Development of Culture-Based Local Instructional Theory through Broad Learning Trajectory of Squares and Rectangulars in Elementary School Students

Abstract

The understanding of the concept of square and rectangle area in elementary school students is still dominated by the use of procedural formulas so that students have difficulty connecting measurements using square units with formal mathematical representations. Previous research on Project-Based Learning (PjBL) and culture-based learning generally focused on improving learning outcomes, while studies on the development of students' conceptual understanding to produce Local Instructional Theory (LIT) are still limited. This study aims to analyze the development of students' conceptual understanding through culture-based learning trajectories and develop Local Instructional Theory for square and rectangular area learning in elementary schools. The research uses a Design Research approach which includes the preliminary design stage, design experiment (pilot experiment and teaching experiment), and retrospective analysis. The research participants consisted of 101 grade V elementary school students in Medan City. Data were collected through observations, interviews, student worksheets, project artifacts, and learning documentation, then analyzed qualitatively using retrospective analysis. The results of the study show that students' conceptual understanding develops gradually through the identification of geometric shapes in miniature North Sumatra traditional houses, measurements using square units, spatial structuring, the formation of multiplicative reasoning, generalization of broad formulas, the application of concepts in projects, and the conclusion of broad concepts. The pilot experiment identified the learning obstacles that became the basis for the reconstruction of the Hypothetical Learning Trajectory (HLT) into Students' Learning Trajectory (LT) which was empirically validated and synthesized into the Final Local Instructional Theory. This research contributed to the development of Design Research by showing that culture-based PjBL facilitates the transformation of HLT into LT and produces adaptive learning design principles for mathematics learning.