In this paper, students’ questions while working in small groups on mathematical problem-solving tasks are investigated. In order to improve students’ reasoning and communication abilities in mathematics, an intervention study was designed in a multilingual upper secondary mathematics classroom in Sweden. In their discussions students used Swedish, which was their second language and also the language of instruction. The changes in students’ ways of using questions across the three cycles of the intervention were analysed. The results showed how students over the cycles changed their ways of framing questions from looking for the correct answer towards clarifying other students’ meaning in order to understand each other’s reasoning. The implication from the study is that it is important to promote interactions between students rather than focusing on students’ need to develop their second language competencies.

Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students' listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, "productive listening," is described which focuses on observable features connected to students' ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker's contribution as being valuable and feeling that one's own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others' mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving.

How can teachers refne their strategies for purposefully engaging students in mathematicaldiscussions when students are working in groups and the teacher enters an ongoing groupconversation? In three educational design research cycles, four teachers collaborated witha researcher for one year to analyse, design and evaluate strategies for engaging students insmall-group mathematical discussions. The idea of noticing (Mason in Researching yourown practice: the discipline of noticing, RoutledgeFalmer, London, 2002; Sherin et al. inMathematics teacher noticing: seeing through teachers’ eyes, Taylor & Francis, New York,2011) was used to organize the fndings—by paying attention to aspects in the mathematical discussions and interpreting the interactions, teachers could together refne their ownactions/responses to better support students’ work. The Inquiry Co-operation Model ofAlrø and Skovsmose (Dialogue and learning in mathematics education: intention, refection, critique, Kluwer Academic Publishers, Dordrecht, 2004) was used as a theoreticalbase for understanding qualities in mathematical discussions. Ehrenfeld and Horn’s (EducStud Math 103(7):251–272, 2020) model of initiation-entry-focus-exit and participationwas for interpreting and organizing the fndings on teachers’ actions. The results show thatteachers became more aware of the importance of explicit instructions and their own role asfacilitators of mathematical questions to students, by directing specifc mathematical questions to all students within the groups. In this article, by going back and forth between whathappened in the teachers’ professional development group and in the classrooms, it waspossible to simultaneously follow the teachers’ development processes and what changedin students’ mathematical discussions.