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.

Techno-Mathematical Discourse: A Conceptual Framework for Analyzing Classroom Discussions

“…Therefore, in order to deeply understand complex concepts, some form of discussion must take place-even if that conversation occurs within one individual. When considered in the classroom context, rich meaningful communication consists of "interactive and sustained discourses of a dialogic nature between teachers and students aligned to the content of the lesson that addresses specific student issues" [11] (p. 378). In other words, meaningful classroom discourse contributes to students' understanding by promoting effective communication and articulation of thought.…”

“…Through these interactions, students analyze and evaluate the mathematical thinking and strategies of others and deepen their own mathematical understanding. Students must organize and consolidate their mathematical thinking in order to communicate effectively with their classmates and with the teacher [7,11,[30][31][32]. Teachers' discourse practices also influence the nature of classroom discussions.…”

“…When students have opportunities to articulate and discuss mathematical concepts, they develop a deep understanding of those concepts. With its roots in Vygotskian social learning theories, the study of the structure and flow of mathematical discourse in the classroom has generally taken a socio-cultural or socio-linguistic perspective, and many researchers have developed different ways to conceptualize and classify how discourse occurs in classrooms and its impact on learning [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Metasynthesis of Factors Contributing to Children’s Communication Development: Influence on Reading and Mathematics

“…Just as vocabulary development is essential for developing early reading skills, mathematics vocabulary development is key to build a foundation for later mathematics conceptual understanding [5,[10][11][12][13] (Samuels & Flor, 1997). These two vocabularies are interwoven in that the earlier a child can be exposed to mathematical vocabulary words representing concepts, the earlier that child could become proficient in the language of mathematics before formal instruction [4,14,15].…”

“…Meanwhile, recent research from both educational and psychological perspectives has suggested that developmental milestones in reading and mathematics can be symbiotic [3,4]. One possible explanation for this connectivity is that students' understanding of mathematics concepts is bound to their mastering of content vocabularies that are used to define, represent, and communicate mathematical concepts [5]. It is feasible that improving children's application of mathematics vocabulary would yield a positive effect on their mathematics achievement.…”