Dwika Saputri
Universitas Islam Riau

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Why do students struggle to understand composition functions? Analysis of learning obstacles in vocational education Dwika Saputri; Reni Wahyuni; Dedek Andrian; Nofriyandi Nofriyandi
AXIOM : Jurnal Pendidikan dan Matematika Vol 15, No 1 (2026)
Publisher : State Islamic University of North Sumatra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30821/axiom.v15i1.29352

Abstract

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.
Analysis of Students' Ability to Understand The Concept of Compositional Function Dwika Saputri; Reni Wahyuni; Raman Kumar
International Journal of Applied Learning and Research in Algebra Vol. 3 No. 2 (2026)
Publisher : EDUPEDIA Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/algebra.v3i2.2393

Abstract

Purpose – This study aims to analyze students' ability to understand the concept of compositional functions based on indicators of understanding mathematical concepts. Understanding concepts is important in learning composition functions because students not only need to be able to do calculations, but also understand and apply concepts appropriately. Methodology – This study uses a qualitative approach with a qualitative descriptive research type. The research subjects consisted of six grade XI students at one of the Vocational High Schools (SMK) in Pekanbaru City in the even semester of the 2025/2026 school year. Subjects were selected using purposive sampling based on the results of the concept comprehension test. Data were collected through a description test consisting of two questions of composition function material. Data analysis is carried out based on two indicators of concept understanding, namely applying concepts algorithmically and presenting concepts in various mathematical representations. The percentage of achievement of each indicator is calculated based on the number of students who meet the indicators. Findings – The results of the study show that students' abilities are in the high category. The indicator applied concepts algorithmically reached a percentage of 83.33%, while the indicator presented concepts in various mathematical representations reached 100%. However, errors are still found in the application of composition procedures, especially in the process of function substitution. Novelty – This study provides an overview of the ability to understand the concept of composition function based on two indicators specifically in vocational school students. Significance – The results of the research can be an input for teachers in designing learning that emphasizes understanding of concepts, procedural accuracy, and the use of various mathematical representations.