Supporting Student Justification in Middle School Classrooms: Teachers’ Work to Create a Context for Justification

• In Event: Productive Talk and Participation in Disciplinary Practices: Perspectives From Science and Mathematics Education

Abstract

Purpose
Justification activity in middle school classrooms is rare in the United States (Bieda, 2010; Jacobs et al., 2006). Despite a growing knowledge base regarding how teachers orchestrate mathematical discussions (e.g., Smith & Stein, 2010; Staples, 2007), few analyses have considered the orchestration of disciplinary practices such as justification. To advance this agenda, we present two cases of 7th-grade teachers who were successful at engaging students in mathematical justification across multiple tasks. Analyses of their pedagogy of justification revealed that their successes resulted from overlapping but distinct pedagogical repertoires.

Theoretical perspectives
Two perspectives informed this work: a disciplinary perspective, which considers justification as a core mathematical practice (Hanna, 2000; Lakatos, 1976); and a community-of-practice perspective (Lave & Wenger, 1991; Wenger, 1998), where justification is viewed as a practice of a specific community, here, a middle school mathematics classroom that is doing and learning mathematics together. These two perspectives allowed us to consider how the disciplinary practice of justification is shaped by (and shapes) the community’s practices. Our analyses privileged teacher actions, as these are critical in creating opportunities and establishing criteria for justification (Bieda, 2010; Nathan & Knuth, 2003).

Methods and data
The case teachers were two of 12 participants in JAGUAR, an NSF-funded project focused on middle grades’ justification. They were selected for this analysis as their classrooms revealed consistent justification activity among students (disciplinary practice) yet revealed different sets of learning practices (community of practice).

Data sources included video-recordings and transcriptions of 12 implementations of justification tasks (six per teacher), corresponding student work, teacher reflective journals, and video-viewing interviews where teachers viewed researcher-selected clips and responded to questions about their pedagogy and student justification activity. The first analysis documented student justification activity in these classrooms. The second analysis focused on the constellation of factors that supported student justification activity.

Findings
We examined dimensions including teachers’ moves (turn level) such as student-to-student orchestration moves (low and high accountability), press moves, and coupling of teacher responses to students’ mathematics (Seymour & Lehrer, 2006), as well as patterns of interaction (Voigt, 1985; Wood, Williams & McNeal, 2006) and task design (Stein & Smith, 1996).

The results documented differences in these teachers’ pedagogies of justification. The teachers’ pedagogies overlapped in many areas such as patterns of interaction to elicit and make public students’ thinking, asking students to consider others’ ideas, and pressing for elaboration. They differed, however, in other dimensions. One teacher created a context for justification through questions that were tightly coupled with students’ mathematics, explicit press for justification, and deliberate task design. The other teacher created a context for justification through high accountability student-to-student orchestration moves and responsiveness to students’ ideas.

Significance
To augment our knowledge base related to mathematical practices such as justification, a consideration of multiple instructional approaches is necessary. This paper offers two instantiations of extensive student justification and the pedagogical repertoires that supported students’ engagement in this practice, thereby advancing the argument that considering constellations of moves might be one effective approach to supporting student justification.

Author

• Megan E. Staples, University of Connecticut