Recent scholarly work in mathematics education has included a focus on learning mathematics with understanding (Hiebert & Carpenter, 1992; Hiebert et al., 1997; Fennema & Romberg, 1999; National Council of Teachers of Mathematics, 2000). Hiebert et al. (1997) discussed two processes that they suggested increase understanding and that are central to this study: reflection and communication. Learning mathematics with understanding requires that the students create a deeper knowledge of mathematics through reflection and communication. The environment in which such learning can take place must include patterns of behavior, known as social norms that promote deeper thinking. When the social norms encourage reflection and communication among the members of the classroom community, or supports learning with understanding, it becomes what I term a productive discourse community. The purpose of this study is to find out what a teacher does to create and maintain a productive discourse community where students can reason and learn with understanding. To accomplish this purpose, this research asks the following question: In what ways does the teacher in the study direct mathematical discourse in order to facilitate understanding? To answer this research question, data was gathered from eight class periods. The classroom discourse was analyzed and six discourse generating tools were found to be used by the teacher: (1) using lower-order questions to engage students, (2) persisting in eliciting students' reasoning, (3) encouraging as many student participations as possible, (4) encouraging students to analyze and evaluate each other's comments, (5) encouraging students to share as many strategies as possible and (6) using a focusing discourse pattern. There were also three social norms found to be established in the classroom at the time of the data collection. These norms are: all students are expected to (a) participate (b) share their reasoning when called upon, and (c) listen to, analyze, and evaluate each other's comments. Through further analysis, it was found that the six discourse generating tools reinforced the social norms, while the social norms supported the six discourse generating tools. Thus creating an environment where reflection and communication occurred in a way that promoted learning mathematics with understanding.



College and Department

Physical and Mathematical Sciences; Mathematics Education



Date Submitted


Document Type





Discourse, Discourse Generating Tools, Social Norms, Discourse Patterns, Learning with Understanding, Productive Discourse Community, Classroom Norms, Classroom Discourse, Teacher Questioning, Discourse Analysis