Analysis of Students' Errors in Solving Recurrence Relation Word Problems Based on Newman's Procedure
Main Article Content
Abstract
Although Newman’s Error Analysis (NEA) has been widely applied to mathematical word problems, contextual recurrence relation problems in undergraduate Discrete Mathematics remain underexamined. This study analysed the types, frequencies, and characteristics of students’ errors in solving a recurrence relation word problem using Newman’s procedure. A qualitative descriptive approach with a document analysis design was employed, examining examination scripts from all 32 students enrolled in a Discrete Mathematics course through total sampling. Written responses to a single contextual savings problem were analysed using NEA-based coding, frequency tabulation, and qualitative description. Only one student (3.1%) produced a complete and correct response, while 59.4% failed before constructing a valid model. The largest decline in successful progression occurred at the comprehension stage. The most frequent error indicators were failure to interpret the result in context (43.8%) and failure to construct a recurrence model (28.1%). The findings suggest that the principal difficulties in this task concerned translating verbal information into mathematical models and interpreting mathematical results within the original context. The study contributes a task-specific account of modelling errors to NEA research in higher education. Instructional implications include explicitly linking temporal expressions to mathematical indices, incorporating contextual validation into assessment rubrics, and designing realistic contextual problems. Further research should triangulate written-response analysis with interviews to clarify the reasoning underlying the observed errors.
Citation Metrics:
Downloads
Citation Metrics & Similar Scopus Articles
-
Kazhikenova S.S. (2028)Modelling and Solving Problems of Sustainable Efficiency of Technological Processes in MetallurgyKompleksnoe Ispolzovanie Mineralnogo Syra, 344(1), 65-78
-
Li R. (2027)IrMn-Cluster-Based Artificial Metalloenzymes with Radiosensitized Systemic Antitumor Responses to Prevent Malignant Tumor Metastasis and RecurrenceNano Micro Letters, 19(1)
-
Afrouz M. (2027)Automatic Detection of Grammatical Errors in English Translations: Assessing the Efficacy and Suggesting Some Recommendations for Boosting Grammarly SoftwareLanguage Related Research, 17(4), 1-33
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Aurelia, D., Ekawati, R., & Arifin, S. (2024). Primary students’ comprehension errors in translating math problems. Edumatica: Jurnal Pendidikan Matematika, 14(3), 213–230. https://doi.org/10.22437/edumatica.v14i3.38814
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 109(2), 205–236. https://doi.org/10.1007/s10649-021-10104-6
Ekasari, A., & Putra, D. J. (2024). Error analysis of learners’ problem-solving abilities in mathematics courses: A Newman error analysis (NEA) approach. Jurnal Pendidikan Sains, 12(1), 44–49. https://doi.org/10.17977/2442-3904.1019
Geisler, S. (2023). Mathematical modelling with experiments: Students’ sense of validation and its relevance. Rivista di Matematica della Università di Parma, 14(2), 265–280. https://www.rivmat.unipr.it/vols/2023-14-2/03-geisler.html
Haerani, A., Novianingsih, K., & Turmudi, T. (2021). Analysis of students’ errors in solving word problems viewed from mathematical resilience. JTAM (Jurnal Teori dan Aplikasi Matematika), 5(1), 246–253. https://doi.org/10.31764/jtam.v5i1.3928
Hidayatullah, A., & Csíkos, C. (2023). Students’ responses to the realistic word problems and their mathematics-related beliefs in primary education. Pedagogika, 150(2), 21–37. https://doi.org/10.15823/p.2023.150.2
Hurrell, D. P. (2021). Conceptual knowledge or procedural knowledge or conceptual knowledge and procedural knowledge: Why the conjunction is important to teachers. Australian Journal of Teacher Education, 46(2), 57–71. https://doi.org/10.14221/ajte.2021v46n2.4
Husenti, N., & Pratama, A. M. I. (2022). Analisis Kesalahan Materi Logika dengan Metode Newman pada Mahasiswa Program Studi Teknik Informatika UMG. Jurnal Pendidikan Informatika dan Sains, 11(2), 88–101. https://doi.org/10.31571/saintek.v11i2.2845
Indriana, I., Pathuddin, P., Lefrida, R., & Alfisyahra, A. (2024). Newman’s error analysis: The students’ errors in solving word problems of proportion. Edumatika: Jurnal Riset Pendidikan Matematika, 7(1), 45–57. https://doi.org/10.32939/ejrpm.v7i1.3642
Irianti, N. P., Barr, F. D., Nurasiah, L., & Irsal, N. A. (2024). Error analysis in solving applied mathematics problems based on the Newman procedure. Inteligensi: Jurnal Ilmu Pendidikan, 7(1), 110–117. https://doi.org/10.33366/ilg.v7i1.5883
Jablonski, S., Barlovits, S., & Ludwig, M. (2023). How digital tools support the validation of outdoor modelling results. Frontiers in Education, 8, Article 1145588. https://doi.org/10.3389/feduc.2023.1145588
Kiesler, N. (2022). Mental models of recursion: A secondary analysis of novice learners’ steps and errors in Java exercises. In Proceedings of the 33rd Annual Workshop of the Psychology of Programming Interest Group (PPIG 2022). Psychology of Programming Interest Group. https://ppig.org/papers/2022-ppig-33rd-kiesler/
Kılıç, Ç., & Şahinkaya, N. (2022). Examining primary school students’ performance in solving problems requiring realistic considerations. Malikussaleh Journal of Mathematics Learning, 5(1), 19–25. https://ojs.unimal.ac.id/mjml/article/view/7191/0
Kirkland, P. K., & McNeil, N. M. (2021). Question design affects students’ sense-making on mathematics word problems. Cognitive Science, 45(4), Article e12960. https://doi.org/10.1111/cogs.12960
Kusmaryono, I., Aminudin, M., Ubaidah, N., & Chamalah, E. (2024). The bridging understanding of language and mathematical symbols between teachers and students: An effort to increase mathematical literacy. Infinity Journal, 13(1), 251–270. https://doi.org/10.22460/infinity.v13i1.p251-270
Magda, D., & Gardner-McCune, C. (2025). Students’ thoughts on discrete mathematics: Insights for practice and implications for future research. In Proceedings of the 56th ACM Technical Symposium on Computer Science Education V. 1 (pp. 736–741). Association for Computing Machinery. https://doi.org/10.1145/3641554.3701948
Marhami, M., Dasari, D., Suryadi, D., & Juandi, D. (2026). Epistemological obstacles in combinatorics as praxeological gaps among pre-service mathematics teachers. Jurnal Elemen, 12(3), 710–723. https://doi.org/10.29408/jel.v12i3.35192
Nicchiotti, B., Donatiello, A., & Bianco, G. (2024). A narrative approach to foster the construction of recursive thinking in high school students. Education Sciences, 14(4), Article 350. https://doi.org/10.3390/educsci14040350
Noorbehbahani, F., Mohammadi, A., & Aminazadeh, M. (2022). A systematic review of research on cheating in online exams from 2010 to 2021. Education and Information Technologies, 27(6), 8413–8460. https://doi.org/10.1007/s10639-022-10927-7
Nuryati, N., Purwaningsih, S. S., & Habinuddin, E. (2022). Analysis of errors in solving mathematical literacy analysis problems using Newman. International Journal of Trends in Mathematics Education Research, 5(3), 299–305. https://doi.org/10.33122/ijtmer.v5i3.164
Parandrengi, M. J., & Hiltrimartin, C. (2023). Students’ errors in solving climate change context mathematical modeling problems. Jurnal Elemen, 9(2), 388–402. https://doi.org/10.29408/jel.v9i2.11422
Permata, J. I., Budiarto, M. T., & Fuad, Y. (2025). Analysis of error in mathematical modeling problems: An exploratory study of middle school students. Edelweiss Applied Science and Technology, 9(7), 947–959. https://doi.org/10.55214/25768484.v9i7.8773
Pinahayu, E. A. R., Awaaludin, A. A. R., Adnyani, L. P. W., Mariko, S., Mulyani, N., & Yono, S. (2023). Analisis Kesalahan Mahasiswa dalam Menyelesaikan Soal Distribusi Sampling Beda Dua Proporsi Berdasarkan Prosedur Newman. Jurnal Pendidikan Tambusai, 7(2), 9191–9198. https://jptam.org/index.php/jptam/article/view/7714
Purba, P. P. N., Sihite, M. A., Hutagalung, E. E., & Al Fath, A. M. (2026). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Cerita Matematika Berdasarkan Tahapan Newman: Systematic Literatur Review. Pendas: Jurnal Ilmiah Pendidikan Dasar, 11(2), 241–253. https://www.journal.unpas.ac.id/index.php/pendas/article/view/45403
Salim, L. F., Noverli, M. F., & Kartika, H. (2026). Stage-specific patterns in students’ statistical problem solving: A qualitative analysis through Pólya’s framework. Jurnal Didactical Mathematics, 8(2), 469–490. https://ejournal.unma.ac.id/index.php/dm/article/view/19208
Sari, N. R., Asyari, S., & Darwis M., M. (2023). Analisis Kesalahan dalam Menyelesaikan Masalah Numerasi Aljabar dengan Menggunakan Prosedur Newman pada Siswa Kelas XI SMA. Issues in Mathematics Education, 7(2), 120–138. https://ojs.unm.ac.id/imed/article/view/51347
Sarwan, S., Fineldi, R. J., & Panjaitan, M. A. (2026). Analysis of student errors in solving algebra problems: A Newman’s error analysis perspective. Journal on Mathematics Education Research, 7(1), 148–159. https://doi.org/10.17509/j-mer.v7i1.885
Schlüter, D., & Besser, M. (2024). Assessing authenticity in modelling test items: Deriving a theoretical model. Frontiers in Education, 9, Article 1343510. https://doi.org/10.3389/feduc.2024.1343510
Schukajlow, S., Kaiser, G., & Stillman, G. (2023). Modeling from a cognitive perspective: Theoretical considerations and empirical contributions. Mathematical Thinking and Learning, 25(3), 259–269. https://doi.org/10.1080/10986065.2021.2012631
Sjaastad, J., & Lorange, C. A. (2026). Pre-service teachers using an app to generalize figural patterns through figural reasoning. LUMAT: International Journal on Math, Science and Technology Education, 14(1), Article 2. https://doi.org/10.31129/LUMAT.14.1.2856
Soto, O., Siy, K., & Harel, G. (2022). Promoting a set-oriented way of thinking in a U.S. high school discrete mathematics class: A case study. ZDM – Mathematics Education, 54(4), 809–827. https://doi.org/10.1007/s11858-022-01337-7
Suddin, S., & Handayani, R. (2026). An analysis of students’ errors based on Newman’s error analysis in solving partial derivative problems in calculus. MATH-EDU: Jurnal Ilmu Pendidikan Matematika, 11(1), 27–38. https://jurnal.unimor.ac.id/index.php/JIPM/article/view/10926
Sukmarini, M. A., & Hermanto, H. (2021). Error analysis in answering system of linear equations with two variables questions based on Newman indicator. International Journal on Teaching and Learning Mathematics, 4(1), 15–25. https://doi.org/10.18860/ijtlm.v4i1.14180
Trigueros-Rodríguez, E., & Montejo-Gámez, J. (2025). Formulación de relaciones de recurrencia utilizadas por estudiantes de ingeniería para la identificación de patrones. In M. Burgos Navarro, M. C. Cañadas Santiago, J. M. Marbán Prieto, & I. Polo-Blanco (Eds.), Investigación en educación matemática XXVIII (pp. 445–452). Sociedad Española de Investigación en Educación Matemática. https://www.seiem.es/acta/actas-xxviii-seiem-melilla-2025/
Zulyanty, M., & Mardia, A. (2022). Do students’ errors still occur in mathematical word problem-solving?: A Newman error analysis. Al-Jabar: Jurnal Pendidikan Matematika, 13(2), 343–353. https://doi.org/10.24042/ajpm.v13i2.13519
Article Sidebar
Page Numbers:
9177-9192
Digital Object ID:
Viewed: 12 times
Downloaded: 5 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:
Copyright :Authors retain copyright and grant the journal right of first publication.
Explore Our Journals
Find the journal that best fits your research. If this journal does not match your manuscript’s scope, explore our portfolio below to select a more suitable publication venue.