Exploring Student Errors in Solving Derivative Problems: A Systematic Literature Review
Abstract
Derivative material is essential in developing students’ critical thinking skills and its application in various scientific fields, specifically in mathematics. However, numerous studies revealed that many students still considered this material difficult, which often causes students to make mistakes in solving derivative problems. This study aims to analyze students' errors in solving derivative problems. This research method used systematic literature review with data synthesis process, qualitative data analysis through thematic analysis, and PRISMA method for data selection which obtained 10 articles from 232 articles on the Google Scholar, Semantic Scholar, and Scopus pages. The analysis results showed uneven fluctuations in the number of studies, peaking in 2022. The distribution of research covers nine provinces in Indonesia, with a dominance in the NTB province, although the distribution is still uneven. Newman’s theory became the primary approach to analyzing student errors. Most of the research was published in SINTA 4 and SINTA 5 journals, while contributions in highly reputable journals are still minimal. The most dominant student error occurred at the encoding/looking back stage, which was caused by a lack of understanding of the derivative concept, inaccuracy, rushing, and lack of habit to re-examine the work. Other errors include conceptual, procedural, and technical errors related to derivative facts, concepts, operations, and principles. As a solution, interactive teaching materials based on the Newman procedure was recommended to improve students’ understanding of derivative concepts.
Keywords: derivative, mathematics, student errors, systematic literature review.
DOI: http://dx.doi.org/10.23960/jpmipa/v25i4.pp1693-1704
Full Text:
PDFReferences
Al-Agili, M. Z. G., Mamat, M. Bin, Abdullah, L., & Maad, H. A. (2012). The factors influence students’ achievement in mathematics: a case for libyan’s students. World Applied Sciences Journal, 17(9), 1224–1230. https://www.researchgate.net/ publication/267246643
Angco, R. J. N. (2021). Error analysis in integral calculus: a modified newman’s approach. American Research Journal of Humanities Social Science (ARJHSS), 04(09), 38–52. https://www.researchgate.net/publication/354556234
Clarkson, P. C. (1991). Language comprehension errors: a further investigation. Mathematics Education Research Journal, 3(2), 24–33. https://doi.org/10.1007/ BF03217225
Clements, M. . (1980). Analyzing children’s errors on written mathematical task. Educational Studies in Mathematics, 11(1), 1–21. https://doi.org/10.1007/ BF00369157
Dj Pomalato, S. W., Ili, L., Ningsi, B. A., Fadhilaturrahmi, Hasibuan, A. T., & Primayana, K. H. (2020). Student error analysis in solving mathematical problems. Universal Journal of Educational Research, 8(11), 5183–5187. https://doi.org/10.13189/ ujer.2020.081118
Esterlina, E., & Dahlan, J. A. (2023). Analysis of students’ errors in mathematical problem solving based on kastolan error analysis. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1505. https://doi.org/10.24127/ ajpm.v12i1.7224
Fahrudin, D., Mardiyana, & Pramudya, I. (2019). The analysis of mathematic problem solving ability by polya steps on material trigonometric reviewed from self-regulated learning. Journal of Physics: Conference Series, 1254(1). https://doi.org/10.1088/1742-6596/1254/1/012076
Fathurrohman, M. T., & Sugandi, A. I. (2023). The implementation of scientific approach to increase mathematical understanding ability on algebraic derivative materials. (Jiml) Journal of Innovative Mathematics Learning, 6(3), 186–193. https://doi.org/10.22460/jiml.v6i3.17612
Feudel, F., & Biehler, R. (2021). Students’ understanding of the derivative concept in the context of mathematics for economics. Journal Fur Mathematik-Didaktik, 42(1), 273–305. https://doi.org/10.1007/s13138-020-00174-z
Hamidah, & Kusuma, J. W. (2024). Developing ethnomathematical-based learning stages on mathematical communication skills with kastolan error analysis. Communications on Applied Nonlinear Analysis, 31(1), 150–176. https://doi.org/10.52783/cana.v31.371
Handayani, D., & Kusnandi. (2023). Analysis of student errors in solving algebraic function derivative problems according to watson theory: a case study in class XI of yayasan atikan sunda high school bandung. EDUSENTRIS: Jurnal Ilmu Pendidikan Dan Pengajaran, 10(March), 22–32. https://ejournal.upi.edu/index.php/edusentris/index
Hoth, J., Larrain, M., & Kaiser, G. (2022). Identifying and dealing with student errors in the mathematics classroom: Cognitive and motivational requirements. Frontiers in Psychology, 13(December), 1–16. https://doi.org/10.3389/fpsyg.2022.1057730
Juandi, D., & Tamur, M. (2021). The impact of problem-based learning toward enchancing mathematical thinking: a meta-analysis study. Journal of Engineering Science and Technology.
Kurniati, U., Setiyani, & Sagita, L. (2021). Error analysis using newman procedures and the mathematical representation ability of pre service english teachers. Anatolian Journal of Education, 6(2), 135–156. https://doi.org/10.29333/aje.2021.6211a
Mahaliyanaarachchi, R. P. (2016). Indexing of journals. Journal of Agricultural Sciences, 11(3). https://doi.org/10.4038/jas.v11i3.8166
Mubarokah, A. A. L., & Amir, M. F. (2024). Primary students’ errors in solving mathematical literacy problems based on newman analysis. Mathematics Education Journal, 18(2), 217–230. https://doi.org/10.22342/jpm.v18i2.pp217-230
Mutia, Kartono, Dwijanto, & Wijayanti, K. (2023). Students’ mathematical creative thinking obstacle and scaffolding in solving derivative problems. Journal of Higher Education Theory and Practice, 23(17), 150–169. https://doi.org/10.33423/jhetp.v23i17.6540
Nguyen, L. C., Thuan, H. T., & Giang, T. T. H. (2023). A application of g. polya’s problem-solving process in teaching high-school physics. Journal La Sociale, 4(1), 26–33. https://doi.org/10.37899/journal-la-sociale.v4i1.761
Pati, J., Jena, U. K., & Beura, M. K. (2024). Attitude of secondary school students’ towards mathematics. Integrated Journal for Research in Arts and Humanities, 4(2), 92–96. https://doi.org/10.55544/ijrah.4.2.15
Polya, G. (2004). How to solve it: a new aspect of mathematical method. in stochastic optimization in continuous time. Princeton University Press. https://doi.org/10.1017/cbo9780511616747.007
Purssell, E., & McCrae, N. (2020). How to perform a systematic literature review. In Springer. https://doi.org/10.1007/978-3-030-49672-2
Quezada, V. D. (2020). Difficulties and performance in mathematics competences: Solving problems with derivatives. International Journal of Engineering Pedagogy, 10(4), 35–53. https://doi.org/10.3991/ijep.v10i4.12473
Raduan, I. H. (2010). Error analysis and the corresponding cognitive activities committed by year five primary students in solving mathematical word problems. Procedia - Social and Behavioral Sciences, 2(2), 3836–3838. https://doi.org/10.1016/ j.sbspro.2010.03.600
Siddaway, A. P., Wood, A. M., & Hedges, L. V. (2019). How to do a systematic review: a best practice guide for conducting and reporting narrative reviews, meta-analyses, and meta-syntheses. Annual Review of Psychology, 70, 747–770. https://doi.org/10.1146/annurev-psych-010418-102803
Singh, P., Rahman, A. A., & Hoon, T. S. (2010). The Newman procedure for analyzing Primary Four pupils errors on written mathematical tasks: A Malaysian perspective. Procedia - Social and Behavioral Sciences, 8(5), 264–271. https://doi.org/10.1016/j.sbspro.2010.12.036
Tasman, F., Yenti, I. N., & Heriyanti, S. (2018). Analysis of students’ error in understanding the mathematical problems. Advances in Social Science, Education and Humanities Research (ASSEHR), 285(ICM2E 2018), 62–65. https://doi.org/10.2991/icm2e-18.2018.16
Tiwari, C., & Fatima, R. (2019). Secondary school students‟ misconceptions in algebra concepts. Mahatma Gandhi Central University Journal of Social Sciences, 1(1), 22–33.https://mgcub.ac.in/pdf/journals/mgcujss_1-1_april-september_2019-32-43.pdf
Triliana, T., & Asih, E. C. M. (2019). Analysis of students’ errors in solving probability based on Newman’s error analysis. Journal of Physics: Conference Series, 1211(1). https://doi.org/10.1088/1742-6596/1211/1/012061
Yarman, Y., Fauzan, A., Armiati, A., & Lufri, L. (2020). Analysis of student errors in solving ordinary differential equations based on SOLO taxonomy. Journal of Physics: Conference Series, 1554(1), 1–7. https://doi.org/10.1088/1742-6596/1554/1/012065
Refbacks
- There are currently no refbacks.
Copyright (c) 2025 Jurnal Pendidikan MIPA
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
The copyright is reserved to The Jurnal Pendidikan Progresif that is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.