Different types of talk in mixed-attainment problem-solving groups: Contributions to individual students’ combinatorial thinking

This study contributes to previous research on collaborative approaches to instruction in mathematics. The study focuses on the relationships between the type of talk in groups and individual students’ combinatorial thinking. Four case studies of mixed-attainment groups of middle-school students working with mathematical problem solving in combinatorics were conducted. Video-recordings of dyad and group work, as well as interviews with four students (one per group), were analyzed. The results reveal how affordances and constraints in different types of talk (exploratory, cumulative, disputational talk) in mixed-attainment groups can contribute to individual students’ combinatorial thinking. The results highlight the interconnectedness of collective and individual reasoning in combinatorics, emphasizing the role of quality of group talk.