Quality of Instruction: Examining Discourse in Middle Schoo Mathematics Instruction

Abstract

According to the NCTM reform suggestions, when teachers are orchestrators of student interactions, students adopt a more active role in explaining and learning mathematics. This research, which mapped the nature and role of meaningful mathematical discourse, provides insights into discursive practices that lead to rich mathematical interactions. We observed, coded, and analyzed middle school algebra, number, and data lessons using a grounded theory approach. We organized the observed paths that emerged into a map depicting actual paths for mathematics discourse. The results indicated that communication pathways between the teacher and students occur in many ways, and certain student-initiated questions may trigger predictable teaching patterns. Conversation that originates with the teacher often results in dialogue that is one-dimensional, mostly provides factual information, and rarely results in rich, meaningful mathematical dialogue. However, when students engage in the teacher's conversation or they are persistent in their own questioning, teachers tended to provide more detailed explanations, and teachers often embellished with new examples and representations using nuanced solution methods. Although results seem to indicate that teaching children to be persistent with their questioning will enhance understanding, this behavior may be interpreted as threatening to some teachers. Therefore, caution is warranted when attempting to turn these findings into action. It is important that, before instructing students about being persistent with questions, teachers understand the students' intentions. Although participants did not have negative reactions to persistent student questioning, some children might experience negative responses without proper professional development for teachers.