Hypothetical Learning Trajectory (HLT) pada Materi Bangun Ruang Sisi Datar

Abstract

Many students still encounter difficulties when learning polyhedra, particularly in understanding the concepts of surface area and volume and applying them to solve contextual problems. These challenges suggest that instruction should support students in constructing mathematical ideas progressively rather than relying on memorization of formulas. This study aimed to develop a Hypothetical Learning Trajectory (HLT) based on Realistic Mathematics Education (RME) for learning polyhedra. A design research approach was adopted through three interconnected phases: preliminary design, teaching experiment, and retrospective analysis. The study began with curriculum analysis, a review of relevant literature, and an examination of students' anticipated ways of thinking to formulate an initial learning trajectory. The proposed trajectory was then implemented in classroom learning to capture students' responses, solution strategies, and learning difficulties. Qualitative data from the implementation were examined by comparing the intended learning trajectory with the trajectory that actually emerged during instruction. The findings indicate that contextual situations, supported by mathematical models and exploratory activities, enabled students to develop a more meaningful understanding of polyhedra concepts, including geometric elements, surface area, and volume. The resulting learning trajectory also provides insight into students' thinking processes and highlights learning obstacles encountered throughout the learning sequence. These findings may serve as a reference for teachers in designing geometry instruction that is more responsive to students' conceptual development.