"Event" and "happening" completely synonymous?

Hi everyone!
My students have the annoying habit of not doing as I told them ... Seriously: I usually insist that they use the word "event" when they refer to any kind of occurence, be it historical or fictional (i.e. when they relate the plot of a novel or a play). However, they carry on using "happening" instead, which sounds rather strange to me, since I associate that term with special kinds of modern art.

Here are a few examples:
In a test on Arthur Miller's "Crucible" some students wrote sentences like: "In Parris's house they talk about the happenings in the woods." (i.e. the dancing of the girls)
In a test on the McCarthy era, some use expressions like "Historians have an objective view on the happenings of that time."

Both examples sound rather strange, if not altogether wrong, to me. I would prefer the word "events" in both cases.
What do native speakers say?
Curious,
Andreas.