Culturally responsive approaches to geometric translation: Exploring Songket motifs and students’ proving trajectories

Research on students’ proving processes in geometry has largely emphasized formal reasoning, with limited exploration of cultural contexts as scaffolds for mathematical understanding. Addressing this gap, this study investigates the integration of South Sumatera Songket motifs as culturally relevant tools to support students’ proving processes in learning geometric translation. Using a Design Research methodology, a validation study was conducted with 30 junior high school students in Palembang. The research progressed through three phases: preparation, design experiments (preliminary and main teaching experiments), and retrospective analysis. Learning tasks were designed based on Habermas’ Construct of Rationality—epistemic, teleological, and communicative—to structure the proving trajectory. Culturally grounded tasks facilitated students’ progression from intuitive exploration to formal justification. In the first activity, the Songket Durian motif supported recognition of translation as an isometric transformation through visual pattern analysis. Subsequent tasks introduced algebraic reasoning with coordinate shifts and vector notation, leading to replication of the Perahu Kajang motif across Cartesian quadrants to formulate general transformation rules. These findings reveal the effectiveness of cultural artifacts in supporting both intuitive and formal dimensions of proof. Embedding cultural artifacts in mathematics instruction fosters culturally responsive and proof-oriented learning, enhancing conceptual understanding while strengthening connections between mathematics and cultural identity. This study contributes a novel approach by systematically employing cultural motifs to design proof-based learning trajectories in geometry, offering a model for integrating cultural heritage with mathematical reasoning in diverse educational settings.