An Exploration of Learners’ Understanding of Euclidean Geometric Concepts: A Case Study of Secondary Schools in the OR Tambo Inland District of the Eastern Cape
Thabisa Maqoqa 
Issue: Vol.5 No.5 Issue Article 7 pp.658 – 675
DOI: https://doi.org/10.38159/ehass.2024557 | Published online 10th May, 2024
© 2024 The Author(s). This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).
A major concern in South Africa is the poor performance of learners in mathematics, particularly in geometry. This paper therefore sought to explore the learners’ understanding of Euclidean geometric concepts. The Van Hiele model was a useful framework for understanding the reasoning and challenges that students encounter with geometry. This study focused on 15 participants from rural South African schools, including 5 grade 10 mathematics learners in each of the three secondary schools and three teachers who are teaching mathematics in grade 10, in three secondary schools. Through face-to-face interviews, learners’ comprehension of geometry was qualitatively assessed. Pedagogical and methodological difficulties, lack of learners’ interest and comprehension of numerous geometrical concepts, as well as the absence of technology use, were found to contribute to the challenges in learning and teaching Euclidean geometry. The recommendations suggest that teachers should plan and prepare their geometry classes with the students’ understanding in mind that Euclidean geometry has been a cornerstone of mathematical education for centuries, teaching students critical thinking, problem-solving, and logical reasoning skills. This study adds to the existing literature on introducing new concepts in mathematics into the educational system of South Africa.
Keywords: Geometry, Students’ Interest, Self-efficacy, Understanding, Three-Dimensional Shape
Adeniji, Saidat Morenike, Saka Khadijat Ameen, B U Dambatta, and Razak Orilonise. “Effect of Mastery Learning Approach on Senior School Students’ Academic Performance and Retention in Circle Geometry.” International Journal of Instruction 11, no. 4 (2018): 951–62.
Adora, Nelia M. “Mathematics Performance of Grade Six Pupils in the National Achievement Test, Division of Northern Samar: Basis in Developing a Workbook in Elementary Mathematics VI.” In Universal Academic Cluster International May Conference in Bangkok, 25–26, 2017.
Ahmad Al-Khateeb, Mohammad. “The Extent of Mathematics Teacher’s Awareness of Their Students’ Misconceptions in Learning Geometrical Concepts in the Intermediate Education Stage.” European Scientific Journal, ESJ 12, no. 31 (November 30, 2016): 357. https://doi.org/10.19044/esj.2016.v12n31p357.
Alex, J. K., and K. J. Mammen. “A Survey of South African Grade 10 Learners’ Geometric Thinking Levels in Terms of the Van Hiele Theory.” The Anthropologist 14, no. 2 (March 17, 2012): 123–29. https://doi.org/10.1080/09720073.2012.11891229.
Alex, Jogymol Kalariparambil, and Kuttickattu John Mammen. “Lessons Learnt From Employing van Hiele Theory Based Instruction In Senior Secondary School Geometry Classrooms.” EURASIA Journal of Mathematics, Science and Technology Education 12, no. 8 (July 2, 2016). https://doi.org/10.12973/eurasia.2016.1228a.
Alharahsheh, Husam Helmi, and Abraham Pius. “A Review of Key Paradigms: Positivism VS Interpretivism.” Global Academic Journal of Humanities and Social Sciences 2, no. 3 (2020): 39–43.
Ali, Imdad, Bhagawati Simarekha, and Sarmah Jnanjyoti. “Performance of Geometry among the Secondary School Students of Bhurbandha CD Block of Morigaon District, Assam, India.” International Journal of Innovative Research and Development 3, no. 11 (2014).
Armah, Robert Benjamin, Primrose Otokonor Cofie, and Christopher Adjei Okpoti. “Investigating the Effect of van Hiele Phase-Based Instruction on Pre-Service Teachers’ Geometric Thinking.” International Journal of Research in Education and Science, January 24, 2018, 314–30. https://doi.org/10.21890/ijres.383201.
Asemani, Emmanuel, Samuel Kwesi Asiedu-Addo, and Richard Asumadu Oppong. “The Geometric Augmented Reality for Junior High School Students .” In IOP Conference Series: Materials Science and Engineering, 1st ed., 306:012029. IOP Publishing, 2018.
Bansilal, Sarah, and Ifunanya Ubah. “The Use of Semiotic Representations in Reasoning about Similar Triangles in Euclidean Geometry.” Pythagoras 40, no. 1 (2019): 1–10.
Bayuningsih, A S, B Usodo, and S Subanti. “Problem Based Learning with Scaffolding Technique on Geometry.” Journal of Physics: Conference Series 1013 (May 2018): 012134. https://doi.org/10.1088/1742-6596/1013/1/012134.
Burger, William F., and J. Michael Shaughnessy. “Characterizing the Van Hiele Levels of Development in Geometry.” Journal for Research in Mathematics Education 17, no. 1 (January 1986): 31–48. https://doi.org/10.5951/jresematheduc.17.1.0031.
Cattaneo, Kelsey Hood. “Telling Active Learning Pedagogies Apart: From Theory to Practice.” Journal of New Approaches in Educational Research (NAER Journal) 6, no. 2 (2017): 144–52.
Chihambakwe, Thabani. “Impact of National Senior Certificate Examination Diagnostic Report on Learner Performance in Mathematics.” University of Zululand, 2017.
Creswell, J. David. “Mindfulness Interventions.” Annual Review of Psychology 68, no. 1 (January 3, 2017): 491–516. https://doi.org/10.1146/annurev-psych-042716-051139.
Department of Basic Education. Curriculum News: Improving the Quality of Learning and Teaching-Strengthening Curriculum Implementation from 2010 and Beyond. Pretoria: Government Printers, 2011.
Department of Education. “A review of the Grade 12 National Senior Certificate” 2016, 2017, 2018, 2019.
Dimla, Robin B. “Probing Students’ Levels of Geometric Thinking in Geometry and Their Enacted Example Space Function.” Journal of Education in Black Sea Region 4, no. 1 (2018): 155–63.
Ester, Pilar, Isabel Morales, Álvaro Moraleda, and Vicente Bermejo. “The Verbal Component of Mathematical Problem Solving in Bilingual Contexts by Early Elementary Schoolers.” Mathematics 9, no. 5 (March 6, 2021): 564. https://doi.org/10.3390/math9050564.
Estonanto, Aldrin John J, and Ryan V Dio. “Factors Causing Mathematics Anxiety of Senior High School Students in Calculus.” Asian Journal of Education and E-Learning (ISSN: 2321–2454) 7, no. 01 (2019).
Giannakopoulos, A. “An Alternative Way of Solving Geometry Riders in Grade 12: Back to Synthesis and Analysis.” Proceedings of the 23rd Annual National Congress of the Association for Mathematics Education of South Africa. Johannesburg: Association for Mathematics Education of South Africa (AMESA), 2017.
Hiele, Pierre M van. “Structure and Insight: A Theory of Mathematics Education.” (No Title), 1986.
Hollweck, Trista. “Robert K. Yin. (2014). Case Study Research Design and Methods (5th Ed.).” Canadian Journal of Program Evaluation 30, no. 1 (March 2015): 108–10. https://doi.org/10.3138/cjpe.30.1.108.
Ismail, Lilliati, Fadzilah Abd Rahman, Moomala Othman, and Noorlila Ahmad. “The Effectiveness of Using a Tracker Chart to Enhance Willingness to Communicate among ESL Learners in a Philosophical Inquiry Classroom Discussion.” Pertanika Journal of Social Sciences & Humanities 28 (2020).
Jones, Keith. “Issues in the Teaching and Learning of Geometry.” In Aspects of Teaching Secondary Mathematics, 137–55. Routledge, 2003.
Kanandjebo, Leena N, and Elizabeth Ndeukumwa Ngololo. “The Effects of ‘Geometry Sketchpad’on Grade 12 Learners’ Performance in Geometry,” 2017.
Kelly, Susan E, I Bourgeault, and R Dingwall. “Qualitative Interviewing Techniques and Styles.” The SAGE Handbook of Qualitative Methods in Health Research 19 (2010): 307–26.
Machisi, Eric. “Grade 11 Students’ Reflections on Their Euclidean Geometry Learning Experiences.” Eurasia Journal of Mathematics, Science and Technology Education 17, no. 2 (February 3, 2021): em1938. https://doi.org/10.29333/ejmste/9672.
Mason, John. “Attention and Intention in Learning about Teaching through Teaching.” In Learning through Teaching Mathematics: Development of Teachers’ Knowledge and Expertise in Practice, 23–47. Springer, 2010.
Mukamba, Edmore, and Chipo Makamure. “Integration of GeoGebra in Teaching and Learning Geometric Transformations at Ordinary Level in Zimbabwe.” Contemporary Mathematics and Science Education 1, no. 1 (July 30, 2020): ep20001. https://doi.org/10.30935/conmaths/8431.
Mwadzaangati, Lisnet. “ Mathematical Knowledge for Teaching Geometric Proof: Learning from Teachers’ Practices.” CERME 9-Ninth Congress of the European Society for Research in Mathematics Education, 2015.
Naidoo, Jayaluxmi, and Winfilda Kapofu. “Exploring Female Learners’ Perceptions of Learning Geometry in Mathematics.” South African Journal of Education 40, no. 1 (2020): 1–11.
Ngirishi, Harrison, and Sarah Bansilal. “An Exploration of High School Learners’ Understanding of Geometric Concepts.” Problems of Education in the 21st Century 77, no. 1 (2019): 82.
Nogues, Camila Peres, and Beatriz Vargas Dorneles. “Systematic Review on the Precursors of Initial Mathematical Performance.” International Journal of Educational Research Open 2 (2021): 100035. https://doi.org/10.1016/j.ijedro.2021.100035.
Novak, Elena, and Janet Lynne Tassell. “Studying Preservice Teacher Math Anxiety and Mathematics Performance in Geometry, Word, and Non-Word Problem Solving.” Learning and Individual Differences 54 (February 2017): 20–29. https://doi.org/10.1016/j.lindif.2017.01.005.
Okoye, Grace Nwakaego, and Edith Chinyere Onyeka. “Application of Geotrigmetric Set and Geoboard on Studentsretention in Mathematics in Rivers State Nigeria.” African Journal of Educational Management, Teaching and Entrepreneurship Studies 7, no. 2 (2022): 82–97.
Olley, P., J. Archer, D. Copley, P. Core, and A. Mincher. “Analysis and Design of a Centrifugal Filter Geometry for Entrained Particle Separation.” Journal of Aerosol Science 41, no. 9 (September 2010): 848–58. https://doi.org/10.1016/j.jaerosci.2010.05.004.
Onyeka, Edith Chinyere, and G N Okoye. “Effectiveness of Demonstration Teaching Method on Student Academic Achievement in Mathematics in Rivers State Nigeria.” African Journal of Educational Management, Teaching and Entrepreneurship Studies 8, no. 2 (2023): 32–42.
Rabuya, Cristobal A. “Factors Related to Mathematics Anxiety among Senior High School Students in Basic and Pre-Calculus: A Descriptive CROSS-Sectional Psychological Study.” Journal for ReAttach Therapy and Developmental Diversities 6, no. 9s (2023): 183–90.
Rahmiati, Rahmiati, Mutia Putri, Engkizar Engkizar, and Marzni Mohamed Mokhtar. “The Effectiveness of Flipbook-Based e-Modules in Increasing Student Creativity in Nail Art Subject in Higher Education.” Jurnal Pendidikan Vokasi 13, no. 2 (2023).
Retnawati, Heri, Janu Arlinwibowo, and Eny Sulistyaningsih. “The Students’ Difficulties in Completing Geometry Items of National Examination.” International Journal 8, no. 4 (2017): 03.
Rohendi, Acep. “Consumer Protection in the E-Commerce: Indonesian Law and International Law Perspective.” Berkman Center Research Publication, Forthcoming, 2015.
Rohendi, D, S Septian, and H Sutarno. “The Use of Geometry Learning Media Based on Augmented Reality for Junior High School Students.” In IOP Conference Series: Materials Science and Engineering, 306:012029. IOP Publishing, 2018.
Scandrett, Hilary. “Using Geoboards in Primary Mathematics: Going… Going… Gone?” Australian Primary Mathematics Classroom 13, no. 2 (2008): 29–32.
Sfard, Anna. Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. Cambridge university press, 2008.
Shulman, Lee. “Knowledge and Teaching:Foundations of the New Reform.” Harvard Educational Review 57, no. 1 (April 1, 1987): 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411.
Siaw, Anthony, Yuansheng Jiang, Martinson Ankrah Twumasi, and Wonder Agbenyo. “The Impact of Internet Use on Income: The Case of Rural Ghana.” Sustainability 12, no. 8 (April 17, 2020): 3255. https://doi.org/10.3390/su12083255.
Sibiya, Mandlenkosi Richard. “The Effect of Geoboard Use on Learners’ Motivation for Learning of Geometry Theorems.” International Journal of Sciences and Research 75, no. 6/1 (2019).
Sulistiowati, D L, T Herman, and A Jupri. “Student Difficulties in Solving Geometry Problem Based on Van Hiele Thinking Level.” Journal of Physics: Conference Series 1157 (February 2019): 042118. https://doi.org/10.1088/1742-6596/1157/4/042118.
Sunzuma, Gladys, and Aneshkumar Maharaj. “In-Service Teachers’ Geometry Content Knowledge: Implications for How Geometry Is Taught in Teacher Training Institutions.” International Electronic Journal of Mathematics Education 15, no. 1 (May 14, 2019). https://doi.org/10.29333/iejme/5776.
Tachie, Simon A. “The Challenges of South African Teachers in Teaching Euclidean Geometry.” International Journal of Learning, Teaching and Educational Research 19, no. 8 (August 30, 2020): 297–312. https://doi.org/10.26803/ijlter.19.8.16.
Tan, Tong Hock, Rohani Ahmad Tarmizi, Aida Suraya Md. Yunus, and Ahmad Fauzi Mohd. Ayub. “Understanding the Primary School Students’ van Hiele Levels of Geometry Thinking in Learning Shapes and Spaces: A Q-Methodology.” EURASIA Journal of Mathematics, Science and Technology Education 11, no. 4 (August 25, 2015). https://doi.org/10.12973/eurasia.2015.1439a.
Dr. Thabisa Maqoqa is currently a permanent lecturer at the Faculty of Educational Sciences in the Department of Adult, Foundation Phase & Educational Foundations Education, Walter Sisulu University, Mthatha, Eastern Cape, South Africa. Her research focuses on Parental Involvement and Technology Integration in Mathematics teaching.
Maqoqa, Thabisa. “An Exploration of Learners’ Understanding of Euclidean Geometric Concepts: A Case Study of Secondary Schools in the OR Tambo Inland District of the Eastern Cape,” E-Journal of Humanities, Arts and Social Sciences 5, no.5 (2024): 658 – 675. https://doi.org/10.38159/ehass.2024557
© 2024 The Author(s). Published and Maintained by Noyam Journals. This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).
Others
