Markdown is fantastic, and I use it everyday. However, there is a learning curve to overcome. Depending on how often the student uses the system, and for how long a period of time, it can be difficult for them to remember the syntax.
Also, this might be a stretch, but if the student is being tutored, one might surmise that they don't pick up on things as quickly.
Additionally, there are some tricky quirks to the markdown syntax that can produce unexpected results (always bad for ux). There is always the case of _unclosed or_wrongly _closed characters that might throw off the user.
As for using Word docs - I can't stand working with Word format, and having to support different versions, handle complex file uploads/downloads, and not being able to track changes as you can with a text based system.
Personally, I would stick with plaintext.