Main Article Content


The purpose of this study is to understand the causes of common errors and misconceptions in the learning attainment of simultaneous equations, specifically on linear and non-linear equations with two unknowns. The participants consisted of 30 Year 9 students in one of the elite government schools in Brunei Darussalam. Further analyses of their work led to the categorisation of four factors derived from the recurring patterns and occurrences. These four factors are complicating the subject, wrong substitution of the subject, mathematical error and irrational error in solving the question. These factors usually cause participants to make errors or simply misconceptions that usually led them to errors in solving simultaneous equations.


Simultaneous equations Errors Misconceptions Secondary Mathematics Brunei Darussalam

Article Details


  1. Chua, G. L. L., Shahrill, M., & Tan, A. (2016). Common misconceptions of algebraic problems: Identifying trends and proposing possible remedial measures. Advanced Science Letters, 22(5/6), 1547-1550. doi:10.1166/asl.2016.6675
  2. Häggström, J. (2008). Teaching systems of linear equations in Sweden and China: What is made possible to learn? Unpublished doctoral dissertation, University of Gothenburg Studies, Sweden.
  3. Jaggi, V. P. (2006). Dictionary of mathematics (1st Ed.). Nigeria: Educational Printing and Publishing, 92, 222.
  4. Khalid, M. (2006). Mathematical thinking in Brunei curriculum: implementation issues and challenges. In APEC-TSUKUBA International Conference. Tokyo. Retrieved on March 12, 2020 from
  5. Khoo, J. S., Shahrill, M., Yusof, N., Chua, G. L. L., & Roslan, R. (2016). Graphic organizer in action: Solving secondary mathematics problems. Journal on Mathematics Education, 7(2), 83-90. doi:10.22342/jme.7.2.3546.83-90
  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. doi:10.22342/jpm.14.2.11261.101-116
  7. Matzin, R., Shahrill, M., Mahalle, S., Hamid, M. H. S., & Mundia, L. (2013). A comparison of learning styles and study strategies scores of Brunei secondary school students by test anxiety, success attributions, and failure attributions: Implications for teaching at-risk and vulnerable students. Review of European Studies, 5(5), 119-127. doi:10.5539/res.v5n5p119
  8. Nordin, N. H., Tengah, K., Shahrill, M., Tan, A., & Leong, E. (2017). Using visual representations as an alternative in teaching simultaneous equations. Proceeding of the 3rd International Conference on Education, 3, 198-204.
  9. Rohmah, M., & Sutiarso, S. (2018). Analysis problem solving in mathematical using theory Newman. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 671-681. doi:10.12973/ejmste/80630
  10. Salam, N. H. A., & Shahrill, M. (2014). Examining classroom interactions in secondary mathematics classrooms in Brunei Darussalam. Asian Social Science, 10(11), 92–103. doi:10.5539/ass.v10n11p92
  11. Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, [Online] 1-10. doi:10.5899/2014/metr-00051
  12. Shahrill, M. (2009). From the general to the particular: Connecting international classroom research to four classrooms in Brunei Darussalam. Unpublished doctoral dissertation, University of Melbourne, Melbourne, Australia.
  13. Shahrill, M. (2018). Teachers’ devotion to review lessons: Insights to the mathematics lessons in Brunei Darussalam. Journal of Physics: Conference Series, 1028(1), 012158. doi:10.1088/1742-6596/1028/1/012158
  14. Shahrill, M., & Clarke, D. J. (2014). Brunei teachers’ perspectives on questioning: Investigating the opportunities to “talk” in mathematics lessons. International Education Studies, 7(7), 1–18. doi:10.5539/ies.v7n7p1
  15. Shahrill, M., & Clarke, D. J. (2019). Pedagogical features that influence mathematics classroom practices – A Bruneian perspective. Kasetsart Journal of Social Sciences, 40(2), 341–348. doi:10.34044/j.kjss.2019.40.2.06
  16. Shahrill, M., Mahalle, S., Matzin, R., Hamid, M. H. S., & Mundia, L. (2013). A comparison of learning styles and study strategies used by low and high math achieving Brunei secondary school students: Implications for teaching. International Education Studies, 6(10), 39-46. doi:10.5539/ies.v6n10p39
  17. Ugboduma, S. O. (2006). Effective methods of teaching mathematics as it affects Nigerian secondary schools. Journal of Knowledge Review, 12(1), 118-124.
  18. Ugboduma, S. O. (2012). Students’ preference of method of solving simultaneous equations. Global Journal of Educational Research, 11(2), 129-136. doi:10.4314/gjedr.v11i2.8
  19. Yahya, N., & Shahrill, M. (2015). The strategies used in solving algebra by secondary school repeating students. Procedia – Social Behavioural and Sciences, 186, 1192-1200. doi:10.1016/j.sbspro.2015.04.168
  20. Yunus, D. H. R. P. H., Shahrill, M., & Abdullah, N. A., & Tan, A. (2016). Teaching by telling: Investigating the teaching and learning of solving simultaneous linear equations. Advanced Science Letters, 22(5/6), 1551-1555. doi:10.1166/asl.2016.6676
  21. Zakir, N. (2018). The impact of educational change processes in Brunei preschools: An interpretive study. Unpublished doctoral dissertation, University of Sheffield, United Kingdom.