Students’ construction of projection concepts through independent exploration in a technology-enhanced learning environment

Authors

  • Aris Hadiyan Wijaksana Universitas Pendidikan Indonesia
  • Yaya Sukjaya Kusumah Universitas Pendidikan Indonesia
  • Turmudi Turmudi Universitas Pendidikan Indonesia

DOI:

https://doi.org/10.29408/jel.v12i2.33973

Keywords:

independent exploration, projection concepts, student knowledge construction, technology-enhanced learning

Abstract

This research report presents a comprehensive and in-depth analysis of the cognitive dynamics and knowledge construction processes of students in the Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences (FMIPA), State University of Jakarta, within the Descriptive Geometry course during the odd semester of the 2025/2026 academic year. This study is motivated by fundamental pedagogical challenges in descriptive geometry instruction, where conventional paper-and-pencil methods often fail to facilitate accurate spatial visualization, leading to construction inaccuracies and the persistence of epistemological misconceptions. Involving 16 research subjects (S1–S16), this study investigates the impact of integrating Technology-Enhanced Learning (TEL) using the dynamic geometry software GeoGebra on students' ability to translate three-dimensional objects into two-dimensional representations via the orthogonal projection system. Employing a descriptive qualitative research design utilizing conceptual understanding test data and structured interviews, the findings indicate that technology functions not merely as a visual aid, but as a cognitive instrument mediating the process of instrumental genesis. Analysis of construction errors regarding lines, planes, and solid intersections reveals that independent exploration featuring dragging and 3D manipulation assists students in overcoming epistemological obstacles resistant to traditional instruction, although variations in instrument adaptation remain observable.

Author Biographies

Aris Hadiyan Wijaksana, Universitas Pendidikan Indonesia

<span style="font-weight: 400;" data-mce-style="font-weight: 400;">This research report presents a comprehensive and in-depth analysis of the cognitive dynamics and knowledge construction processes of students in the Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences (FMIPA), State University of Jakarta, within the Descriptive Geometry course during the odd semester of the 2025/2026 academic year. This study is motivated by fundamental pedagogical challenges in descriptive geometry instruction, where conventional paper-and-pencil methods often fail to facilitate accurate spatial visualization, leading to construction inaccuracies and the persistence of epistemological misconceptions. Involving 16 research subjects (S1–S16), this study investigates the impact of integrating Technology-Enhanced Learning (TEL) using the dynamic geometry software GeoGebra on students' ability to translate three-dimensional objects into two-dimensional representations via the orthogonal projection system. Employing a descriptive qualitative research design utilizing conceptual understanding test data and structured interviews, the findings indicate that technology functions not merely as a visual aid, but as a cognitive instrument mediating the process of instrumental genesis. Analysis of construction errors regarding lines, planes, and solid intersections reveals that independent exploration featuring dragging and 3D manipulation assists students in overcoming epistemological obstacles resistant to traditional instruction, although variations in instrument adaptation remain observable.</span>

Yaya Sukjaya Kusumah, Universitas Pendidikan Indonesia

<span style="font-weight: 400;" data-mce-style="font-weight: 400;">This research report presents a comprehensive and in-depth analysis of the cognitive dynamics and knowledge construction processes of students in the Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences (FMIPA), State University of Jakarta, within the Descriptive Geometry course during the odd semester of the 2025/2026 academic year. This study is motivated by fundamental pedagogical challenges in descriptive geometry instruction, where conventional paper-and-pencil methods often fail to facilitate accurate spatial visualization, leading to construction inaccuracies and the persistence of epistemological misconceptions. Involving 16 research subjects (S1–S16), this study investigates the impact of integrating Technology-Enhanced Learning (TEL) using the dynamic geometry software GeoGebra on students' ability to translate three-dimensional objects into two-dimensional representations via the orthogonal projection system. Employing a descriptive qualitative research design utilizing conceptual understanding test data and structured interviews, the findings indicate that technology functions not merely as a visual aid, but as a cognitive instrument mediating the process of instrumental genesis. Analysis of construction errors regarding lines, planes, and solid intersections reveals that independent exploration featuring dragging and 3D manipulation assists students in overcoming epistemological obstacles resistant to traditional instruction, although variations in instrument adaptation remain observable.</span>

Turmudi Turmudi, Universitas Pendidikan Indonesia

<span style="font-weight: 400;" data-mce-style="font-weight: 400;">This research report presents a comprehensive and in-depth analysis of the cognitive dynamics and knowledge construction processes of students in the Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences (FMIPA), State University of Jakarta, within the Descriptive Geometry course during the odd semester of the 2025/2026 academic year. This study is motivated by fundamental pedagogical challenges in descriptive geometry instruction, where conventional paper-and-pencil methods often fail to facilitate accurate spatial visualization, leading to construction inaccuracies and the persistence of epistemological misconceptions. Involving 16 research subjects (S1–S16), this study investigates the impact of integrating Technology-Enhanced Learning (TEL) using the dynamic geometry software GeoGebra on students' ability to translate three-dimensional objects into two-dimensional representations via the orthogonal projection system. Employing a descriptive qualitative research design utilizing conceptual understanding test data and structured interviews, the findings indicate that technology functions not merely as a visual aid, but as a cognitive instrument mediating the process of instrumental genesis. Analysis of construction errors regarding lines, planes, and solid intersections reveals that independent exploration featuring dragging and 3D manipulation assists students in overcoming epistemological obstacles resistant to traditional instruction, although variations in instrument adaptation remain observable.</span>

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

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Published

10-05-2026

How to Cite

Wijaksana, A. H., Kusumah, Y. S., & Turmudi, T. (2026). Students’ construction of projection concepts through independent exploration in a technology-enhanced learning environment. Jurnal Elemen, 12(2), 577–590. https://doi.org/10.29408/jel.v12i2.33973

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