Ordinary-level learners’ errors in solving simultaneous linear equations at a Zimbabwean secondary school
Young Mudavanhu 1 * , Conilius Jaison Chagwiza 2, Andrew Mashungu 3
More Detail
1 Bindura University of Science Education, Zimbabwe
2 Department of Science and Mathematics Education, Faculty of Science Education, Bindura, Zimbabwe
3 Department of Science and Mathematics Education, Faculty of Science Education, Bindura, Zimbabwe
* Corresponding Author


This study sought to reveal the ordinary level learners’ errors in solving simultaneous linear equations using any method of their choice at a secondary school in Chikomba district of Zimbabwe. The study used convenience sampling to select 100 learners. In the qualitative methodology adopted, data was gathered using transcripts of an achievement test and structured interviews. The study used content analysis of selected tasks to expose learners’ mental construction when solving the simultaneous linear equations.  The Ordinary Level learners consistently made procedural errors when they used the substitution, the elimination, and the matrix methods. The researchers recommend future studies to build on the loopholes of these ever-present methods and invest in hybrid ways of solving simultaneous linear equations.



  • Alghazo, Y. M., & Alghazo, R. (2017). Exploring common misconceptions and errors about fractions among college students in Saudi Arabia. International Education Studies, 10(4), 133-140. https://doi.org/10.5539/ies.v10n4p133
  • Banerjee, R., & Subramaniam, K. (2012). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics, 6(4), 351-367. https://doi.org/10.1007/s10649-011-9353-y
  • Chagwiza, C. J., Mutambara, L. H., & Sunzuma, G. (2021). Exploring Zimbabwean A-Level Mathematics Learners’ Understanding of the Determinant Concept. European Journal of Mathematics and Science Education, 2(2), 85-100.
  • Channon, J. B., Smith, A. M., Head, H. C., Macrae, M. F., & Chasakara, A. F. (2004). New general mathematics book 1: A Junior Certificate Course. Longman.
  • Chikwanha, P., Mudavanhu, Y. & Chagwiza, C. J. (2022). Exploring Errors and Misconceptions in Differentiation: A Case Study Of Advanced Level Students in Zimbabwe. International journal of Social Science Research, 10(2), 1-19. https://doi.org/10.5296/ijssr.v10i2.1981
  • Clark, M. K. (2012). History of mathematics: Illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educational studies in Mathematics, 81, 67-84. https://doi.org/10.1007/s10649-011-9361-y
  • Ellis, M. (2021). Recognising Misconceptions as opportunities for Learning Mathematics with Understanding. Carlifonia State University.
  • Godden, H., Mbekwa, M., & Julie, C. (2013). An analysis of errors and misconceptions in the 2010 grade 12 mathematics examination: A focus on quadratic equations and inequalities. In Z. Davis & S. Jaffer (Eds.) Proceedings of the 19th Annual Congress of the Association for Mathematics Education of South Africa (pp. 70-79). Association for Mathematics Education of South Africa.
  • Hansen, A. (2006). Children’s errors in mathematics. Learning Matters.
  • Johari, M.A.R, & Shahrill , M. (2020). The common errors in the learning of the simultaneous equations. In Infinity, 9(2), 263-274. https://doi.org/10.22460/infinity.v912.p263-274
  • Kazunga, C., & Bansilal, S. (2020). An APOS analysis of solving systems of equations using the inverse matrix method. Educ Stud Math, 103, 339-358. https://doi.org/10.1007/s10649-020-09935-6
  • Low, J., Shahrill, M., & Zakir, N. (2020). Solving fractions by applying the bar model concept with the butterfly method. Jurnal Pendidikan Matematika, 14(2), 101-116. https://doi.org/10.22342/jpm.14.2.11261.101-116
  • Lucariello, J., & Naff, D. (2014). How do I get my students over their alternative conceptions (misconceptions) for learning? Removing barriers to aid in the development of the student. American Psychological Association Coalition for Psychology in the Schools. http://www.apa.org/education/k12/misconceptions.aspx
  • Luneta, K., & Makonye, P. J. (2010). Learner errors and misconception in elementary analysis: A case study of a grade 11 class in South Africa. Acta Didactica Napocensia, 3(3), 35-46.
  • Makonye, J. P. (2014). Learner mathematical errors in introductory differential calculus [Unpublished doctoral dissertation]. University of Johannesburg, Johannesburg Gauteng.
  • Msomi, A. M., & Bansilal , S. (2022). Analysis of Students’ Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform. International Electronic Journal of Mathematics Education, 17(2), em0670. https://doi.org/10.29333/iejme/11474
  • Mulungye, M. M. (2016). Sources of students’ errors and misconceptions in algebra and influence of classroom practice remediation in secondary schools Machakos Sub-County, Kenya [Unpublished master’s thesis]. Kenyatta University, Nairobi.
  • Mutambara, L., & Bansilal, S. (2019). An exploratory study on the understanding of the vector subspace concept. African Journal of Research in Mathematics, Science and Technology, 23(1), 14-26. https://doi.org/10.1080/18117295.2018.1564496
  • Naseer, M. S. (2015). Analysis of students’ errors and misconceptions in pre-university mathematics courses. In M. N. Salleh, & N. F. Z. Abedin, (Eds.), Proceedings: First International Conference on Teaching & Learning 2015 (pp. 34-39). MNNF Publisher.
  • Orton, A. (1983). Students’ understanding of differentiation. Educational Studies in Mathematics, 14, 235-250. https://doi.org/10.1007/BF00410540
  • Roselizawati, H., Sawardi, H., & Shahrill, M. (2014). Understanding stuents' mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, metr-00051. https://doi.org/10.5899/2014/metr-00051
  • Sadler, P. M., Sonnert, G., Coyle, H. P., Cook-Smith, N., & Miller, J. L. (2013). The influence of teachers’ knowledge on student learning in middle school physical science classrooms. American Educational Research Journal, 50(5), 1020-1049. https://doi.org/10.3102/0002831213477680
  • Siyepu, S. W. (2013). Students’ interpretations in learning derivatives in a university mathematics classroom. In Z. Davis & S. Jaffer (Eds.), Proceedings of the 19th annual congress of the association for mathematics education of South Africa (pp.183−193). AMESA. https://doi.org/10.15700/saje.v33n2a714
  • Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric. International Journal of STEM Education, 2(1), 1-16.
  • Tendere, J., & Mutambara, L. H. (2020). An analysis of errors and misconceptions in the study of quadratic equations. European Journal of Mathematics and Science Education, 1(2), 81-90. https://doi.org/10.12973/ejmse.1.2.81
  • Ugboduma, S. O. (2012). Students' preference of method of solving simultaneous equations. Global Journal of Educational Research, 11(2), 129-136. http://doi.org/10.4314/gjedr.v11i2.8
  • Welder, R. M. (2012). Improving Algebra Preparation: Implications from Research on Student Misconceptions and Difficulties. School Science and Mathematics, 112(4), 255-264. https://doi.org/10.1111/j.1949-8594.2012.00136.x
  • Ministroy of Primary and Secondary Education. (2023). Zimbabwe curriculum framework for primary and secondary education 2015-2022. Retrieved March 23, 2023 from http://mopse.co.zw


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.