A prevailing challenge in teacher education is the "problem of enactment," a discrepancy in what teacher candidates (TCs) know or say about practice and what they can actually do or enact (Kennedy, 1999). Current practice-based teacher education research focuses on articulating pedagogies of practice and core practices to integrate theory and practice, attend to the sociocultural nature of TC learning, and support TCs to "enact" practices (Grossman, Compton, et al., 2009; Grossman et al., 2019; McDonald et al., 2013). While there is research on practice-based learning cycles, core practices, and pedagogies of practice, there is limited research documenting how TCs participate in these types of contexts and how they enact core practices. Purpose and Research Question. The purpose of this study was to understand TC participation: How does TC participation manifest and change in their practice-based mathematics methods course? I sought to characterize TCs' participation around the practice of facilitating a productive mathematical discussion. Data and Methodology. Relevant data sources for this study included videotaped observations of TCs' participation in the course, TC assessments and lesson plans, and field notes. Data was analyzed for broad themes and categories related to TC participation around facilitating discussion. Coding was guided by my conceptual framework, which focused on TC learning as participation in a community of practice. Iterative passes of the data looked for patterns and reoccurring themes related to development of a shared repertoire and joint enterprise. Findings. Findings documented changes in TCs' talk about and enactment of facilitating productive mathematical discussion. TCs' "specificity" in articulating the instructional goal, "intentionality" in facilitating discussions to reach these goals, and "ownership" over articulating and working on goals increased over the 10-week course. TCs were able to use tools (particularly lesson plans, board work, and talk moves) more intentionally in response to student thinking and in service of their instructional goal as they became familiar with these tools and routinized their use. As part of the shared repertoire, these tools reified practice as representations, decompositions, and approximations of practice and provided routines and opportunities for deliberate practice. Implications. Understanding what TCs learn in practice-based courses, particularly how they enact practice, contributes to understanding the efficacy of current practice-based approaches in teacher education. This study is one of a limited number of studies that examines TCs' participation and what they learn and enact. My dissertation makes two contributions that address gaps in the literature: (1) Existence proof that there are shifts in TC beliefs and talk about teaching and enactment of the practice of facilitating a productive mathematical discussion in a 10-week practice-based methods course. (2) An image of TC participation to contribute to trajectories of TC learning and enactment of core practices in teacher education. My study considered the sociocultural approach common in teacher education and operationalized learning from that perspective, laying the groundwork for research on what particular pedagogies offer for TC learning. Understanding the changes in how TC participate and enact practice is useful to support teacher educators to continually refine and improve their practices and coursework. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]