Eksplorasi Konsep Segitiga pada Geometri Euclid dan Non-Euclid untuk Meningkatkan Pemahaman Siswa SMA

Abstract

This study aims to analyze students' conceptual understanding of triangle concepts in Euclidean and Non-Euclidean geometry through the implementation of exploratory learning. The study was conducted using a quantitative descriptive approach involving 30 twelfth-grade students at SMA Methodist Antiokhia Pancur Batu. Data were collected through observation and a Likert-scale questionnaire consisting of 20 statement items based on four indicators, namely understanding of Euclidean geometry, understanding of Non-Euclidean geometry, conceptual understanding of triangles, and cognitive impact of learning. The data were analyzed using descriptive statistical techniques by calculating the mean score of each indicator, which generally fell into the high category (range 2.98–3.41), with understanding of Non-Euclidean geometry still slightly lagging behind the other three indicators. The key finding of this study is that exploratory learning effectively encourages students to build a deeper conceptual understanding of triangles through observation, analysis, and discussion, rather than relying on rote procedural memorization. More importantly, integrating Euclidean and Non-Euclidean geometry within a single learning sequence was shown to broaden students' way of thinking: students came to understand not only the properties of triangles on flat planes but also that these properties can change on curved surfaces, resulting in a more flexible and contextual understanding of geometry. These findings imply that an integrative approach combining Euclidean and Non-Euclidean geometry has potential as an alternative strategy for teaching geometry at the senior high school level to foster students' critical and analytical thinking skills, while also addressing the gap in Non-Euclidean geometry instruction that remains rarely introduced at the secondary education level.