Students’ construction of projection concepts through independent exploration in a technology-enhanced learning environment
DOI:
https://doi.org/10.29408/jel.v12i2.33973Keywords:
independent exploration, projection concepts, student knowledge construction, technology-enhanced learningAbstract
Conventional descriptive geometry instruction often fails to facilitate accurate spatial visualization, perpetuating epistemological obstacles. This study investigates how integrating independent exploration via GeoGebra impacts students' knowledge construction of orthogonal projection concepts. A descriptive qualitative case study was conducted involving 16 mathematics education students at the State University of Jakarta during the odd semester of 2026. Data were collected using a conceptual understanding test comprising three hierarchical questions and a structured interview guide, and then analyzed through an interactive qualitative model. Findings indicate that GeoGebra functions beyond a mere visual aid; it acts as a cognitive instrument mediating instrumental genesis. Specifically, independent exploration utilizing dragging and 3D manipulation empowered students to diagnose and dismantle persistent epistemological obstacles related to dimensional transformations and planar intersections. However, varying levels of student dependence on instructor scaffolding highlight that successful instrument adaptation relies on individual learning dispositions. The study implies that effectively integrating technology in geometry education requires a differentiated pedagogical approach and a shift toward orchestrated digital exploration.
References
Akyüz, D. (2015). The role of dynamic geometry software in teaching geometry. Journal of Mathematics Education, 8(2), 112–125.
Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. ZDM – The International Journal on Mathematics Education, 34(3), 66–72. https://doi.org/10.1007/BF02655708
Aziiza, Y. F., Rosjanuardi, R., & Juandi, D. (2022). Didactic design of the concept of surface area of flat-sided prism based on van Hiele’s theory in online learning. Jurnal Pendidikan Matematika, 16(1), 73–88. https://doi.org/10.22342/jpm.16.1.13789.73-88
Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.). Kluwer Academic Publishers.
Capone, R., & Lepore, M. (2020). From static to dynamic: The role of augmented reality in geometry learning. Journal of Educational Technology Systems, 49(1), 35–50. https://doi.org/10.1177/0047239520914972
Flores Salazar, J. V., Théry Romero, M. C., Neira Fernández, V., & Peñaloza Vara, T. N. (2025). In-service teachers’ mathematical work on quadrilaterals and their technological knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 21(3), em2604. https://doi.org/10.29333/ejmste/16069
Gorjanc, S. (n.d.). Introduction to the Monge’s method of projections. In Descriptive geometry materials. Retrieved January 20, 2026, from https://www.grad.hr/geomteh3d/Monge/01uvod/uvod_eng.html
Gutiérrez de Ravé, S., Gutiérrez de Ravé, E., & Jiménez-Hornero, F. J. (2025). Integrating CAD and orthographic projection in descriptive geometry education: A comparative analysis with Monge’s system. Education Sciences, 15(11), 1492. https://doi.org/10.3390/educsci15111492
Herrera, C., Saputra, E., & Morales, M. (2024). Spatial visualization and dynamic geometry: A comprehensive analysis. Journal of Educational Technology, 12(3), 45–60.
Hwang, G. J., Lai, C. L., Liang, J. C., & Chu, H. C. (2020). A ubiquitous geometry system for improving geometric reasoning. Computers & Education, 156, 103943. https://doi.org/10.1016/j.compedu.2020.103943
Izzati, N., & Al Farizi, R. (2025). Analysis of students’ spatial ability using GeoGebra in the spatial geometry course. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 10(3), 98–107. https://doi.org/10.17977/jptpp.v10i3.25624
Lowrie, T., & Logan, T. (2023). The role of spatial reasoning in problem solving. Mathematics Education Research Journal, 35(1), 15–30. https://doi.org/10.1007/s13394-021-00360-1
Misfeldt, M. (2013). Instrumental genesis in GeoGebra based board game design. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp. 2664–2673). Middle East Technical University. http://cerme8.metu.edu.tr/wgpapers/WG15/WG15_Misfeldt.pdf
Modestou, M., & Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity.” Educational Psychology, 27(1), 75–92. https://doi.org/10.1080/01443410601061462
NCSM. (2024). Leading with technology position paper. National Council of Supervisors of Mathematics. https://www.mathedleadership.org/wp-content/uploads/2024/09/53502_NCSM_Leading-with-Technology-Position-Paper_digital-version.pdf
Parra Lara, H., & Ospina Parra, C. A. (2024). Bolstering the spatial rotation ability to understand the topics of point and line in descriptive geometry. Ingeniería, 29(3), e21253. https://doi.org/10.14483/23448393.21253
Pfeiffer, C., Ndlovu, M., & Oladele, J. I. (2025). The effectiveness of GeoGebra for developing mathematical knowledge in transformations of functions and graphs. Futurity Education, 5(4), 331–356. https://doi.org/10.57125/FED.2025.12.19
Resnick, I., Newcombe, N. S., & Jordan, N. C. (2020). The relationship between spatial reasoning and mathematical achievement. Journal of Cognition and Development, 21(1), 1–18. https://doi.org/10.1080/15248372.2019.1706155
Rigopouli, K., Kotsifakos, D., & Psaromiligkos, Y. (2025). Vygotsky’s creativity options and ideas in 21st-century technology-enhanced learning design. Education Sciences, 15(2), 257. https://doi.org/10.3390/educsci15020257
Sebsibe, A. S., & Abdella, N. M. (2025). The effect of GeoGebra integrated instruction on students' learning of the quadratic function concept. F1000Research, 14, 671. https://doi.org/10.12688/f1000research.163113.1
Shittu, M., & Alex, J. K. (2025). The 5E instructional model of constructivism in mathematics education: Teachers’ beliefs and classroom practices. Eurasia Journal of Mathematics, Science and Technology Education, 21(9), em2704. https://doi.org/10.29333/ejmste/16884
Sianturi, A., & Ningsih, Y. L. (2025). Integrating GeoGebra in learning right triangle geometry: A descriptive study of first-year university students’ responses. Perpendicular: Journal of Mathematics Education and Learning, 1(2), 90–100. https://doi.org/10.61994/perpendicular.v1i2.1531
Siregar, T. (2025). Literature review: The use of GeoGebra software on mathematical comprehension ability. Preprints. https://doi.org/10.20944/preprints202510.0925.v1
Sudirman, Runisah, Kusumah, Y. S., & Martadiputra, B. A. P. (2023). Epistemological obstacle in 3D geometry thinking: Representation, spatial structuring, and measurement. Pegem Journal of Education and Instruction, 13(4), 292–301. https://doi.org/10.47750/pegegog.13.04.34
Suparman, S., Marasabessy, R., & Helsa, Y. (2024). Fostering spatial visualization in GeoGebra-assisted geometry lesson: A systematic review and meta-analysis. Eurasia Journal of Mathematics, Science and Technology Education, 20(9), em2509. https://doi.org/10.29333/ejmste/15170
Sweller, J. (2020). Cognitive load theory and educational technology. Educational Technology Research and Development, 68(1), 1–16. https://doi.org/10.1007/s11423-019-09701-3
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Aris Hadiyan Wijaksana, Yaya Sukjaya Kusumah, Turmudi Turmudi
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
