re: the apostrophe.
If it’s the possessive, as in “this is Jane’s lunchbox” I understand the apostrophe use no problem.
What I don’t get is how to contract (is that the right word?) “Jane is” as in “Jane is going to the movies”.
Would that be Jane’s going to the movies? It doesn’t look right to me.
This is the kind of stuff I think about on the bus when my book on tape gets a bit slow 
“Jane’s” is correct. In this case the possessive and the contraction are the same.
“Jane’s going to the movies” is correct. The apostrophe indicates a missing letter or letters, and goes where the missing letter goes. So “Jane is” becomes “Jane’s”, just like “do not” becomes “don’t” and “cannot” becomes “can’t”.
You’re right in the first place. “Jane is going to the movies” would be contracted to “Jane’s going to the movies.” Furthermore, “Jane has gone to the movies” would be contracted to “Jane’s gone to the movies.” So “Jane’s” can be either the possessive of “Jane” or a contraction of “Jane is” or a contraction of “Jane has.” The reason that this doesn’t look right to you is that you don’t often see noun-verb contractions in print, while you do see pronoun-verb contractions fairly often in print. Even though in speech people often make noun-verb contractions, they tend not to write them even when trying to reproduce their speech.
thanks to all, that’s been bugging me all day!
I think you would want to avoid that usage in formal writing, but other than that, it’s fine.
you’re right, I would never write it that way. I would say it that way though, which is what got me wondering.
That’s all. There’s nothing to see here. It’s time to go.
it’s been fun.
The question’s been answered. Y’all’re fast. I couldn’t’ve said it better myself.
Hold on, not so fast there…what’s Jane going to see?
So, in the possessive, “Jane’s book,” what does the apostrophe-s stand for? Does it stand for anything?
It’s a remnant of the genitive case inflection that Old English used to have, centuries ago. There’s some more detail about it here, under section 4.
Can’t we quibble a little? Surely we can find something. After all, it’s the Fourth of July and all. (I changed that from “Independence Day” so that I wouldn’t be exclusive.)
I know that it is grammatical to use a possessive pronoun before a gerund as in:
I admire your walking to work every day. (“Your” instead of “you”)
What happens when a proper name is substituted for "your’?
I admire (Caroline, Caroline’s) walking to work every day
And if Jane took her lunchbox to the movies with her, you could say, “Jane’s lunchbox’s going to the movies.”
We can also say things like, “Bob’s supposed make sure that whoever’s not here’s spot’s plowed each day”.
That’s correct too.
Both of those’re correct. But they have different meanings. “I admire Caroline walking to work every day” means you’re admiring the person. Maybe she’s good-looking. “I admire Caroline’s walking to work every day” means you’re admiring the act. Maybe she’s determined.
Ah yes, accusative, genetive, dative…my German professor always warned me I was the unfortunate victim of a progressive education! 