Open-ended questions, as discussed in this article, are questions that can be solved or explained in a variety of ways, that focus on conceptual aspects of mathematics, and that have the potential to expose students' understanding and misconceptions. When working with teachers who are using open-ended questions with their students for the first time, the author found that they learn a considerable amount about what their students both know and do not know--much more than what they knew before they started using open-ended questions. Teachers are almost always surprised, a little disappointed, but often excited about what they discover. Open-ended questions can help teachers focus their instruction and assessment on NCTM's Process Standards and on reasoning and sense making, which really is the heart of mathematics. Moreover, responses to open-ended questions give teachers so much more information about students' ways of thinking and misconceptions, and these can provide important avenues for further investigation of mathematics.