Learning Trajectory of Linear Equation Systems with an Ethnomathematical Approach Using Outdoor Balinese Panglipuran Village: A Design Research Study

Abstract

Mathematics learning, particularly Linear Equation Systems (SPLs), often presents significant challenges for students in different parts of the world, characterized by difficulties in problem modeling, conceptual understanding, and mastery of solving procedures. The nature of SPL that tends to be abstract is often independent of the real experience of students. Addressing this gap requires an innovative and culturally relevant pedagogical approach. This study explores the development and potential effectiveness of a Hypothetical Learning Trajectory (HLT) for SPL integrated with an ethnomathematical approach, utilizing the rich outdoor context  of Panglipuran Traditional Village in Bali. Panglipuran Village, with its preserved traditional architecture, unique spatial layout, and socio-cultural activities of its people, is believed to hold various mathematical ideas that can be the starting point for learning. Using  the Design Research framework, this study involves an in-depth analysis of the concept of SPL and the potential of ethnomathematics in Panglipuran, the design of HLT, and a limited teaching experiment to investigate how the HLT facilitates the development of students' understanding. Data was collected through observations, student work results, and interviews during the trial. The proposed HLT guides students through the stages of exploration of mathematical situations in the context of villages, informal and symbolic representations, formalization into SPL models, development of solution strategies, and applications. The findings of the retrospective analysis show that the ethnomathematical context of Panglipuran Village, through  designed outdoor activities , successfully provides a concrete experience that facilitates students' transition from informal understanding to formal understanding of SPL. The HLT developed appears to be effective in guiding the development of students' understanding, although challenges remain at the modeling and formalization stages. This study contributes to the literature on ethnomathematics-based learning trajectories and provides practical insights into the use of local cultural heritage as a globally relevant source of mathematics learning.