Local Instructional Theory for Ratio and Proportion through Yogyakarta Cultural Tour Packages for Inclusive Education Students - Irma Risdiyanti; Zulkardi; Ratu Ilma Indra Putri; Rully Charitas Indra Prahmana (Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS), 2026)
Students with mild learning difficulties in inclusive classrooms frequently encounter substantial challenges in developing conceptual understanding of ratio and proportion, particularly when required to connect abstract mathematical relationships with meaningful real-world situations. Rather than reasoning proportionally, many students interpret proportional situations as routine arithmetic procedures, while limitations in working memory and difficulties in processing abstract information often result in inefficient or inappropriate computational strategies. Consequently, mathematics instruction in inclusive settings should provide contextualized, concrete, and sensorimotor-based learning experiences that facilitate conceptual understanding while simultaneously reducing unnecessary cognitive load. This study aimed to develop a Local Instructional Theory (LIT) for teaching and learning ratio and proportion through the integration of the Indonesian Realistic Mathematics Education known as PMRI approach and Embodied Learning within the authentic context of Yogyakarta cultural tour packages. The study employed design research of the validation studies type, comprising three iterative phases: preliminary design, design experiment, and retrospective analysis. The resulting learning trajectory consisted of four interconnected instructional activities: recommending cultural tourism destinations, organizing efficient travel routes, selecting appropriate transportation, and calculating tour package prices. The findings demonstrate that students progressively developed proportional reasoning from concrete embodied experiences toward formal mathematical understanding by comparing quantities, representing proportional relationships through ribbon diagrams and double number lines, and applying concepts of direct and inverse proportion to solve contextual decision-making problems. Furthermore, the integration of culturally meaningful tourism contexts with embodied learning activities effectively reduced students’ cognitive load and facilitated their transition from intuitive, informal reasoning to formal proportional understanding, thereby providing empirical support for the effectiveness of the proposed LIT in inclusive mathematics education.