This study aimed at investigating and analysing the communication occurring during whole class discussions, with a specific focus on the nature of the mathematical arguments. The investigation was a qualitative case study where the communication during eight whole class discussions in grade 3-5 were analysed. Three types of arguments, wich are functional in the communication and convey different aspects of mathematics, were identified in the study. The types are (a) argument conveying a solution to a task/ a problem (b) argument conveying conceptual properties, and (c) argument conveying a mathematical relationship. The arguments types explain why an answer to a task is correct (type a), illuminate properties of a mathematical object (b), and clarify a mathematical relationship (c). The findings also reveal that arguments may be expressed through the use of a broad range of communicative resources, such as spoken language, written language, symbols, drawings, the use of manipulatives, and gestures. This highlights the importance of taking into account more than speech when construing arguments/reasoning communicated in mathematics classroom. The study also points to the importance of paying attention to arguments/reasoning that are created during other occasions than during task work or problem solving, and that arguments can enable the discerning of mathematical aspects for learners.

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.