The Use of Lesson Study to Unpack Learning Trajectories and Deepen Teachers’ Horizon Knowledge

Abstract

We highlight a learning trajectory-based professional development (PD) routine used during Lesson Study to deepen teachers’ and coaches’ understanding of the development of children’s fraction knowledge through the analysis of student work. One of the key elements in the design of the coach-facilitated Lesson Study was a team of teachers from multiple grade levels who focused on a rich task that engaged all in vertical articulation of the progression of mathematical learning. Using a case study approach, we examine how the intentional introduction of the learning trajectory by the coach/mathematics teacher educator promoted the teachers’ use of the learning trajectory and contributed to the expansion of teachers’ horizon content knowledge, in terms of how they gained knowledge of content of students, teaching, and curriculum. In particular, we highlight the phases of the Lesson Study process, particularly the planning, the live lesson, and the debrief, which focused teachers’ attention on their understanding of the learning trajectories through student work and discussion during the Lesson Study. Teachers used the curriculum standards, pacing guide, and teaching materials along with research-based learning trajectories to negotiate the appropriate conceptual corridor for learning. Teacher’s experimentation with curriculum pacing guides and learning trajectories in Lesson Study not only benefited from the jugyokenkyu, the research “kenkyu” around “jugyo” which means teaching and learning, but also deepened their understanding of how student learning progresses around fraction knowledge.