"school shootings" is also misleading, because it includes negligent discharge of a police officer's gun into the wall on school property, gang/crime related shootings (even non-fatal) on the school parking lot after hours, and so on.

What we think of as "school shootings" - an active shooters targeting individuals in a school systematically - is still exceedingly rare and you know them all by name. 1-2 per year, if memory serves. Pretty bad, yea, but not nearly what it's made out to be. Pretty much chance of being struck by lightning.