One possible approach is a forum with posts limit set to 1 per student and only the teacher/administrator is subscribed. Every post will be emailed to the teacher/administrator. The only thing left to feature is to make the forum private per student (if that's a requirement).
Another approach is a database activity set up in a similar way with a patch which emails a notification to the teacher upon adding an entry. The privacy feature is worked around in the database activity by enabling approval and not approving. But I'm not sure that the email patch is updated to v 2.0.
hth