This paper presents an investigation of mathematical problem solving in two small groups of students in grade 6, as well as the groups’ orientation to social and sociomathematical norms. The interaction within the groups was analysed with proof schemes as analytical tool, in combination with principles and procedures of Ethnomethodological conversation analysis (EMCA). The analysis showed that one group oriented to social and sociomathematical norms that gave rise to a potentially positive learning opportunity, whereas the other group primarily oriented to a socialnorm of equality that overshadowed the mathematical discussion. This study serves as a pre-study for the analysis of larger material, where EMCA appears as a promising methodological contribution.

In this study, we focused on grade-6 students’ justifications during mathematical problem solving in small group interaction. Video recordings from two classrooms were analyzed, using Harel and Sowder’s (2007) taxonomy of proof schemes as a tool to categorize students’ justifications, which showed that the frequency of various types of justifications corresponded to previous studies of adult students’ demonstrations of proof schemes. Results also showed that both Non-referential Symbolic and Transformational justifications contributed to students’ formulations of general arguments. In addition, agreements between proximately located justifications based on examples and calculations supported students’ improvements of solutions. However, in cases of disagreements, justifications based on calculations often had most influence on the proving process even when the calculation was incorrect. Our results imply that teachers should emphasize the importance of agreement between calculations and empirical examples, as well as the significance of counterexamples, as a support to students’ progression towards mathematical proving.

This study focused on Grade 6 students’ handling of differing proposals when discussing solutions to mathematical problems in small groups. Using conversation analysis, we analysed video recordings of naturally occurring student–student interaction. Findings show that students avoided criticizing peers’ proposed solutions, whereas they either advocated or rejected their own. Furthermore, rejections were immediately followed by conceding to someone else’s proposal, with the concession emphasized through the conceder’s affect-laden embodied actions. Students’ interactional work not only maintained their social relations but also offered opportunities to display epistemic independence. These findings imply that teachers should support students’ argumentation in the mathematics classroom in presenting critical reviews of peer’s differing proposals in ways that are not face-threatening.

This study investigated young students' (11–12 years old) generalising while discussing solutions to mathematical tasks with peers. Generalising was operationalised as identifying regularities among cases or transferring argumentation into new contexts. Findings emphasise the importance of agreement between general arguments and empirical examinations. Students often formulated general arguments after empirical examinations but the opposite ordering also occurred; in both cases, students' generalisations involved 'for all' arguments. When generalising was accomplished by referring to mathematical facts, the argument was marked by the Swedish modal particle ju which can indicate that knowledge is treated as shared. The findings can inform teachers' didactic choices, for example, by emphasising what type of arguments and linguistic resources students should pay attention to.