The case of Mrs. Purl: Using a learning trajectory as a tool for teaching

Abstract

Researchers have hypothesized and, in some cases, shown that hypothetical learning trajectories (LT)s can be effective tools in teaching, but implementation, across individual teachers, varies. From the literature base, we have identified six ways researchers have hypothesized teachers might be able to use LTs in their work as teachers: formatively assess students over time, attend to student thinking, provide appropriate differentiation, design and modify mathematical tasks, choose appropriate learning goals, and relate lesson goals to broader curriculum goals. To gain greater insight from the teachers’ perspective, we followed one teacher, Mrs. Purl, and chronicled her efforts in using the LT to design and enact student interviews and lessons. During data collection, Mrs. Purl participated in in-the-moment noticing in which she noted events during interviews or instruction that she found significant. Following interviews and lessons, Mrs. Purl was asked to reflect on each of the events and describe what she noticed, what she could infer about student understanding, and instructional implications. Using literature on teacher noticing, we qualitatively analyzed each of the three components and then related them back to the ways in which researchers have hypothesized teachers might be able to use learning trajectories. Findings suggest that the LT supported Mrs. Purl in attending to students’ thinking, designing and modifying mathematical tasks, and choosing appropriate learning goals, but she did not refer to the LT to provide differentiation, formatively assess students over time, or relate lesson goals to broader curriculum goals.