HomeUniversal Journal of Educational Researchvol. 3 no. 3 (2024)

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

Sieng Veasna

Discipline: Education

 

Abstract:

This study aims toanalyzestudents’ 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 inlearningdifficulty. 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.



References:

  1. Baiduri, B., Ismail, A. D., & Sulfiyah, R. (2020). Understanding the concept of visualization phase student in geometry learning. International Journal of Scientific Technology Research, 9(2), 2353-2359.
  2. Bhatta, S. D., S.Katwal, T.Pfutze, V.Ros, & Y.N.Wong. (2022). Learning Loss in Cambodia and the Use of EdTech during COVID-19.
  3. Darmofal, D. L., Soderholm, D. H., & Brodeur, D. R. (2002). Using concept maps and concept questions to enhance conceptual understanding. 32nd annual frontiers in education,
  4. Dray, T., & Manogue, C. A. (2023). Vector line integrals in mathematics and physics. International Journal of Research in Undergraduate Mathematics Education, 9(1), 92-117.
  5. Dundar, S., Gokkurt, B., & Soylu, Y. (2012). The efficiency of visualization through geometry at mathematics education: a theoretical framework. Procedia-Social and Behavioral Sciences, 46, 2579-2583.
  6. Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Educational studies in mathematics, 74, 163-183.
  7. Hwang, W.-Y., Chen, N.-S., Dung, J.-J., Yang, Y.-L. J. J. o. E. T., & Society. (2007). Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. 10(2), 191-212.
  8. Jones, K., & Tzekaki, M. (2016a). Research on the teaching and learning of geometry. The second handbook of research on the psychology of mathematics education, 109-149.
  9. Jones, K., & Tzekaki, M. (2016b). Research on the Teaching and Learning of Geometry. In Á. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues (pp. 109-149). SensePublishers. https://doi.org/10.1007/978-94-6300-561-6_4
  10. Khalil, I. A., Al-Aqlaa, M. A., Al-Wahbi, T. A., & Wardat, Y. (2024). Evaluating Students’ Perception of Visual Mathematics in Secondary Geometry Education: A Mixed Methods Investigation. International Journal of Information and Education Technology, 14(4), 542-551.
  11. Lowrie, T., Logan, T., Hegarty, M. J. J. o. C., & Development. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. 20(5), 729-751.
  12. Majeed, B. H., & ALRikabi, H. T. S. (2022). Effect of Augmented Reality Technology on Spatial Intelligence among High School Students. Int. J. Emerg. Technol. Learn., 17(24), 131-143.
  13. Mammarella, I. C., Giofrè, D., & Caviola, S. (2017). Learning Geometry: the Development of Geometrical Concepts and the Role of Cognitive Processes.
  14. MoEYS. (2018a). Education in Cambodia: Finding from Cambodia's experience in PISA for Development. Author.
  15. MoEYS. (2018b). The Revised Mathematics Syllabus for Upper Secondary Education: Science track (Khmer version). Ministry of Education, Youth and Sport.
  16. MoEYS. (2018c). The Revised Mathematics Syllabus for Upper Secondary Education: Social Science track (Khmer version).
  17. MoEYS. (2020a). Mathematics 10th Grade Part 1 (Khmer Version). Publishing and Distribution House. (Ministry of Education Youth and Sport)
  18. MoEYS. (2020b). Mathematics 10th Grade Part 2 (Khmer Version). Publishing and Distribution House. (Ministry of Education Youth and Sport)
  19. MoEYS. (2022). Analysing Report on the G12 National Examination in the Year 2021 by Subjects (Khmer version).
  20. MoEYS. (2023). Technical Report: Grade 8 National Learning Assessment in Academic Year 2021 -2022.
  21. MoEYS. (2024). A Country Report: PISA 2022 Results for Cambodia. Phnom Penh. Author.
  22. Naron, D. H. C. (2015). The Vision of Education Reform in Cambodia. http://moeys.gov.kh/en/media-center/education-congress/vision-of-education-reform-in-cambodia/
  23. Perry, E. L., & Len-Ríos, M. E. (2019). Conceptual understanding. In Cross-Cultural Journalism and Strategic Communication (pp. 3-19). Routledge.
  24. Porat, R., & Ceobanu, C. (2024). Enhancing Spatial Ability: A New Integrated Hybrid Training Approach for Engineering and Architecture Students. Education Sciences, 14(6), 563.
  25. Ramdjid, N. R., Sukestiyarno, S., Rochmad, R., & Mulyono, M. (2022). Students' difficulties in solving geometry problems. Sciences, 17(12), 4628-4640.
  26. Samphantakul, N., & Thinwiangthong, S. (2019). Mathematical Conceptual Understanding about Geometry of 8th Grade Students in Classroom Using Lesson Study and Open Approach with The Geometer’s Sketchpad. Journal of Physics: Conference Series,
  27. Sari, P., & Slamet, I. (2018). Cooperative learning model with high order thinking skills questions: an understanding on geometry. Journal of Physics: Conference Series,
  28. SEM, R., & HEM, k. (2016). Education Reform in Cambodia: Progress and Challenges in Basic Education. https://pcasia.org/pic/wp-content/uploads/simple-file-list/20170523-Education_Reform_Cambodia_Eng.pdf
  29. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School, 77(1), 20-26.
  30. UNICEF. (2022). Learning Loss in the Covid-19 Pandamic Era: Evidence from the 2016-2021 Grade Six National Learning Assessment in Cambodia. United Nations Childrent's Fund (UNICEF), Cambodia Country Office. https://www.unicef.org/cambodia/media/6166/file/Grade%206%20NLA%20Report%20Final%20April%205_clean_Final.pdf
  31. Utami, C., Mardiyana, & Triyanto. (2019). Profile of students’ mathematical representation ability in solving geometry problems. IOP Conference Series: Earth and Environmental Science, 243.
  32. van Garderen, D., Scheuermann, A., Poch, A., Murray, M. M. J. T. E., & Education, S. (2018). Visual representation in mathematics: Special education teachers’ knowledge and emphasis for instruction. 41(1), 7-23.
  33. Yurmalia, D., & Herman, T. (2021). Student visualization in solving geometry problem: the case of reflection. Journal of Physics: Conference Series,
  34. Žakelj, A., & Klancar, A. (2022). The Role of Visual Representations in Geometry Learning. European Journal of Educational Research, 11(3), 1393-1411.
  35. Zhang, D., Wang, Q., Ding, Y., & Liu, J. J. (2014). Testing accommodation or modification? The effects of integrated object representation on enhancing geometry performance in children with and without geometry difficulties. Journal of learning disabilities, 47(6), 569-583.