I'm so glad I got assigned this as my editing assignment. It was by far my favourite!
I'll go through the story bit by bit, and make any recommendations as I go through. Sometimes it'll be grammar, sometimes suggestions on style, and sometimes I'll just mention things that I think could be improved (but often don't know how). I'll italicise bits from the story so you know where I am.
avoiding the only one that was occupied I think this would be a little more powerful if you swapped the 'the' and 'only': avoiding only the one that was occupied
switch his pen from the right hand to the left You could just say switch his pen from his right hand as the left is implied; I can't decide if it would be best to do this and shorten an already quite long sentence as I quite like the wording you've picked. But it's something to consider.
William put his pen down, and looking straight at the blank blackboard, recited Again, nothing actually wrong with this, but I think it would be better as William put his pen down, looked at the blank blackboard, and recited:
slate-pencil Chalk? Slate-pencil seems clumsy when chalk would do just as well.
And, uhm, that's pretty much all I can come up with. There are no obvious spelling or grammar errors, the story flows really nicely (well, chillingly!). Perhaps the only criticism I'd have would be that you do lots of long sentences - most of the short sentences tend to be dialogue. It might be nice to have a little more variety.
Edit!
I'll go through the story bit by bit, and make any recommendations as I go through. Sometimes it'll be grammar, sometimes suggestions on style, and sometimes I'll just mention things that I think could be improved (but often don't know how). I'll italicise bits from the story so you know where I am.
avoiding the only one that was occupied
I think this would be a little more powerful if you swapped the 'the' and 'only': avoiding only the one that was occupied
switch his pen from the right hand to the left
You could just say switch his pen from his right hand as the left is implied; I can't decide if it would be best to do this and shorten an already quite long sentence as I quite like the wording you've picked. But it's something to consider.
William put his pen down, and looking straight at the blank blackboard, recited
Again, nothing actually wrong with this, but I think it would be better as William put his pen down, looked at the blank blackboard, and recited:
slate-pencil
Chalk? Slate-pencil seems clumsy when chalk would do just as well.
And, uhm, that's pretty much all I can come up with. There are no obvious spelling or grammar errors, the story flows really nicely (well, chillingly!). Perhaps the only criticism I'd have would be that you do lots of long sentences - most of the short sentences tend to be dialogue. It might be nice to have a little more variety.