I don't know if Wordpress would be the best place to start for something like this. What you're looking for is something more "application-based."
I would recommend looking at something more along the lines of Moodle : http://moodle.org/
Or this one, based on the Drupal CMS: https://elms.psu.edu/
If all you need is a way for students to submit assignments, then I would just use Google Docs, or have them email them to you.