One armed person isn't enough to provide adequate security to a facility the size of most schools.
Israel had some horrific school massacres. Their solution? Train and arm the teachers. It works. They haven't had a major incident since, despite being surrounded by madmen sworn to kill all Jews and wipe Israel from the face of the planet.
From my point of view, as a father of three and grandfather of 10, if the teachers aren't willing to take responsibility for the defense of their charges they should find another job and let someone who will defend the children take the position.
The principal in CT bravely tried to defend her students, but she was doomed from the start and had no chance. Train and arm the teachers - it works.