Kalchman describes and discusses preservice teachers' changing views of what it means to know and do mathematics both inside and outside the classroom walls. The context for change is a weekly assignment for methods students to describe and solve mathematical problems in situations that they confront in day-to-day life. The assignment supports growth in personal and professional mathematical understanding in at least three ways: It provides: (1) a window into students' growth as mathematical thinkers; (2) a curriculur and instructional approach ensuring authentic mathematics while meeting NCTM and local standards for content, process, and professionalism; and (3) a model for classroom teaching that shows how students' everyday mathematical experiences are relevant to and inform school mathematics, and how school mathematics are relevant to and inform students' everyday mathematical experiences. (Contains 4 figures.)