Hello Rachel,
Yes you can. Use the "announcements" template and "allow comments". Another way to accomplish this is to create a blog in Blogger. Once again - allow comments. You can either link to this, or embed the blog in one of your pages with a blogger gadget. There may be a discussion board gadget out there for SItes - I have to check.
One method I am considering is creating a "circle" of students in Google+ and then using that small social group to create discussion threads.
I am sure that there are other possibilities out there - but at least these are some options to consider.
Good luck with your site,