If you look at the breadcrumbs after you click on a participant's name, you'll notice that the classroom/course name does not appear.
- CTYOnline ► Participants ► CTY Staff - Ben Reynolds
So, I am pretty sure you would have to give that capability system wide.
One other way to approach your problem is to give teachers the ability to login as students. Since every user is generally able to change his own password, the teacher logged in as the student could change the password.
You do want to think about what else teachers could do while logged in as someone else.