Zulkardi
Doctoral Program in Mathematics Education, Universitas Sriwijaya, Palembang, Indonesia

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Local Instructional Theory on Ratio and Proportion through Yogyakarta Cultural Tour Packages for Inclusive Education Students Irma Risdiyanti; Zulkardi; Ratu Ilma Indra Putri; Rully Charitas Indra Prahmana
Mathematics Education Journal Vol. 20 No. 3 (2026): Mathematics Education Journal
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/mej.v20i3.pp569-598

Abstract

Students with mild learning difficulties in inclusive education often experience challenges in understanding ratio and proportion, particularly in relating abstract mathematical concepts to meaningful real-world situations. Many tend to interpret proportional relationships as simple arithmetic procedures rather than as relationships between quantities, while limitations in working memory and difficulties in processing abstract information frequently lead to inappropriate calculation strategies. Therefore, mathematics instruction in inclusive classrooms requires contextual, concrete, and sensorimotor-based learning activities that support conceptual understanding while reducing cognitive load. This study aimed to develop a Local Instructional Theory (LIT) for learning ratio and proportion through the integration of the Indonesian Realistic Mathematics Education known as PMRI approach and Embodied Learning using the context of Yogyakarta cultural tour packages. The study employed design research of the validation studies type, consisting of preliminary design, design experiment, and retrospective analysis phases. The learning trajectory comprised four activities: recommending cultural tourism destinations, organizing efficient travel routes, selecting appropriate transportation, and calculating tour package prices. The findings indicate that students gradually developed proportional reasoning from concrete experiences toward formal mathematical understanding by comparing quantities, representing proportional relationships using ribbon diagrams and double number lines, and applying direct and inverse proportion concepts in contextual decision-making situations. Furthermore, the integration of cultural tourism contexts and embodied learning activities reduced cognitive load and effectively supported students’ transition from informal reasoning to formal proportional understanding.