@FredFriendly People also say "would of", "could of", etc. as opposed to would've and could've these days. Point being, colloquial usages can be hideous and should be ignored in some instances. Granted, these characters are high schoolers and speaking colloquially to each other. But if I'm choosing between a word and its already extant counterpart, I'm going to choose the correct counterpart. Plus, Fukami-kun seems anal(i.e. pedantic) enough to use the proper term. It also reflects the difference between 復習(fukushuu) and 予習(yoshuu) in Japanese.
Edit: Also, I have worded it differently in the past, when I had more room left in a bubble. But I still feel previewing should be used sometimes, anyway.