In this multicase study (Stake, 2005), I studied a semester-long online implementation of the "Mathematics Discourse in Secondary Classrooms" (Herbel-Eisenmann, Cirillo, et al., 2017) (MDISC) teaching professional development (T-PD)-slightly modified for the university context-which I offered to three mathematics-teaching graduate teaching assistants (GTAs) (i.e., Finnegan, Valeria, and Alice) who were no longer in their first year of teaching. I sought to understand: (a) How does the classroom discourse change in each of the participant's classes over the course of their participation in the MDISC T-PD?; and (b) How do participants talk about their use of the teacher discourse moves (TDMs) (e.g., Cirillo et al., 2014; Herbel-Eisenmann et al., 2013)? To analyze the change in classroom discourse, I studied two sets of classroom discourse dimensions: (a) the TDMs (i.e., waiting, inviting student participation, revoicing, asking students to revoice, probing a student's thinking, and creating opportunities to engage with another's reasoning), which were a central set of practical tools offered by the T-PD; and (b) student discourse dimensions drawn from the discourse dimensions of the "Equity QUantified In Participation" (EQUIP) tool (Reinholz & Shah, 2018).In line with a multicase approach, this study consists of one case report for each participant, with each report driven by an emic issue, as well as a multicase report thereafter in which the participants' similarities and differences with respect to the research questions are explored. Finnegan, Valeria, and Alice's respective emic issues were: (a) How can an instructor who wants students to participate in their class invite student participation?; (b) How does an instructor who weighs wielding her authority to engage students against respecting students' agency (even if that agency is used to not participate) implement the TDMs?; and (c) How does an instructor who finds herself in a stage of "survival" (Beisiegel et al., 2019; Katz, 1972) implement and talk about the TDMs? Finnegan, who sought to invite student participation, especially took to TDMs that helped him do so: waiting (particularly wait time 1 [Rowe, 1986]), probing a student's thinking, and inviting student participation via cold-calling. Valeria, who did not want to force students to do things, felt more comfortable implementing TDMs that relied more on what she was doing than on what students were doing. She mainly used waiting (particularly wait time 1), revoicing, and inviting student participation via inviting further responses. Last, Alice, who found herself in a stage of survival, continued using those TDMs that she was already familiar with, that is, waiting and revoicing.This study contributes to the emerging area of T-PD for GTAs beyond their first year of teaching. In addition, it offers a refinement of the TDMs and a detailed account of how and why participants used (or did not) each TDM. The TDM refinement includes: (a) a refinement of "waiting" that builds on work by Rowe (1986) and Ingram and Elliott (2016); (b) a refinement of "probing a student's thinking" that distinguishes between two types of probing (i.e., to clarify a student's turn or to go deeper with it) enacted in two ways (i.e., instructor- or student-centric) in response to student statements or questions; and (c) a refinement of "creating opportunities to engage with another's reasoning" by distinguishing between five types of such engagement (i.e., adding to, anticipating, comparing to, evaluating, and understanding). Further, the participants' uses for revoicing add to work on different uses of revoicing (e.g., Herbel-Eisenmann et al., 2009), and the participants' hesitations about asking students to revoice provide insight into the challenges of learning to use this TDM.
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