Pola dan Lintasan Kesalahan Mahasiswa dalam Pemecahan Masalah Trigonometri Open-Ended
DOI:
https://doi.org/10.53696/venn.v5i5.664Keywords:
Analisis Kesalahan, Lintasan Kesalahan, Masalah Open-Ended, Polya, TrigonometriAbstract
This study aims to identify error patterns and trace students’ error trajectories in solving open-ended trigonometry problems based on Polya’s problem-solving stages. An exploratory qualitative approach with cross-case analysis was employed. The participants were 85 first-year undergraduate students enrolled in a Trigonometry course in the second semester of the 2025/2026 academic year. Four open-ended problems yielded 340 responses, which were analyzed across four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. Errors were categorized as conceptual, representational, strategic, procedural, and verification errors. Eight students were purposively selected for interviews to clarify their problem-solving processes in specific cases. The findings revealed that error patterns varied according to the demands of each problem. Strategic and procedural errors predominated in general triangle problems, conceptual and verification errors were prominent in trigonometric identity proofs, whereas representational and strategic errors dominated function modeling and graphing problems. Cross-case analysis identified four main error trajectories: representational errors that propagated into strategic and procedural errors; adequate problem understanding accompanied by inappropriate or undeveloped strategies; appropriate strategies followed by errors during execution; and correct execution followed by inadequate verification. These findings extend Polya-based error analysis beyond stage-specific classification by tracing the relationships among errors across successive stages of the problem-solving process.
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Ade Mirza, Winarji, A., Metia Novianti, Ferah Ningtias, & Muhammad Arjuna. (2026). Exploring learning trajectories in trigonometric identity proof construction through didactic transposition. Al-Jabar : Jurnal Pendidikan Matematika, 17(1), 493–509. https://doi.org/10.24042/ajpm.v17i1.30223
Buchbinder, O., & McCrone, S. (2023). Preparing prospective secondary teachers to teach mathematical reasoning and proof: The case of the role of examples in proving. ZDM – Mathematics Education, 55(4), 779–792. https://doi.org/10.1007/s11858-023-01493-4
Eva Wulanningtyas, M., Arfin, A., Linling, Y., Slamet Setiana, D., & Boriboon, G. (2024). Learning Mathematics through Students’ Worksheets with Open-Ended Approach: A Students’ Errors Analysis on Mathematical Problem-Solving Ability. Jurnal Pendidikan MIPA, 25(1), 468–485. https://doi.org/10.23960/jpmipa/v25i1.pp468-485
Fauzi, K. M. A., & Hia, Y. (2022). Types of student errors in the trajectory of thinking solving analytical geometry questions based on Newman’S Error Analysis (NEA). AIP Conference Proceedings, 2659(1), 100011. https://doi.org/10.1063/5.0113797
Gradini, E., Yustinaningrum, B., & Safitri, D. (2022). Kesalahan Siswa Dalam Memecahkan Masalah Trigonometri Ditinjau dari Indikator Polya. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 49–60. https://doi.org/10.31980/mosharafa.v11i1.686
Herizal. (2025). Identifikasi kesalahan pembuktian matematis siswa pada materi aplikasi trigonometri. Jurnal Pendidik Indonesia, 6(2), 64–74. https://doi.org/10.61291/jpi.v6i2.74
Hidayat, W., & Aripin, U. (2020). Identifikasi Kesalahan Jawaban Mahasiswa Pada Mata Kuliah Trigonometri Berdasarkan Dimensi Pengetahuan Krathwohl. JNPM (Jurnal Nasional Pendidikan Matematika), 4(1), 142. https://doi.org/10.33603/jnpm.v4i1.3316
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
Maharani, R., & Murtiyasa, B. (2023). Analysis Of Students’ Error In Solving Trigonometry Comparison Problems With The Polya Criteria Guiden. Prima: Jurnal Pendidikan Matematika, 7(2), 157. https://doi.org/10.31000/prima.v7i2.8482
Msi, Y., Matsepe, M. E., & Sehowa, K. (2026). Errors in trigonometric proof-related reasoning tasks: Insights from Grade 10 learners at a rural Eastern Cape school. African Journal of Teacher Education and Development, 5(1), a132. https://doi.org/10.4102/AJOTED.v5i1.132
Murtafiah, W., Lestari, N. D. S., Yahya, F. H., Apriandi, D., & Suprapto, E. (2023). How Do Students’ Decision-Making Ability In Solving Open-Ended Problems? Infinity Journal, 12(1), 133. https://doi.org/10.22460/infinity.v12i1.p133-150
Nabie, M. J., Akayuure, P., Ibrahim-Bariham, U. A., & Sofo, S. (2018). Trigonometric Concepts: Pre-Service Teachers’ Perceptions And Knowledge. Journal on Mathematics Education, 9(2), 169–182. https://doi.org/10.22342/jme.9.2.5261.169-182
Obeng, B. A., Banson, G. M., Owusu, E., & Owusu, R. (2024). Analysis of senior high school students’ errors in solving trigonometry. Cogent Education, 11(1), 2385119. https://doi.org/10.1080/2331186X.2024.2385119
Pólya, G. (2014). How to solve it: A new aspect of mathematical method. Princeton University Press. https://doi.org/10.1515/9781400828678
Ramadhan, D., & Santoso, E. (2025). Newman’s Error Analysis of Trigonometry: Critical Thinking Perspective. Jurnal Pendidikan MIPA, 26(4), 2321–2342. https://doi.org/10.23960/jpmipa.v26i4.pp2321-2342
Setiawan, Y. E. S. & Sunardi. (2023). Classification of errors in determining trigonometry function values at standard positions. JRAMathEdu (Journal of Research and Advances in Mathematics Education). https://doi.org/10.23917/jramathedu.v8i2.1625
Sulistyaningsih, D., Purnomo, E. A., & Purnomo, P. (2021). Polya’s Problem Solving Strategy in Trigonometry: An Analysis of Students’ Difficulties in Problem Solving. Mathematics and Statistics, 9(2), 127–134. https://doi.org/10.13189/ms.2021.090206
Wahab A, A., Kusuma, Y. S., Juandi, D., Turmudi, T., Buhaerah, B., & Syaiful, S. (2024). Understanding Students’ Struggles in Solving Mathematical Problems: A Systematic Literature Review Using Polya’s Framework. Jurnal Pendidikan Progresif, 14(3), 1728–1753. https://doi.org/10.23960/jpp.v14.i3.2024118
Wardhani, T. A. W., & Argaswari, D. P. A. D. (2022). High School Students’ Error In Solving Word Problem Of Trigonometry Based On Newman Error Hierarchical Model. Infinity Journal, 11(1), 87. https://doi.org/10.22460/infinity.v11i1.p87-102
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
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