The Impact of Teaching Strategies on Students’ Understanding of Circle Theorems

This action research focused on improving the understanding of Circle Theorems among Grade 11 students. Geometry is a core area of secondary school mathematics, yet many learners experience ongoing difficulties when working with geometric ideas, especially in reasoning and application. The purpose of this study was to examine the use of selected teaching strategies and visual aids to support students’ understanding of Circle Theorems. The study used a mixed-methods approach. A pre-test and a post-test were used before and after the intervention to obtain quantitative information about students’ performance. Qualitative information was gathered through classroom observations and semi-structured interviews. For quantitative analysis, descriptive statistics, a paired-samples t-test, the Wilcoxon Signed-Rank Test, and effect size measures were applied. The qualitative information was examined thematically to understand changes in students’ learning behavior and the difficulties they encountered during the intervention. The findings showed that students’ understanding of Circle Theorems improved after the intervention. Many students demonstrated better reasoning and were more confident when explaining geometric ideas. Classroom observations and interview data showed that students slowly shifted away from rote procedures and developed a better understanding of how concepts were connected, while the study also noted several changes during the intervention. These included limited lesson time, lack of access to digital devices, difficulty adjusting to new learning approaches, and anxiety when solving problems that required several steps. Based on these findings, the study concludes that the use of carefully planned teaching strategies and visual aids can support students’ learning of Circle Theorems. Addressing the identified challenges may help to improve the effectiveness of geometry teaching in similar classroom contexts

circle theorems, inquiry- based learning, visualization

1. 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 [Google Scholar] [Crossref]

2. Adelabu, O. A., Marange, C. S., & Alex, J. K. (2022). The use of GeoGebra in teaching and learning circle geometry at Grade 11 level. African Journal of Research in Mathematics, Science and Technology Education, 26(2), 1–12. [Google Scholar] [Crossref]

3. Aidoo Bervell, B., & Akayuure, P. (2022). Female senior high school students’ thinking levels in solving circle geometry problems. International Journal of Secondary Education, 10(4), 95–103. https://doi.org/10.11648/j.ijsedu.20221004.11 [Google Scholar] [Crossref]

4. Ali, L. (2023). Enhancing problem-solving skills in geometry through van Hiele’s theory: A study on motivation and collaboration. [Google Scholar] [Crossref]

5. Ambonza, M. O. (2022). Effect of GeoGebra-assisted instruction on students’ academic performance in geometry in secondary schools in Kenya (Master’s thesis, University of Nairobi). University of Nairobi Repository. https://erepository.uonbi.ac.ke/handle/11295/161520 [Google Scholar] [Crossref]

6. Armah, R. B., & Kissi, P. S. (2019). Use of the van Hiele theory in investigating teaching strategies used by college of education geometry tutors. Eurasia Journal of Mathematics, Science and Technology Education, 15(4), em1694. https://doi.org/10.29333/ejmste/103562 [Google Scholar] [Crossref]

7. Asare, B. (2024). Investigating the philosophical view of teaching circles theorem. Mathematics Education Journals, 8(1), 114–119. http://ejournal.umm.ac.id/index.php/MEJ [Google Scholar] [Crossref]

8. Assan-Donkoh, I., Susuoroka, G., Baah, D., Baah-Duodu, S., & Zutaah, P. (2019). Cooperative learning strategy in teaching and learning of circle theorem in mathematics: A case of Nana Brentu Senior High School in Aowin Municipality in Ghana. Open Science Journal of Mathematics and Application, 7(1), 1–13. [Google Scholar] [Crossref]

9. Assan-Donkoh, M., Quaigrain, K., & Torto, G. (2019). The effect of cooperative learning on students’ achievement in circle theorems. International Journal of Mathematics Education, 7(2), 35–50. [Google Scholar] [Crossref]

10. Chimuka, A. (2017). The effect of integration of GeoGebra software in the teaching of circle geometry on Grade 11 students’ achievement (Master’s thesis). University of South Africa. [Google Scholar] [Crossref]

11. Department of Examinations, Sri Lanka. (2018). G.C.E. (O/L) Mathematics evaluation report. Retrieved from https://www.doenets.lk/evaluationreports [Google Scholar] [Crossref]

12. Department of Examinations, Sri Lanka. (2020). G.C.E. (O/L) Mathematics evaluation report. Retrieved from https://www.doenets.lk/evaluationreports [Google Scholar] [Crossref]

13. Department of Examinations, Sri Lanka. (2021). G.C.E. (O/L) Mathematics evaluation report. Retrieved from https://www.doenets.lk/evaluationreports [Google Scholar] [Crossref]

14. Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 273–280). Kluwer Academic Publishers. [Google Scholar] [Crossref]

15. Enoch, S. K. (2024). Using applicable theorems for solving circle geometry problems: A correlational study of senior high school students’ academic performance in circle geometry. Research Square https://doi.org/10.21203/rs.3.rs-3694470/v2 ⁠ [Google Scholar] [Crossref]

16. Erebakyere, S., & Agyei, D. D. (2022). Effects of social-interaction and self-exploration strategies with Dynamic Autograph Software on senior high school students’ learning of Circle Theorems. *African Journal of Educational Studies in Mathematics and Sciences, 18*(1), 31–41. https://doi.org/10.4314/ajesms.v18i1.3 [Google Scholar] [Crossref]

17. Fuys, H., Geddes, D., & Tischler, R. (1984). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, 15(3), 141–158. https://doi.org/10.5951/jresematheduc.15.3.0141 [Google Scholar] [Crossref]

18. Lwanga, A. (2023). The application of van Hiele’s theory of instructional design to facilitate the learning of circle geometry in Grade 11 [Master’s thesis, Cape Peninsula University of Technology]. [Google Scholar] [Crossref]

19. Magalhães, D., & Magalhães, R. (2021). Discussion Circle for the teaching-learning of statistics: A contribution based on Vygotsky’s Cultural-Historical Theory. *Statistics Education Research Journal, 20*(2), 1–18. https://doi.org/10.52041/serj.v20i2.355 [Google Scholar] [Crossref]

20. Mensah-Wonkyi, T., & Adu, E. (2016). Effect of the inquiry-based teaching approach on students’ understanding of circle theorems in plane geometry. African Journal of Educational Studies in Mathematics and Sciences, 12, 61–73. [Google Scholar] [Crossref]

21. Mifetu, R. K. (2023). Using activity method to address students’ problem-solving difficulties in circle geometry. Contemporary Mathematics and Science Education, 4(1), ep23016. https://doi.org/10.30935/conmaths/13079 [Google Scholar] [Crossref]

22. Naidoo, J., & Kapofu, W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education, 40(1), Article 1727. https://doi.org/10.15700/saje.v40n1a1727 [Google Scholar] [Crossref]

23. Ntow, F. D., & Hissan, Y. (2021). The impact of concept-based instruction on senior high school students’ achievement in circle theorems. African Journal of Educational Studies in Mathematics and Sciences, 17(1),113 132. https://dx.doi.org/10.4314/ajesms.v17i1.8 [Google Scholar] [Crossref]

24. Nxumalo, M., Chibisa, A., & Mabusela, M. S. (2022). Acceptance of the GeoGebra application in learning circle theorems. African Journal of Research in Mathematics, Science and Technology Education, 26(1), 1–12. [Google Scholar] [Crossref]

25. Ochoma, M. U. (2020). Curriculum content and the issue of relevance in the 21st century classroom. International Journal on Integrated Education, 3(9), 158–164. [Google Scholar] [Crossref]

26. Salifu, A. S. (2020). Effect of GeoGebra on pre-service teachers’ achievement and perception of circle theorems at E. P. College of Education, Bimbilla–Ghana. International Journal of Innovative Science and Research Technology, 5(8), 1202–1215. [Google Scholar] [Crossref]

27. Sudihartinih, S., Sari, E. Y., & Fatmasari, R. (2024). Learner-centered teaching: A guide for teachers and trainers. Journal of Physics: Conference Series, 1157(4), 042090. https://doi.org/10.1088/1742-6596/1157/4/042090 [Google Scholar] [Crossref]

28. Sudihartinih. (2019). Learner-centered learning model to improve mathematics learning outcomes. Journal of Physics: Conference Series, 1157(4), 042090. https://doi.org/10.1088/1742-6596/1157/4/042090 [Google Scholar] [Crossref]

29. Suglo-Kabinaa, E. (2024). Using applicable theorems for solving circle geometry problems: A correlational study of senior high school students’ academic performance in circle geometry. Research Square https://doi.org/10.21203/rs.3.rs 3694470/v2 [Google Scholar] [Crossref]

30. Tay, C. K., & Mensah-Wonkyi, C. (2018). The effect of using GeoGebra on senior high school students’ performance in circle theorems. African Journal of Educational Studies in Mathematics and Sciences, 14, 49–62. https://doi.org/10.4314/ajesms.v14i1.5 [Google Scholar] [Crossref]

31. van Hiele, P. M. (1985). The child's thought and geometry. In D. Tall (Ed.), Selected papers of Pierre van Hiele (pp. 243–252). University of Warwick. [Google Scholar] [Crossref]

32. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. [Google Scholar] [Crossref]

33. Žakelj, A., & Klančar, A. (2022). The role of visual representations in geometry learning. European Journal of Educational Research, 11(3), 1393–1411. https://doi.org/10.12973/eu-jer.11.3.1393 [Google Scholar] [Crossref]

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