Developing a local instruction theory for fraction learning through a cultural context

Purpose: Learning fractions at the elementary school level remains challenging due to the abstract nature of fraction concepts and students’ difficulties in interpreting multiple representations. This study aims to develop a structured learning trajectory that supports students’ understanding of fractions by integrating the local cultural context of melemang from Muara Enim, thereby reducing abstraction and enhancing meaningful learning. Method: The study employed a design research methodology in the form of validation studies, consisting of three iterative stages: preliminary design, teaching experiment, and retrospective analysis. The participants were 28 lower-grade students from an elementary school in Muara Enim Regency. Data were collected through student worksheets (LKPD), classroom observations, and documentation of students’ learning activities. The analysis focused on examining the alignment between the Hypothetical Learning Trajectory (HLT) and students’ actual learning processes. Findings: The results indicate that the designed HLT was largely consistent with students’ learning trajectories, particularly in supporting the transition from concrete experiences to visual and symbolic representations of fractions. However, several students required additional instructional scaffolding to connect visual models with formal notation and to recognize fraction equivalence. The retrospective analysis led to the formulation of a Local Instructional Theory (LIT) emphasizing three key principles: the use of meaningful cultural contexts, progressive representational development, and adaptive scaffolding to address misconceptions. Significance: This study contributes theoretically by developing a culturally grounded LIT that integrates Realistic Mathematics Education (RME) with local culture and practically by providing teachers with a contextual instructional model to enhance students’ conceptual and procedural understanding of fractions.