An Analysis of Errors and Misconceptions in the Study of Quadratic Equations
This study attempts to investigate the errors and misconception that form three students reveal using symbolic equation and word-problem representatio.
- Pub. date: December 15, 2020
- Pages: 81-90
- 1840 Downloads
- 1488 Views
- 0 Citations
This study attempts to investigate the errors and misconception that form three students reveal using symbolic equation and word-problem representations. The participants were thirty form three students, from a high school in Zimbabwe. Three mathematics teachers from the same school also took part. Data was collected from the students through a questionnaire, a test, follow up interviews and semi-structured interviews. Semi structured interviews were also conducted with the three mathematics teachers. In data analysis, the students’ written responses and data from questionnaire were qualitatively analysed to determine the nature of the students’ errors when solving quadratic equations. The results revealed that the students had difficulties in solving symbolic quadratic equations by the factorisation method as well as the use of the quadratic formula such that many misconceptions were exposed. The following types of errors were revealed: conceptual, procedural and technical. It was found out that it is an advantage for teachers to teach students with the knowledge of these errors in an effort to eliminate them.
Keywords: Error, misconception, quadratic equation.
0
References
Alkan, H., & Altan, M. (1998). Matematik öğretimi [Mathematics teaching]. Anadolu Üniversitesi Açık Öğretim Fakültesi/ Anadolu University Open Education Faculty.
Bertram, C., & Christiansen, I. (2014). Understanding research: An introduction to reading research. Van Schaik Publishers.
Bosse, M. J., & Nandakumar, N. R. (2005). The factorability of quadratics: Motivation for more techniques (Section A). Teaching Mathematics and Its Applications, 24(4), 143-153.
Brodie, K. (2014). Learning about learner errors in professional learning communities. Educational Studies in Mathematics, 85(2), 221-239.
Clark, M, K. (2012). History of mathematics: Illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educational studies in Mathematics, 81, 67-84.
Cohen, L., Manion, L, & Morrison, L. (2011). Surveys, longitudinal, cross sectional and trend studies. Routledge.
de Lima, R. N., & Tall, D. (2008). Procedural embodiment and quadratic equations. Educational Studies in Mathematics, 67, 3-18.
Didis, M.G., & Erbas, A.K. (2015). Performance and difficulties of students in formulating and solving quadratic equation with one unknown. Educational Science, Theory and Practice, 15(4), 1137-1150.
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. (Ed.). (2006). Children’s errors in mathematics. Learning Matters Ltd.
Kazunga, C., & Bansilal, S. (2017). Zimbabwean in-service mathematics teachers’ understanding of matrix operations. The Journal of Mathematical Behavior, 47, 81-95.
Kiat, S. E. (2005). Analysis of students’ difficulties in solving integration problems. The Mathematics Educator, 9(1), 39-59.
Kufakowadya, M. B., & Nyamakura, A. (2010). Mathematics today. Zimbabwe Publishing House.
Luneta , K., & Makonye, P.J. (2010). Learner errors and misconceptions in elementary analysis: A case study of a grade 12 class in South Africa. Acta Didactica Napocensia, 3(3), 35-46.
Makgakga, S. (2016). Errors and miscanceptions in solving quadratic equations by completing a square. Association for Mathematics Education of South Africa. http://shorturl.at/hzALU
Mbewe, T. L., & Nkhata, B. (2019). secondary teachers’ mathematics knowledge for teaching quadratic equations: A case of selected secondary schools in Katete district. Zambia Journal of Teacher Professional Growth, 5(1), 38 – 55.
Nyaumwe, L., & Buzuzi G. (2007). Teachers attitudes towards proof of mathematical results in the secondary school curriculum. Mathematics Educational Research Journal, 19(3), 21-32.
Makonye, J. P. (2014). Learner mathematical errors in introductory differential calculus tasks: A study of misconceptions in the senior certificate examinations [Unpublished doctoral dissertation]. University of Johannesburg.
Makonye, J. P. (2012). Learner errors on calculus tasks in the NSC examinations: Towards an analytical protocol for learner perturbable concepts in introductory differentiation. International Journal of Learning, 18(6), 339-357.
Makonye, J., & Nhlanhla, S. (2014). Exploring ‘non-science’ grade 11 learners’ errors in solving quadratic equations. Mediterranean Journal of Social Sciences, 5(27) 634-644. https://doi.org/10.5901/mjss.2014.v5n27p634
Makonye, J. P. (2012). Learner errors on calculus tasks in the NSC examinations: Towards an analytical protocol for learner perturbable concepts in introductory differentiation. International Journal of Learning, 18(6), 339-357.
Ojose, B. (2015). Misconceptions in mathematics: Strategies to correct them. University Press of America.
Owusu, J. (2015). The impact of constructivist-based teaching method on secondary school learners' errors in algebra [Unpublished Doctoral dissertation]. University of South Africa.
Saglam, R., & Alacaci, C. (2012). A comparative analysis of quadratics unit in Singaporean, Turkish and IMDP mathematics textbooks. Turkish Journal of Computer and Mathematics Education, 3(3), 131-147.
Vaiyavutjamai, P., Ellerton, N. F., & Clements, M. A. (2005). Students’ attempts to solve two elementary quadratic equations: A study in three nations. In P. C. Clarkson (Ed.), Proceeding of Building connections research, theory and practice: MERGA 28 (pp. 735-742). Mathematics Education Research Group of Australasia.
White, A. L. (2005). Active mathematics in classrooms: Finding out why children mistakes – And then doing something. Square One, 15(4), 15-19.