Analisis Pemahaman Mahasiswa Terhadap Konsep Interval Dalam Mata Kuliah Analisis Real

Abstract

This study aims to analyze students' understanding of the concept of interval in the Real Analysis course, particularly in understanding the properties of intervals, such as supremum, infimum, and nested intervals. The research method used is a qualitative descriptive approach with a case study. Data were collected through proof-based essay tests, semi-structured interviews, and participant observation during the learning process using GeoGebra 3D AR. The sample consisted of 35 fourth semester students from the Mathematics Education program enrolled in the Real Analysis course. Data analysis was carried out with a thematic approach based on the APOS theory (Action, Process, Object, Schema). The results showed that most students struggled to transfer the visual understanding obtained through GeoGebra 3D AR into formal proofs. While 68.6% of students showed an improvement in visual understanding, only 8.5% could formally prove the property of nested interval intersections. The implications of this study highlight the importance of integrating interactive technology with deeper proof exercises, as well as the application of problem-based approaches to enhance understanding of the interval concept. The limitations of this study include the small sample size and the focus on one type of learning technology. Future research is recommended to explore the use of other technologies and more varied teaching methods.