If a certain slot or day of a teacher is already taken/booked out, then it could be nice to receive a notification in case it becomes available again (because someone else canceled his lesson).
This would not even need to be too complex, IMHO scheduling a notification request for a certain day would be sufficient. See example:
In that case I would set a marker like "watch that date" for the 16th and receive an email if a slot becomes available. If the canceled slot suits me I could book that one (first come first serve).