Development of a Three-Dimensional Geometry Instrument to Measure Mathematics Students’ Problem-Solving Ability

The ability to solve three-dimensional (3D) geometry problems is an essential competence for mathematics education students, particularly because geometry requires skills in representation, reasoning, and spatial visualization. However, instruments specifically designed to measure students’ problem-solving ability in 3D geometry are still limited. This study aimed to develop a test instrument to measure the problem-solving ability of prospective mathematics teachers in solving 3D geometry problems. The developed instrument was an essay-type test based on geometric concepts, focusing on three-dimensional geometry and consisting of four items. The instrument was developed using the ADDIE R&D model (Analysis, Design, Development, Implementation, and Evaluation). The validation process included expert validation and empirical validation. The results of expert validation indicated that the instrument had high validity, as shown by a Gregory index of 1. The results of empirical validation showed that all test items were valid and reliable, with a reliability coefficient of 0.666. The validated instrument was then implemented to measure students’ problem-solving ability. The findings revealed that the average score of students’ problem-solving ability was 40 (SD = 20.37), with the highest score of 85 and the lowest score of 6 on a scale of 0–100. Therefore, it can be concluded that the developed test instrument is valid and can be used to measure students’ problem-solving ability in solving 3D geometry problems.

Three-dimensional geometry, Instrument, Problem-solving

1. Abd Rahim, F., Ujang, N., & Said, M. T. (2018). Geometri dan peranannya dalam reka bentuk bandar Islamik. Malaysian Journal of Society and Space, 14(2), 82–96. https://doi.org/10.17576/geo-2018-1402-07 [Google Scholar] [Crossref]

2. Abdul Hanid, M. F., Mohamad Said, M. N. H., Yahaya, N., & Abdullah, Z. (2022). Effects of augmented reality application integration with computational thinking in geometry topics. In Education and Information Technologies (Vol. 27, Issue 7). Springer US. https://doi.org/10.1007/s10639-022-10994-w [Google Scholar] [Crossref]

3. Adelabu, F. M., Makgato, M., & Ramaligela, M. S. (2019). Enhancing learners’ geometric thinking using dynamic geometry computer software. Journal of Technical Education and Training, 11(1), 44–53. https://doi.org/10.30880/jtet.2019.11.01.006 [Google Scholar] [Crossref]

4. Alex, J. K., & Mammen, K. J. (2016). Lessons Learnt from Employing van Hiele Theory Based Instruction in Senior Secondary School Geometry Classrooms. Eurasia Journal of Mathematics, Science and Technology Education, 12(8), 2223–2236. https://doi.org/10.12973/eurasia.2016.1228a [Google Scholar] [Crossref]

5. Arikunto, S. (2012). Dasar-Dasar Evaluasi Pendidikan: Edisi 2. Jakarta: Buni Aksara. [Google Scholar] [Crossref]

6. Bendall, R. C. A., Galpin, A., Marrow, L. P., & Cassidy, S. (2016). Cognitive style: Time to experiment. Frontiers in Psychology, 7(NOV), 1–4. https://doi.org/10.3389/fpsyg.2016.01786 [Google Scholar] [Crossref]

7. Hourigan, M., & Leavy, A. M. (2017). Preservice Primary Teachers ’ Geometric Thinking : Is Pre-Tertiary Mathematics Education Building Sufficiently Strong Foundations ? Mathematics Education Building Suf fi ciently Strong Foundations? The Teacher Educator, 52(4), 346–364. https://doi.org/10.1080/08878730.2017.1349226 [Google Scholar] [Crossref]

8. İbili, E., Çat, M., Resnyansky, D., Şahin, S., & Billinghurst, M. (2019). An assessment of geometry teaching supported with augmented reality teaching materials to enhance students’ 3D geometry thinking skills. International Journal of Mathematical Education in Science and Technology, 1–23. https://doi.org/10.1080/0020739X.2019.1583382 [Google Scholar] [Crossref]

9. Jones, K., & Tzekaki, M. (2016). Research on the teaching and learning of geometry. In The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues. https://doi.org/10.1007/978-94-6300-561-6_4 [Google Scholar] [Crossref]

10. Komala, K., Manfaat, B., & Haqq, A. A. (2021). Development of Geometry Test Based on Van Hiele’s Theory in Exploration Profile of Student’s Spatial Reasoning Ability Level. Eduma : Mathematics Education Learning and Teaching, 10(1), 83. https://doi.org/10.24235/eduma.v10i1.8518 [Google Scholar] [Crossref]

11. Krawec, J., & Huang, J. (2017). Modifying a Research-Based Problem-Solving Intervention to Improve the Problem-Solving Performance of Fifth and Sixth Graders With and Without Learning Disabilities. Journal of Learning Disabilities, 50(4), 468–480. https://doi.org/10.1177/0022219416645565 [Google Scholar] [Crossref]

12. Maqoqa, T. (2024). An Exploration of Learners’ Understanding of Euclidean Geometric Concepts: A Case Study of Secondary Schools in the OR Tambo Inland District of the Eastern Cape. E-Journal of Humanities, Arts and Social Sciences, 5(5), 658–675. https://doi.org/10.38159/ehass.2024557 [Google Scholar] [Crossref]

13. Montague, M., Krawec, J., Enders, C., & Dietz, S. (2014). The effects of cognitive strategy instruction on math problem solving of middle-school students of varying ability. Journal of Educational Psychology, 106(2), 469–481. https://doi.org/10.1037/a0035176 [Google Scholar] [Crossref]

14. Olivares, D., Lupianez, J. L., & Segovia, I. (2020). Roles and characteristics of problem solving in the mathematics curriculum: a review. International Journal of Mathematical Education in Science and Technology, 52(7), 1–18. https://doi.org/10.1080/0020739X.2020.1738579 [Google Scholar] [Crossref]

15. Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191–212. https://doi.org/10.1007/s10649-010-9251-8 [Google Scholar] [Crossref]

16. Rahman, A., & Ahmar, A. S. (2016). Exploration of mathematics problem solving process based on the thinking level of students in junior high school. International Journal of Environmental and Science Education, 11(14), 7278–7285. [Google Scholar] [Crossref]

17. Rahman, M. M. (2019). 21st Century Skill “Problem Solving”: Defining the Concept. Asian Journal of Interdisciplinary Research, 2(1), 64–74. https://doi.org/10.34256/ajir1917 [Google Scholar] [Crossref]

18. Retnawati, H. (2016). Proving content validity of self-regulated learning scale (The comparison of Aiken index and expanded Gregory index). REID (Research and Evaluation in Education), 2(2), 155–164. https://doi.org/10.21831/reid.v2i2.11029 [Google Scholar] [Crossref]

19. Shi, L., Dong, L., Zhao, W., & Tan, D. (2023). Improving middle school students’ geometry problem solving ability through hands-on experience: An fNIRS study. Frontiers in Psychology, 14(March), 1–10. https://doi.org/10.3389/fpsyg.2023.1126047 [Google Scholar] [Crossref]

20. Silitonga, R. H. Y., Molle, J. S., & Ngilawajan, D. A. (2023). Increasing Mathematical Problem-Solving Abilities Using Video Tutorials of the Three-Dimensional Coordinate System in Spatial Analytic Geometry. JOHME: Journal of Holistic Mathematics Education, 7(2), 212–226. https://doi.org/10.19166/johme.v7i2.7575 [Google Scholar] [Crossref]

21. Sudirman, Andrés Rodríguez-Nieto, C., Bongani Dhlamini, Z., Singh Chauhan, A., Baltaeva, U., Abubakar, A., Dejarlo, J. O., & Andriani, M. (2023). Ways of Thinking 3D Geometry: Exploratory Case Study in Junior High School Students. Polyhedron International Journal in Mathematics Education, 1(1), 15–34. [Google Scholar] [Crossref]

22. Sudirman, García-García, J., Rodríguez-Nieto, C. A., & Son, A. L. (2024). Exploring Junior High School Students’ Geometry Self-Efficacy in Solving 3D Geometry Problems Through 5E Instructional Model Intervention: A Grounded Theory Study. Infiniti, Journal of Mathematics Education, 13(1), 215–232. https://doi.org/10.22460/infinity.v13i1.p215-232 [Google Scholar] [Crossref]

23. Sudjana, N. (2014). Penilaian Hasil Proses Belajar Mengajar. Bandung: PT Remaja Rosdakarya. [Google Scholar] [Crossref]

24. Tachie, S. A. (2019). Meta-cognitive skills and strategies application: How this helps learners in mathematics problem-solving. Eurasia Journal of Mathematics, Science and Technology Education, 15(5). https://doi.org/10.29333/ejmste/105364 [Google Scholar] [Crossref]

25. Tajudin, N. M., & Chinnappan, M. (2016). The link between higher order thinking skills, representation and concepts in enhancing TIMSS tasks. International Journal of Instruction, 9(2), 199–214. https://doi.org/10.12973/iji.2016.9214a [Google Scholar] [Crossref]

26. Tambunan, H. (2019). The Effectiveness of the Problem Solving Strategy and the Scientific Approach to Students’ Mathematical Capabilities in High Order Thinking Skills. International Electronic Journal of Mathematics Education, 14(2), 293–302. https://doi.org/10.29333/iejme/5715 [Google Scholar] [Crossref]

27. Türkoğlu, H., & Yalçınalp, S. (2024). Investigating Problem-solving Behaviours of University Students Through an Eye-tracking System Using GeoGebra in Geometry: A Case Study. In Education and Information Technologies (Vol. 29, Issue 12). Springer US. https://doi.org/10.1007/s10639-024-12452-1 [Google Scholar] [Crossref]

28. Widodo, S. A., Ibrahim, I., Hidayat, W., Maarif, S., & Sulistyowati, F. (2021). Development of Mathematical Problem Solving Tests on Geometry for Junior High School Students. Jurnal Elemen, 7(1), 221–231. https://doi.org/10.29408/jel.v7i1.2973 [Google Scholar] [Crossref]

• Assessment of the Role of Artificial Intelligence in Repositioning TVET for Economic Development in Nigeria
• Teachers’ Use of Assure Model Instructional Design on Learners’ Problem Solving Efficacy in Secondary Schools in Bungoma County, Kenya
• “E-Booksan Ang Kaalaman”: Development, Validation, and Utilization of Electronic Book in Academic Performance of Grade 9 Students in Social Studies
• Analyzing EFL University Students’ Academic Speaking Skills Through Self-Recorded Video Presentation
• Major Findings of The Study on Total Quality Management in Teachers’ Education Institutions (TEIs) In Assam – An Evaluative Study