I'm starting to think of fountain pens as something I enjoy using, rather than automatically the best choice for school. When I'm trying to keep up with notes in class, a gel pen is often easier. I don't have to think about the paper, whether the ink will dry quickly enough, or what happens if someone needs to borrow it. I still like using a fountain pen when I have more time to write.
I keep a gel pen in the front pocket of my bag for exactly that reason. If my fountain pen runs out of ink halfway through the day, I can just grab the backup and carry on taking notes.
A spare only helps if you can find it. Mine stays in the same pocket of my pencil case, or it vanishes into the depths of my bag between lessons.
I'd clip the spare to the pencil case or use a pen loop, so it's not loose in the bag.