Interferensi Jenis Besaran: Mengapa Definisi Variabel yang Dinyatakan dalam Soal Gagal Mengatur Pemodelan Siswa
Keywords:
asesmen kontekstual, interferensi jenis besaran, literasi matematika, pemodelan matematis, penskoran bersyarat
Abstract
Soal kontekstual di Indonesia sering langsung menuliskan arti variabel, misalnya "misalkan x adalah harga satu noken", agar siswa mudah membuat model, tetapi belum diketahui apakah siswa benar-benar memakainya. Penelitian ini menguji hal itu, menelusuri kesalahan menghitung, dan memeriksa pengaruh cara penskoran terhadap penilaian kemampuan menafsirkan. Studi kasus ini melibatkan 17 siswa kelas IX sebuah madrasah negeri di Kota Jayapura yang mengerjakan enam soal bertahap tentang sistem persamaan linear dua variabel berkonteks Papua; tujuh di antaranya diwawancarai. Dua soal menyusun model (formulate) sama-sama menuliskan arti variabel. Saat yang dicari harga di antara data harga, hampir semua siswa berhasil (rerata 1,76 dari 2). Saat yang dicari berat di antara data yang didominasi harga, hampir semua gagal (rerata 0,18) dan banyak yang mencampuradukkan berat dengan harga. Gejala ini disebut interferensi jenis besaran: jenis angka yang mendominasi soal mengalahkan arti variabel yang tertulis. Kesalahan menghitung (employ) terutama berasal dari pengurangan bilangan besar, dan hanya satu siswa memeriksa jawaban pada kedua persamaan. Penskoran biasa berdasarkan kunci jawaban menilai kemampuan menafsirkan (interpret) sangat rendah (0,35). Penskoran bersyarat, yang berpatokan pada angka hasil siswa sendiri pada langkah sebelumnya, menaikkannya menjadi 1,00, tetapi seluruh kenaikan itu berasal dari jawaban identik yang kemungkinan disalin. Jadi, menuliskan arti variabel dalam soal tidak menjamin siswa mampu menyusun model sendiri. Penyusun soal perlu menyertakan soal yang besaran dicarinya berbeda jenis dari angka yang dominan, sedangkan guru perlu melaporkan kedua skor dan memastikan siswa bekerja mandiri.
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References
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fostering. Educational Studies in Mathematics, 109(2), 205–236. https://doi.org/10.1007/s10649-021-10104-6
Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and Representation of Physics Problems by Experts and Novices*. Cognitive Science, 5(2), 121–152. https://doi.org/10.1207/s15516709cog0502_2
Darmawijoyo, D., Zulkardi, Z., Putri, R. I. I., Hapizah, H., & Syutaridho, S. (2025). How do students use mathematical reasoning to solve PISA-type mathematics problems based on making kite contexts? Infinity Journal, 14(4), 1065–1080. https://doi.org/10.22460/infinity.v14i4.p1065-1080
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Efendi, R., & Kulimbang, E. (2025). Pengaruh Self-Regulated Learning dan Gaya Belajar terhadap Kemampuan
Pemecahan Masalah Matematika Siswa MTs Negeri Kota Jayapura. Jurnal Cendekia : Jurnal Pendidikan Matematika, 10(1), 25–39. https://doi.org/10.31004/cendekia.v10i1.4601
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Educational Review, 70(1), 7–17. https://doi.org/10.1080/00131911.2018.1396806
Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87(3), 215–251. https://doi.org/10.1037/0033-295X.87.3.215
Filloy, E., & Rojano, T. (1989). Solving Equations: the Transition from Arithmetic to Algebra. For the Learning of Mathematics, 9(2), 19–25. https://www.jstor.org/stable/40247950
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143–162. https://doi.org/10.1007/BF02655886
Gustiningsi, T., Pasaribu, F. T., Junita, R., & Ismail, Z. (2026). Investigating students’ mathematical literacy: How students solve PISA-like problems in the Jambi context. Jurnal Elemen, 12(2), 631–651. https://doi.org/10.29408/jel.v12i2.34156
Hamidy, A., & Jailani, J. (2019). Kemampuan proses matematis siswa Kalimantan Timur dalam menyelesaikan soal matematika model PISA. Jurnal Riset Pendidikan Matematika, 6(2), 133–149. https://doi.org/10.21831/jrpm.v6i2.26679
Khairani, A., Hakiki, N. I., & Yopan, M. (2025). Analisis Faktor Penyebab Angka Putus Sekolah di Tingkat SD dan SMP di Papua: Kajian Studi Pustaka Berbasis Teori Struktural. JIIP - Jurnal Ilmiah Ilmu Pendidikan, 8(1), 45–51. https://doi.org/10.54371/jiip.v8i1.6510
Kirshner, D. (1989). The Visual Syntax of Algebra. Journal for Research in Mathematics Education, 20(3), 274. https://doi.org/10.2307/749516
Klingbeil, K., & Moons, F. (2025). The omnipresence of the Letter-as-Object misconception: a multilevel Latent Transition Analysis on understanding variables. Educational Studies in Mathematics, 120(3), 455–476. https://doi.org/10.1007/s10649-025-10428-7
Krawitz, J., Chang, Y.-P., Yang, K.-L., & Schukajlow, S. (2022). The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan. Educational Studies in Mathematics, 109(2), 337–359. https://doi.org/10.1007/s10649-021-10058-9
Krawitz, J., Schukajlow, S., Yang, X., & Geiger, V. (2025). A Systematic Review of International Perspectives on Mathematical Modelling: Modelling Goals and Task Characteristics. ZDM – Mathematics Education, 57(2–3), 193–212. https://doi.org/10.1007/s11858-025-01683-2
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
May, T. A., Koskey, K. L. K., Bostic, J. D., Stone, G. E., Kruse, L. M., & Matney, G. (2023). Examining how using dichotomous and partial credit scoring models influence sixth-grade mathematical problem-solving assessment outcomes. School Science and Mathematics, 123(2), 54–67. https://doi.org/10.1111/ssm.12570
Medrano, J., & Miller‐Cotto, D. (2025). Understanding working memory as a facilitator of math problem‐solving: Offloading as a potential strategy. British Journal of Educational Psychology, 95(3), 871–887. https://doi.org/10.1111/bjep.12767
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (3rd ed.). SAGE Publications, Inc.
Muskens, M., Frankenhuis, W. E., & Borghans, L. (2024). Math items about real-world content lower test-scores of students from families with low socioeconomic status. Npj Science of Learning, 9(1), 19. https://doi.org/10.1038/s41539-024-00228-8
OECD. (2023a). PISA 2022 Assessment and Analytical Framework. OECD Publishing. https://doi.org/10.1787/dfe0bf9c-en
OECD. (2023b). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing. https://doi.org/10.1787/53f23881-en
OECD. (2026). PISA 2025 Results (Volume I): Future-Ready Students. OECD Publishing. https://doi.org/10.1787/73451bc5-en
Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2025). Revisiting the Relationship of Arithmetical Thinking and Letter-Symbolic Algebra. International Journal of Science and Mathematics Education, 23(3), 689–711. https://doi.org/10.1007/s10763-024-10493-z
Pradana, D. A. Y., & Murtiyasa, B. (2020). Kemampuan siswa menyelesaikan masalah berbentuk soal cerita sistem persamaan linear ditinjau dari kemampuan penalaran. Pythagoras: Jurnal Pendidikan Matematika, 15(2). https://doi.org/10.21831/pg.v15i2.35419
Prahmana, R. C. I., & D’Ambrosio, U. (2020). Learning Geometry and Values from Patterns: Ethnomathematics on the Batik Patterns of Yogyakarta, Indonesia. Journal on Mathematics Education, 11(3), 439–456. https://doi.org/10.22342/jme.11.3.12949.439-456
Rubel, L. H., & McCloskey, A. V. (2021). Contextualization of mathematics: which and whose world? Educational Studies in Mathematics, 107(2), 383–404. https://doi.org/10.1007/s10649-021-10041-4
Säfström, A. I., Lithner, J., Palm, T., Palmberg, B., Sidenvall, J., Andersson, C., Boström, E., & Granberg, C. (2024).
Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving. Educational Studies in Mathematics, 115(2), 125–149. https://doi.org/10.1007/s10649-023-10278-1
Schoenfeld, A. H. (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint). Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Schukajlow, S., Krawitz, J., Kanefke, J., Blum, W., & Rakoczy, K. (2023). Open modelling problems: cognitive barriers and instructional prompts. Educational Studies in Mathematics, 114(3), 417–438. https://doi.org/10.1007/s10649-023-10265-6
Sidenvall, J., Boström, E., Granberg, C., Lithner, J., Säfström, A. I., Andersson, C., Palmberg, B., & Palm, T. (2026).
Teachers’ in-the-moment diagnosis of students’ problem-solving difficulties in mathematics. Frontiers in Education, 11. https://doi.org/10.3389/feduc.2026.1831773
Soneira, C., Bansilal, S., & Govender, R. (2021). Insights into the reversal error from a study with South African and Spanish prospective primary teachers. Pythagoras, 42(1). https://doi.org/10.4102/pythagoras.v42i1.613
Stefana, A., Damiani, S., Granziol, U., Provenzani, U., Solmi, M., Youngstrom, E. A., & Fusar-Poli, P. (2025). Psychological, psychiatric, and behavioral sciences measurement scales: best practice guidelines for their development and validation. Frontiers in Psychology, 15. https://doi.org/10.3389/fpsyg.2024.1494261
Strohmaier, A. R., Schons, C., Knabbe, A., Vogel, M., Saado, K., & Obersteiner, A. (2026). The relation between text comprehension and computation in mathematical word-problem solving. Learning and Instruction, 101,
102235. https://doi.org/10.1016/j.learninstruc.2025.102235
Toalongo, X., Trelles, C., & Alsina, Á. (2022). Design, Construction and Validation of a Rubric to Evaluate Mathematical Modelling in School Education. Mathematics, 10(24), 4662. https://doi.org/10.3390/math10244662
Vessonen, T., Dahlberg, M., Hellstrand, H., Widlund, A., Korhonen, J., Aunio, P., & Laine, A. (2024). Task
Characteristics Associated with Mathematical Word Problem-Solving Performance Among Elementary School-Aged Children: A Systematic Review and Meta-Analysis. Educational Psychology Review, 36(4), 117. https://doi.org/10.1007/s10648-024-09954-2
Wahyuni, R., Suwanto, F. R., Sthephani, A., & Ahyan, S. (2025). Students’ obstacles in solving algebra form problems viewed from mathematical problem-solving ability. Infinity Journal, 14(3), 587–606. https://doi.org/10.22460/infinity.v14i3.p587-606
Wijaya, A., van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584. https://doi.org/10.54870/1551-3440.1317
Published
2026-10-30
How to Cite
Efendi, R., Sitepu, R., Ruamba, M., & Margareta, H. (2026). Interferensi Jenis Besaran: Mengapa Definisi Variabel yang Dinyatakan dalam Soal Gagal Mengatur Pemodelan Siswa. Jurnal Cendekia : Jurnal Pendidikan Matematika, 10(3), 2064-2079. https://doi.org/10.31004/cendekia.v10i3.5593
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Copyright (c) 2026 Rian Efendi, Rina Ananta Sumawardani Sitepu, Marthinus Yohanes Ruamba, Histia Sisilia Margareta
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