Enhancing Students' van Hiele Geometric Thinking Levels Through the Integration of Geometer's Sketchpad (GSP) in Geometry Learning
DOI:
https://doi.org/10.48161/qaj.v5n2a1639Abstract
Van Hiele’s theory of geometric thinking describes a hierarchical progression through distinct levels, from basic visualization to advanced deductive reasoning. Students typically struggle to transition between these levels without appropriate instructional support. Dynamic geometry software, such as Geometer’s Sketchpad (GSP), has been shown to facilitate this transition by providing interactive visualizations and exploratory learning experiences. By allowing students to manipulate geometric shapes and observe properties dynamically, GSP enhances conceptual understanding and promotes higher-order thinking. This study aims to analyze the development of students' geometric thinking levels on geometry topics based on Van Hiele's theory after instruction using Geometer's Sketchpad (GSP). The research employed a qualitative approach, involving three participants from Class VIIG of a junior high school in Mojokerto, Indonesia, representing high, medium, and low ability levels. Data were collected through a test consisting of three questions designed to assess students' geometric understanding across various indicators of Van Hiele's thinking levels, followed by in-depth interviews. The findings revealed that GSP-based learning was effective in enhancing students' geometric thinking. Subjects ST and SD demonstrated significant progress, with several indicators advancing from Level 0 (Visualization) to Level 2 (Informal Deduction). In contrast, subject SR exhibited limited improvement, with most indicators remaining at Level 1 (Analysis). These results highlight GSP's potential to support students in developing a deeper understanding of geometric concepts. This study provides valuable insights for designing learning strategies tailored to the diverse needs and abilities of students, aiming to facilitate higher levels of geometric thinking.
Downloads
References
Hartono, S. (2020). Effectiveness of Geometer's Sketchpad Learning in Two-Dimensional Shapes. Mathematics Teaching Research Journal, 12(3), 84-93.
Judijanto, L., Manu, C. M. A., Sitopu, J. W., Mangelep, N. O., & Hardiansyah, A. (2024). The Impact of Mathematics In Science And Technology Development. International Journal of Teaching and Learning, 2(2), 451-458.
Darmayanti, R., Laila, A. R. N., Khan, S., Fitriyah, I. D., Bausir, U., Setio, A., & Usmiyatun, U. (2023). Students' Attitudes Towards Learning Mathematics:" Too Soft Attitudes-Very Difficult-Boring-In A Good Way". Indonesian Journal of Learning and Educational Studies, 1(1), 29-50.
Stylianides, G. J., Stylianides, A. J., & Moutsios-Rentzos, A. (2024). Proof and proving in school and university mathematics education research: a systematic review. ZDM–Mathematics Education, 56(1), 47-59.
Mukuka, A., & Alex, J. K. (2024). Student Teachers’ Knowledge of School-level Geometry: Implications for Teaching and Learning. European Journal of Educational Research, 13(3).
Khusna, N., Widiyono, Y., & Khaq, M. (2023). Improving Activity and Learning Outcomes Through the Student Team Achievement Divisions Learning Model for Elementary School Students. Pedagogik Journal of Islamic Elementary School, 6(1), 39-50.
Birgin, O., & Özkan, K. (2024). Comparing the concept images and hierarchical classification skills of students at different educational levels regarding parallelograms: a cross-sectional study. International Journal of Mathematical Education in Science and Technology, 55(4), 850-882.
Nuraeni, Z., Simarmata, R. H., & Tarigan, A. H. Z. (2024). Develop of learning tools based on worked example of geometry materials to improve students’ mathematical representations ability in junior high school. In AIP Conference Proceedings (Vol. 3052, No. 1). AIP Publishing.
Haqq, A. A., Suyitno, A., & Zaenuri, Z. (2023). The use of van Hiele theory as a theoretical framework for technology-assisted geometry learning. In AIP Conference Proceedings (Vol. 2614, No. 1). AIP Publishing.
Restrepo-Ochoa, J. F., Gualdrón-Pinto, E., & Ávila-Ascanio, L. F. (2023). Improving the learning of geometric proportionality using van Hiele’s model, mathematical visualization, and GeoGebra. EURASIA Journal of Mathematics, Science and Technology Education, 19(9), em2324.
Gurmu, F., Tuge, C., & Hunde, A. B. (2024). Effects of GeoGebra-assisted instructional methods on students’ conceptual understanding of geometry. Cogent Education, 11(1), 2379745.
Meng, C., C. (2009). Enhancing Students' Geometric Thinking Through Phase-Based Instruction Using Geometer's Skechpad: A Case Study, Jurnal Pendidik dan Pendidikan, 24, 89–107.
Leong, K. E. (2013). Impact of Geometer's Sketchpad on Students Achievement in Graph Functions. Malaysian Online Journal of Educational Technology, 1(2), 19-33.
Idris, N. (2009). The Impact of Using Geometers’ Sketchpad on Malaysian Students’ Achievement and Van Hiele Geometric Thinking: A case study in Malaya, Journal of Mathematics Teacher Education,2 (2), 94-107.
Presmeg, N. (2020). Visualization and learning in mathematics education. Encyclopedia of mathematics education, 900-904.
Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., & Ihsan, H. (2021). Reviewing the Van Hiele Model and the Application of Metacognition on Geometric Thinking. International Journal of Evaluation and Research in Education, 10(2), 597-605.
Yee, L., P. (2007). Teaching Secondary School Mathematics a Resource Book. Singapore: Mathematics and Mathematics Education National Institute of Education Nanyang Tehnoloogical University.
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for research in mathematics education, 17(1), 31-48.
Abdullah, A. H., & Zakaria, E. (2013). Enhancing students’ level of geometric thinking through van Hiele’s phase-based learning. Indian Journal of Science and Technology, 6(5), 4432-4446.
Hodiyanto, H., & Santoso, D. (2020). How Geometer’s Sketchpad (GSP) Develops Geometry Concept Understanding. International Journal of Trends in Mathematics Education Research, 3(1), 31-35.
Kotu, A., & Weldeyesus, K. M. (2022). Instructional use of Geometer’s Sketchpad and students’ geometry learning motivation and problem-solving ability. Eurasia Journal of Mathematics, Science and Technology Education, 18(12).
Meng, C. C., & Sam, L. C. (2013). Enhancing primary pupils' geometric thinking through phase-based instruction using the geometer's sketchpad. Asia Pacific Journal of Educators and Education, 28, 33-51.
Uygun, T. (2020). An inquiry-based design research for teaching geometric transformations by developing mathematical practices in dynamic geometry environment. Mathematics Education Research Journal, 32(3), 523-549.
Li, H. L., & Zulnaidi, H. (2024). Effects of Geometer’s Sketchpad on Algebraic Reasoning Competency amongst Students in Malaysia. Edunesia: Jurnal Ilmiah Pendidikan, 5(1), 488-499.
Kotu, A., & Weldeyesus, K. M. (2022). Instructional use of Geometer’s Sketchpad and students geometry learning motivation and problem-solving ability. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2201.
Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. CDASSG Project.
Patsiomitou, S., Barkatsas, A., & Emvalotis, A. (2010). Secondary students'" dynamic reinvention of geometric proof" through the utilization of linking visual active representations. Journal of Mathematics and Technology, 5, 43-56.
Sun, Z., Smith, C., Gemmiti, A., & Zhang, G. (2024). Analysis of the Intention of Chinese High School Students to Study Abroad in the Post-Pandemic Era, Based on the Push-Pull Theory. In Proceedings of the 3rd International Conference on Education, Language and Art (ICELA 2023) (Vol. 831, p. 173). Springer Nature.
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. Creativity in mathematics and the education of gifted students, 9, 129-145.
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in mathematics, 67, 255-276.
Belbase, S. (2013). Beliefs about teaching geometric transformations with geometers’ Sketchpad: A reflexive abstraction. Journal of Education and Research, 3(2).
İbili, E. (2019). The use of dynamic geometry software from a pedagogical perspective: current status and future prospects. Journal of Computer and Education Research, 7(14), 337-355.
Machisi, E. R. I. C. (2020). Van Hiele theory-based instruction, geometric proof competence and grade 11 students' reflections. Unpublished doctoral dissertation]. University of South Africa.
Wilson, A. M. (2011). One teacher’s experience with implementing Geometer’s Sketchpad to promote student engagement. Unpublished Master’s Thesis, The Evergreen State College, Olympia, Washington.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Qubahan Academic Journal

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.