Our study investigates preservice teachers' perceptions of real-world problems; their beliefs about teaching real-world contexts, especially ones sociopolitical in nature; and their ability to pose meaningful real-world problems. In this paper we present cases of three preservice teachers who participated in interviews that probed their thinking about real-world problems, and asked them to create problems they would consider using in their future classrooms. We use the three cases to propose a potential trajectory for preservice teachers from ambivalence to certainty about teaching mathematics through real-world and controversial contexts. [For the complete proceedings, see ED583608.]