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All Journal JPPM (JURNAL PENELITIAN DAN PEMBELAJARAN MATEMATIKA)
Dilham Fardian
Laboratoire d’Informatique de Grenoble, Université Grenoble Alpes, Grenoble, France.
Mathematics

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Uncovering Student Errors and Learning Obstacles in Composition and Inverse Functions through An AVAEM Error Analysis Nadia nadia Ulfa; Al Jupri; Dadang Juandi; Dilham Fardian; Ulfah Nur Azizah
Jurnal Penelitian dan Pembelajaran Matematika Vol 19, No 1 (2026): JPPM (Jurnal Penelitian dan Pembelajaran Matematika) Volume 19 Nomor 1 Februari
Publisher : Universitas Sultan Ageng Tirtayasa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62870/jppm.v19i1.39246

Abstract

Our study aims to analyze the learning obstacles experienced by students in understanding the concepts of composition of functions and inverse functions using the AVAEM error categorization framework (ARITH, VAR, AE, EQS, and MATH). We employed a qualitative approach with triangulation techniques, collecting data through written tests, interviews, and document analysis. A total of 70 students aged 14–15 years participated in our study. Our findings indicate three types of learning obstacles: epistemological, ontogenetic, and didactical. Epistemological obstacles arise from students' limited conceptual understanding, especially when they encounter unfamiliar problem contexts. Ontogenic obstacle were found in two forms: conceptual (stemming from a weak understanding of prerequisite concepts) and instrumental (related to technical errors in applying key procedures in the composition of function). Didactical obstacles arise from the presentation of material in textbooks that does not align with scientific concepts. Mapping these learning obstacles through the AVAEM error categorization framework provides valuable insights for mathematics education. One of the main implications of this research is the development of learning designs based on students learning obstacles. This kind of learning design is expected to help reduce students' difficulties in learning composition of functions and inverse functions in the future, especially in online or distance learning environments.
Co-Authors Al Jupri Dadang Juandi Nadia nadia Ulfa Ulfah Nur Azizah