Classrooms Socio-Mathematical Discourse: Two Nine-Grade-Dyads’ Non-Routine Problem-Solving Engagement

Abstract

The purpose of this case study is to explore the complex interplay among student beliefs, problem solving engagement, problem type, and mathematics understanding as well as dynamics within group discourse among four ninth-grade mathematics students. The analysis of both these dyad’s 16-week long collaboration reveals that the role of conversation, prolonged problem solving interactions, and on-going negotiations and relationships is key in their transformation. The results suggest, as students developed a culture within their dyads, of problem solving and problem posing, and collaboration, that engagement was increased. After evaluating the various data relating to problem type and participant engagement, it became evident that certain problem types engaged the students more than the others. While it was no surprise that routine problems were not engaging to them, it was also evident that their collaboration and discourse were very different under these circumstances. They were much less likely to question, challenge, argue, negotiate, or probe each other’s thinking, and were much more likely to rely on and accept the first answer. There were no efforts to modify, extend, or apply these routine problems to other contexts. The implication of this study for 21st Century classrooms discourse sheds light on the envisioning of curriculum alternatives for mathematics education amidst the many constraints of current and traditional problem solving contexts. This implication for today's technological and information-sensitive classrooms environment is a key for developing learners who are mathematically literate and intellectually autonomous.