A Qualitative Analysis of Students' Errors in Fraction Word Problems Based on Polya’s Stages of Problem Solving: Evidence from Papua, Indonesia

Yosefin Rianita Hadiyanti; Mayor M.H. Manurung

doi:10.22437/edumatica.v15i2.43746

Authors

Yosefin Rianita Hadiyanti Universitas Cenderawasih
Mayor M.H. Manurung Universitas Cenderawasih

DOI:

https://doi.org/10.22437/edumatica.v15i2.43746

Keywords:

Error analysis, Fractions, Polya’s method, problem solving

Abstract

This study investigates the types and causes of student errors in solving fraction word problems using Pólya’s four-step problem-solving framework: understanding the problem, devising a plan, carrying out the plan, and reviewing the solution. Employing a descriptive qualitative design, data were collected from three Grade VII students at SMP Negeri 2 Sentani, Papua, Indonesia, through written tests and semi-structured interviews. The findings reveal that students made errors at each stage of problem solving. Misidentification of known and unknown quantities, improper selection of operations, computational mistakes, and the absence of solution verification were frequently observed. These errors were attributed to weak conceptual understanding, limited procedural fluency, representational difficulties, and insufficient metacognitive awareness. Furthermore, cultural and contextual factors including linguistic challenges in interpreting mathematical terminology, classroom norms emphasizing speed over reflection, and limited exposure to diverse problem types contributed to students’ difficulties. The study suggests that mathematics instruction in similar educational settings should incorporate language support, structured scaffolding aligned with Pólya’s framework, and explicit metacognitive training to enhance students' problem-solving abilities.

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References

A, A. W. (2024). The Influence of the Use of Polya’s Heuristic Strategies on Students’ Mathematical Problem Solving: A Meta Analysis. Jmlipare, 3(2), 156–167. https://doi.org/10.35905/jmlipare.v3i2.10664

Amalia, L., Makmuri, M., & Hakim, L. (2024). Learning Design: To Improve Mathematical Problem-Solving Skills Using a Contextual Approach. Jiip - Jurnal Ilmiah Ilmu Pendidikan, 7(3), 2353–2366. https://doi.org/10.54371/jiip.v7i3.3455

Andrini, V. S. (2023). Integrating Adaptive E-Learning Platform to Enhance Mathematical Problem-Solving Abilities. Edutec Journal of Education and Technology, 7(2), 344–352. https://doi.org/10.29062/edu.v7i2.709

Balayan, R., Oliveros, R. T., & Tagalog, L. B. (2024). Participation of Math Students in Online and Face-to-Face Hybrid Mathematics Instruction. Mathematics Education Journal, 8(1), 21–38. https://doi.org/10.22219/mej.v8i1.29954

Bernedo, F. E. F., & Fuentes, A. M. B. (2022). Libro: MATEMÁTICA BÁSICA. https://doi.org/10.34893/r4514-8213-9481-k

Braithwaite, D. W., & Siegler, R. S. (2021). Putting Fractions Together. Journal of Educational Psychology, 113(3), 556–571. https://doi.org/10.1037/edu0000477

Chiu, B., Randles, C., & Irby, S. M. (2022). Analyzing Student Problem-Solving With MAtCH. Frontiers in Education, 6. https://doi.org/10.3389/feduc.2021.769042

Cui, Z., & Ng, O.-L. (2021). The interplay between mathematical and computational thinking in primary school students’ mathematical problem-solving within a programming environment. Journal of Educational Computing Research, 59(5), 988–1012.

Difinubun, F. A., Makmuri, M., & Hidayat, F. A. (2024). Preliminary Study on the Development of Project-Based Learning Module to Improve Students’ Mathematical Problem Solving Ability. Mathline Jurnal Matematika Dan Pendidikan Matematika, 9(2), 605–628. https://doi.org/10.31943/mathline.v9i2.638

Diputra, K. S., Suryadi, D., Herman, T., & Jupri, A. (2023). Analysis of the Elementary School Students’ Learning Obstacles: A Case Study on the Concept of Fractions. Al Ibtida Jurnal Pendidikan Guru Mi, 10(1), 13. https://doi.org/10.24235/al.ibtida.snj.v10i1.13078

Ekasari, A., & Putra, D. J. (2024). Error Analysis of Learners’ Problem-Solving Abilities in Mathematics Courses: A Newman Error Analysis (NEA) Approach. J. Pendidik. Sains, 12(1), 44–49. https://doi.org/10.17977/jps.v12i12024p044

Erlin, E., Rahmat, A., & Purwianingsih, W. (2024). Metacognitive Self Regulation Integrated With Science Technology Society to Improving Problem Solving Ability in Microbiology Courses. Biosfer Jurnal Pendidikan Biologi, 17(1), 204–214. https://doi.org/10.21009/biosferjpb.38102

Fitriani, F., Hayati, R., Sugeng, S., Srimuliati, S., & Herman, T. (2022). Students’ ability to solve mathematical problems through polya steps. Journal of Engineering Science and Technology, 17, 25–32.

GÖKTAŞ, O., & Yazıcı, E. (2020). Effectiveness of Teaching Mathematical Problem-Solving Strategies to Students With Mild Intellectual Disabilities. Turkish Journal of Computer and Mathematics Education (Turcomat). https://doi.org/10.16949/turkbilmat.662461

Gopinath, S., & Lertlit, S. (2022). The Implementation of Polya’s Model in Solving Problem-Questions in Mathematics by Grade 7 Students. Suranaree Journal of Social Science, 11(1), 47–59. https://doi.org/10.55766/ffnz6417

Herawati, R., & Marfuah, I. (2021). Analysis of Student Errors in Solving Mathematics Problems at Muhammadiyah Senior High School Special Program of Kottabarat Surakarta City. Jurnal Cendekia Jurnal Pendidikan Matematika, 5(3), 3239–3252. https://doi.org/10.31004/cendekia.v5i3.952

Iilonga, H. K., & Chirimbana, M. (2024). Errors Made by 8th Grade Students while Solving Mathematical Word Problems. Journal of Research in Science and Mathematics Education, 3(3), 120–129.

Kabael, T., & Baran, A. A. (2023). An Investigation of Mathematics Teachers’ Conceptions of Mathematical Literacy Related to Participation in a Web-Based PISA Course. Bartın University Journal of Faculty of Education, 12(2), 315–324. https://doi.org/10.14686/buefad.1053557

Kamid, K., Dewi, R. K., Kurniawan, D. A., Azzahra, M. Z., & Nawahdani, A. M. (2023). Student Learning Difficulties in Terms of the STIF in Framework of Fractional Material. Jurnal Penelitian Dan Pengembangan Pendidikan, 7(2), 187–194. https://doi.org/10.23887/jppp.v7i2.57371

Keazer, L., & Phaiah, J. (2023). Analyzing Prospective Elementary Teachers’ Evidence of Conceptual Understanding and Procedural Fluency. Investigations in Mathematics Learning, 15(2), 135–148.

Khofifah, K., Rosyadi, R., Gunadi, F., Nandang, N., & Runisah, R. (2024). Students’ Difficulties in Solve Trigonometry Problem Solving According to Step Polya’s. Mathline Jurnal Matematika Dan Pendidikan Matematika, 9(3), 919–946. https://doi.org/10.31943/mathline.v9i3.571

Kusaka, S. (2021). Analysis of Learning Difficulties With Fractions in Three African Countries: Focusing on the Scope, Sequence and Models of Fractions. African Journal of Education and Practice, 7(2), 77–91. https://doi.org/10.47604/ajep.1267

Li, T., Chen, C., & Zhou, X. (2022). How Are Different Math Knowledge Presentations Associated With Math Anxiety? Annals of the New York Academy of Sciences, 1520(1), 153–160. https://doi.org/10.1111/nyas.14951

Lisnani, L. (2023). Fraction Learning Using Daily Context for Pre-Service Primary School Teacher Education. Jurnal Pendidikan Matematika (Jupitek), 6(2), 73–81. https://doi.org/10.30598/jupitekvol6iss2pp73-81

Miles, M. B., Huberman, A. M., & Saldana, J. (2020). Qualitative Data Analysis. Sage Publications, Inc.

Mohammed, A. (2021). The effect of cooperative problem-solving approach on secondary school students’ mathematics performance and perceptions: The case of Awi-zone.

Muhassanah, N., & Setiani, A. (2024). Analysis of Student Errors Based on Polya’s Steps in Three-Dimensional Geometry. Union Jurnal Ilmiah Pendidikan Matematika, 12(2), 340–349. https://doi.org/10.30738/union.v12i2.17575

Nashiroh, F., & Zainuddin, A. (2023). Development of GeoGebra-Based Fraction Gap Learning Media to Improve Understanding of the Fraction Concept of Grade v Elementary School. Didaktika Tauhidi Jurnal Pendidikan Guru Sekolah Dasar, 10(1), 55–69. https://doi.org/10.30997/dt.v10i1.8238

Ndukwe, Nnachi, O., Egbe, I., Ndubuisi, N., & Patrick, O. (2022). Effect of Polya Problem Solving Teaching Method on the Achievement of Students in Algebra. RHSS. https://doi.org/10.7176/rhss/12-6-04

Ng, Y. X., & Toh, T. L. (2024). On Some Guiding Principles of Enacting Mathematical Problem Solving for Classroom Instruction. Dinamika Jurnal Ilmiah Pendidikan Dasar, 16(1), 1. https://doi.org/10.30595/dinamika.v16i1.20441

Nofrianto, A., Gulo, A. D., Amri, M. A., & Rafulta, E. (2022). Student Errors in Mathematics Word Problem: What Can Be Learned? Jurnal Gantang, 7(1), 59–67. https://doi.org/10.31629/jg.v7i1.4426

Pambudi, D. S., Hobri, H., Putri, I. W. S., Trapsilasiwi, D., & Jatmiko, D. D. H. (2023). Analisis Pemecahan Masalah Siswa Dalam Menyelesaikan Soal Sharing Task Dan Jumping Task Berdasarkan Gaya Kognitif. Educator Jurnal Inovasi Tenaga Pendidik Dan Kependidikan, 3(1), 1–13. https://doi.org/10.51878/educator.v3i1.2184

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

Pradana, L. N. (2024). Problem-Solving Strategy: Mathematical Problem-Solving Model Within the Polya’ Framework. Kne Social Sciences. https://doi.org/10.18502/kss.v9i6.15327

Rahmah, N., & Darsikin, D. (2021). Student’s Problem-Solving Skills in Thermodynamics at Dampelas 1 Senior High School. Jurnal Ilmiah Pendidikan Fisika, 5(2), 258. https://doi.org/10.20527/jipf.v5i2.2797

Ramadhani, S., Ismaimuza, D., Sukayasa, S., & Meinarni, W. (2024). Analysis of Students’ Errors in Solving Story Problems Based on Newman’s Error Analysis (NEA) on the Subject Matter of Linear Program in View of Students’ Mathematical Ability. Prisma Sains Jurnal Pengkajian Ilmu Dan Pembelajaran Matematika Dan Ipa Ikip Mataram, 12(1), 110. https://doi.org/10.33394/j-ps.v12i1.10310

Rott, B., Specht, B. J., & Knipping, C. (2021). A Descriptive Phase Model of Problem-Solving Processes. ZDM, 53(4), 737–752. https://doi.org/10.1007/s11858-021-01244-3

Safrina, Y., Ikhsan, M. F., & Zubainur, C. M. (2022). Improving Student Geometry Problem-Solving Skills Through Spatial Training. https://doi.org/10.2991/assehr.k.211229.005

Shah, M. N., Anjum, F., Chand, S., & Tabassum, P. D. R. (2021). Enhancing Mathematical Word Problem Solving Skills: Using Bar Model Visualization Technique. International Research Journal of Education and Innovation, 2(3), 119–128. https://doi.org/10.53575/irjei.v2.03(21)11.119-128

Singh, P., Hoon, T. S., Nasir, N. A. M., Han, C. T., Rasid, S. M., & Hoong, J. B. Z. (2021). Obstacles Faced by Students in Making Sense of Fractions. The European Journal of Social & Behavioural Sciences, 30(1), 34–51. https://doi.org/10.15405/ejsbs.287

Starling‐Alves, I., Wronski, M. R., & Hubbard, E. M. (2021). Math Anxiety Differentially Impairs Symbolic, but Not Nonsymbolic, Fraction Skills Across Development. Annals of the New York Academy of Sciences, 1509(1), 113–129. https://doi.org/10.1111/nyas.14715

Sulistyani, D., Subekti, E. E., & Wardana, M. Y. S. (2021). Students’ Learning Difficulties Review From Mathematics Problem-Solving Ability in Third-Grade Elementary School. Indonesian Journal of Educational Research and Review, 4(2), 345. https://doi.org/10.23887/ijerr.v4i2.30310

Tay, Y. K., & Toh, T. L. (2023). A Model for Scaffolding Mathematical Problem-Solving: From Theory to Practice. Contemporary Mathematics and Science Education, 4(2), ep23019–ep23019. https://doi.org/10.30935/conmaths/13308

Tohir, M., Muhasshanah, M., Hidayat, R., Valentino, E., & Wijaya, T. T. (2023). Mathematical Olympiad Issues to Identify Students’ Reasoning Ability Using Polya’s Model. Alifmatika Jurnal Pendidikan Dan Pembelajaran Matematika, 5(2), 264–281. https://doi.org/10.35316/alifmatika.2023.v5i2.264-281

Unaenah, E., Suryadi, D., & Turmudi, T. (2024). Epistemological Learning Obstacles on Fractions in Elementary School. Jurnal Elemen, 10(1), 1–12. https://doi.org/10.29408/jel.v10i1.18306

Utomo, D. P., & Syarifah, D. L. (2021). Examining mathematical representation to solve problems in trends in mathematics and science study: Voices from Indonesian secondary school students. International Journal of Education in Mathematics, Science and Technology, 9(3), 540–556. https://doi.org/10.46328/IJEMST.1685

Verzosa-Quinto, E. M., & Mabansag, A. B. (2023). Error Analysis in Solving Word Problems Among Grade-8 Students. International Journal of Current Science Research and Review, 06(10). https://doi.org/10.47191/ijcsrr/v6-i10-10

Viseu, F., Pires, A., Menezes, L., & Costa, A. M. (2021). Semiotic Representations in the Learning of Rational Numbers by 2nd Grade Portuguese Students. Lnternational Electronic Journal of Elementary Education, 13(5), 611–624. https://doi.org/10.26822/iejee.2021.216

Wahyu, K., Kuzu, T. E., Subarinah, S., Ratnasari, D., & Mahfudy, S. (2020). Partitive Fraction Division: Revealing and Promoting Primary Students’ Understanding. Journal on Mathematics Education, 11(2), 237–258. https://doi.org/10.22342/jme.11.2.11062.237-258

Widodo, S. A., Ibrahim, I., Hidayat, W., Maarif, S., & Sulistyowati, F. (2021). Development of Mathematical Problem Solving Tests on Geometry for Junior High School Students. Jurnal Elemen, 7(1), 221–231. https://doi.org/10.29408/jel.v7i1.2973