Drive & Docs

Most private - Most work
Create a folder for each course/section and within that create a folder for each student.  Then share each folder with the respective student.
This process takes time in the beginning but you would only have to set it up once per year or semester depending on the duration of the course.

Note: If multiple teachers are doing the same thing, then the students are getting multiple folders from differnt teachers with the student's name on it. I would consider distiguishing yours in some way. Perhaps adding your initials to the end of the folder name. e.g. Student Name (Teacher initials) would look like: Andrew Student (JB).
Another option could be Student Name (Course) | Andrew Student (Eng7)

Alternatively:
You can only make the folders of each course/section.
Make each student share with you a folder with their name on it and edit rights. Then move the folder they shared with you, from "Shared with me", into the course/section folder.

Less Private - Less Work
Create a folder for each course/section. Share that folder with all the students in that section all at once. 
Tell the students to create a folder with their name on it in that folder.