Thank you for contacting The Elder Scrolls Online support team!
I understand that you are having difficulty with the quest School Daze and I apologize for the inconvenience this may be causing you during your game time.
This particular quest bug is a known issue, and the team is currently working on a solution. In the meantime, there are a couple of things to try that may resolve this issue:
Type /reloadui in the command line of the Chat Box
Try performing a soft reset: log out of the game and launcher completely for at least 15 minutes. This will reset the character's instance information and may cause quest NPCs to work properly.
Abandon and restart the quest, which also causes quest NPCs and objectives to restart; this generally gets positive results.
Keep your blades sharp, friend!