A Hybrid Didactical Design through Gendang Beleq Ethnomathematics to Address Students’ Learning Obstacles in Understanding Relations and Functions

Abstract

Understanding relations and functions remains challenging for many junior secondary students due to difficulties in distinguishing relations from functions, identifying domains and ranges, and coordinating multiple mathematical representations. This study aims to develop a hybrid didactical design through Gendang Beleq ethnomathematics to address students’ learning obstacles in understanding relations and functions.

This study employed Didactical Design Research (DDR) integrated with the Theory of Didactical Situations (TDS). The research involved eighth-grade students from junior secondary schools on Lombok Island, Indonesia, through iterative phases of a priori analysis, didactical design and anticipation, didactical experimentation, and retrospective analysis. Gendang Beleq was utilized as a culturally meaningful learning resource by transforming rhythmic patterns and musical relationships into mathematical representations, including ordered pairs, mappings, domain–range relationships, and graphs.

Data were collected through diagnostic tests, observations, interviews, students’ written work, and teacher reflections. The findings are expected to produce a learning obstacle map, a hypothetical learning trajectory, and a validated Gendang Beleq-based instructional design. This study contributes to inclusive mathematics education by demonstrating how culturally responsive didactical designs can support students experiencing conceptual and representational difficulties in mathematics learning.