Set up a Professional Audience for the Writing Assignment
Even though they might be dismissive of you because you're a teacher, students rarely are so flippant about giving shoddy work to potential employers. Most students have heard the horror stories (urban legend or not) about the person highly qualified for a job whose letter of application went into the wastebasket because of a typo.
If you raise the stakes for writers by setting a professional context for their writing - submission to a journal, a stakeholder audience, or a potential employer - then students are much more likely to care about the final product. So try building in an audience other than the teacher for your writing assignments.