of the killers at any of these schools would have been deterred by anything. In fact, they probably would have taken it as a challenge. Again, once someone is inside the building, people are going to get shot. The key is to have better preventation such as outside cams and automatic locking doors.