Teachers’ task-specific questions when monitoring students’ combinatorial reasoning in mathematics

The aim of this paper is to contribute to what kinds of task-specific questions teachers pose when students solve problems and reason mathematically in combinatorics. With departure in creative mathematical reasoning (CMR), which entails constructing and arguing for solutions on mathematical problems, two lessons with similar mathematical problems on combinatorics in grades 5 and 6 from two teachers participating in the same professional development program were analyzed and contrasted. The analysis was supported by the four principles for CMR-teaching: encouraging students to initiate, develop, justify, and verify their own reasoning. The results show that despite that both teachers have very high mathematical knowledge for teaching, they pose different kinds of task-specific questions – adhering to the four principles – in relation to combinatorial reasoning. The first teacher poses questions according to the first two principles of initiating and developing students’ reasoning as well as funnels students towards answers and solutions, the latter which does not align with CMR-teaching. The second teacher poses questions according to all four principles for CMR-teaching. It is discussed how the differences in results between the two teachers’ lessons regarding the four principles underline the importance of preparing task-specific questions. It is also discussed how the results may contribute to teacher education activities aimed at developing teacher’s question-posing skills.