...of problem-solving is to take a deep breath and head for the library.
Yep, Rule One is to see if someone already solved that problem before you, then look at that solution to see if it worked, or could work, in your situation.
Problem: How do we better secure our schools against attack?
History: This is exactly the same problem that the Israelis faced ever since the Paleoswinians and other assorted middle-earth middle east dwellers decided to eradicate their country by terroristic attacks.
Research: Google "israel arms school teachers" and this Wiki will come up. Read the Wiki and it discusses arming school personnel, and near the end of the article, under "Impact", is a paragraph devoted entirely to armed educational facilities.
Perhaps instead of ginning up to ban more guns or lock up a bunch of people pre-emptively, we could just do point-defense at the schools. Of course, the Ivory Tower school bureaucrats would have to be gotten around, but Obama's Bully Pulpit could accomplish that, couldn't it?