Teachers' noticing to promote students' mathematical dialogue in group work

How can teachers refine their strategies for purposefully engaging students in mathematical discussions when students are working in groups and the teacher enters an ongoing group conversation? In three educational design research cycles, four teachers collaborated with a researcher for one year to analyse, design and evaluate strategies for engaging students in small-group mathematical discussions. The idea of noticing (Mason in Researching your own practice: the discipline of noticing, RoutledgeFalmer, London, 2002; Sherin et al. in Mathematics teacher noticing: seeing through teachers' eyes, Taylor & Francis, New York, 2011) was used to organize the findings-by paying attention to aspects in the mathematical discussions and interpreting the interactions, teachers could together refine their own actions/responses to better support students' work. The Inquiry Co-operation Model of Alro and Skovsmose (Dialogue and learning in mathematics education: intention, reflection, critique, Kluwer Academic Publishers, Dordrecht, 2004) was used as a theoretical base for understanding qualities in mathematical discussions. Ehrenfeld and Horn's (Educ Stud Math 103(7):251-272, 2020) model of initiation-entry-focus-exit and participation was for interpreting and organizing the findings on teachers' actions. The results show that teachers became more aware of the importance of explicit instructions and their own role as facilitators of mathematical questions to students, by directing specific mathematical questions to all students within the groups. In this article, by going back and forth between what happened in the teachers' professional development group and in the classrooms, it was possible to simultaneously follow the teachers' development processes and what changed in students' mathematical discussions