Learning Trajectory of Arithmetic Sequences and Series with a PMRI Approach Using the Context of Yogyakarta's Kawung Batik Fabric

Mathematics learning is often perceived as abstract and disconnected from students’ real-life experiences. To bridge this gap, this study developed a culturally contextualized learning trajectory using Kawung Batik patterns from Yogyakarta to support students' understanding of arithmetic sequences and series. Employing the Indonesian Realistic Mathematics Education (PMRI) approach within a design research framework, this study followed three main phases: preliminary phase, design experiments (pilot and teaching experiments), and retrospective analysis. The participants were 32 tenth-grade science students at SMAS Muhammadiyah Kedawung. The findings indicate that the Kawung Batik context facilitated students’ transition from informal to formal reasoning in learning arithmetic sequences and series. Students actively identified patterns, organized batik motifs into arithmetic sequences, and formulated the general term and the sum of the first n terms through meaningful contextual engagement. Visual strategies and group discussions promoted active participation and conceptual understanding in solving culturally grounded mathematical problems. This study contributes to the development of culturally contextual mathematics instruction in Indonesia and provides a practical model for designing meaningful arithmetic sequence and series lessons. The proposed learning trajectory serves as a reference for teachers seeking to connect mathematics learning with students' cultural environments.