back when I was a student I used to look after groups of american school students on their london trips in the summer holidays.
One day the teacher had announced that they needed to be back at the coach at a quarter of two and reminded the class as it was their first day that they needed to be in good time.
I turned up at , so I turned up at two o'clock as being the guide you were supposed to be there for the really early ones and was shocked to find everybody there.
Cue one angry teacher saying that she had distinctly said to be there at a quarter of two. Cue one very confused me saying yes, I'm quarter of an hour early, I know you told people to be early but for everybody to be quarter of an hour early is almost unheard of (and also a waste of their time in a foreign land when they could have had that time looking around a bit more in the gift shop orchatting up locals--)
Obviously them being american, turned out they had been waiting since a quarter to two...
I later did a straw poll of my friends and found that everybody thought it sounded just wrong to talk about 'a quarter of' time and it went 50:50 as to those that thought it probably meant quarter to or quarter past.
Logically most were convinced by the fact that if something is 'of' something then it shouldn't be before it IYSWIM.
The american students (typically 16-18 year olds) also had real problems with the 24 hour clock, sevens written with a bar across the 7, the facts that Shakespeare wrote in English and that apple pie was also a traditional English dish (and that France, Germany etc also had their own traditional apple pies) so that the phrase as American as apple pie caused confusion amongst the British kids.
They also assumed that everybody in Britain had met the 'king' and queen and that if they knew someone in the UK then you would too. I used to laugh at the last one until once it turned out that I did 
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