Paradoxical writing is exploring two sides of an idea. Students are given quotations to chose from for this assignment. They are to respond to the quotation, then "flip it" and respond to the other side. Students also apply the same ideas to literary characters and historical figures. This is excellent "brain work" for AP and Pre-AP students as well as on-level students. Debate classes could also incorporate this assignment.
If you need a prep exercise for STAAR persuasive writing, or just a "break" from the traditional short answer response practice, this is another way to get students to think critically.