I hate to have to ask this, but don't American schools all have some kind of campus police / security people running around. Or does that not apply to primary schools?
No. If it's in a good neighborhood you can probably walk right in and wander around.
That wasn't true in this case, nor is it very true any more in general. At Sandy Hook Elementary School, the doors were locked after 9:30am, and all visitors were required to check in at the front entrance and would only be admitted after visual review over a video monitor. It's likely that the shooter either (1) knew about this policy and deliberately entered the school before 9:30 in order to make the entrance a bit easier or (2) was let in after visual inspection because someone recognized him as someone who might have a valid reason to enter. I know that my high school implemented a similar policy during my senior year of high school. All the elementary schools I volunteered at during undergrad had similar policies, though they were much more lax about locking entrances.
EDIT: Ah, I
stand corrected... it looks like the school had appropriate security measures that they attempted to follow, but the shooter still forced his way in regardless.