Analysis of Student Errors in Solving Problems on Three-Dimensional Shapes with Flat Surfaces: A Qualitative Study on Eighth-Grade Students
Main Article Content
Abstract
This study analyzes errors made by eighth-grade students in solving problems involving three-dimensional geometric shapes with flat surfaces and examines the factors causing these errors. Using a qualitative descriptive approach, three students with varying error levels (high, medium, low) were selected for analysis through written tests and in-depth interviews. Data were processed using the Miles and Huberman model: data reduction, data presentation, and conclusion drawing. Findings identified four main error types: factual, conceptual, principle, and operational. High-error students mainly struggled with conceptual understanding and operations, while low-error students primarily made operational errors. The results highlight that weak conceptual understanding and cognitive overload were the key factors in these errors. This study implies that teaching strategies should enhance both conceptual and procedural knowledge, utilizing interactive and manipulative learning methods to reduce cognitive load and improve student performance in geometry.
Article Details
References
Alibali, M. W., Nathan, M. J., & Fujimori, Y. (2019). Learning mathematics in the era of cognitive science. Cognitive Science, 43(6), e12748. https://doi.org/10.1111/cogs.12748
Asipi, L. S., Rosalina, U., & Nopiyadi, D. (2022). The analysis of reading habits using Miles and Huberman interactive model to empower students’ literacy at IPB Cirebon. International Journal of Education and Humanities, 2(3), 117-125.
Booth, J. L., Barbieri, C., Eyer, F., & Paré-Blagoev, J. (2021). Comparing worked example and problem-solving instruction for improving algebraic equation solving. Journal of Educational Psychology, 113(4), 754-771. https://doi.org/10.1037/edu0000655
Carpenter, T. P., Franke, M. L., & Levi, L. (2015). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Journal of Mathematics Teacher Education, 18(1), 1-9. https://doi.org/10.1007/s10857-014-9280-1.
De Koning, B. B., & van der Schoot, M. (2019). Learning by doing versus learning by viewing: Comparing two instructional approaches for solving geometry problems. Learning and Instruction, 62, 1-10. https://doi.org/10.1016/j.learninstruc.2019.02.004
Fyfe, E. R., DeCaro, M. S., & Rittle-Johnson, B. (2018). The relation between conceptual understanding and procedural skill: Does it matter how you measure it? British Journal of Educational Psychology, 88(1), 13-27. https://doi.org/10.1111/bjep.12181
Haser, Ç., & Star, J. R. (2020). Preservice mathematics teachers' knowledge and implementation of multiple strategies in the classroom. Mathematical Thinking and Learning, 22(2), 105-129.
Kania, N., Kusumah, Y. S., Dahlan, J. A., Nurlaelah, E., & Kyaruzi, F. (2024). Decoding Student Struggles in Geometry: Newman Error Analysis of Higher-Order Thinking Skills. International Journal of Geometry Research and Inventions in Education (Gradient), 1(01), 31–47. https://doi.org/10.56855/gradient.v1i01.1146
Khosroshahi, L. G., & Rosli, R. (2019). The nature of students' conceptual and procedural errors in solving mathematical word problems. International Journal of Mathematical Education in Science and Technology, 50(7), 1070-1083. https://doi.org/10.1080/0020739X.2018.1533674
Lamon, S. J. (2017). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge.
Litke, E. G. (2019). The nature and quality of algebra instruction: Using a content-focused observation tool as a lens for understanding and improving instructional practice. Cognition and Instruction, 37(3), 273-301.
Mason, M. (2018). Mathematical thinking in the classroom: A critical analysis of the Van Hiele theory. Journal of Mathematical Behavior, 52, 157-165.
Mubarak, H., Nordin, N., & Aman, R. (2020). Exploring the errors in solving algebraic problems among high school students. Journal of Mathematics Education, 11(3), 457-472. https://doi.org/10.1080/17940031.2019.1584543
OECD. (2018). PISA 2018 results: Combined executive summaries. OECD Publishing.
Reeve, J., Jang, H., & Carrell, D. (2020). Enhancing students' engagement by increasing teachers' autonomy support. Journal of Educational Psychology, 112(3), 499-518. https://doi.org/10.1037/edu0000412
Schneider, M., & Preckel, F. (2017). Variables associated with achievement in higher education: A systematic review of meta-analyses. Psychological Bulletin, 143(6), 565-600. https://doi.org/10.1037/bul0000098
Schoenfeld, A. H. (2020). Learning to think mathematically: Problem-solving, metacognition, and sense-making in mathematics. Journal for Research in Mathematics Education, 51(4), 300-324. https://doi.org/10.5951/jresematheduc-2020-015
Sweller, J., Ayres, P., & Kalyuga, S. (2019). Cognitive load theory. Springer.
Valentine, V. E., Alawiyah, T., Dewi, I. L. K., & Nopriana, T. (2024). Identifying the Mathematical Concept Understanding Ability of Junior High School Students in Learning Linear Function Material. International Journal of Contemporary Studies in Education (IJ-CSE), 3(2), 115-126. https://doi.org/10.56855/ijcse.v3i2.994
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Wijaya, A., Doorman, M., & Keijer, T. (2019). Difficulties in solving context-based PISA mathematics tasks: An analysis of students' errors. Mathematics Education Research Journal, 31(4), 351-371.