They don't always need to be corrected or graded. A very common kind of assignment involves writing paragraphs for different purposes. Again, they are not tests. Rather, they allow a teacher to understand if the student is understanding the concepts. Students need to know why they are reading an assignment, what they are reading for.
Writing helps students prepare readings and promotes better class discussion.
A journal or reading notebook, developed throughout the semester, can help students summarize, respond to, compare, or analyze reading assignments. Five minutes before the end of class, ask students to write a paragraph that summarizes the main points of the lecture. Then ask three or four people to read their paragraphs. Such writing improves note taking and listening skills. The instructor can respond to problems immediately, reviewing points students did or did not grasp.