I'm not sure if it should be "to write (something) on the board" or "to write (something) onto the board" . To me both versions sound correct, but I'm always wondering which is the better / more correct one.
It's better to say "to write something on the board". Although "onto the board" might not be technically incorrect, it doesn't sound very natural to my ears. Likewise you should say "write it in the book" and not "into the book"
"on" the board is what the majority of native speakers would use in conversation.
''We drove on the beach'' [location]
''We drove onto the beach'' [direction]
Is it really clear though, if you are writing something in a book or on a board, whether it is location or direction. It's a bit ambiguous isn't it. I suppose once the pen is on the paper, it is indeed 'on' it, but as you have to bring the pen to it, and you lift the pen off again intermittently, it does also have the sense of direction. Sorry, don't mean to be picky, and am not saying it's wrong in English to use 'on', it's definitely right. I'm just wondering about the logic, as German would use the equivalent of 'onto' or 'into', and I think if you used 'on the board' in that language, it would imply you yourself were on the board while you were writing :O