Uncovering Learning Obstacles in Elementary Students Fraction Understanding: A Multi-Dimensional Analysis for Didactical Design

Abstract

Learning fractions in elementary school remains difficult for students because the concept is abstract and requires strong conceptual understanding. Although prior studies have examined epistemological, didactical, or ontogenic learning obstacles separately, few have triangulated multiple data sources to capture how these three dimensions interact, particularly within a Didactical Design Research (DDR) framework at the lower-grade elementary level, this gap in integrated, multi-source analysis is what the present study addresses. This study identifies and analyzes the three types of learning obstacle experienced by third-grade students in learning fractions at UPT SDN 060817 Medan and examines how these obstacles interact as a basis for designing DDR-based instruction. A qualitative descriptive approach was used with 15 third-grade students and one classroom teacher as subjects. Data was collected through a mathematical concept-understanding test, classroom observation, semi-structured interviews, and instructional-artifact analysis, then triangulated. Results show that only 33.33% of students reached mastery, with a class average of 53.2. Fifteen learning obstacles were identified: five epistemological, five didactical, and five ontogenic, and these interact with one another rather than occurring independently. Identifying these three obstacle categories carries direct practical significance for guiding teachers in designing more contextual, concrete-media- and technology-supported fraction instruction. The findings provide an empirical foundation for a Hypothetical Learning Trajectory (HLT) integrating concrete media, PhET Simulation, Problem-Based Learning, and local Medan contextualization.