Developing Productive Dispositions during Small-Group Work in Two Sixth-Grade Mathematics Classrooms: Teachers' Facilitation Efforts and Students' Self-Reported Benefits.

Through this exploratory study, I developed conjectures about classroom conditions that had the potential to support (or not) the development of productive dispositions toward mathematics. To do so, I listened to sixth-grade students' voices about their experiences with small-group work in 2 mathematics classrooms and contrasted their teachers' efforts to facilitate small-group work. I interviewed 12 students from each classroom (N = 24) to examine the benefits and drawbacks of small-group work that students noticed. Interview data were interpreted to assess the degree to which students' self-reports reflected productive dispositions toward mathematics, and they were reported in the form of 2 composite cases from each classroom. Video recordings of mathematics lessons were analyzed to characterize how each teacher facilitated small-group work. Results indicated that students were more likely to hold productive dispositions (autonomy, belief that mathematical competence is malleable rather than fixed, focus on understanding over task completion) in a classroom in which the teacher transferred responsibility to students, solicited multiple solution strategies, provided process scaffolding, and pressed for conceptual understanding. In contrast, students were less likely to hold productive dispositions (relying on external authorities, belief that mathematical competence is fixed rather than malleable, focus on task completion over understanding) in a classroom in which the teacher provided content help that lowered the cognitive demand for students, focused on obtaining an answer rather than understanding strategies, and placed 1 "genius" in each small group (explicitly grouped students heterogeneously). Students' self-report data provided insights for recommendations of dispositional outcomes to be assessed in future research on students' experiences with small-group work.BACKGROUNDSmall-group work can be implemented during mathematics classes to achieve a range of purposes. Some teachers use group work to provide opportunities to leam mathematics content through explicitly teaching students how to interact (e.g., Fuchs et al., 1997). Other teachers implement group work to provide opportunities for students to develop productive dispositions and intellectual autonomy (Yackel, Cobb, & Wood, 1991). Additionally, other teachers use group work to help students develop interpersonal skills and an appreciation for engaging in democratic processes (Dewey, 1916, as cited in Noddings, 1989). Some teachers pursue still other purposes or multiple purposes. Following Florez and McCaslin (2008), students' voices about their experiences can serve as a measure of students' awareness of benefits (or drawbacks) of group work in their mathematics classrooms. Among the potential purposes for and benefits of group work, which do students notice and report?How students experience group work is likely to differ according to teachers' expectations for group work (Webb, 1995). A range of research has demonstrated that careful structuring of group work matters; teachers who have worked with researchers to structure group work in particular ways have elicited positive outcomes (Fuchs et al., 1997; Yackel et al., 1991). However, it is worth exploring naturalistically how teachers facilitate group work when they are not implementing interventions developed by researchers (Florez & McCaslin, 2008). Comparing and contrasting teachers' instructional practices qualitatively can inspire conjectures about conditions for effective group work (to be tested in future interventions). In particular, more research is needed to identify conditions that lead to the development of students' productive dispositions toward mathematics in the context of group work. It seems particularly important to investigate how middle school teachers facilitate group work, as prior research indicates that middle school teachers exert more control over students' experiences (compared to elementary school teachers) at a developmental period in which students are starting to desire more autonomy (Eccles et al. …