...said the sheep on the way into the slaughterhouse.
Steingar is no coward. And well-applied intelligence is a far stronger weapon than any firearm.
That said, where I work is private property. I will therefore obey the wishes of its administrators. Even if I couldn't get fired for carrying a firearm (I can), I wouldn't just out of courtesy. I feel carrying a weapon onto private property against the wishes of the owners is outright discourteous.
Of course, intelligence is also useful for risk assessment. The number of school shootings in the nation is actually very, very low, spectacularly so for the number of firearms in private hands. The cost of obtaining and maintaining said firearm, along with the risk of discovery far outweighs the risk of a school shooter. Had the fellow responsible for the "incident" showed up in my classroom I'd not have hesitated to engage him. Sorry, just can't get worked up over a cleaver.