Students Proportional Reasoning Level in Solving Ill Structured Problem on Proportion Material in Terms of Gregorc’s Thinking Style
Abstract
This study examines the level of proportional reasoning in students when solving ill-structured problems concerning proportions, in terms of Gregorc's cognitive styles. A qualitative approach was used, involving 8 participants from grade VIII-B of MTsN Kota Batu. Based on the analysis, it can be concluded that students' cognitive styles affect their understanding of proportional reasoning. Students with a concrete sequential (CS) thinking style showed difficulty in understanding the concept of proportional and still relied on trial-and-error approaches, indicating they are at Level 0 (Non-proportional reasoning). Students with a abstract sequential (AS) and concrete random (CR) thinking style have used some visual or concrete aids, although they have not fully transitioned to a more systematic mathematical approach, placing them at Level 1 (Manipulative Proportional Reasoning). Meanwhile, students with an abstract random (AR) thinking style were able to use mathematical models to solve proportional problems but still faced challenges in consistently applying the correct method, leading them to Level 3 (Pre-multiplicative Proportional Reasoning). The differences in students' cognitive styles affect how they understand and apply the concept of proportional reasoning, including their ability to choose the appropriate method and maintain consistency in its application.
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References
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Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2021). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24(2), 179–202. https://doi.org/10.1007/s10857-019-09453-0
Zulkarnaen, R. (2017). Kesalahan Siswa Dalam Menyelesaikan Soal Penalaran Proposional. Seminar Matematika Dan Pendidikan Matematika UNY, M–8, 49–54.
Dole, S., Clarke, D., Wright, T., & Hilton, G. (2012). Student’s Proportional Reasoning in Mathematics and Science. Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, 2, 195–202. https://espace.library.uq.edu.au/view/UQ:279214
Dwirahayu, G., & Firdausi. (2016). Pengaruh Gaya Berpikir Terhadap Kemampuan Koneksi Matematis Mahasiswa. 9(2), 210–221. https://repository.uinjkt.ac.id/dspace/bitstream/123456789/46363/1/15
Eka, R., & Susanah. (2013). Penalaran Proporsional Siswa Kelas VII SMP Negeri II Beji Pasuruan Berdasarkan Tingkat Kemampuan Matematika. Jurnal Pendidikan Matematika, 2(1), 15–21. https://jurnalmahasiswa.unesa.ac.id/index.php/3/article/view/1209
Fadillla, D. M. N., & Siswono, T. Y. E. (2022). Penalaran Proporsional Siswa Bergaya Kognitif Sistematis dan Intutif dalam Menyelesaikan Masalah Numerasi. Jurnal Ilmiah Pendidikan Matematika, 11(3).
Fauzi, F. A., Ratnaningsih, N., & Nimah, K. (2020). Analisis Kemampuan Berpikir Kritis Matematis Peserta Didik Ditinjau Dari Gaya Berpikir Gregorc. Journal of Authentic Research on Mathematics Education (JARME), 2(2), 96–107. http://jurnal.unsil.ac.id/index.php/jarme/article/view/1734
Febriani, C., & Rosyidi, A. H. (2013). Identifikasi Penalaran Induktif Siswa dalam Memecahkan Masalah Matematika. Mathedunesa, 2(1), 1–6.
Fitri, S. N., Liana, M., & T, L. R. (2023). Penalaran Matematis Siswa Ditinjau dari Gaya Berpikir menurut Gregorc. AKSIOMA: Jurnal Matematika Dan Pendidikan Matematika, 14(2), 131–146.
Fuat, F., & Wulan, M. P. (2021). Kemampuan Penalaran Proporsional Siswa dalam Menyelesaikan Masalah Pra-Multiplikatif. JKPM (Jurnal Kajian Pendidikan Matematika), 6(2), 179. https://doi.org/10.30998/jkpm.v6i2.9047
Hariyanti, U. (2016). Penalaran Proposional Dalam Menyelesaikan Masalah Multiplikatif Bagi Siswa Kelas VIII SMP. Universitas Negeri Malang.
Hariyanti, U., Irawan, E. B., & Widayanti, E. (2017). Penalaran Proporsional dalam Menyelesaikan Masalah Multiplikatif Tipe Product of Measurement. Jurnal Kajian Pembelajaran Matematika, 1(April), 1. http://journal2.um.ac.id/index.php/jkpm
Hawk, T. F., & Shah, A. J. (2007). Using Learning Style Instruments to Enhance Student Learning. Decision Sciences Journal of Innovative Education, 5(1), 1–19. https://doi.org/10.1111/j.1540-4609.2007.00125.x
Hidayat, A. F., Amin, S. M., & Fuad, Y. (2017). Profil Penalaran Proporsional Siswa SMP dalam Memecahkan Masalah Matematika Berdasarkan Gaya Kognitif Sistematis dan Intuitif. Jurnal Matematika Kreatif-Inovatif, 2, 162–170. https://doi.org/http://dx.doi.org/10.15294/kreano.v8i2.9635
Hobri, H., Arifin, S., Murtikusuma, R. P., Oktavianingtyas, E., & Setya Putri, I. W. (2021). Students’ Critical Thinking Process in Solving Jumping Task According to Gregorc’s Thinking Style. Jurnal Didaktik Matematika, 8(1), 15–31. https://doi.org/10.24815/jdm.v8i1.19776
Holzrichter, R. (2016). Proportional Reasoning in Middle Level Mathematics TextBooks. https://scholarworks.uni.edu/hpt/221
Indillah, Z. E. C., Agustina, E. N. S., & Susilo, T. A. B. (2019). Penalaran Proporsional Siswa SMP Kelas VIII Dalam Menyelesaikan Soal Matematika Ditinjau Dari Jenis Kelamin.
Kariadinata, R. (2012). Menumbuhkan Daya Nalar (Power Of Reason) Siswa Melalui Pembelajaran Analogi Matematika. Jurnal Ilmiah Program Studi Matematika STKIP Siliwangi Bandung, 1(1).
Khotimah, K., & Shodikin, A. (2021). An Analysis of Proportional Reasoning Ability of Secondary School Students on Opportunity Material Viewed from Gender Prespective. Hipotenusa: Jurnal of Mathematical Society, 3(1). https://doi.org/10.18326/hipotenusa.v3i1.111-128
Khumairoh, B., Amin, S. M., & Wijayanti, P. (2020). Penalaran Proporsional Siswa Kelas Menengah dalam Menyelesaikan Masalah Matematika Ditinjau dari Adversity Quotient. Pedagogia?: Jurnal Pendidikan, 9(1), 67–80. https://doi.org/10.21070/pedagogia.v9i1.259
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. In National Academy Press. ftp://129.132.148.131/EMIS/journals/ZDM/zdm026r1.pdf
Laili, A. N. (2023). Level Penalaran Proporsional Siswa Dalam Menyelesaikan Masalah Proporsi Ditinjau Dari Tingkat Kemampuan Koneksi Matematis Siswa Kelas VII MTS Al Amien Ambulu Jember [Universitas Islam Negeri Kiai Haji Achmad Siddiq Jember]. http://digilib.uinkhas.ac.id/31848/1/Tanti Arsy Asriana_T20191212.pdf
Langrall, C. W., & Swafford, J. (2000). Three Balloons for Two Dollars: Developing Proportional Reasoning. The National Council of Teachers of Mathematics, 6(4), 254.
Lobato, J., & Ellis, A. (2010). Developing Essential Understanding of Ratios, Proportions & Proportional Reasoning.
Nurlela, N., Sumarni, S., Riyadi, M., Adiastuty, N., & Syafari, R. (2022). Proportional Reasoning Level Based on Student Self-Efficacy Review. https://doi.org/10.4108/eai.2-12-2021.2320311
Öztürk, M., Demir, Ü., & Akkan, Y. (2021). Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students?: A Mixed Method. International Journal on Social and Education Sciences, 3(1), 48–67. https://doi.org/https://doi.org/10.4632/ijonses.66
Patimah, D., & Murni. (n.d.). Analisis Kualitatif Gaya Berpikir Siswa dalam Memecahkan Masalah Fisika Pada Materi Gerak Parabola. Inovasi Dan Pembelajaran Fisika, 106–118.
Permatasari, D. I., Amin, S. M., & Wijayanti, P. (2017). Penalaran Proporsional Siswa SMP Kelas IX dalam Menyelesaikan Masalah Matematika Ditinjau dari Gender. Jurnal Matematika Kreatif-Inovatif, 8(2), 199–207.
Prayitno, A., Rossa, A., & Widayanti, F. D. (2019). Level penalaran proporsional siswa dalam memecahkan missing value problem. Jurnal Riset Pendidikan Matematika, 6(2), 177–187. https://doi.org/10.21831/jrpm.v6i2.19728
Prayitno, A., Rossa, A., Widayanti, F. D., Rahayuningsih, S., Hamid, A., & Baidawi, M. (2018). Characteristics of Students’ Proportional Reasoning in Solving Missing Value Problem. Journal of Physics: Conference Series, 1114(1). https://doi.org/10.1088/1742-6596/1114/1/012021
Putra, A., Tensa, Y., & Erita, S. (2020). Analisis Penalaran Proporsional Siswa dengan Gaya Belajar Auditori dalam Menyelesaikan Soal Perbandingan. Journal on Education, 2(4), 323–330. https://doi.org/10.31004/joe.v2i4.326
Risdianti, A. (2016). Analisis Kemampuan Penalaran Proporsional Siswa Kelas X Dalam Pembelajaran Discovery Learning Ditinjau Dari Gaya Belajar Menurut Kolb. Universitas Negeri Semarang.
Rizal, A. H. (2019). Analisis Penalaran Proporsional Siswa Dalam Menyelesaikan Soal Perbandingan. Universitas Islam Negeri (UIN) Mataram.
Sari, D. N. (2019). Analisis Kemampuan Penalaran Proporsional Siswa SMA dalam Memecahkan Masalah Matematika. Jurnal Math Didactic?: Jurnal Pendidikan Matematika, 5(2). https://repository.uksw.edu//handle/123456789/19274
Sugiyono. (2019). Metode Penelitian Kualitatif Kuantitatif dan R&D (Sutopo (ed.); Kedua).
Suryadi. (2008). Analisis Penalaran Proporsional Siswa Kelas VIII Berdasarkan Gaya Kognitif Field Dependent dan Field Independent Pada Materi Bangun Ruang. Jurnal Ekuivalen, 222–227. http://ejournal.umpwr.ac.id/index.php/ekuivalen/article/view/4235
Wahyuni, I. (2022). Pelanaran Proporsional (U. Farihah (ed.)). Lembaga Ladang Kata.
Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2021). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24(2), 179–202. https://doi.org/10.1007/s10857-019-09453-0
Zulkarnaen, R. (2017). Kesalahan Siswa Dalam Menyelesaikan Soal Penalaran Proposional. Seminar Matematika Dan Pendidikan Matematika UNY, M–8, 49–54.
Published
2025-01-06
How to Cite
PRAMONO, Yasmine Az Zahra Awwalina et al.
Students Proportional Reasoning Level in Solving Ill Structured Problem on Proportion Material in Terms of Gregorc’s Thinking Style.
Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, [S.l.], v. 9, n. 1, p. 25-37, jan. 2025.
ISSN 2549-5070.
Available at: <https://e-journal.ivet.ac.id/index.php/matematika/article/view/3568>. Date accessed: 12 july 2025.
doi: https://doi.org/10.31331/medivesveteran.v9i1.3568.
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