Abstract
Non-Euclidean Geometry is a complex subject for students. It is necessary to analyze the weaknesses of Euclidean geometry to provide a basis for thinking about the need for learning non-Euclidean geometry. The starting point of learning must be close to students' local minds and culture. The purpose of this study is to describe the weaknesses of Euclidean geometry as a step in analyzing the needs of non-Euclidean geometry learning through an ethnomathematics approach. This research uses qualitative descriptive methods. The subjects of this study were students of Mathematics Education at State Islamic University (UIN) Fatmawati Soekarno Bengkulu, Indonesia. The researcher acts as a lecturer and the main instrument in this research. Researchers used a spatial ability test instrument to explore qualitative data. The data were analyzed qualitatively descriptively. The result of this research is that there are two weaknesses of Euclidean geometry, namely Euclid’s attempt to define all elements in geometry, including points, lines, and planes. Euclid defined a point as one that has no part. He defined a line as length without width. The words "section", "length", and "width" are not found in Euclidean Geometry. In addition, almost every part of Euclid’s proof of the theorem uses geometric drawings, but in practice, these drawings are misleading. Local culture and ethnomathematics approach design teaching materials and student learning trajectories in studying Non-Euclid Geometry.
Highlights
Geometry learning is one of the mandatory materials for students
Euclid attempted to define all elements in geometry, including points, lines, and planes
If asked what is meant by section? In Euclidean geometry, there is no explanation of "parts"
Summary
Geometry is an abstract subject that is difficult for students to learn (Widada, Herawaty, Ma’rifah, & Yunita, 2019). It is necessary to analyze the weaknesses of Euclidean geometry to provide a basis for thinking about the need for learning non-Euclidean geometry. Spatial ability is essential in understanding geometry and solving geometry problems (Eskisehir & Ozlem, 2015). Spatial thinking is a core skill of human life. It can be learned through formal education. Learning geometry in a system presents its challenges for students (Widada, Herawaty, Widiarti, Aisyah, & Tuzzahra, 2020). Learning Euclidean geometry and its comparison with non-Euclidean geometry is one of the exciting studies for students of mathematics and mathematics education
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