Parents and teachers occasionally express concern that their children are too focused on the discovery of mathematics. The author remembers clearly one upset father who told him, "Just teach my daughter what she needs to know. Don't worry if she understands why it works. She just needs to know how to get the right answer." The author agrees with part of that parent's remark. His daughter does need the skills and experiences to be able to find a meaningful and accurate solution to a problem. However, if teachers focus only on the answer, student learning becomes passive, centered on the content and problems the teacher chooses. Inquiry, inference, and reflection are essential skills in the development of creative mathematical thinking. Students need to struggle with ill formed problems, as well as explore and experiment with their ideas on how to solve problems. They need opportunities to refine and generalize their methodologies and solutions. This article discusses several criteria for measuring creative ability in mathematics.