Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school teachers' understandings of math were insufficient for teaching. Observable knowledge gaps surfaced as preservice teachers demonstrated their procedural knowledge of a topic but could not explain its underlying concepts. The authors have endeavored to create experiences for preservice elementary school teachers to confront gaps in their mathematical knowledge for teaching and, in the process, deepen their mathematical understanding. The experiences include three tasks focused on children's mathematical thinking: (1) Analyzing videotapes; (2) Writing cases based on tutoring sessions; and (3) Connecting coursework experiences to student interviews. This article discusses these experiences which were intentionally developed to challenge preservice teachers' knowledge in various content areas. (Contains 1 table and 2 figures.)