I was stuck on this last night as well. I even leveled up a couple times thinking I was too low, or didn't have enough mana (he tells you you'll need alot). Still, every time I went to see the Prof for those schools, nothing happened.
Then by chance I happened to look at my map. There is an icon on your map for each of the three monsters you need to defeat. The doors to get to them are located across the street from the school towers.
I think they should reword the quest details on that one as it is a little confusing. And seriously, how often does one need to look at your map in Ravenwood. I clicked mine by accident, but if I hadn't, I'm sure I'd still have that quest open.
Ah I remember this....I went to the professors for each school but it didn't work. Try this, open your spell book and look at the task. If I remember right you had to talk to "other" people who were of those schools....
Yes. For ice school you must talk to Proffessor Greyrose, but for fire you need that girl outside Golem Tower who needs help with her project (whose name I cannot remember at the moment) and for storm Boris Tallstaff, the guy in the library.