Analyzing Students’ Difficulty in Learning Geometry at Upper Secondary School in Cambodia: A Case Study on Vector

Abstract

This study aims to analyze students’ difficulties in learning Geometry at upper secondary schools in Cambodia, focusing on vectors through visual representation and conceptual understanding. The research involved 226 10th-grade students, including 139 females. It used an explanatory sequential mixed-methods design and collected data through tests on vector contents adapted from the Cambodia 10th-grade textbook. The instrument consisted of five test items, each assessing visual representation and conceptual understanding, and semi-structured interview questions. The data analysis employed statistical analysis to see a central tendency of visual representation and conceptual understanding and Wilcoxon Signed Ranks to examine their differences in learning difficulty. The result showed that students solved vector problems related to visual representations better than those requiring conceptual understanding. Students’ mean visual representation and conceptual understanding format scores were 6.74 and 4.88, respectively. Wilcoxon Signed Ranks Tests of students’ difficulty in solving vector problems, which were significant differences between visual representation and conceptual understanding (N=226, z=-10.76, p<.001, r=-0.71), indicating that the difference between students’ difficulties in visual representation and conceptual understanding is significant. The study highlighted that (1) students struggled with creating geometrical drawings, including difficulties with visual, symbolic, and verbal representations, and (2) students had difficulty grasping correct mathematical concepts and performing correct mathematical procedures related to visual presentation. The findings suggest focusing on various representations and connecting the meanings of vector operations across these representations to improve students’ understanding of Geometry concepts. Additionally, future research should explore visual perception and visual-spatial skills to enhance students’ achievement in Geometry.

Keywords

• cambodia
• conceptual understanding
• students’ difficulty
• visualization
• geometry