The Use of GeoGebra as an Instrument to Facilitate Grade 11 Learners’ Understanding of Cyclic Quadrilateral and Tangent Theorems: A Case Study
DOI:
https://doi.org/10.57125/FED.2026.03.09Keywords:
GeoGebra, Circle geometry, Cyclic quadrilaterals, Tangent theorems, Instrumental genesis, Constructivism.Abstract
This study explores the use of GeoGebra as a teaching tool to improve Grade 11 learners' understanding of cyclic quadrilaterals and tangent theorems in circle geometry. Persistent challenges in Euclidean geometry in South African schools are often linked to traditional teaching methods that rely heavily on memorisation and offer limited opportunities for meaningful visual engagement. In response, a qualitative case study was conducted with one Grade 11 mathematics teacher and thirty-nine learners at a public secondary school in the Western Cape. The intervention involved three GeoGebra-supported teaching cycles over three weeks. Data were collected through classroom observations, interviews with learners and the teacher, and a post-intervention learner survey. The analysis focused on how learners utilised GeoGebra as a tool for geometric reasoning and understanding. The findings show that GeoGebra enhanced learners’ ability to visualise geometric relationships, improved their conceptual understanding, and increased their engagement during circle geometry lessons. Learners demonstrated a greater ability to explore relationships, form conjectures, and collaborate during problem-solving activities. Evidence further indicated that learners shifted from seeing GeoGebra as a simple drawing tool to using it as a reasoning resource to test and verify geometric ideas. While notable advances in conceptual understanding were observed, additional support was still necessary to strengthen learners’ ability to construct formal proofs. The study concludes that GeoGebra can be an effective instructional tool for fostering conceptual understanding in circle geometry when integrated into a learner-centred teaching approach.
References
Adler, J., & Pillay, V. (2024). Teaching mathematics for understanding in constrained contexts. Pythagoras, 45(1), Article a789. https://doi.org/10.4102/pythagoras.v45i1.789
Bozkurt, G., & Uygan, C. (2020). Instrumental genesis of pre-service mathematics teachers in a dynamic geometry environment. International Journal of Research in Education and Science, 6(2), 292–309. https://doi.org/10.46328/ijres.v6i2.1013
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
Chimuka, L., & Ogbonnaya, U. I. (2015). Students' response to teachers' use of GeoGebra in Euclidean geometry. African Journal of Research in Mathematics, Science and Technology Education, 19(1), 70–84. https://doi.org/10.1080/10288457.2014.942959
Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.
Department of Basic Education. (2011). Curriculum and assessment policy statement (CAPS): Mathematics grades 10–12. Department of Basic Education.
Department of Basic Education. (2014–2019). National senior certificate diagnostic examination reports: Mathematics. Department of Basic Education.
Diković, L. (2009). Implementing dynamic mathematics resources with GeoGebra at the college level. International Journal of Emerging Technologies in Learning, 4(3), 51–54. https://doi.org/10.3991/ijet.v4i3.784
Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234. https://doi.org/10.1007/s10649-010-9254-5
Duval, R. (1999). Representation, vision and visualisation: Cognitive functions in mathematical thinking. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3–26).
Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805–842). Information Age.
Hohenwarter, M., & Fuchs, K. (2004). A combination of dynamic geometry, algebra, and calculus in the software system GeoGebra. Proceedings of the Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching Conference. https://www.geogebra.org
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Sage.
Mhlolo, M. K. (2021). Learners' errors and misconceptions in geometry: Implications for teaching. African Journal of Research in Mathematics, Science and Technology Education, 25(2), 156–168. https://doi.org/10.1080/18117295.2021.1917562
Mthethwa, S. (2015). Learners' perceptions of GeoGebra as a tool for learning circle geometry. South African Journal of Education, 35(2), 1–10. https://doi.org/10.15700/saje.v35n2a1073
Mudaly, V., & Fletcher, T. (2022). Technology-mediated learning in South African mathematics classrooms. South African Journal of Education, 42(3), 1–12. https://doi.org/10.15700/saje.v42n3a2103
Ng, O. L., Sinclair, N., & Patahuddin, S. M. (2023). Digital tools and proof construction in geometry classrooms. Educational Studies in Mathematics, 112(1), 1–20. https://doi.org/10.1007/s10649-022-10168-4
Rabardel, P. (1995). Les hommes et les technologies: Approche cognitive des instruments contemporains [People and technologies: A cognitive approach to contemporary instruments]. Armand Colin.
Rabardel, P., & Béguin, P. (2005). Instrument mediated activity: From subject development to anthropocentric design. Theoretical Issues in Ergonomics Science, 6(5), 429–461. https://doi.org/10.1080/14639220500078179
Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Developing geometric reasoning with dynamic geometry. ZDM – Mathematics Education, 48(5), 701–714.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Trouche, L. (2004). Managing complexity of human/machine interactions in computerised learning environments: Guiding students' command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307. https://doi.org/10.1023/B:IJCO.0000049018.97134.2e
van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage.
Zengin, Y., Furkan, H., & Kutluca, T. (2012). The effect of dynamic mathematics software GeoGebra on student achievement in teaching trigonometry. Procedia – Social and Behavioral Sciences, 31, 183–187. https://doi.org/10.1016/j.sbspro.2011.12.038
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