What "is" mathematics? What does it mean to "do" mathematics? The answers to these two questions critically influence the ways in which learners respond to a mathematical problem. On the other hand, if they see questions as having only one correct answer and as needing to be solved in one particular way, they will be prone to treat mathematics as a rigid discipline. They will likely view it as a subject that one is either good at or not. On the other hand, if they see problems as opportunities to explore, create, and prove, they will experience the beauty and wonder of mathematics and realize that the unknown provides a chance for new learning. In this article, the author describes her experience teaching an eighth-grade heterogeneous mathematics class in a suburban middle school that used reform-oriented curriculum materials. With this class, she aimed to achieve her goal of employing problem solving to allow students to discover mathematical relationships and pose new questions of their own.