Abstract :
This study aims to develop GeoGebra-assisted instructional materials on circle topics based on the van Hiele model that meet the criteria of validity, practicality, and effectiveness. The study employed a Research and Development (R&D) approach using the 4D model, consisting of the Define, Design, Develop, and Disseminate stages. The participants were high school students divided into an experimental group and a control group. Data were collected through validation sheets, observation sheets, student response questionnaires, readability tests, and learning outcome assessments. The results indicate that the developed materials are valid, with average validity scores ranging from 3.58 to 3.85. Practicality was demonstrated by a high level of instructional implementation (3.75), very high student activity (93.2%), and highly positive student responses (92.68%). Effectiveness was confirmed by a classical mastery rate of 89%, a high N-Gain score (0.77), and a statistically significant difference between the experimental and control groups (p < 0.05). These findings suggest that GeoGebra-assisted instructional materials based on the van Hiele model are effective in improving students’ mathematics learning outcomes, particularly in geometry.
Keywords :
circle geometry, dynamic geometry software, GeoGebra, instructional material development, van Hiele modelReferences :
- Amaliah, D., Khotimah, K., & Lestari, I. (2022). Perancangan media pembelajaran interaktif berbantuan GeoGebra untuk mendukung students’ geometric thinking skills. SENTRI: Jurnal Riset Ilmiah, 1(1), 150–154. https://doi.org/10.55681/sentri.v1i1.215
- Balladares-Pico, L. M., Espinosa-Pinos, C. A., & Núñez-Torres, M. G. (2023). Development and evaluation of a computerized didactic guide with mathematical foundations for the teaching–learning of physics. In 2023 IEEE 3rd International Conference on Advanced Learning Technologies on Education & Research (ICALTER) (pp. 1–4). https://doi.org/10.1109/ICALTER61411.2023.10372903
- Budiman, H. (2014). Pembelajaran geometri lingkaran dengan metode konvensional dan pengaruhnya pada siswa. Jurnal Kajian Pendidikan, 4(1), 61–72.
- Budiman, H., & Rosmiati, M. (2020). Penerapan Teori Belajar Van Hiele Berbantuan Geogebra untuk Meningkatkan Kemampuan Penalaran Matematis Siswa. PRISMA, 9(1), 47–56.
- Fakhri, A. (2023). Kurikulum Merdeka dan pengembangan perangkat pembelajaran: Menjawab tantangan sosial dalam meningkatkan keterampilan abad 21. C.E.S (Conference of Elementary Studies), 1(1), 32–40.
- Fiangga, S., Rosyidi, A. H., Wijayanti, P., Harini, N. V., Romadhon, A., & Roberta, A. P. (2025). Task design analysis in mathematics teacher’s TPACK: A case study in Pasuruan. In AIP Conference Proceedings, 3316(1). https://doi.org/10.1063/5.0290656
- Firmansyah, F. F., Aribowo, B. E., Damayanti, R., Sari, M. P., Sunardi, & Yudianto, E. (2020). Students’ metacognition profile in solving PISA shape and space problems based on van Hiele levels. Journal of Physics: Conference Series, 1563(1). https://doi.org/10.1088/1742-6596/1563/1/012049
- Firmansyah, F. F., Sa’dijah, C., Subanji, S., & Qohar, A. (2022). Characterizations of Students ’ Metacognition in Solving Geometry Problems through Positioning Group Work. TEM Journal, 11(3), 1391–1398. https://doi.org/10.18421/TEM113
- Firmansyah, F. F., Sunardi, Susanti, & Ambarwati, R. (2019). The uniqueness of visual levels in resolving geometry of shape and space content based on van hieles ’ s theory. Journal of Physics: Conference Series, 1211(1), 012076. https://doi.org/10.1088/1742-6596/1211/1/012076
- Giovanni, L. D. A., Susanto, & Yudianto, E. (2022). Analisis berpikir siswa dalam memecahkan masalah segiempat berdasarkan level van Hiele. Journal of Mathematics Education and Learning, 2(1), 84. https://doi.org/10.19184/jomeal.v2i1.24829
- Gurmu, F., Tuge, C., & Hunde, A. B. (2024). Effects of GeoGebra-assisted instruction on students’ conceptual understanding of geometry. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2024.2379745
- Hohenwarter, M., & Lavicza, Z. (2024). MATHEMATICS TEACHER DEVELOPMENT WITH ICT : Proceedings of the British Society for Research into Learning Mathematics, 27(3), 49–54.
- Kurt, G., Önel, F., & Çakıoğlu, Ö. (2023). An Investigation of Middle School Students ’ Spatial Reasoning Skills. International Electronic Journal of Elementary Education, 16(1), 123–141.
- Loureiro, A. C., Ibáñez-cubillas, P., & Miranda-pinto, S. (2023). Content validity by expert evaluation to measure the digital competences of master’s degree students in Special Education. Texto Livre, 17, 1–12. https://doi.org/10.1590/1983–3652.2024.52564
- Lusyana, E., & Lestari, T. K. (2022). Pengembangan perangkat pembelajaran matematika SMK menggunakan teori van Hiele. CV. Azka Pustaka.
- Mayadi, S. (2021). Meningkatkan Keaktifan dan Hasil Belajar Matematika Dengan Implementasi Media Geogebra Pada Siswa SMA. Educatio: Jurnal Ilmu Kependidikan, 16(1), 1–8. https://doi.org/10.29408/edc.v16i1.2691
- Nwabuaku, L., & Iroriteraye-Adjekpovu, J. I. (2021). Effect of Cooperative Learning Strategy on Students’ Achievement in and Attitude to Mathematics. European Journal of Arts, Humanities and Social Sciences, 6(1), 37. https://doi.org/10.59324/ej
- Pattanapiboon, W., & Nishizawa, H. (2024). Impact on Student Learning Outcomes in Mathematics Using GeoGebra. In Proceedings of the Asian Technology Conference in Mathematics (pp. 258 – 267). https://www.scopus.com/inward/record.uri?eid=2-s2.085217668592&partnerID=40&md5=abe3b6e904fac6e507bf4b145bd73b82
- Puspita, W., Nst, S. A., Saragih, A. K., & Nurbaiti. (2023). Analisis penggunaan software dalam pembelajaran matematika berbasis multimedia interaktif. Jurnal Informatika dan Rekayasa Perangkat Lunak, 3(4), 415–421. https://doi.org/10.33365/jatika.v3i4.2262
- Rindi Fatmawati, & Yahfizham Yahfizham. (2024). Systematic literature review on GeoGebra in geometry learning. International Journal of Mathematics and Science Education, 1(2), 1–11. https://doi.org/10.62951/ijmse.v1i2.17
- Salfate, L. E., Guerrero, G., Farré, J. B., & Salinas, F. M. (2023). Design and Validation of a Classroom Observation Instrument to Evaluate the Quality of Mathematical Activity from a Gender Perspective. Education Sciences, 13(3), 266.
- Sari, C. K., Machromah, I. U., & Zakkiyah. (2020). Developing Circle Module Based on Van Hiele Theory. In SEMANTIK Conference of Mathematics Education (SEMANTIK 2019), 467, 72–77.
- Sari, H. A., Susanto, & Yudianto, E. (2022). Pengembangan perangkat pembelajaran geometri berbantuan GeoGebra. AKSIOMA, 11(3), 2441. https://doi.org/10.24127/ajpm.v11i3.5568
- Septian, A., Setiawan, E., & Noersapitri, Y. (2023). Peningkatan kemampuan representasi matematis siswa menggunakan GeoGebra. Jurnal Padegogik, 6(1), 1–9. http://doi.org/10.35974/jpd.v6i1.2905
- Yudianto, E., Sunardi, Sugiarti, T., Setiawan, T. B., & Maghfiroh, A. (2022). Pengaruh penerapan fase-fase pembelajaran van Hiele terhadap tingkat berpikir geometri siswa SMA. Jurnal Cendekia, 6(1), 710–720. https://doi.org/10.31004/cendekia.v6i1.1289
- Zakariya, Y. F. (2022). Cronbach’s alpha in mathematics education research: Its appropriateness and alternatives. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2022.1074430
- Annizar, A. M., Kurniati, D., Yudianto, E., & Susanto, S. (2025). Towards a comprehensive framework for complex problem-solving in mathematics: A development and validation study. TEM Journal, 14(3), 2860–2869. https://doi.org/10.18421/TEM143-85
- Kurniati, D., Annizar, A. M., Yudianto, E., & Susanto, S. (2026). Developing dynamic contextual mathematics problems with SDGs perspectives: Assessing students’ problem-solving flexibility. Perspectives of science and Education, 79(1), 374–385. https://doi.org/10.32744/pse.2026.1.23

