I went into this in great detail at the other place. I worked a conference of Homicide Investigators several years in a row, and one case study was on the Sandy Hook shooting. This was not a press conference, but a closed door presentation of active HI's for other HI's, sharing experiences and techniques both good and bad. Another year they presented the Christopher Dorner case, and another the Grim Sleeper. For someone not in that world, I found it fascinating and sobering, and that the guys that were 40 looked like they were 50, and they guys that were 45 looked like they were 65, it's fascinating, but I couldn't do it for any length of time.
Anyway, it came down to Adam Lanza killing his mother with a .22 rifle, destroying the hard drive on his computer, loading up with an AR15, two pistols and a shotgun, (which was left in the car and not used in the attack). Walking up to the locked, (SOP for that school), front door and shooting out the adjoining window, shot the school principal and the school psychologist. The school intercom was used to alert the presence of an active shooter, and 911 was called. The whole shooting took less than 6 minutes, and the first on scene police could still hear rifle shots, and were able to find the classroom where he was and he had taken his own life with one of the handguns. The response time was very rapid, a matter of 5 minutes or less.
The school had a protocol in place, and teachers were locking and barricading doors, but obviously it wasn't enough. I don't know how you effectively harden all the schools, but I do think armed school police is a good idea, as these crazy's all seem to be sane enough to go on these rampages where they know they won't get return fire.
The big problem is not guns, or hardening schools, it's mental illness and/or the treatment of such.