"Strategy sharing" is a certain type of discussion that centers on students' ideas and occurs when children present different approaches to problems and provide information about how they solved the problem (Wood, Williams, and McNeal 2004). A teacher may orchestrate a strategy-sharing discussion to achieve one or more of the following goals (NCTM 2000): (1) Elicit students' mathematical ideas; (2) Represent students' diverse strategies; (3) Make connections between mathematical ideas; (4) Compare similarities and differences across strategies; and (5) Develop students' repertoire of strategies and flexible thinking. During the author's years of teaching and research in elementary school classrooms, she has focused on understanding and supporting students' experiences during strategy-sharing discussions. Building on the work of other researchers, she wanted to understand how to cultivate a classroom atmosphere that encourages problem solving and inquiry (e.g., Yackel and Cobb 1996) and that fosters mathematical discourse where students' problem-solving strategies, no the answers, are the foundation of the discussion (e.g., Lampert 1990). She also wanted to understand how strategy sharing could be mathematically productive and socially supportive for students. In this article, she draws on a larger study in which she spent a year observing and interviewing first-grade and fourth-grade mathematics students who regularly enacted strategy-sharing discussions (Hintz 2010).