Students’ Word-Problem Errors Identified Through Newman’s Procedure in a Problem-Based Learning Classroom

1 Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Medan
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Low mathematics achievement, particularly in solving word problems, remains a persistent challenge for students. This study aims to analyze (1) whether students’ errors in solving word problems through the Problem-Based Learning (PBL) model are lower than those in conventional learning, (2) whether students’ mastery learning in the PBL model is higher than that in conventional learning, and (3) how well students are able to solve mathematical word problems based on Newman’s procedure when taught using the PBL model. A mixed methods approach was employed, combining a quasi-experimental design with a qualitative descriptive method. Data were collected through written tests for the quantitative component and in-depth interviews for the qualitative component. The quantitative data were analyzed using an Independent Sample t-test. The findings indicate that students taught with the PBL model experienced a notable reduction in errors across all stages of Newman’s procedure. These results demonstrate that the PBL model effectively minimizes student errors, increases mastery learning, and strengthens students’ ability to solve mathematical word problems. Overall, the study recommends the use of the PBL model in mathematics classrooms to foster deeper understanding and enhance the relevance of learning to students’ everyday experiences.

Anggraini, H., & Surya, E. (2025). Students’ Word-Problem Errors Identified Through Newman’s Procedure in a Problem-Based Learning Classroom. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 5(4), 1550–1570. https://doi.org/10.51574/kognitif.v5i4.2638

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  1. Amelia Safitri, F., Sugiarti, T., & Fajar Surya Hutama, dan. (2019). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Cerita Bangun Datar Berdasarkan Newman’s Error Analysis (NEA). In JPK (Vol. 5, Issue 1). https://journal.unnes.ac.id/nju/index.php/jpk
  2. Björklund, C., & Palmér, H. (2022). Teaching toddlers the meaning of numbers—connecting modes of mathematical representations in book reading. Educational Studies in Mathematics, 110(3), 525–544. https://doi.org/10.1007/s10649-022-10147-3
  3. Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., & Newman-Owens, A. (2015). A Learning Trajectory in 6-Year-Olds’ Thinking About Generalizing Functional Relationships. Journal for Research in Mathematics Education, 46(5), 511–558. https://doi.org/10.5951/jresematheduc.46.5.0511
  4. Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., & Newman-Owens, A. (2017). A progression in first-grade children’s thinking about variable and variable notation in functional relationships. Educational Studies in Mathematics, 95(2), 181–202. https://doi.org/10.1007/s10649-016-9745-0
  5. Chronaki, A., & Planas, N. (2018). Language diversity in mathematics education research: a move from language as representation to politics of representation. ZDM - Mathematics Education, 50(6), 1101–1111. https://doi.org/10.1007/s11858-018-0942-4
  6. Fonger, N. L. (2019). Meaningfulness in representational fluency: An analytic lens for students’ creations, interpretations, and connections. Journal of Mathematical Behavior, October, 1–26. https://doi.org/10.1016/j.jmathb.2018.10.003
  7. Hughes, E. M., Riccomini, P. J., & Lee, J. (2020). Investigating written expressions of mathematical reasoning for students with learning disabilities. Journal of Mathematical Behavior, 58(February), 100775. https://doi.org/10.1016/j.jmathb.2020.100775
  8. Ikram, M., Purwanto, Parta, I. N., & Susanto, H. (2020). Exploring the potential role of reversible reasoning: Cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591–611. https://doi.org/10.17478/jegys.665836
  9. Kotto, M. A., Babys, U., & Gella, N. J. M. (2022). Meningkatkan Kemampuan Penalaran Matematika Siswa Melalui Model PBL (Problem Based Learning). Jurnal Sains Dan Edukasi Sains, 5(1), 24–27. https://doi.org/10.24246/juses.v5i1p24-27
  10. Lee, H. S., Sanei, H., Famularo, L., Masters, J., Bradshaw, L., & Schellman, M. (2023). Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle. Journal of Mathematical Behavior, 71(June), 101081. https://doi.org/10.1016/j.jmathb.2023.101081
  11. Lee, Y., Capraro, R. M., & Bicer, A. (2019). Affective Mathematics Engagement: a Comparison of STEM PBL Versus Non-STEM PBL Instruction. Canadian Journal of Science, Mathematics and Technology Education, 19(3), 270–289. https://doi.org/10.1007/s42330-019-00050-0
  12. Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the Visual Representation of a Figural Pattern. Mathematical Thinking and Learning, 20(2), 91–107. https://doi.org/10.1080/10986065.2018.1441599
  13. Nolaputra, A. P., Wardono, & Supriyono. (2018). Analisis Kemampuan Literasi Matematika pada Pembelajaran PBL Pendekatan RME Berbantuan Schoology Siswa SMP. Prisma, Prosiding Seminar Nasional Matematika, 1.
  14. Nurwita, F., Kusumah, Y. S., & Priatna, N. (2022). Exploring students’ mathematical computational thinking ability in solving pythagorean theorem problems. Al-Jabar : Jurnal Pendidikan Matematika, 13(2). https://doi.org/10.24042/ajpm.v13i2.12496
  15. OECD. (2018). Programme for International Students Assesment (PISA) Result From PISA 2018.
  16. Paichi Pat Shein. (2012). Seeing With Two Eyes: A Teacher’s Use of Gestures in Questioning and Revoicing to Engage English Language Learners in the Repair of Mathematical Errors. Journal for Research in Mathematics Education, 43(2), 182. https://doi.org/10.5951/jresematheduc.43.2.0182
  17. Rich, K. M., Yadav, A., & Schwarz, C. V. (2019). Computational thinking, mathematics, and science: Elementary teachers’ perspectives on integration. Journal of Technology and Teacher Education, 27(2), 165–205.
  18. Scheiner, T., & Pinto, M. M. F. (2019). Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-019-9879-y
  19. Sevinc, S., & Lesh, R. (2022). Preservice mathematics teachers’ conceptions of mathematically rich and contextually realistic problems. Journal of Mathematics Teacher Education, 25(6), 667–695. https://doi.org/10.1007/s10857-021-09512-5
  20. Swidan, O. (2020). A learning trajectory for the fundamental theorem of calculus using digital tools. International Journal of Mathematical Education in Science and Technology, 51(4), 542–562. https://doi.org/10.1080/0020739X.2019.1593531
  21. Swidan, O., & Fried, M. (2021). Focuses of awareness in the process of learning the fundamental theorem of calculus with digital technologies. Journal of Mathematical Behavior, 62(June 2020), 100847. https://doi.org/10.1016/j.jmathb.2021.100847
  22. Tallman, M. A., & Frank, K. M. (2020). Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base. Journal of Mathematics Teacher Education, 23(1), 69–95. https://doi.org/10.1007/s10857-018-9409-3
  23. Tan Sisman, G., & Aksu, M. (2016). A Study on Sixth Grade Students’ Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume. International Journal of Science and Mathematics Education, 14(7), 1293–1319. https://doi.org/10.1007/s10763-015-9642-5
  24. Thompson, P., Carlson, M. P., Byerley, C., & Hatfield, N. (2014). Schemes for thinking with magnitudes: An hypothesis about foundational reasoning abilities in algebra. Epistemic Algebra Students: Emerging Models of Students’ Algebraic Knowing, September, 1–24.
  25. van Lieshout, E. C. D. M., & Xenidou-Dervou, I. (2018). Pictorial representations of simple arithmetic problems are not always helpful: a cognitive load perspective. Educational Studies in Mathematics, 98(1), 39–55. https://doi.org/10.1007/s10649-017-9802-3
  26. Wilkie, K. J., & Hopkins, S. (2024). Primary students’ relational thinking and computation strategies with concrete-to-symbolic representations of subtraction as difference. Journal of Mathematical Behavior, 73(April 2023), 101121. https://doi.org/10.1016/j.jmathb.2023.101121
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