A design research study of a curriculum and diagnostic assessment system for a learning trajectory on equipartitioning

Abstract

Design research studies provide significant opportunities to study new innovations and approaches and how they affect the forms of learning in complex classroom ecologies. This paper reports on a two-week long design research study with twelve 2nd through 4th graders using curricular materials and a tablet-based diagnostic assessment system, both designed around a learning trajectory on equipartitioning. A learning trajectory is a conceptual model of how students move from naive to more sophisticated understandings as they engage with a carefully sequenced set of tasks. The equipartitioning construct describes how students come to understand the ideas involved in sharing fairly an evenly divisible collection, a single shape or multiple shapes. The paper is organized around the three phases of design research: planning, conduct, and retrospective analysis Cobb et al. (Educ Res 32(1):9–13, 2003). It illustrates how the conjectures of the study are subjected to testing and revision, based on the students’ and teachers’ behaviors during the study, and how interpretations and theories evolve during the different phases.