Systematic literature review on learning obstacles in set materials for designing hypothetical learning trajectory

Abstract

This study aims to synthesize various learning obstacles experienced by students in the subject of sets as a basis for designing a Hypothetical Learning Trajectory (HLT) through a Systematic Literature Review (SLR) using the PRISMA 2020 framework. This study was conducted to overcome the limitations of previous studies that generally identified learning difficulties separately without explaining the structural relationships between the dimensions of these difficulties. A total of 20 empirical research articles published in 2020–2024 and obtained from Scopus, ERIC, ScienceDirect, SpringerLink, and Google Scholar were analyzed using thematic synthesis techniques. The results of the synthesis showed that conceptual difficulties were the most dominant finding and were consistently reported in almost all studies, followed by procedural, representational, and problem-solving difficulties. Conceptual difficulties are related to a weak understanding of definitions, symbols, notations, membership, and set operations, which then affect students' abilities to apply procedures, represent concepts through Venn diagrams, and solve contextual problems. In addition, three types of learning obstacles, namely ontogenic, epistemological, and didactic, were consistently identified as factors that strengthen the emergence of these various learning difficulties. Based on the results of this synthesis, the study proposes a Multidimensional Dependency Model (MDM) that describes the hierarchical relationships between dimensions of mathematics learning difficulties and explains how identifying learning obstacles can serve as a conceptual foundation in designing HLT. The research findings emphasize that strengthening conceptual understanding needs to be prioritized as a foundation for developing students' procedural, representational, and problem-solving abilities sustainably. 

Penelitian ini bertujuan untuk menyintesis berbagai hambatan belajar yang dialami siswa pada materi himpunan sebagai dasar perancangan Hypothetical Learning Trajectory (HLT) melalui Systematic Literature Review (SLR) dengan menggunakan kerangka kerja PRISMA 2020. Studi ini dilakukan untuk mengatasi keterbatasan penelitian sebelumnya yang umumnya mengidentifikasi kesulitan belajar secara terpisah tanpa menjelaskan hubungan struktural antar-dimensi kesulitan tersebut. Sebanyak 20 artikel penelitian empiris yang diterbitkan pada tahun 2020–2024 dan diperoleh dari Scopus, ERIC, ScienceDirect, SpringerLink, serta Google Scholar dianalisis menggunakan teknik sintesis tematik. Hasil sintesis menunjukkan bahwa kesulitan konseptual merupakan temuan yang paling dominan dan dilaporkan secara konsisten dalam hampir semua studi, diikuti oleh kesulitan prosedural, representasional, dan pemecahan masalah. Kesulitan konseptual berkaitan dengan lemahnya pemahaman terhadap definisi, simbol, notasi, keanggotaan, dan operasi himpunan, yang kemudian memengaruhi kemampuan siswa dalam menerapkan prosedur, merepresentasikan konsep melalui diagram Venn, dan menyelesaikan masalah kontekstual. Selain itu, tiga jenis hambatan belajar—yaitu ontogenik, epistemologis, dan didaktis—diidentifikasi secara konsisten sebagai faktor yang memperkuat munculnya berbagai kesulitan belajar tersebut. Berdasarkan hasil sintesis ini, penelitian mengusulkan Multidimensional Dependency Model (MDM) yang menggambarkan hubungan hierarkis antar-dimensi kesulitan belajar matematika serta menjelaskan bagaimana identifikasi hambatan belajar dapat menjadi landasan konseptual dalam merancang HLT. Temuan penelitian ini menekankan bahwa penguatan pemahaman konseptual perlu diprioritaskan sebagai landasan untuk mengembangkan kemampuan prosedural, representasional, dan pemecahan masalah siswa secara berkelanjutan.