Grade 11 Students’ Reflections on their Euclidean Geometry Learning Experiences

Eric Machisi

doi:10.29333/ejmste/9672

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Eric Machisi ¹ ^*

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¹ University of South Africa, SOUTH AFRICA^* Corresponding Author

Abstract

The teaching of Euclidean geometry is a matter of serious concern in South Africa. This research, therefore, examined the Euclidean geometry learning experiences of 16 Grade 11 students from four South African secondary schools. Data were obtained using focus group discussions and student diary records. Students who were taught using a Van Hiele theory-based approach reported positive learning experiences in Euclidean geometry, while those who were taught using conventional methods reported negative learning experiences. It was concluded that the Van Hiele theory-based approach seems to meet students’ needs better than conventional approaches in learning Euclidean geometry. The use of unconventional teaching approaches such as Van Hiele theory-based instruction in the teaching and learning of Euclidean geometry is therefore recommended. Furthermore, teachers should give students an opportunity to evaluate the teaching approaches used in mathematics classrooms. Student input will help teachers change their teaching methods to suit the needs of the students.

Keywords

conventional instruction
Euclidean geometry
students’ reflections
Van Hiele theory-based instruction

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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.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 17, Issue 2, February 2021, Article No: em1938

https://doi.org/10.29333/ejmste/9672

Publication date: 03 Feb 2021

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Article Downloads: 6620

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

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. https://doi.org/10.17485/ijst/2013/v6i5.13
Abrahams, K., & Matthews, T. (2011). Child rights manual: Handbook for parliamentarians. Cape Town: Parliament of the Republic of South Africa.
Adeniji, S. M., Ameen, S. K., Dambatta, B., & Orilonise, R. (2018). Effects of mastery learning approach on senior school students’ academic performance and retention in circle geometry. International Journal of Instruction, 11(4), 951-962. https://doi.org/10.12973/iji.2018.11460a
Al-Khateeb, M. A. (2016). The extent of mathematics teachers’ awareness of their students’ misconceptions in learning geometrical concepts in the intermediate education stage. European Scientific Journal, 12(31), 357-372. https://doi.org/10.19044/esj.2016.v12n31p357
Anney, V. N. (2014). Ensuring the quality of the findings of qualitative research: looking at trustworthiness criteria. Journal of Emerging Trends in Educational Research and Policy, 5(2), 272-281.
Armah, R. B., Cofie, P. O., & Okpoti, C. A. (2018). Investigating the effect of Van Hiele phase-based instruction on pre-service teachers’ geometric thinking. International Journal of Research in Education and Science (IJRES), 4(1), 314-330. https://doi.org/10.21890/ijres.383201
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.
Baral, S., Uprety, S., & Lamichhane, B. (2016, March). Focus group discussion. Retrieved from Herd: http://www.herd.org.np/uploads/frontend/Publications/PublicationsAttachments1/1480653060-Focus%20Group%20Discussion_0.pdf
Bazeley, P., & Jackson, K. (2013). Qualitative data analysis with NVIVO. London: Sage Publications Ltd.
Bill, A., & Giles, D. (2016). Repositioning diagnostic school reviews using appreciative inquiry: A way of eliciting student voice for school improvement. Journal of Educational Leadership, Policy and Practice, 31(1), 165-179.
Bonnie, L., & Lawes, E. (2016). Assessing students’ maths self-efficacy and achievement. Assessment News, 2, 60-63. https://doi.org/10.18296/set.0048
Bowie, L. (2009, June). What is Mathematics Paper 3 for? Marang News, 5.
Bramlet, D. C., & Drake, C. T. (2013). The role of proof in the curriculum. Journal of Mathematical Sciences and Mathematics Education, 8(1), 62-72.
Busher, H. (2012). Students as expert witnesses of teaching and learning. Management in Education, 26(3), 113-119. https://doi.org/10.1177/0892020612445679
Bytheway, B. (2012). The use of diaries in qualitative longitudinal research. In B. Neale, & K. Henwood (Eds.), Timescapes Methods Guides Series 2012 Guide No. 7. Leeds: Economic and Social Research Council. Retrieved from http://www.timescapes.leeds.ac.uk/assets/files/methods-guides/timescapes-bytheway-use-of-diaries.pdf
Cato, N. (2018). Student voice in secondary schools: Purpose, value and characteristics. Auckland, New Zealand: Unitec Institute of Technology.
Craig, T., & Morgan, C. (2015). Language and communication in mathematics education. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematics Education (pp. 529-533). Cham: Springer. https://doi.org/10.1007/978-3-319-12688-3_53
De Villiers, M., & Heideman, N. (2014). Conjecturing, refuting and proving within the context of dynamic geometry. Learning and Teaching Mathematics, 17, 20-26.
Dell EMC. (2018, May). Empowering student voice and choice to deliver personalized education. Student Voice and Choice Whitepaper, 1-14.
Department of Education and Training. (2018). Amplify: Empowering students through voice, agency and leadership. East Melbourne, Victoria: State of Victoria.
Dilshad, R. M., & Latif, M. I. (2013). focus group interview as a tool for qualitative research: an analysis. Pakistan Journal of Social Sciences, 33(1), 191-198.
Dube, N. V. (2016). Teachers’ experiences of the implementation of the mathematics curriculum and assessment policy statement at the further education and training (FET) phase: Case Study. University of Fort Hare, Faculty of Education. East London: University of Fort Hare.
Duke, J. (2012). Joining the dots: Piloting the work diary as a data collection tool. Issues in Educational Research, 22(2), 111-126.
Elo, S., Kääriäinen, M., Kanste, O., Pölkki, T., Utriainen, K., & Kyngäs, H. (2014). Qualitative content analysis: A focus on trustworthiness. SAGE Open January-March 2014, 1-10. https://doi.org/10.1177/2158244014522633
Engelbecht, J., Harding, A., & Phiri, P. (2010). Are OBE-trained learners ready for university mathematics? Pythagoras, 72, 3-13. https://doi.org/10.4102/pythagoras.v0i72.16
Govender, R. (2014). Rider strategies for solving school geometry problems. In M. Lebitso, & A. Maclean (Eds.), Proceedings of the 20th Annual National Congress of the Association for Mathematics Education of South Africa: Demystifying Mathematics (pp. 4-5). Kimberley: AMESA.
Holloway, I., & Wheeler, S. (2010). Qualitative research in nursing and healthcare. Oxford, UK: Blackwell.
Jones, K., Fujita, T., & Kunimune, S. (2012). Promoting productive reasoning in the teaching of geometry in lower secondary school: Towards a future research agenda. In S. J. Cho (Ed.), Pre-proceedings of the 12th International Congress on Mathematical Education ICME-12 (pp. 2387-2396). Seoul, Korea: ICME.
Kanandjebo, L. N., & Ngololo, E. N. (2017). The effects of ‘geometry sketchpad’ on Grade 12 learners’ performance in geometry. International Electronic Journal of Mathematics Education, 12(3), 735-747.
Keiler, L. S. (2018). Teachers’ roles and identities in student-centered classrooms. International Journal on STEM Education, 5(1), 1-20. https://doi.org/10.1186/s40594-018-0131-6
Knight, W. E. (2012). Using focus groups. In W. E. Knight, & R. A. Costomiris (Ed.), Ball State University Assessment Workbook (pp. 49-54). Muncie: Office of Institutional Effectiveness, Ball State University. Retrieved from https://www.bsu.edu/-/media/www/departmentalcontent/effectiveness/pdfs/wkbk/assessment%20workbook%20-%2020121.pdf?la=en
Köǧce, D., Aydιn, M., & Yιldιz, C. (2010). The views of high school students about proof and their levels of proof: The case of Trabzon. Procedia Social and Behavioral Sciences, 2, 2544-2549. https://doi.org/10.1016/j.sbspro.2010.03.370
Krueger, R. A. (2002, October). Designing and conducting focus group interviews. St. Paul, MN: University of Minnesota. Retrieved from https://www.eiu.edu/ihec/Krueger-FocusGroupInterviews.pdf
Kuhn, G. (2016, November 16). What is a moderator’s guide? Focus groups upstate NY. Retrieved from Drive Research: https://www.driveresearch.com/single-post/2016/10/30/What-is-a-Moderators-Guide-Focus-
Machisi, E., & Feza, N. N. (in press). Van Hiele theory-based instruction and Grade 11 students’ geometric proof competencies. Contemporary Mathematics and Science Education.
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.
Mostafa, M., Javad, L. M., & Reza, O. H. (2017). The effect of Van Hiele theory-based teaching educational package on achievement goal orientation of student teachers. Review of European Studies, 9(1), 93-105. https://doi.org/10.5539/res.v9n1p93
Mouton, N., Louw, G. P., & Strydom, G. L. (2012). A historical analysis of the post-apartheid dispensation education in South Africa (1994-2011). International Business and Economics Research Journal, 11(11), 1211-1222. https://doi.org/10.19030/iber.v11i11.7369
Mudaly, V. (2016). Pre-service teachers’ understanding of the concept of proof. International Scientific Researches Journal, 72(5), 137-158. https://doi.org/10.21506/j.ponte.2016.5.15
Mukamba, E., & Makamure, C. (2020). Integration of GeoGebra in teaching and learning geometric transformations at Ordinary Level in Zimbabwe. Contemporary Mathematics and Science Education, 1(1), ep20001. https://doi.org/10.30935/conmaths/8431
Mulwa, E. C. (2014). The role of language of mathematics in students’ understanding of number concepts in Eldoret Municiplaity, Kenya. International Journal of Humanities and Social Science, 4(3), 264-274.
Mwadzaangati, L. (2015). Mathematical knowledge for teaching geometric proof: Learning from teachers’ practices. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 3308-3308). Prague, Czech Republic: CERME.
Naidoo, J., & Kapofu, W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education, 40(1), 1-11. https://doi.org/10.15700/saje.v40ns2a1717
Naziev, A. (2018). The role of language in teaching and learning mathematics. BRAIN-Broad Research In Artificial Intelligence and Neuroscience, 9(1), 114-124.
Ndlovu, M. (2013). The learning of geometry as moving from one thinking level to the next: revising Van Hiele. In Z. Davies, & S. Jaffer (Ed.), Proceedings of the 19th Annual Congress of the Association for Mathematics Education of South Africa (pp. 277-279). Cape Town: AMESA.
Ngirishi, H., & Bansilal, S. (2019). An exploration of high school learners’ understanding of geometric concepts. Problems of Education in the 21st Century, 77(1), 82-96. https://doi.org/10.33225/pec/19.77.82
Olivier, W. (2013, May). Reflection on the training of teachers for the CAPS mathematics curriculum - a brief report. Retrieved from SAMF: http://www.samf.ac.za/documents/CAPS_mathematics_curriculum.pdf
Olivier, W. (2014, April). Reflections on the Implementation of CAPS Mathematics in the Classroom. Retrieved from SAMF: http://www.samf.ac.za/documents/Reflections_on_implementation_of_CAPS_Mathematics_in_the_Classroom.pdf
Oueini, S. (2019). The impact of intelligent tutoring software on geometry students. University of South Carolina. California: University of South Carolina Scholar Commons.
Padayachee, P., Boshoff, H., Olivier, W., & Harding, A. (2011). A blended learning Grade 12 intervention using DVD technology to enhance teaching and learning of mathematics. Pythagoras, 32(1), 1-8. https://doi.org/10.4102/pythagoras.v32i1.24
Pearson, D., & Vossler, A. (2016). Methodological issues in focus group research. Counselling Psychology Review, 31(1), 8-16.
Rausch, A. (2014). Using diaries in research on work and learning. In C. Harteis, A. Rausch, J. Seifried, C. Harteis, A. Rausch, & J. Seifried (Eds.), Discourses on Professional Learning: On the Boundary Between Learning and Working (pp. 341-366). Dordrecht: Springer.
Reid, S., & Mash, B. (2014). African primary care research: Qualitative interviewing in primary care. African Journal of Primary Health Care and Family Medicine, 6(1), 1-6. Retrieved from https://doi.org/10.4102/phcfm.v6i1.632
Rennie Center for Education Research and Policy. (2019). Student voice: How young people can shape the future of education. Boston, MA: Rennie Center for Education Research and Policy.
Robertson, S.-A., & Graven, M. (2019). Language as an including or excluding factor in mathematics teaching and learning. Mathematics Education Research Journal, 32(1), 77-101. https://doi.org/10.1007/s13394-019-00302-0
Saldana, J. (2013). The coding manual for qualitative researchers. London: Sage Publications Ltd.
Sheble, L., & Wildemuth, B. (2009). Research diaries. In B. Wildemuth (Ed.), Applications of Social Research Methods to Questions in Information and Library Science (pp. 211-221). Santa Barbara, CA: Libraries Unlimited.
Siyepu, S. (2014). Analysis of Van Hiele’s theory in circle geometry: A Focus in FET level. In M. Lebitso, & A. Maclean (Eds.), Proceedings of the 20th Annual National Congress of the Association for Mathematics Education of South Africa: Demystifying Mathematics (pp. 61-63). Kimberley: AMESA.
Sun, H. (2014). Rapport and its impact on the disclosure of sensitive information in standardized interviews. University of Maryland, Faculty of Graduate School. College Park: University of Maryland.
Tachie, S. A. (2020). The challenges of South African teachers in teaching euclidean geometry. International Journal of Learning, Teaching and Educational Research, 19(8), 297-312. https://doi.org/10.26803/ijlter.19.8.16
Tahani, A. (2016). Effects of Van Hiele Model in geometric concepts acquisition: The attitudes towards geometry and learning transfer effect of the first three grades students in Jordan. International Education Studies, 9(4), 87-98. https://doi.org/10.5539/ies.v9n4p87
Thomas, E., & Magilvy, J. K. (2011). Qualitative rigour or research validity in qualitative research. Journal for Specialists in Pediatric Nursing, 16(2), 151-155. https://doi.org/10.1111/j.1744-6155.2011.00283.x
Usman, H., Yew, W. T., & Saleh, S. (2019). Effects of Van Hiele’s phase-based teaching strategy and gender on pre-service mathematics teachers’ attitude towards geometry in Niger State, Nigeria. African Journal of Educational Studies in Mathematics and Sciences, 15(1), 61-75.
Van Hiele, P. M. (1984). A Child’s thought and geometry. In D. Fuys, D. Geddes, & R. Tischler (Eds.), English Translation of Selected Writings of Dina Van Hiele-Geldof and Pierre M. Van Hiele (pp. 247-256). Brooklyn, NY: Brooklyn College.
Van Hiele-Geldof, D. (1984). The didactic of geometry in the lowest class of secondary school. In D. Fuys, D. Geddes, & R. Tischler (Eds.), English Translation of Selected Writings of Dina Van Hiele-Geldoff and Pierre M. Van Hiele (pp. 10-222). Brooklyn, NY: Brooklyn College.
Wang, X. (2013). Why students choose STEM majors: Motivation, high school learning and postsecondary context of support. American Educational Research Journal, 50(5), 1081-1121. https://doi.org/10.3102/0002831213488622
White, K. (2006). Self-selected sample. In K. White, The Sage Dictionary of Health and Society (p. 188). London: Sage. https://doi.org/10.4135/9781446215159
Woll, H. (2013). Process diary as methodological approach in longitudinal phenomenological research. Indo-Pacific Journal of Phenomenology, 13(2), 1-11. https://doi.org/10.2989/IPJP.2013.13.2.2.1176A
Wolmarans, N., Smit, R., Collier-Reed, B., & Leather, H. (2010). Addressing concerns with the NSC: An analysis of first-year student performance in Mathematics and Physics. In V. Mudaly (Ed.), Proceedings of the 18th Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (pp. 274-284). KwaZulu-Natal.
Yi, J.-Y. (2008). The use of diaries as a qualitative research method to investigate teachers’ perception and use of rating schemes. Journal of Pan-Pacific Association of Applied Linguistics, 12(1), 1-10.
Yılmazer, Z., & Keklikci, H. (2015). The effects of teaching geometry on the academic achievement by using puppet method. Procedia-Social and Behavioral Sciences, 191, 2355-2358. https://doi.org/10.1016/j.sbspro.2015.04.463

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APA

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

Vancouver

Machisi E. Grade 11 Students’ Reflections on their Euclidean Geometry Learning Experiences. EURASIA J Math Sci Tech Ed. 2021;17(2):em1938. https://doi.org/10.29333/ejmste/9672

AMA

Machisi E. Grade 11 Students’ Reflections on their Euclidean Geometry Learning Experiences. EURASIA J Math Sci Tech Ed. 2021;17(2), em1938. https://doi.org/10.29333/ejmste/9672

Chicago

Machisi, Eric. "Grade 11 Students’ Reflections on their Euclidean Geometry Learning Experiences". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 2 (2021): em1938. https://doi.org/10.29333/ejmste/9672

Harvard

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

MLA

Machisi, Eric "Grade 11 Students’ Reflections on their Euclidean Geometry Learning Experiences". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 2, 2021, em1938. https://doi.org/10.29333/ejmste/9672