Chapter 4: Two Approaches to Describing the Development of Students’ Reasoning about Length: A Case Study for Coordinating Related Trajectories

This chapter compares two different learning trajectories describing length and its measurement. By analyzing the origin of these two trajectories within the respective research projects, we offer a case study for the coordination and consolidation of different trajectories. The analysis commences with a detailed comparison of both learning trajectories.

Comparative analysis of these research projects and the resulting accounts of student learning and development in the form of learning trajectories helped us pursue several questions about the use of trajectories as integrative tools for research, curriculum development, evaluation, and standard setting. This case study illustrates the importance of finding broadly common terminology for describing the growth of children’s knowledge and strategies for a topic—length measurement in this case. We identified a common partial sequence of increasingly sophisticated reasoning consistent with both trajectories but did not find a completely consistent system allowing a comprehensive coordination. Nevertheless, by relying on this common partial sequence, we examined the correspondence of sections of both research-based trajectories and produced a visual mapping to represent our analysis. We developed a rubric of five types of correspondence between related trajectories and used this rubric to characterize the degree of fit between these two trajectories. Thus, we provide one example that blends related trajectories to forge a common recommendation for content-specific pedagogy that may help teachers improve instruction.