Journal of Pedagogical Sociology and Psychology
Rethinking the teaching of Euclidean geometry
Kambila J. Kyabuntu 1, Hlamulo W. Mbhiza 1 *
More Detail
1 Department of Mathematics Education, University of South Africa
* Corresponding Author
Open Access Full Text (PDF)
ARTICLE INFO

Journal of Pedagogical Sociology and Psychology, 2024 - Volume 6 Issue 3, pp. 49-63
https://doi.org/10.33902/jpsp.202427063

Article Type: Research Article

Published Online: 12 Jul 2024

Views: 373 | Downloads: 213

ABSTRACT
Euclidean geometry teaching and learning in South Africa has a unique history. It is one of the topics that are characterised by teaching-learning difficulties as demonstrated by learner underachievement related to the topic. There is death of research that explored teachers’ explanatory talk during Euclidean geometry lessons. Thus, to address this research gap, within qualitative research approach, we employed non-structured classroom observations with 6 teachers, to explore and understand how they make Euclidean geometry concepts and principles available for the learners. We used Adler and Ronda’s concept of explanatory talk to make sense of teachers’ classroom practices. We used content analysis to understand what teachers said and write on the board during teaching. In this paper, we focus on one of the four teachers’ lesson, to demystify how their explanatory talk or lack thereof made geometry concepts available for learners to learn. The findings reveal that the teacher used questions-and-answer strategy to engage learners in the lessons but did not provide explanations to the learners during the lesson, to guide them on the nature of the concepts and their relatedness.     
KEYWORDS
Euclidean geometry explanatory talk teaching teachers observations
In-text citation: (Kyabuntu & Mbhiza, 2024)
Reference: Kyabuntu, K. J., & Mbhiza, H. W. (2024). Rethinking the teaching of Euclidean geometry. Journal of Pedagogical Sociology and Psychology, 6(3), 49-63. https://doi.org/10.33902/jpsp.202427063
In-text citation: (1), (2), (3), etc.
Reference: Kyabuntu KJ, Mbhiza HW. Rethinking the teaching of Euclidean geometry. Journal of Pedagogical Sociology and Psychology. 2024;6(3), 49-63. https://doi.org/10.33902/jpsp.202427063
In-text citation: (1), (2), (3), etc.
Reference: Kyabuntu KJ, Mbhiza HW. Rethinking the teaching of Euclidean geometry. Journal of Pedagogical Sociology and Psychology. 2024;6(3):49-63. https://doi.org/10.33902/jpsp.202427063
In-text citation: (Kyabuntu and Mbhiza, 2024)
Reference: Kyabuntu, Kambila J., and Hlamulo W. Mbhiza. "Rethinking the teaching of Euclidean geometry". Journal of Pedagogical Sociology and Psychology 2024 6 no. 3 (2024): 49-63. https://doi.org/10.33902/jpsp.202427063
In-text citation: (Kyabuntu and Mbhiza, 2024)
Reference: Kyabuntu, K. J., and Mbhiza, H. W. (2024). Rethinking the teaching of Euclidean geometry. Journal of Pedagogical Sociology and Psychology, 6(3), pp. 49-63. https://doi.org/10.33902/jpsp.202427063
In-text citation: (Kyabuntu and Mbhiza, 2024)
Reference: Kyabuntu, Kambila J. et al. "Rethinking the teaching of Euclidean geometry". Journal of Pedagogical Sociology and Psychology, vol. 6, no. 3, 2024, pp. 49-63. https://doi.org/10.33902/jpsp.202427063
REFERENCES
  • Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching. African Journal of Research in Mathematics, Science and Technology Education, 19(3), 237-254. https://doi.org/10.1080/10288457.2015.1089677
  • Adler, J., & Ronda, E. (2017). Mathematical discourse in instruction matters. In J. Adler & A. Sfard (Eds.), Research for educational change. Transforming researchers’ insights into improvement in mathematics teaching and learning, (pp. 64-81). Routledge.
  • Adler, J., Venkat, H., (2014). Teachers’ mathematical discourse in instruction: focus on examples and explanations. In Venkat, H., Rollnick, M., Loughran, J., Askew, M. (Eds.), Exploring Mathematics and Science Teachers’ Knowledge: Windows into Teacher Thinking (pp. 132-146). Routledge. https://doi.org/10.4324/9781315883090
  • Alex, J. K., & Mammen, J. K. (2016). Geometrical sense making: Findings of analysis based on the characteristics of the van Hiele theory among a sample of South African grade 10 learners. Eurasia Journal of Mathematics, Science and Technology Education, 12(2), 173-188. https://doi.org/10.12973/eurasia.2016.1211a
  • Baiduri, B., Ismail, A. D., & Sulfiyah, R. (2020). Understanding the concept of visualization phase student in geometry learning. International Journal of Scientific & Technology Research, 9(2), 2353-2359.
  • Bansilal, S., & Ubah, I. (2019). The use of semiotic representations in reasoning about similar triangles in Euclidean geometry. Pythagoras, 40(1), 1-10. https://doi.org/10.4102/pythagoras.v40i1.480
  • Bell, A. J. (2005). "Oh yes, I remember it well!" Reflections on using the life-grid in qualitative interviews with couples. Qualitative Sociology Review, 1(1), 51-67. https://doi.org/10.18778/1733-8077.1.1.04
  • Bonnie, L., & Lawes, E. (2016). Assessing students’ maths self-efficacy and achievement. Assessment News, 2, 60-63. https://doi.org/10.18296/set.0048
  • Charalambous, C. Y., Hill, H. C., & Ball, D. L. (2011). Prospective teachers’ learning to provide instructional explanations: How does it look and what might it take?. Journal of Mathematics Teacher Education, 14, 441-463. https://doi.org/10.1007/s10857-011-9182-z
  • Cohen, L., Manion, L., & Morrison, K. (2013). Research methods in education. Hoboken. https://doi.org/10.4324/9780203720967
  • Cohen, M. F. (2011). An introduction to logic and scientific method. Read Books Ltd.
  • Couto, A., & Vale, I. (2014). Pre-service teachers’ knowledge on elementary geometry concepts. Journal of the European Teacher Education Network, 9, 57–73.
  • Department of Basic Education. (2011). Curriculum and assessment policy statement. Mathematics Grades 10–12. DBE.
  • Department of Basic Education. (2017). National senior certificate schools subject report. DBE. https://www.education.gov.za/Portals/0/Documents/Reports/2017%20School%20Subject%20Report.pdf?ver=2018-01-04-034704-000
  • Department of Basic Education. (2018). National Senior Certificate Schools Subject Report. Pretoria: DBE. https://www.education.gov.za/Portals/0/Documents/Reports/NSC%202018%20School%20Subject%20Report%20WEB.pdf?ver=2019-01-03-093412-000
  • Department of Basic Education. (2019). National Senior Certificate Schools Subject Report. Pretoria: DBE. https://www.education.gov.za/Portals/0/Documents/Reports/2019%20NSC%20School%20Subject%20Report.pdf?ver=2020-01-07-135604-000
  • Gresham, G., & Shannon, T. (2017). Building mathematics discourse in students. Teaching Children Mathematics, 23(6), 360-366. https://doi.org/10.5951/teacchilmath.23.6.0360
  • Guthrie, G. (2011). The progressive education fallacy in developing countries: In favour of formalism. Springer. https://doi.org/10.1007/978-94-007-1851-7
  • Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 65–97). Macmillan Pub.
  • Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1-11. https://doi.org/10.4102/pythagoras.v36i1.261
  • Lynch, S. D., & Bolyard, J. J. (2012). Putting mathematical discourse in writing. Mathematics Teaching in the Middle School, 17(8), 486-492. https://doi.org/10.5951/mathteacmiddscho.17.8.0486
  • Mabotja, K. S. (2017). An exploration of folding back in improving grade 10 students’ reasoning in geometry [Unpublished master’s thesis]. University of Limpopo, Mankweng, South Africa.
  • Machisi, E. (2021). Grade 11 students’ reflections on their Euclidean geometry learning experiences. EURASIA Journal of Mathematics, Science and Technology Education, 17(2), em1938. https://doi.org/10.29333/ejmste/9672
  • Marange, I. Y., & Tatira, B. (2023). Teaching Euclidean geometry with GeoGebra: Perceptions for in-service mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 19(12), em2367. https://doi.org/10.29333/ejmste/13861
  • Maree, K. (2007). First steps in research. Van Schaik Publishers.
  • Mbhiza, H. W. (2021). Grade 10 mathematics teachers’ discourses and approaches during algebraic functions lessons in Acornhoek, rural Mpumalanga Province, South Africa [Unpublished doctoral dissertation]. University of the Witwatersrand, Johannesburg.
  • McAndrew, E. M., Morris, W. L., & Fennell, F. (2017). Geometry‐related children's literature improves the geometry achievement and attitudes of second‐grade students. School Science and Mathematics, 117(1-2), 34-51. https://doi.org/10.1111/ssm.12202
  • McMillan, J. H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry. Pearson.
  • Ngirishi, H., & Bansilal, S. (2019). An exploration of high school learners’ understanding of geometric concepts. Problems of Education in the 21st Century, 77(1), 82. https://doi.org/10.33225/pec/19.77.82
  • Ozkan, A., Ozkan, E. M., & Karapıcak, S. (2018). On the misconceptions of 10th grade students about analytical geometry. The Educational Review, 2(8), 417-426. https://doi.org/10.26855/er.2018.08.002
  • Scott, P., Mortimer, E., & Ametller, J. (2011). Pedagogical link-making: A fundamental aspect of teaching and learning scientific conceptual knowledge. Studies in Science Education, 47(1), 3–36. https://doi.org/10.1080/03057267.2011.549619
  • Sequeira, J., & Ferreira, I. (2014). The concept of [Robot] in children and teens: Some guidelines to the design of social robots. International Journal of Signs and Semiotic Systems (IJSSS), 3(2), 43-57. https://doi.org/10.4018/IJSSS.2014070104
  • Sfard, A. (2019). Learning, discursive faultiness and dialogic engagement. In N. Mercer, R. Wegerif, & L. Major (Eds.), The Routledge international handbook of research on dialogic education (pp. 89-99). Routledge. https://doi.org/10.4324/9780429441677-9
  • Sibiya, M. R. (2020). A reconsideration of the effectiveness of using geoboard in teaching euclidean geometry. EURASIA Journal of Mathematics, Science and Technology Education, 16(9), em1876. https://doi.org/10.29333/ejmste/8360
  • Siyepu, S. W., & Mtonjeni, T. (2014, July). Geometrical concepts in real-life context: A case of South African traffic road signs [Paper presentation]. 20th Annual National Congress of the Association for Mathematics Education of South Africa, Kimberley, Northern Cape.
  • Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20-26.
  • Tachie, S. A. (2020). Teachers' attitudes towards lesson study as a viable strategy to improve the teaching and learning of mathematics. Universal Journal of Educational Research, 8(6), 2326-2334. https://doi.org/10.13189/ujer.2020.080616
  • Tutak, F. A., & Adams, T. L. (2015). A study of geometry content knowledge of elementary preservice teachers. International Electronic Journal of Elementary Education, 7(3), 301-318.
  • Ugorji, I. O., & Alfred, C. (2017, October). The impact of using GeoGebra to teach circle geometry on grade 11 students' achievement [Paper presentation]. UNISA/ISTE Conference on Mathematics, Science and Technology Education, Mopani Camp in Kruger National Park, Limpopo, South Africa.
  • Utami, A. K. D., Mardiyana, M., & Pramudya, I. (2017, August). Analysis of junior high school students’ difficulty in resolving rectangular conceptual problems. AIP Conference Proceedings, 1868(1), 050008. https://doi.org/10.1063/1.4995135
  • Vygotsky, L. S. (1987). The collected works of LS Vygotsky: Problems of the theory and history of psychology. Springer.
  • Wei, R. C., Darling-Hammond, L., Andree, A., Richardson, N., & Orphanos, S. (2017). An alternative way of solving geometry riders in grade 12: Back to synthesis and analysis. In T. Penlington & C. Chikiwa (Eds.), Proceedings of the 23rd Annual National Congress of the Association for Mathematics Education of South Africa (pp. 19-27). Association for Mathematics Education of South Africa.
  • Wentzel, V. D. (2016). Primary school teachers' experiences of providing learning support for learners with mild intellectual disabilities (Doctoral dissertation, University of South Africa).
  • Wittwer, J., & Renkl, A. (2008). Why instructional explanations often do not work: A framework for understanding the effectiveness of instructional explanations. Educational Psychologist, 43(1), 49-64. https://doi.org/10.1080/00461520701756420
LICENSE
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.