Understanding Teacher and Student Learning Situated in a School-wide Implementation of Fractions Instruction

Thesis (Ph.D.)--University of Washington, 2016-06

The current push to improve fractions instruction is in response to studies that have aptly demonstrated the deficits in student and teacher understanding of fractions (e.g., Chinnappan & Desplat, 2012; Kloosterman, 2010; Ma, 1999; Rittle-Johnson, Siegler, & Alibali, 2001). While these studies have built an argument of the weaknesses in our current systems for supporting student learning, we have not studied how schools focused on improvement coordinate teacher and student learning. This qualitative study was designed to advance our understanding of how to support teachers’ instructional practices and students’ learning of fractions by focusing on what teachers and students do know and understand and how both teacher and student learning were intentionally considered and coordinated. A case study of one elementary school where teachers implemented a school-wide approach to fractions instruction and were positioned as learners alongside their students provided the opportunity to study how students’ thinking developed over multiple years and what teachers know and understand about teaching fractions through their participation in a school-wide effort to implement fractions instruction. Three major findings related to student learning emerged: (1) over time, students demonstrated more sophisticated understandings of fractions, (2) at the start of each subsequent school year, the cohort of students entering a particular grade level brought with them more sophisticated strategies for partitioning and sharing as well as more accurate representations, and (3) the understanding and strategies for students with one year of instruction were noticeably less sophisticated than students with two or three years of instruction, whose understandings and strategies were much more aligned with one another. Related to teacher learning, I offer examples of three kinds of intellectual resources that teachers generated, drew upon, made meaning of, and coordinated as they engaged in teaching mathematics and learning to teach mathematics: mathematical knowledge for teaching, instructional visions, and understanding of trajectories of student learning. In addition, I examine how the school-based professional learning opportunities supported the development of mutual understanding among teachers and instructional leaders such that there was instructional alignment across the school. I offer four findings from looking across the three professional learning contexts: (1) I argue that all three learning contexts provided opportunities for teachers and instructional leaders to develop mutual understanding around various kinds of intellectual resources, (2) I argue that the interactions in which teachers generated and used various intellectual resources varied across the different settings but worked together to support the development of mutual understanding, (3) I argue that mutual understanding both allowed the coach to develop unit plans that had meaning to the teachers and supported them to teach fractions in ways that were aligned within classrooms at the same grade level and across classrooms at different grade levels, and (4) I argue that teachers were positioned as both “listeners” and “sources” and that because of these different positionings, participants have different perspectives that shape the interpretations and functions of their contributions.