This qualitative study documents the establishment of new social and sociomathematical norms in a second grade classroom. The teacher allowed students to speak directly to one another without having to raise their hands first during whole group mathematics instruction. Reform efforts in mathematics and the standards for mathematical practice contained in the Common Core State Standards call for students to discuss their reasoning with each other. Data were collected through interviews with the teacher and students, field notes, and video-recorded lessons over the course of 23 days. An online survey tool was utilized to share selected video of the teacher's instruction. Initial professional development topics were chosen from research in mathematics education related to the social construction of understanding. Ongoing professional development was responsive to what occurred during instruction. The literature suggests that teachers often utilize traditional teaching methods and struggle to deviate from established patterns regardless of their desire to implement change. The teacher in this study learned that allowing students to talk openly provided him with insight into their mathematical conceptions and misconceptions. The students initially viewed mathematics as a set of rules to follow and exhibited the role of passive recipients of information. This changed as students were provided opportunities to participate in discussions and in doing so developed a new understanding of their role during mathematics lessons. Mathematical errors became a catalyst for communication and were viewed by students as opportunities for assisting their peers.

The researcher in this case study sought to determine the ways in which teachers support their students to create viable arguments and critique the reasoning of others (SMP3). In order to achieve this goal, the self-conceived classroom roles of two teachers, one experienced and one novice, were elicited and then compared to their actualized roles observed in the classroom. Both teachers were provided with professional development focused on supporting student engagement in SMP3. This professional development was informed by the guidelines that describe the behaviors students should exhibit as they are engaged in the standards for mathematical practice contained in the Common Core State Standards for Mathematics. The teachers were observed, video recorded, and interviewed during and immediately after the professional development. A final observation was performed four weeks after the PD. The marked differences in the teachers' characteristics depicted in each case added to the robustness of the results of the study. A cross-case analysis was performed in order to gauge how the novice and experienced teachers' roles compared and contrasted with each other. The comparison of the teachers' self-perception and their actual roles in the classroom indicated that they were not supporting their students as they thought they were. The analysis yielded specific ways in which novice and experienced teachers might support their students. Furthermore, the cross-case analysis established the support that teachers are able to provide to students depends on (a) teaching experience, (b) teacher content and pedagogical knowledge, (c) questioning, (d) awareness of communication, (e) teacher expectations, and (f) classroom management. Study results provide implications regarding the kinds of support teachers might need given their teaching experience and mathematics content knowledge as they attempt to motivate their students to engage in SMP3.