W/ respect to suggestion of arming civilian school administrators (absurd in my view) and the comparison with airlines:  Pilots who receive authorization to carry guns on commercial airlines have annual health screenings including mental health issues.  They get extensive training on use of the handgun in a volatile situation (very different than target practice) and I think annual recertification.  Many of them have prior military training.  They keep themselves and their handgun in a locked cockpit while in flight which keeps the gun away from other passengers and attendants, and gives the pilot time to prepare to use the gun properly and effectively in an emergency situation.  Schools just aren't like that.   

However, it would be possible to combine regional law enforcement facilities w/ school facilities to increase the probability of on-site law enforcement and faster responses.  Just design new schools with/in conjunction with law enforcement facilities.  Same or adjacent buildings or properties.  Would take a long time to get this accomplished on a wide spread basis, but start with all new schools and all new law enforcement facilities.  In the meantime, just providing an office in every school for our bicycle cops to use to do paperwork between their patrols would create some police presence.  Developing personal relationships between young children and police officers could create some positive long term outcomes as well.

We presently have police office space in all our high schools (all 4 of them) with police "school resource" officers assigned to each.  There is usually a highly visible police car parked on a special pad up on the school entry way.  I don't know if any of this helps, but it might.   (FYI - bit of humor:  my husband pulled up in front of the  high school in his classic '67 Impala to pick up one of our kids.  The on campus police  officer came over to admire the car.  Within 3 minutes, both of our children - one who is in College - had received texts saying that their father had been arrested in front of the high school.)

I'm not saying this idea would have prevented the recent tragedy.  Lots of practical problems with implementation, but something to think about.  

Liz