Responding to student thinking in the moment : examining conferring practices and teacher learning in the elementary mathematics classroom
Keywords: Education.

Research, policies, and standards have called for math classrooms to engage students in the work of doing mathematics as a joint, discourse-driven endeavor (e.g., Boaler & Staples, 2008; Common Core State Standards Initiative, 2010; National Council of the Teachers of Mathematics, 2014). Collaborative problem solving provides just such an opportunity and offers multiple demonstrated benefits to students (c.f., Boaler, 2010; Johnson & Johnson, 1999; Laughlin, Hatch, Silver, & Boh, 2006; Pantiz, 1999), but raises questions about the role of the teacher when students are co-constructing understanding in small groups. Prior research provides evidence that teachers can support student learning during collaborative problem solving by asking questions to uncover student thinking (Franke et al., 2009; Kazemi & Stipek, 2001), however there is also the potential for teachers to undermine students' mathematical authority and derail their thinking (Brodie, 2000; Cohen & Lotan, 2014). How teachers navigate the discursive challenges of intervening in students' work-in-progress productively has yet to be fully illustrated, and researchers in this area have called for greater attention to these conversations (Jacobs & Empson, 2016). The pedagogical work involved in responding productively to student thinking in the moment is demanding because it cannot be fully planned for in advance and requires skillful improvisation (Ball & Cohen, 1999; Lampert & Graziani, 2009). Responding to student thinking in the moment is difficult work, and we don't yet know how best to support teachers in learning to do so. Professional development structures typically do not provide opportunities to learn how to respond to the emergent thinking of students because they take place in the absence of students and the demands of the moment, compounding the challenge of learning responsiveness. Efforts toward practice-based teacher education seek to bridge this gap, by decomposing practice, trying on practices in low-stakes environments, and maintaining the complexity of pedagogies (Grossman, Hammerness, & McDonald, 2009; Lampert et al., 2013). To inform teachers' efforts to respond to student thinking in the moment and better understand the professional learning involved, my dissertation seeks to define and illustrate how teacher-student interactions, which I refer to as conferring, can uncover and advance student thinking in the moment. I also undertake an examination of how an embedded professional development structure can support teacher learning of responsiveness through conferring. I conducted two studies to address these twin goals. In Study 1, I examine the conferring interactions of two fourth grade teachers with their students and use cross-case analysis to compare how different interactions were structured. Using video and audio records of teachers' interactions with collaborating students, I determined the structures of more and less productive conferring interactions and the specific discursive moves teachers used in these interactions which contributed to their productivity. In Study 2, I designed a coaching intervention embedded directly in teachers' own classrooms, which I call side-by-side coaching, and explored the impact of this intervention on the conferring practices of three elementary teachers. The multiple layers of analysis of video records compare teachers' conferring interactions before and after side-by-side coaching, which are triangulated with interview data. Findings from Study 1 are detailed in Chapters 3 and 4. In Chapter 3, I present analysis of teachers' conferring interactions with students in which there was evidence that student thinking was advanced in the discourse. I describe the characteristics and the types of these discursive episodes, which I refer to as nudges. Nudges build on student thinking in the moment. In Chapter 4, I contrast these conferring interactions with those that do not evidently advance student thinking and provide an analysis of the types of structures of conferring interactions without a nudge. These findings illuminate what makes conferring challenging for teachers and what specific discursive routines may undermine or support teachers' efforts to advance student thinking. Findings from Study 2 are detailed in Chapters 5 and 6. In Chapter 5, I examine quantitatively whether teachers learned to nudge student thinking more frequently from pre- to post-coaching. I found statistical evidence that all three teachers did learn to do so, and I explore three competing hypotheses for what might explain the increased frequency of nudging in the data, finding only a shift in the nature of conferring interactions a plausible explanation. In Chapter 6, I provide an in-depth analysis of the shift in the nature of teachers' conferring interactions from pre- to post-coaching. I found that changes were clustered around changes in teachers' enacted identities and practices, and this chapter describes a total of eight dimensions of teacher learning. These eight shifts are united by a shared arc of teacher learning: developing and enacting a genuinely curious stance toward student thinking. The findings from these studies have implications for research and practice. First, the nudge provides an articulation of how teachers can effectively build on student thinking in the moment without succumbing to the pitfalls identified by earlier research. Within the broader context of conferring interactions, these finding provide the first clear illustration of how teachers and students can co-construct interactions in the midst of problem solving that both uncover and advance student thinking. Second, the findings from Study 2 offer a model for teacher learning of responsive pedagogy and emphasize the complex interdependence of teacher identity and practice. These finding underscore the need for professional developers and teacher educators to consider how to attend to shifts in both identity and practice to support teacher learning. Third, the development of a curious orientation to student thinking and the practices to enact that curiosity was a central theme of teachers' learning. Teacher curiosity matters and can be learned. This study raises questions about the role teacher curiosity about student thinking in the learning or other teaching practices. Finally, the specific embedded professional development model used in Study 2, side-by-side coaching, effectively supports teachers' learning of a complex and responsive pedagogy, conferring. Side-by-side coaching offers the field a new professional development structure to support teachers directly in the classroom to learn and teach simultaneously and has implications for researchers aiming to understand how teacher learning unfolds in the moment.