Creating Cultures of Participation to Promote Mathematical Discourse

Abstract

IntroductionAs a former eighth grade mathematics teacher, I was aware of the impact discourse had in shaping students' thinking and thus often implemented strategies that supported these efforts. However, a reality became clear when pursuing these National Board Certification, which demanded a 15-minute unedited video of me facilitating a whole-class discussion. While recording the lesson, which centered on an introduction to irrational numbers, I thought students were engaged in lively discussion. However, analysis of the video-taped lesson revealed that I was doing almost all of the talking! The perceptions of my practice were not aligned with my actual practice. After this revelatory experience, I was curious to learn more about how other teachers perceived the use of discourse to support adolescents reasoning in mathematics and particularly how they created cultures of participation to support equitable discursive interactions with adolescent students from diverse backgrounds.Consistent with my own experience, equitable access to mathematically rich and meaningful learning experiences continues as a critical need in the classroom (Cobb 8c Hodge, 2011; National Middle School Association [NMSA], 2010). Rich learning experiences also are fundamental in supporting and developing students' mathematical reasoning and sense making (Chapin, O'Connor, 8c Canavan Anderson, 2003), which is of particular concern during the middle grades as the level of abstraction in mathematics increases greatly. As a means of openly engaging in understanding meaningful and rich mathematics, discourse offers one avenue for teachers to create equitable and mathematically rich learning environments and interactions; this article demonstrates why an emphasis on mathematical discourse should be a common practice within the middle level classroom (Bartolini Bussi, 1998).Discourse requires students to evaluate and interpret the perspectives, ideas, and mathematical arguments of others as well as construct valid arguments of their own. That is, students develop deeper understandings of mathematics when they engage in meaningful social interactions such as whole class discourse (Cobb, Yackel, W NCTM, 1991; Rigleman, 2010). The adoption of the Common Core State Standards in many states reinforces the importance of creating classrooms that focus on reasoning, deep conceptual understanding, and the communication of mathematics (Larson, 2012;NCTM, 2000). In addition, the teacher's efforts and attitudes in creating a caring and well-structured classroom environment with high expectations for all students are more likely to increase student engagement (Klem 8c Connell, 2004), which can lead to greater achievement (Smith, Rook, 8c Smith, 2007). Such classrooms exemplify cultures of participation. With that said, knowing that discourse can support student learning and creating the structures to help discourse come alive are not the same thing. Creating a classroom culture of participation is a necessary first step in implementing meaningful discourse and creating equitable learning experiences.What follows is a compilation of strategies and classroom structures from 13 middle level teachers from highly urban communities with tremendous cultural, linguistic, and ethnic diversity. …