An Examination of Common Errors in Geometric Concepts among Senior Secondary School Students in Lagos State
Keywords:
error analysis, geometry, geometry concept, mathematics, mathematics achievementAbstract
This study examined students' performance in geometry and the specific errors related to their understanding of certain mathematical concepts. The emphasis was on five geometry subjects: constructions, angles, circles, volume, and polygon properties. A quantitative research design was utilised, and data were gathered through the Mathematics Achievement Test (MAT). Students' answers were scored in a systematic way, and an error analysis was done using a structured coding scheme to put mistakes into the following groups: conceptual, procedural, symbolic, reasoning, and careless. Descriptive statistical methods were employed to examine overall achievement, performance across geometric concepts, and the distribution of error types. The results showed that the students' overall mathematics achievement in geometry concept was at a moderate level. But the results were very different for the different geometry concepts that were tested. Students did better on volume and properties of polygons. The analysis of the errors showed that most of the mistakes were conceptual and procedural, which means that many students relied on memorised steps without really understanding what they were doing. Mistakes in reasoning were especially clear in topics that were more abstract and required more thought, like constructions and tasks related to angles. The results show that students' understanding of geometry is not developing evenly, and they stress the need for teaching methods that help students understand concepts, reason, and visualise space. The research emphasises the significance of employing diagnostic assessments to pinpoint particular error patterns and guide focused instructional interventions. The results add to what is already known about how students learn geometry by showing how well they do and what kinds of mistakes they make. This has useful implications for teaching mathematics, developing curricula, and testing methods.
References
Abdul Rahman, T.F. & Mohamad Foad, M.S. (2021). Quadratic functions in additional mathematics and mathematics: An analysis on students' errors. Academic Journal of Business and Social Sciences, 5(1), 1-16, available at: https://ir.uitm.edu.my/id/eprint/59114/.
Aguele, L.I., Omo-Ojugo, M.O. & Imhanlahimi, E.O. (2010). Effectiveness of selected teaching strategies in the remediation of process errors committed by senior secondary school students in mathematics. Journal of Social Sciences, 22(2), 139-144, available at: https://www.tandfonline.com/doi/abs/10.1080/09718923.2010.11892803.
Arhin, J. & Hokor, E. (2021). Analysis of high school students’ errors in solving trigonometry problems. Journal of Mathematics and Science Teacher, 1(1), 1-16. DOI: https://doi.org/10.29333/mathsciteacher/11058.
Ashcraft, M.H. & Kirk, E.P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. DOI: https://doi.org/10.1037/0096-3445.130.2.224.
Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). Charlotte, NC: Information Age Publishing.
Borasi, R. (1987). Exploring mathematics through the analysis of errors. For the learning of Mathematics, 7(3), 2-8, available at: https://www.jstor.org/stable/40248041.
Chamundeswari, S. (2014). Conceptual errors encountered in mathematical operations in algebra among students at the secondary level. International Journal of Innovative Science, Engineering & Technology, 1(8), 24-38.
Clements, D.H. & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. DOI: https://doi.org/10.1126/science.1204537.
Dawkins, P. (2006). Common math errors, available at: http://tutorial.math.lamar.edu/pdf/Common_Math_Errors.pdf.
Durkaya, M., Aksu, Z., Öçal, M.F., Şenel, E.Ö., Konyalıoğlu, A.C., Hızarcı, S. & Kaplan, A. (2011). Secondary school mathematics teachers’ approaches to students’ possible mistakes. Procedia-Social and Behavioral Sciences, 15, 2569-2573. DOI: https://doi.org/10.1016/j.sbspro.2011.03.368.
Gierl, M.J., Alves, C. & Majeau, R.T. (2010). Using the attribute hierarchy method to make diagnostic inferences about examinees’ knowledge and skills in mathematics: An operational implementation of cognitive diagnostic assessment. International Journal of Testing, 10(4), 318-341. DOI: https://doi.org/10.1080/15305058.2010.509083.
Haghverdi, M., Semnani, A.S. & Seifi, M. (2012). The relationship between different kinds of students' errors and the knowledge required to solve mathematics word problems. Bolema: Boletim de Educação Matemática, 26, 649-666. DOI: https://doi.org/10.1590/S0103-636X2012000300006.
xe, S. (2025). How do preservice mathematics teachers analyze and respond to student errors in solving probability problems using tree diagrams? Teaching and Teacher Education, 168, 105250. DOI: https://doi.org/10.1016/j.tate.2024.105250.
Laborde, C. (2005). The hidden role of diagrams in students’ construction of meaning in geometry. In J. Kilpatrick, C. Hoyles, O. Skovsmose, & P. Valero (Eds.), Meaning in mathematics education (pp. 159–179). New York, NY: Springer, available at: https://link.springer.com/chapter/10.1007/0-387-24040-3_9.
McGowen, M.A. & Davis, G.E. (2019). Spectral analysis of concept maps of high and low gain undergraduate mathematics students. The Journal of Mathematical Behavior, 55, 100686.
Mitchelmore, M.C. & White, P. (2000). Development of angle concepts by progressive abstraction and generalization. Educational Studies in Mathematics, 41(3), 209–238. DOI: https://doi.org/10.1023/A:1003927811079.
Molina, M., Rodríguez-Domingo, S., Cañadas, M.C. & Castro, E. (2017). Secondary school students’ errors in the translation of algebraic statements. International Journal of Science and Mathematics Education, 15(6), 1137-1156. DOI: https://doi.org/10.1007/s10763-016-9739-7.
Newman, M.A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin, 39, 31–43.
Nwoke, B.I., Duru, D.C., Ahanotu, C. & Ifediba, C.P. (2024). Analyzing errors pattern in mathematics achievement among senior secondary school students: A case study. Journal of Instructional Mathematics, 5(1), 24-33. DOI: https://doi.org/10.37640/jim.v5i1.1948.
Piaget, J. (1978). Piaget's theory of intelligence (Vol. 2). Englewood Cliffs, NJ: Prentice Hall.
Priyani, H.A. & Ekawati, R. (2018). Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students. In IOP Conference Series: Materials Science and Engineering, 296(1), 012010). DOI: https://doi.org/10.1088/1757-899X/296/1/012010
Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10(3), 163-172. DOI: https://doi.org/10.2307/748804.
Sapire, I., Shalem, Y., Wilson-Thompson, B. & Paulsen, R. (2016). Engaging with learners' errors when teaching mathematics. Pythagoras, 37(1), 1-11. DOI: https://doi.org/10.4102/pythagoras.v37i1.348.
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, 1-10.
Schcolnik, M., Kol, S. & Abarbanel, J. (2006). Constructivism in theory and in practice. In English Teaching Forum, 44(4), 12-20), available at: https://americanenglish.state.gov/files/ae/resource_files/06-44-4-c.pdf.
Schoenfeld, A.H. (2013). Cognitive science and mathematics education. Abingdon: Routledge. DOI: https://doi.org/10.4324/9780203813924.
Sia, C.J.L. & Lim, C.S. (2018). Cognitive diagnostic assessment: An alternative mode of assessment for learning. In Classroom assessment in mathematics: Perspectives from around the globe, 123-137. New York, NY: Springer International Publishing. DOI: https://doi.org/10.1007/978-3-319-73748-5.
Sinclair, N. & Bruce, C.D. (2015). New opportunities in geometry education at the primary school. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed.), 319–340). Abingdon: Routledge. DOI: https://doi.org/10.4324/9780203096143.
Skemp, R.R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Van Hiele, P.M. (1986). Structure and insight: A theory of mathematics education. Cambridge, MA: Academic Press.
Veloo, A.K.H.N., Krishnasamy, H.N. & Wan Abdullah, W.S. (2015). Types of student errors in mathematical symbols, graphs and problem-solving. Asian Social Science, 11(15), 324-334. DOI: https://doi.org/10.5539/ass.v11n15p324.
Von Glasersfeld, E. (1995). Despedida de la objetividad. El ojo del observador, available at: https://sotraem.izt.uam.mx/wp-content/uploads/2022/10/Glasersfeld.pdf.
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