Teacher education programs have a critical role in supporting prospective teachers' connections between theory and practice. In this study, we examined three prospective secondary mathematics teachers' discourses regarding collective argumentation during and after a unit of instruction addressing collective argumentation and ways they recontextualized their on-campus coursework (theory) into their student teaching (practice) as demonstrated by their support for students' mathematical arguments during student teaching. Through a recursive process of coding data from interviews, reflections, and classroom discussions, we constructed descriptions of participants' discourses about argumentation based in their coursework and identified three themes about collective argumentation in the prospective teachers' discourses: the purposes of argumentation, the role of the teacher in argumentation, and characteristics of effective mathematical arguments. Analysis using extended Toulmin diagrams of classroom data from participants' student teaching showed that these three interrelated themes were visible in the participants' enactment of moves supporting collective argumentation. Our study opens spaces for future investigations into how teachers recontextualize their learning from coursework (theory) into their practice.