Why do students struggle to understand composition functions? Analysis of learning obstacles in vocational education - Dwika Saputri; Reni Wahyuni; Dedek Andrian; Nofriyandi Nofriyandi (State Islamic University of North Sumatra, 2026)
Difficulties in understanding abstract mathematical concepts, particularly functions and function composition, are still commonly experienced by students, especially those in Vocational High Schools (SMKs). This study aimed to identify the learning obstacles experienced by eleventh-grade Vocational High School (SMK) students in learning functions and function composition. This study employed a qualitative descriptive approach as the initial stage of Didactical Design Research (DDR). Data were collected through diagnostic tests, semi-structured interviews, and documentation to identify learning obstacles related to function composition. The results indicate that students experienced various learning obstacles. They had difficulty understanding the concepts of functions and function composition, as reflected in their inability to distinguish between the two concepts and their dependence on examples provided by teachers, indicating epistemological obstacles. In addition, students experienced difficulty performing substitutions, determining the order of function composition, and applying solution procedures systematically, indicating instrumental ontogenic obstacles. The interview results also revealed that learning practices oriented toward memorization contributed to these difficulties, indicating didactical obstacles. Therefore, students’ difficulties in learning function composition were influenced by epistemological, instrumental ontogenic, and didactical obstacles. These findings provide a basis for developing more effective learning designs that emphasize conceptual understanding.