Analyzing Student Difficulties on Geometric Translation through Polya’s Stages
DOI:
https://doi.org/10.31980/mosharafa.v14i2.3045Keywords:
Kesulitan Siswa, Pemecahan Masalah, Tahapan Polya, Translasi Geometri, Student Difficulties, Problem Solving, Polya’s Stages, Geometric TranslationAbstract
Abstrak
Rendahnya kemampuan pemecahan masalah siswa dalam translasi geometri ditunjukkan oleh kesulitan memahami arah pergerakan, representasi koordinat, dan strategi penyelesaian. Penelitian ini bertujuan menganalisis jenis dan penyebab kesulitan siswa berdasarkan tahapan Polya. Metode yang digunakan adalah kualitatif deskriptif dengan subjek 20 siswa kelas IX SMP Negeri di Tasikmalaya. Instrumen penelitian berupa dua soal tes uraian berbasis translasi geometri yang divalidasi ahli serta wawancara semi-terstruktur. Analisis data dilakukan melalui reduksi, penyajian, dan penarikan kesimpulan. Hasil menunjukkan kesulitan dominan pada tahap memahami masalah (65%) dan memeriksa kembali (65%), diikuti merencanakan penyelesaian (25%) dan melaksanakan rencana (17,5%). Temuan ini menegaskan perlunya pembelajaran berbasis soal kontekstual dan strategi reflektif. Penelitian ini berkontribusi dengan memberikan gambaran terarah mengenai letak kesulitan siswa yang dapat dijadikan dasar perbaikan pembelajaran translasi geometri.
Abstract
Students’ low problem-solving ability in geometric translation is reflected in their difficulties in understanding movement direction, representing coordinates, and applying solution strategies. This study aims to analyze the types and causes of students’ difficulties based on Polya’s problem-solving stages. A qualitative descriptive method was employed with 20 ninth-grade students from a public junior high school in Tasikmalaya as subjects. The research instruments included two essay-based problem-solving tests on geometric translation, validated by experts, and semi-structured interviews. Data were analyzed through reduction, display, and conclusion drawing. The findings revealed that the dominant difficulties occurred in understanding the problem (65%) and looking back (65%), followed by devising a plan (25%) and carrying out the plan (17.5%). These results highlight the need for contextual problem-based tasks and reflective strategies. The study contributes by providing a structured overview of students’ difficulties, which can serve as a foundation for improving instructional practices in teaching geometric translation.
References
Adu‐Gyamfi, K., Stiff, L. V, & Bossé, M. J. (2012). Lost in translation: Examining Translation Errors Associated with Mathematical Representations. School Science and Mathematics, 112(3), 159–170. https://doi.org/10.1111/j.1949-8594.2011.00129.x
Afhami, A. H. (2022). Aplikasi Geogebra Classic terhadap Pemahaman Konsep Matematika Siswa pada Materi Transformasi Geometri. Plusminus: Jurnal Pendidikan Matematika, 2(3), 449-460. https://doi.org/10.31980/plusminus.v2i3.1119
Agusfianuddin, A., Herman, T., & Turmudi, T. (2024). Difficulties in Mathematical Language and Representation among Elementary School Students when Solving Word Problems. Jurnal Elemen, 10(3), 567–581.
https://doi.org/10.29408/jel.v10i3.25814
Alashwal, H. A., & Barham, A. I. (2025). Sustaining Problem-Based Learning: A Mixed-Methods Exploration of Its Long-Term Effects on Primary Students’ Mathematical Problem Solving. Social Sciences & Humanities Open, 12, 101717.
https://doi.org/10.1016/j.ssaho.2025.101717
Amrullah, A., Chelladurai, S., Zulihi, Z., Ramdhani, M. I., Sukma, F. A. O., Patil, A. B., & Durgayan, A. (2024). Analysis of Students’ Learning Problem Solving Skills through the Application of Polya’s Steps. International Journal of Education Research and Development, 4(1), 25–36.
https://doi.org/10.52760/ijerd.v4i1.53
ARGÜN, Z. (2020). Self-Reflections of Gifted Students in the Context of Mathematical Problem Solving. MOJES: Malaysian Online Journal of Educational Sciences, 8(2), 14–27.
Balaban, L.-M. (2024). Autoevaluărea: Instrument Al Dezvoltării Competenței A Învăța Să Înveți A Elevilor De Liceu. Univers Pedagogic, 84(4), 23–28. https://doi.org/10.52387/1811-5470.2024.4.03
Bandara, F., Halini, H., & Suratman, D. (2022). Analisis Kesalahan Siswa Menyelesaikan Soal Cerita Sistem Persamaan Linear Dua Variabel Smp. Jurnal AlphaEuclidEdu, 3(2), 144–151. https://doi.org/10.26418/ja.v3i2.53172
Barana, A., Boetti, G., & Marchisio, M. (2022). Self-Assessment in the Development of Mathematical Problem-Solving Skills. Education Sciences, 12(2), 81. https://doi.org/10.3390/educsci12020081
Flores, A., & Yanik, H. B. (2016). Geometric Translations: An Interactive Approach Based on Students’ Concept Images. North American GeoGebra Journal, 5(1).
Fujita, T., Kondo, Y., Kumakura, H., Kunimune, S., & Jones, K. (2020). Spatial Reasoning Skills About 2D Representations of 3D Geometrical Shapes in grades 4 to 9. Mathematics Education Research Journal, 32, 235–255. https://doi.org/10.1007/s13394-020-00335-w
Gianto, E. K. A., Mampouw, H. L., & Setyadi, D. (2018). The Development of MOSIRI (Geometry Transformation Module) for High School Students. Al-Jabar: Jurnal Pendidikan Matematika, 9(2), 121–134. https://doi.org/10.24042/ajpm.v9i2.3402
Gilligan-Lee, K. A., Hawes, Z. C. K., & Mix, K. S. (2022). Spatial Thinking as the Missing Piece in Mathematics Curricula. Npj Science of Learning, 7(1), 10. https://doi.org/10.1038/s41539-022-00128-9
Giovanni, L. D. A., Parta, I. N., Susanto, H., & Anwar, L. (2023). Analisis Kesalahan Siswa Berbakat Matematika Dalam Memecahkan Masalah Transformasi Geometri Berdasarkan Langkah Polya. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1039–1049. https://doi.org/ 10.24127/ajpm.v12i1.6653
Hagge, J., & Appova, A. (2025). The Technical Subtechnical Nontechnical Vocabulary Model: Helping Students to Make Sense of Math Story Problems. The Reading Teacher.
https://doi.org/10.1002/trtr.2375
Hapsari, Z. M., Muhtadi, D., & Sukirwan. (2024). Analisis Kesulitan Peserta Didik Dan Faktor-Faktor Penyebabnya Pada Materi Luas Permukaan Kerucut Dan Tabung. Uninus Journal of Mathematics Education and Science (UJMES), 9(2), 55–67. https://doi.org/10.30999/ujmes.v9i2.3203
Harris, D., Logan, T., & Lowrie, T. (2021). Unpacking Mathematical-Spatial Relations: Problem-Solving in Static and Interactive Tasks. Mathematics Education Research Journal, 33(3), 495–511. https://doi.org/10.1007/s13394-020-00316-z
Hernández, R. V. (2016). Errores Matemáticos En El Conocimiento Procedimental Al Resolver Problemas De Superficies Cuadráticas. Revista Logos, Ciencia & Tecnología, 8(1), 67–76. https://doi.org/10.22335/rlct.v8i1.348
Huberman, M., & Miles, M. B. (1992). Analisis Data Kualitatif. Universitas Indonesia: Jakarta.
Ignacio, F., López, B., Margarita, C., Rodríguez, O., Adriana, J., & Escamilla, A. (2020). Research Questions and Design Perspectiva Teórica Preguntas de Investigación y Diseño. 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1048–1050.
https://doi.org/10.51272/pmena.42.2020-164
Karagöz Akar, G., Zembat, İ. Ö., Arslan, S., & Belin, M. (2023). Geometric Transformations Through Quantitative Reasoning. In Quantitative Reasoning in Mathematics and Science Education (pp. 199–219). Springer.
https://doi.org/10.1007/978-3-031-14553-7_8
Kop, P. M. G. M., Janssen, F. J. J. M., Drijvers, P. H. M., & van Driel, J. H. (2021). Promoting Insight Hnto Algebraic Formulas Through Graphing by hand. Mathematical Thinking and Learning, 23(2), 125–144. https://doi.org/10.1080/10986065.2020.1765078
Maryati, M., & Prahmana, R. C. I. (2020). Designing Learning Translation Using the Motifs of Anyaman Bambu. IndoMath: Indonesia Mathematics Education, 3(2), 61.
https://doi.org/10.30738/indomath.v3i2.7725
Maulani, F. I., & Zanthy, L. S. (2020). Analisis Kesulitan Siswa Dalam Menyelesaikan Soal Materi Transformasi Geometri. Gammath: Jurnal Ilmiah Program Studi Pendidikan Matematika, 5(1), 16–25. https://doi.org/10.32528/gammath.v5i1.3189
Monteleone, C., Miller, J., & Warren, E. (2023). Conceptualising Critical Mathematical Thinking in Young Students. Mathematics Education Research Journal, 35(2), 339–359. https://doi.org/10.1007/s13394-023-00445-1
NCTM, N. C. of T. of M. (2000). Principles and Standards for School Mathematics. NCTM.
Nguyen, H. A., Guo, Y., Stamper, J., & McLaren, B. M. (2020). Improving Students’ Problem-Solving Flexibility in Non-Routine Mathematics. Artificial Intelligence in Education: 21st International Conference, AIED 2020, Ifrane, Morocco, July 6–10, 2020, Proceedings, Part II 21, 409–413. https://doi.org/10.1007/978-3-030-52240-7_74
Nizar, H., Zulkardi, Z., Putri, R. I. I., Mulyono, B., & Susanti, E. (2025). Learning Translation Using Gobak Sodor Game. Mosharafa: Jurnal Pendidikan Matematika, 14(1), 279-290. https://doi.org/10.31980/mosharafa.v14i1.2607
Nurizlan, A., Komala, E., & Monariska, E. (2022). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Cerita pada Materi Trigonometri Ditinjau dari Langkah Polya. Prisma, 11(2), 639. https://doi.org/10.35194/jp.v11i2.2530
Octaviyanti, L., & Wahyuni, I. (2023). Konstruksi Konsep Geometri Berdasarkan Teori Apos Konteks Budaya Damar Kurung Ditinjau Dari Perbedaan Gender. Radian Journal: Research and Review in Mathematics Education, 2(3), 103-113. https://doi.org/10.35706/rjrrme.v2i3.9011
Paradesa, R. (2019). Learning Trajectory in Problem-Based Mathematics Learning with Literacy and Numeracy Reinforcement an Implementation of Lesson Study at Junior High School. Jurnal Pendidikan Matematika JPM RAFA, 2(1), 56–84.
https://doi.org/10.31764/jtam.v7i2.12883
Pebriyanti, Y., & Amelia, R. (2023). Analysis of Students’ Problem-Solving Ability on Set Material According to Polya Model. JIML: Journal of Innovative Mathematics Learning, 6(4), 272–279. https://doi.org/10.22460/jiml.v6i4.18504
Pitriyani, P., Sundayana, R., & Maryati, I. (2024). Efektivitas Model Problem-Based Learning terhadap Kemampuan Spasial Matematis Siswa. Plusminus: Jurnal Pendidikan Matematika, 4(2), 347-356. https://doi.org/10.31980/plusminus.v4i2.2203
Polya, G. (1973). How To Solve It. Princeton: Princeton University Press.
Polya, G. (2014). How to Solve It: A New Aspect of Mathematical Method. In How to solve it. Princeton university press.
Qi, H. (2024). Understanding Students’ Challenges in Using Their Metacognition to Enact Effective Learning Strategies. 2024 ASEE PSW Conference. https://doi.org/10.18260/1-2--46068
Ramnarain, U. (2014). Empowering Educationally Disadvantaged Mathematics Students through a Strategies-Based Problem-Solving Approach. The Australian Educational Researcher, 41, 43–57.
https://doi.org/10.1007/s13384-013-0098-8
Rehman, N., Huang, X., Mahmood, A., AlGerafi, M. A. M., & Javed, S. (2024). Project-Based Learning as a Catalyst for 21st-Century Skills and Student Engagement in the Math Classroom. Heliyon, 10(23), e39988.
https://doi.org/10.1016/j.heliyon.2024.e39988
Rodríguez-Sánchez, M. M., Sánchez-García, A. B., & López-Fernández, R. (2020). Subtraction: More than an Algorithm? Sustainability, 12(21), 9148. https://doi.org/10.3390/su12219148
Sa’dijah, C., & Muksar, M. (2021). Assessing Students’ Errors in Mathematical Translation: From Symbolic to Verbal and Graphic Representations. International Journal of Evaluation and Research in Education, 10(1), 115–125. https://doi.org/10.11591/ijere.v10i1.20819
Samosir, C. M., Herman, T., Prabawanto, S., Melani, R., & Mefiana, S. A. (2024). Students’ Difficulty in Understanding Problems in the Contextual Problem-Solving Process. PRISMA, 13(1), 20–29. https://doi.org/10.35194/jp.v13i1.3726
Saputri, M., Miza, H., & Hamid, A. (2024). Analysis of Students’ Difficulties in Solving Physics Problems Using Polya’s Theory. Jurnal Penelitian Pendidikan IPA, 10(9), 6525–6532.
https://doi.org/10.29303/jppipa.v10i9.7127
Sholihah, S. Z., & Afriansyah, E. A. (2017). Analisis kesulitan siswa dalam proses pemecahan masalah geometri berdasarkan tahapan berpikir Van Hiele. Mosharafa: Jurnal Pendidikan Matematika, 6(2), 287-298. https://doi.org/10.31980/mosharafa.v6i2.451
Sudirman, S., Kusumah, Y. S., Martadiputra, B. A. P., & Runisah, R. (2023). Epistemological obstacle in 3D geometry thinking: Representation, spatial structuring, and measurement. Pegem Journal of Education and Instruction, 13(4), 292–301. https://doi.org/10.24127/ajpm.v14i1.10763
Sumartono. (2023). Student Mistakes in Solving Math Story Problems (Class V Study at SDN Sedatigede I Sidoarjo). Asian Journal of Applied Education (AJAE), 2(3), 367–380.
https://doi.org/10.55927/ajae.v2i3.5043
Sunariah, L., & Mulyana, E. (2020). The Didactical and Epistemological Obstacles on the Topic of Geometry Transformation. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032089
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of Problem-Solving Strategies in Mathematics Education Supporting the Sustainability of 21st-century skills. Sustainability, 12(23), 10113. https://doi.org/10.3390/su122310113
Wang, G., Kang, Y., Jiao, Z., Chen, X., Zhen, Y., Zhang, D., & Su, M. (2022). Development and Application of Intelligent Assessment System for Metacognition in Learning Mathematics Among Junior High School students. Sustainability, 14(10), 6278. https://doi.org/10.3390/su14106278
Wongsa, S., & Cojorn, K. (2024). Enhancing the Students’ Problem-Solving Ability through Situation-Based Learning with the Six Thinking Hats Technique. Journal of Advanced Sciences and Mathematics Education, 4(2), 95–112. https://doi.org/10.58524/jasme.v4i2.447
Yim, J., & Lee, H. S. (2022). Students’ Use of Prior Conceptions of Symbols in Finding an Equation for a Horizontal Translation of the Graph of a Function. International Journal of Science and Mathematics Education, 1–19. https://doi.org/10.1007/s10763-021-10230-w
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