Reform-based mathematics instruction is a complex process, involving an interaction of students, content, and pedagogical approaches (Cohen & Ball, 1999). To implement such instruction, teachers not only need to have the knowledge of content, students, and pedagogy, but be able to integrate the different forms of knowledge (Davis, 2003, 2006; Lampert, 2001). The aim of the current study was to describe how elementary teachers related aspects of mathematics content and pedagogy to student learning during collaborative lesson planning meetings. The teachers were engaged in mathematics lesson study, which is a form of practice-based PD with substantial empirical and theoretical underpinnings for teacher learning and knowledge reorganization (Lewis et al., 2009). While capturing how teachers interconnect aspects of their practice, my goal in this study was to characterize the potentially evolving nature of teachers’ knowledge integrations as well as to explore the role of a teacher leader involved in facilitating the lesson study process in shaping participants’ knowledge integration across lesson study planning meetings. I conceptualized teacher knowledge integration in terms of the connections among the foci on students, mathematics content, and teaching (Murata et al., 2012), and I assumed the students’ engagement with mathematics content to be at the core of the 3D knowledge integration, with teaching positioned dynamically in relation to this core. Moreover, I was informed by the perspective on teacher knowledge as situated in practice, mediated by talk-in-interaction (Vygotsky, 1986). This research was a qualitative case study (Stake, 1995) of a group of four primary grade teachers and one teacher leader, who was the facilitator, participating in one lesson study cycle focused on primary-grades mathematics. The lesson study team had four meetings to plan a research lesson focused on the topic of number decomposition. The main data for this study included videotapes and transcripts of the four lesson planning meetings. Other forms of data included facilitator and teacher interviews, post research lesson written reflections, videotape of the research lesson, research lesson plan, and a teacher background survey. To answer the research questions, I used the qualitative data analysis methods (Miles & Huberman, 1994). Inductive analysis strategies (Strauss & Corbin, 1998), as well as the existing frameworks for facilitation of PD discussions (van Es et al., 2014; Zhang et al., 2011), also informed the data analysis. Analysis in this study revealed two broad categories of 3D knowledge integration statements, demonstrating that when participants connected aspects of teaching, students, and mathematics during collaborative lesson planning discussions, they positioned teaching either as responsive to students’ work with mathematics (i.e., responsive statements) or as impacting students’ work with mathematics (i.e., impact statements). Given that each broad category of 3D knowledge integration statements was further organized into three sub-categories each, one of the contributions of the current study is the identification of specific teacher knowledge markers that integrate the foci of teaching, students, and mathematics. Throughout the lesson planning meetings, participants used the 3D knowledge integration statements primarily to offer resolutions to the research lesson implementation issues and to visualize the implementation of the lesson, which suggests that these statements were used as part of conversational routines (Horn & Little, 2010). The majority of 3D knowledge integration statements, particularly where the teacher assessed, advanced, directed, and represented students’ work with mathematics, were in form of rehearsals, or portrayals of classroom interactions that included teacher or student anticipated talk, which were also identified in prior research (Horn, 2005, 2010). There was a concentrated presence of 3D knowledge integration statements in discussions centered on anticipating students’ mathematical responses to the lesson tasks along with the identification of student-related issues and associated instructional actions. Moreover, in the current study, discussions that involved disagreements among the participants also tended to feature a concentrated presence of 3D knowledge integration statements. The teacher leader’s approach to facilitation of lesson study was to stand back, giving space to other participants to drive the lesson planning process and perhaps allowing teachers to begin developing a disposition towards their practice as a site for learning, which may be the first step in developing pedagogical content knowledge and analytic skills in a practice-based learning environment. Overall, while participants seemed to adopt the student lens and curriculum developer lens during the lesson planning process, more work is needed to facilitate the development of the researcher lens (Fernandez et al., 2003). Detailed limitations and implications of the study are discussed.
