Designing a GeoGebra-Integrated Learning Trajectory for Fractions Using Jombang’s Traditional Land Measurement

Abstract

The low level of understanding of fractions among students indicates the need for more contextual, meaningful, and relevant learning in everyday life. This study aims to develop a Hypothetical Learning Trajectory (HLT) based on Realistic Mathematics Education (RME) integrated with GeoGebra. The HLT uses the context of traditional land measurement in Jombang to support students’ understanding of fractions. This study employs a design research method consisting of three main stages: preliminary design, design experiment, and retrospective analysis. It focuses on the preliminary design stage and the pilot experiment phase, involving six seventh-grade students selected through purposive sampling. The instruments used included HLT-based Student Worksheets, observation sheets, and interview guidelines. Data were collected through the implementation of HLT in the pilot experiment stage, observation of student activities during the completion of Student Worksheets, and interviews after the activity. Data were analyzed descriptively and qualitatively. The results showed that the developed HLT was able to facilitate students' transition from informal to formal understanding, as indicated by an improvement in the quality of their conceptual understanding in connecting the context, visual representations, and symbolic notation of fractions. GeoGebra was found to help students visualize fraction concepts more concretely, while the local context made learning more relatable and meaningful. Theoretically, these findings reinforce the RME principles of guided reinvention and phenomenological exploration within a learning trajectory. This HLT can serve as a reference for designing interactive, contextual, and culturally aligned fraction learning experiences that align with students' experiences and cultural backgrounds.

Rendahnya tingkat pemahaman siswa terhadap pecahan menunjukkan perlunya pembelajaran yang lebih kontekstual, bermakna, dan relevan dalam kehidupan sehari-hari. Penelitian ini bertujuan untuk mengembangkan Hypothetical Learning Trajectory (HLT) berbasis Realistic Mathematics Education (RME) yang diintegrasikan dengan GeoGebra. HLT ini menggunakan konteks pengukuran lahan tradisional di Jombang untuk mendukung pemahaman siswa terhadap pecahan. Penelitian ini menggunakan metode design research yang terdiri dari tiga tahap utama: preliminary design, design experiment, dan retrospective analysis. Fokus penelitian ini adalah pada tahap preliminary design dan fase pilot experiment, yang melibatkan enam siswa kelas tujuh yang dipilih melalui purposive sampling. Instrumen yang digunakan meliputi Lembar Kerja Peserta Didik (LKPD) berbasis HLT, lembar observasi, dan pedoman wawancara. Data dikumpulkan melalui penerapan HLT pada tahap pilot experiment, observasi aktivitas siswa selama pengerjaan LKS, serta wawancara setelah kegiatan. Data dianalisis secara deskriptif dan kualitatif. Hasil penelitian menunjukkan bahwa HLT yang dikembangkan mampu memfasilitasi siswa dalam transisi dari pemahaman informal ke formal, yang ditunjukkan oleh peningkatan kualitas pemahaman konseptual mereka dalam menghubungkan konteks, representasi visual, dan notasi simbolik pecahan. GeoGebra terbukti membantu siswa memvisualisasikan konsep pecahan secara lebih konkret, sementara konteks lokal membuat pembelajaran lebih relevan dan bermakna. Secara teoretis, temuan ini memperkuat prinsip RME mengenai guided reinvention dan phenomenological exploration dalam sebuah learning trajectory. HLT ini dapat menjadi referensi dalam merancang pengalaman pembelajaran pecahan yang interaktif, kontekstual, dan sesuai budaya, yang selaras dengan pengalaman serta latar budaya siswa.