At a time when students are expected to participate in inquiry-oriented mathematical lessons, this dissertation presents the findings of a qualitative study of the mathematical and interactional demands students experience during the common mathematical discourse pattern of strategy sharing. Mathematical demands were identified as the subject matter knowledge a student must make use of and work with in order to engage in the discourse. Interactional demands were identified as what a child must be able to do socially because s/he is a student in a classroom with other children engaging in the discourse. This study draws upon a sociocultural perspective of learning to frame the study of the demands students' experience. A sociocultural lens focuses the analysis of students' experiences as they engage in mathematical learning through interaction with other people and participate in mathematical discussions where the structured activities have particular mathematical goals. To examine the mathematical and interactional demands students experience during strategy sharing, and how students' histories as well as the classroom context shape their experiences with the demands, data from two elementary classroom cases (a primary and an intermediate classroom) and seven student cases, including twenty-four videotaped focus lessons and individual interviews with focus students across the 2008-2009 school year, were collected. Analyses of this data revealed that (1) There is a wide range of mathematical and interactional demands present in strategy sharing lessons for all students. (2) The classroom context and who students are as learners and people shape how different students experience the demands. (3) Students' narrations reveal important reasons why children share (or do not share), reasons why students listen and what they chose to do with what they hear, and students' experiences working through mathematical mistakes publicly. This dissertation concludes with implications for teaching practices, and future research, that may help support all students through mathematically productive and socially supportive strategy sharing.