The best way to improve student writing is to encourage revision. You might invite students to submit an outline or working draft to you a week or more before the deadline; then briefly confer with those who do or make a few written suggestions. You can also encourage students to take their drafts to the Writing Center. A more radical idea: you could collect drafts from all students a week early and just check them in and return them without comment. By doing this, you encourage students to write early and rework the draft later with a more critical eye. Or you could encourage (not mandate) small writing groups where students review each others' drafts before the final paper is submitted to you. Students benefit greatly from interacting with an audience and considering alternative approaches to a paper they are working on.