From Misconception To Conceptual Understanding: Hypothetical Learning Trajectory Design In Similarity Learning - Vira Pitriatunnazwa; Dedi Muhtadi; Sukirwan (Koordinat Jurnal MIPA, 2026)
Similarity is a fundamental topic in geometry, yet many students continue to experience difficulties in understanding proportional relationships, identifying corresponding elements, and constructing geometric reasoning. This study aimed to synthesize empirical evidence on students’ difficulties in learning geometric similarity and to develop a Hypothetical Learning Trajectory (HLT) to support instruction. A Systematic Literature Review (SLR) was conducted following the PRISMA 2020 guidelines. Data were collected from six databases: Scopus, ScienceDirect, SpringerLink, Taylor & Francis Online, ERIC, and Google Scholar. From 142 identified records published between 2015 and 2025, 15 empirical studies met the inclusion criteria and were selected for analysis. Data were analyzed using thematic synthesis through open coding, axial coding, and selective coding. The findings revealed six major categories of students’ difficulties: conceptual errors, transformation errors, procedural errors, visual–spatial difficulties, metacognitive misconceptions, and reasoning-and-proof difficulties. These difficulties form a developmental pattern, progressing from visual and conceptual misunderstandings to higher-order reasoning challenges. Based on the synthesis, a five-phase Hypothetical Learning Trajectory consisting of visual recognition, correspondence identification, proportional reasoning, contextual application, and deductive justification was developed. The proposed HLT provides an evidence-based framework for improving geometry instruction and supporting students’ conceptual understanding of similarity