Impact of the Analytical Geometry Teaching Based on Flipped Classroom and Augmented Reality (AR) Assistance on 3D Geometric Thinking Skills
Keywords:
analytical geometry; flipped classroom; augmented reality (AR), 3D animation; 3D geometric thinking skillsAbstract
This study aims to examine the impact of the analytical geometry teaching based on flipped classroom and augmented reality (AR) on 3D geometric thinking skills. This study used a quasi-experimental method involving 250 students. Participants were divided into two equal groups. The experimental group received the analytical geometry teaching based on flipped classroom and augmented reality (AR), while the control group received traditional geometry teaching interventions. Several instruments were developed in this study, including a 3D thinking ability scale, 3D animation-based teaching materials, and the development of a geometry training system, along with the implementation and assessment of geometry teaching supported by the training system. Data analysis used in the study included regression tests, t-tests, and ANCOVA tests to investigate the impact of the intervention on students' 3D geometric thinking skills. The results showed that analytical geometry teaching based on flipped classroom and augmented reality (AR) effectively improved 3D geometric thinking skills in all six dimensions. The most significant improvement in 3D geometric thinking skills, from the lowest to the highest, was found in the manipulation dimension, nets dimension, structuring dimension, calculation dimension, properties dimension, and finally the comparison dimension. All of these improvements occurred because the web media and AR scaffolding presented interactive 3D animations depicting the nets of 3D object spaces, thereby enhancing students' imagination and improving their understanding of 3D geometric space. This study implies that the integration of flipped classrooms and AR technology in 3D analytical geometry teaching can improve 3D geometric thinking skills.
https://doi.org/10.26803/ijlter.24.11.2
References
Abakah, F., & Brijlall, D. (2024). Finding an Effective Assessment Approach to Enhance the Teaching and Learning of Circle Geometry. Africa Education Review, 20(3), 93–116. https://doi.org/10.1080/18146627.2024.2402772
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
Arik Karamik, G., Özkaya, A., Gürel Selimo?lu, Ö., & Kalkan, S. (2025). The effect of enriched environments in teaching geometric shapes to students with visual impairment. Humanities and Social Sciences Communications, 12(1), 1–15. https://doi.org/10.1057/s41599-025-04631-3
Astatke, M., Weng, C., & Yohannes, A. (2025). What is the role of immersive virtual reality (IVR) in the development of creativity skills and engagement among students in STREAM (Science, Technology, Religion, Engineering, Art, and Mathematics)-based learning? Education and Information Technologies, 0123456789. https://doi.org/10.1007/s10639-025-13610-9
Avcu, R. (2019). Turkish Pre-service Middle Level Mathematics Teachers’ Knowledge for Teaching Fractions. RMLE Online, 42(9), 1–20. https://doi.org/10.1080/19404476.2019.1681624
Bergdahl, L., & Langmann, E. (2018). Pedagogical postures: a feminist search for a geometry of the educational relation. Ethics and Education, 13(3), 309–328. https://doi.org/10.1080/17449642.2018.1477088
Bergström, T., Gunnarsson, G., & Olteanu, C. (2023). The importance of flow for secondary school students’ experiences in geometry. International Journal of Mathematical Education in Science and Technology, 54(6), 1067–1091. https://doi.org/10.1080/0020739X.2021.1989511
Bertrand, M. G., Sezer, H. B., & Namukasa, I. K. (2024). Exploring AR and VR Tools in Mathematics Education Through Culturally Responsive Pedagogies. Digital Experiences in Mathematics Education, 10(3), 462–486. https://doi.org/10.1007/s40751-024-00152-x
Boonstra, K., Kool, M., Shvarts, A., & Drijvers, P. (2025). Primary school teachers’ practices for fostering embodied abstraction in geometry. Journal of Mathematics Teacher Education, 0123456789. https://doi.org/10.1007/s10857-025-09702-5
Bozan, I., & Taslidere, E. (2025). Effect of the 5E model enriched with coding and digital game design activities on gifted students’ academic achievement and problem-solving skills. In Education and Information Technologies (Vol. 30, Issue 10). Springer US. https://doi.org/10.1007/s10639-024-13281-y
Dilek Eryigit, C., Kucuk, S., & Tasgin, A. (2025). Impact of augmented reality technology on geometry skills and motivation of preschool children. Education and Information Technologies. https://doi.org/10.1007/s10639-025-13631-4
Fényes, D., Fazekas, M., Németh, B., & Gáspár, P. (2022). Implementation of a variable-geometry suspension-based steering control system. Vehicle System Dynamics, 60(6), 2018–2035. https://doi.org/10.1080/00423114.2021.1890798
Frenken, L., Libbrecht, P., Becker, B., & Greefrath, G. (2024). Dynamic geometry tasks in standardized assessment–analysis of solution processes and consequences for practice. International Journal of Mathematical Education in Science and Technology, 55(5), 1117–1133. https://doi.org/10.1080/0020739X.2022.2036838
Gerla, G., & Miranda, A. (2020). Point-free foundation of geometry looking at laboratory activities. Cogent Mathematics & Statistics, 7(1), 1761001. https://doi.org/10.1080/25742558.2020.1761001
Hidajat, F. A. (2023). Augmented reality applications for mathematical creativity: a systematic review. In Journal of Computers in Education (Vol. 11, Issue 4). Springer Berlin Heidelberg. https://doi.org/10.1007/s40692-023-00287-7
Huang, W., Walkington, C., & Nathan, M. J. (2023). Coordinating modalities of mathematical collaboration in shared VR environments. In International Journal of Computer-Supported Collaborative Learning (Vol. 18, Issue 2). Springer US. https://doi.org/10.1007/s11412-023-09397-x
Ka?mierczak, R., Grunwald, G., Skowro?ski, R., Ka?mierczak, L., & Kowalczyk, C. (2025). Augmented reality tools for mathematics and geoscience education. Scientific Reports, 15(1), 1–16. https://doi.org/10.1038/s41598-025-02090-z
Khajehei, H., Ahmadi, A., Soleimanmeigouni, I., Haddadzade, M., Nissen, A., & Latifi Jebelli, M. J. (2022). Prediction of track geometry degradation using artificial neural network: a case study. International Journal of Rail Transportation, 10(1), 24–43. https://doi.org/10.1080/23248378.2021.1875065
Kus, M., & Newcombe, N. S. (2025). Facilitation of students’ disembedding in an online visual arts and mathematics education program. International Journal of STEM Education, 12(1). https://doi.org/10.1186/s40594-024-00524-0
Lane, D., & Sorby, S. (2022). Bridging the gap: blending spatial skills instruction into a technology teacher preparation programme. International Journal of Technology and Design Education, 32(4), 2195–2215. https://doi.org/10.1007/s10798-021-09691-5
Lee, C. Y., Lei, K. H., Chen, M. J., Lee, C. R., & Chen, C. C. (2023). Helping low-achieving students to comprehend the area of basic geometric shapes using an enclosing-rectangle scaffold via computer-assisted instruction. Cogent Education, 10(2). https://doi.org/10.1080/2331186X.2023.2277576
Li, W., Xie, Q., Ao, J., Lin, H., Ji, S., Yang, M., & Sun, J. (2025). Systematic review: a scientometric analysis of the status, trends and challenges in the application of digital technology to cultural heritage conservation (2019–2024). Npj Heritage Science, 13(1), 1–17. https://doi.org/10.1038/s40494-025-01636-8
Miyazaki, M., Fujita, T., Iwata, K., & Jones, K. (2024). Level-spanning proof-production strategies to enhance students’ understanding of the proof structure in school mathematics. International Journal of Mathematical Education in Science and Technology, 55(7), 1597–1618. https://doi.org/10.1080/0020739X.2022.2075288
Mjenda, M., & Kyaruzi, F. (2025). Investigating the integration of technology-aided assessment methods in teaching and learning 3D geometry in Tanzanian secondary schools. Cogent Education, 12(1). https://doi.org/10.1080/2331186X.2025.2464358
Mwadzaangati, L., Adler, J., & Kazima, M. (2022). Mathematics Mediational Means and Learner Centredness: Insights from ‘traditional’ Malawian Secondary School Geometry Lessons. African Journal of Research in Mathematics, Science and Technology Education, 7295. https://doi.org/10.1080/18117295.2022.2055910
Ng, O. L., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing. International Journal of STEM Education, 7(1), 1–13. https://doi.org/10.1186/s40594-020-00244-1
Ortiz-Laso, Z., Diego-Mantecón, J. M., Lavicza, Z., & Blanco, T. F. (2023). Teacher growth in exploiting mathematics competencies through STEAM projects. ZDM - Mathematics Education, 55(7), 1283–1297. https://doi.org/10.1007/s11858-023-01528-w
Oughton, R., Nichols, K., Bolden, D. S., Dixon-Jones, S., Fearn, S., Darwin, S., Mistry, M., Peyerimhoff, N., & Townsend, A. (2024). Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematicians. Mathematical Thinking and Learning, 26(3), 306–325. https://doi.org/10.1080/10986065.2022.2119497
ÖZKUL, H. (2025). Identifying the entrepreneurship and problem-solving skills of fourth-grade students through engineering design-based STEM activities. Humanities and Social Sciences Communications, 12(1), 1–15. https://doi.org/10.1057/s41599-025-05612-2
Pawlak-Jakubowska, A., & Terczy?ska, E. (2023). Evaluation of STEM students’ spatial abilities based on a novel net cube imagination test. Scientific Reports, 13(1), 1–15. https://doi.org/10.1038/s41598-023-44371-5
Pratama, R. A., & Yelken, T. Y. (2024). Effectiveness of ethnomathematics-based learning on students’ mathematical literacy: a meta-analysis study. Discover Education, 3(1). https://doi.org/10.1007/s44217-024-00309-1
Sheynikhovich, D., Alkachroum, M., Arleo, A., & Bécu, M. (2025). Landmarks and environmental geometry in spatial navigation: insights for architecture in the context of human aging. Architectural Science Review, 8628. https://doi.org/10.1080/00038628.2025.2476647
Siller, H. S., & Ahmad, S. (2024). The Effect of Concrete and Virtual Manipulative Blended Instruction on Mathematical Achievement for Elementary School Students. In Canadian Journal of Science, Mathematics and Technology Education (Vol. 24, Issue 2). Springer International Publishing. https://doi.org/10.1007/s42330-024-00336-y
Simsek, A., Clark-Wilson, A., Bretscher, N., & Hoyles, C. (2025). Exploring mathematics teachers’ integration of technology into classroom teaching practice: a focus on geometric similarity. International Journal of Mathematical Education in Science and Technology, 5211. https://doi.org/10.1080/0020739X.2025.2469865
Triviño-Tarradas, P., Mohedo-Gatón, A., Fernández, R. E. H., Mesas-Carrascosa, F. J., & Carranza-Cañadas, P. (2022). Preliminary results of the impact of 3D-visualization resources in the area of graphic expression on the motivation of university students. Virtual Reality, 26(3), 963–978. https://doi.org/10.1007/s10055-021-00606-2
Turgut, M. (2022). Reinventing Geometric Linear Transformations in a Dynamic Geometry Environment: Multimodal Analysis of Student Reasoning. International Journal of Science and Mathematics Education, 20(6), 1203–1223. https://doi.org/10.1007/s10763-021-10185-y
Villa-Ochoa, J. A., Molina-Toro, J. F., & Borba, M. C. (2023). Roles of technologies for future teaching in a pandemic: activity, agency, and humans-with-media. ZDM - Mathematics Education, 55(1), 207–220. https://doi.org/10.1007/s11858-022-01429-4
Weigand, H. G., Hollebrands, K., & Maschietto, M. (2025). Geometry education at secondary level – a systematic literature review. ZDM - Mathematics Education, 57(4), 829–843. https://doi.org/10.1007/s11858-025-01703-1
Weigand, H. G., Trgalova, J., & Tabach, M. (2024). Mathematics teaching, learning, and assessment in the digital age. ZDM - Mathematics Education, 56(4), 525–541. https://doi.org/10.1007/s11858-024-01612-9
Wu, J., Jiang, H., Long, L., & Zhang, X. (2024). Effects of AR mathematical picture books on primary school students’ geometric thinking, cognitive load and flow experience. Education and Information Technologies, 29(18), 24627–24652. https://doi.org/10.1007/s10639-024-12768-y
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