From Learning Obstacles to Conceptual Understanding: Developing GeoGebra-Assisted Teaching Materials for Elementary Fractions through Educational Design Research

Abstract

Learning fractions remains a significant challenge in elementary education, often hindered by specific learning obstacles. This study aims to develop GeoGebra-assisted teaching materials integrated with a Hypothetical Learning Trajectory (HLT) to bridge the gap between these obstacles and conceptual understanding. Adopting an Educational Design Research (EDR) approach, the study progressed through three iterative phases: analysis and exploration, design and construction, and evaluation and reflection. The development was grounded in an initial pedagogical analysis of student learning obstacles, which informed the HLT design. Data were collected through expert validation, teacher interviews, and field testing with 161 elementary students (divided into small-scale and large-scale trials), then analyzed qualitatively using retrospective analysis and constant comparative methods.The quantitative results indicate that the GeoGebra-based materials are highly valid (92.75% from media experts) and practical (81.75% in large-scale trials), effectively transforming the HLT into a verified learning path. However, qualitative findings revealed a critical nuance: while students engaged enthusiastically with dynamic visualizations, some faced challenges in transitioning from visual area models to formal symbolic notation. This underscores the necessity of teacher-led instrumental orchestration to scaffold mathematical generalizations. This research concludes that the synergy between dynamic geometry software and a structured learning trajectory provides a robust framework for overcoming cognitive barriers, provided it is integrated within a dialogic instructional environment.