Analysis of the Refractive Thinking of Students in Decision Making on Open Problems in Mathematics

Ardiana Ardiana

doi:10.37680/qalamuna.v17i2.8113

Authors

Ardiana Ardiana Universitas Khairun

DOI:

https://doi.org/10.37680/qalamuna.v17i2.8113

Keywords:

Decision Making, Decision Making Styles, Open-ended Problems, Math Education, Refractive Thinking

Abstract

This study aims to describe students’ decision-making processes in solving open mathematical problems based on refractive thinking. The research employed a qualitative approach with a descriptive design. The participants were undergraduate students of the Mathematics Education Study Program at the State University of Malang, selected purposively based on decision-making style, domicile, and understanding of the problem context. Research instruments included validated open-ended problem sets based on graph theory and semi-structured interview guides. Data were collected through problem-solving tasks and in-depth interviews, and then analyzed using Miles and Huberman’s interactive model, which consists of data reduction, data display, and conclusion drawing. The findings reveal that students experienced five stages of reflective thinking—perplexity, investigation, construction, evaluation, and decision—throughout the decision-making process. Students with a rational style demonstrated more systematic and consistent reasoning, while intuitive, dependent, and avoidant students tended to perform incomplete evaluations. These results highlight that refractive thinking plays a crucial role in forming logical and adaptive decisions. The study implies that open-ended, context-based mathematics learning can effectively enhance students’ higher-order thinking through reflective and evaluative reasoning. Future research should explore the development of instructional models and digital-based learning environments that systematically foster reflective thinking and decision-making skills across diverse cognitive styles and educational levels.

Downloads

Download data is not yet available.

References

Agbo, F. J., Olaleye, S. A., Bower, M., & Oyelere, S. S. (2023). Examining the relationships between students’ perceptions of technology, pedagogy, and cognition: The case of immersive virtual reality mini games to foster computational thinking in higher education. Smart Learning Environments, 10(1), 16. https://doi.org/10.1186/s40561-023-00233-1

Allsop, Y. (2019). Assessing the computational thinking process using a multiple evaluation approach. International Journal of Child-Computer Interaction, 19, 30–55. https://doi.org/10.1016/j.ijcci.2018.10.004

Alvinaria, A., Lukito, A., & Wijayanti, P. (2022). Identifikasi Berpikir Aljabar Siswa Field Independent dan Field Dependent Menggunakan Taksonomi SOLO. Jurnal Riset Pendidikan Dan Inovasi Pembelajaran Matematika, 5(2), 142–165. https://doi.org/10.26740/jrpipm.v5n2.p142-165

Ansari, B., Taufiq, T., & Saminan, S. (2020). The use of the creative problem-solving model to develop students’ adaptive reasoning ability: Inductive, deductive, and intuitive. International Journal on …, Query date: 2023-09-06 09:20:59. https://scholar.archive.org/work/ep52usovzbbohbcbytvtav4i3y/access/wayback/http://ejournal.uin-malang.ac.id/index.php/ijtlm/article/download/9439/pdf

Atikah, Fitroh Adhilla, & Zunan Setiawan. (2025). Pengaruh Iklan Media Sosial, Electronic Word of Mouth dan Citra Merek Terhadap Keputusan Pembelian Smartphone Oppo: Studi Kasus pada Pengguna Smartphone OPPO di Yogyakarta. Economic Reviews Journal, 4(2). https://doi.org/10.56709/mrj.v4i2.698

Attallah, B., Change, Y.-K., & Il-Agure, Z. (2019). Developing IoT Competencies in Non-Computer Science Students in Higher Education. 2019 Sixth HCT Information Technology Trends (ITT), 240–246. https://doi.org/10.1109/itt48889.2019.9075075

Benakli, N., Kostadinov, B., Satyanarayana, A., & Singh, S. (2017). Introducing computational thinking through hands-on projects using R with applications to calculus, probability, and data analysis. International Journal of Mathematical Education in Science and Technology, 48(3), 393–427. https://doi.org/10.1080/0020739X.2016.1254296

Boonjeam, W., Tesaputa, K., & Sri-ampai, A. (2017). Program Development for Primary School Teachers’ Critical Thinking. International Education Studies, 10(2), 131–138. https://doi.org/10.5539/ies.v10n2p131

Bulent, D., Erdal, B., Ceyda, A., Betul, T., Nurgul, C., & Cevahir, D. (2016). An analysis of teachers' questioning strategies. Educational Research and Reviews, 11(22), 2065–2078. https://doi.org/10.5897/ERR2016.3014

Bull, G., Garofalo, J., & Hguyen, N. R. (2020). Thinking about computational thinking: Origins of computational thinking in educational computing. Journal of Digital Learning in Teacher Education, 36(1), 6–18. https://doi.org/10.1080/21532974.2019.1694381

Cansoy, R., & Turkoglu, M. E. (2017). Examining the Relationship between Pre-Service Teachers’ Critical Thinking Disposition, Problem-Solving Skills, and Teacher Self-Efficacy. International Education Studies, 10(6), 23. https://doi.org/10.5539/ies.v10n6p23

Dumas, D. (2018). Relational reasoning and divergent thinking: An examination of the threshold hypothesis with quantile regression. Contemporary Educational Psychology, 53(January), 1–14. https://doi.org/10.1016/j.cedpsych.2018.01.003

Dwi Prastika, A., & Nugroho, Y. S. (2025a). Klasifikasi Efektivitas Iklan di E-Commerce dan Media Sosial terhadap Minat Beli Mahasiswa UMS dengan Decision Tree. Jurnal Pendidikan Dan Teknologi Indonesia, 5(4), 919–933. https://doi.org/10.52436/1.jpti.727

Dwi Prastika, A., & Nugroho, Y. S. (2025b). Klasifikasi Efektivitas Iklan di E-Commerce dan Media Sosial terhadap Minat Beli Mahasiswa UMS dengan Decision Tree. Jurnal Pendidikan Dan Teknologi Indonesia, 5(4), 919–933. https://doi.org/10.52436/1.jpti.727

Dwyer, C. P., Hogan, M. J., Harney, O. M., & Kavanagh, C. (2017). Facilitating a student-educator conceptual model of dispositions towards critical thinking through interactive management. Education Technology Research, 65, 47–73. https://doi.org/10.1007/s11423-016-9460-7

Fauzan, H. R., Hidayanto, E., & Chandra, T. D. (2024). Reversible thinking in solving mathematics problems in terms of cognitive style. Al-Jabar : Jurnal Pendidikan Matematika, 15(2), 559–576. https://doi.org/10.24042/ajpm.v15i2.24527

Imaniyati, N., Ramdhany, M. A., Rasto, R., Nurjanah, S., Solihah, P. A., & Susilawati, A. (2024). Neuroscience Intervention for Implementing Digital Transformation and Organizational Health Completed with Literature Review, Bibliometrics, and Experiments. Indonesian Journal of Science & Technology, 9(2). https://doi.org/10.17509/ijost.v9i2.67763

Istichomah, N. (2021). Pengembangan lembar kerja siswa berbasis learning trajectory menggunakan motif anyaman pada materi transformasi refleksi.

Johnson, C. A. N., Bin Daud, M. F., Bin Arsat, M., Hussin, W. N. Bt. W., & Egba, E. I. (2021). The Effect of Computer Software Interaction on Students' Cognitive Abilities Enhancement: The Case of Engineering Educators’ Perspective. International Journal of Emerging Technologies in Learning (iJET), 16(18), 228–241. https://doi.org/10.3991/ijet.v16i18.24379

Khaesarani, I. R., & Ananda, R. (2022). Students’ mathematical literacy skills in solving higher-order thinking skills problems. Al-Jabar : Jurnal Pendidikan Matematika, 13(1), 81–99. https://doi.org/10.24042/ajpm.v13i1.11499

Kholid, M. N., Imawati, A., Swastika, A., Maharani, S., & Pradana, L. N. (2021). How is Students’ Conceptual Understanding for Solving Mathematical Problems? Journal of Physics: Conference Series, 1776(1). https://doi.org/10.1088/1742-6596/1776/1/012018

Lestari, K. I., Arcana, I. N., Susetyo, A. E., & Kuncoro, K. S. (2022). Development of Online Learning Quiz and Educational Game Using Word Walls in Mathematics for Grade 10. INSANIA : Jurnal Pemikiran Alternatif Kependidikan, 27(2), 145–159. https://doi.org/10.24090/insania.v27i2.6924

Nouri, J., Zhang, L., Mannila, L., & Norén, E. (2020). Development of computational thinking, digital competence, and 21st-century skills when learning programming in K-12. Education Inquiry, 11(1), 1–17. https://doi.org/10.1080/20004508.2019.1627844

Özsoy-Güneş, Z., Güneş, İ., Derelioğlu, Y., & Kırbaşlar, F. G. (2015). The Reflection of Critical Thinking Dispositions on Operational Chemistry and Physics Problems Solving of Engineering Faculty Students. Procedia - Social and Behavioral Sciences, 174(February), 448–456. https://doi.org/10.1016/j.sbspro.2015.01.688

Presmeg, N. (2016). Semiotics as a Tool for Learning Mathematics: How to Describe the Construction, Visualisation, and Communication of Mathematical Concepts by Adalira Sáenz-Ludlow & Gert Kadunz (Eds.). Mathematical Thinking and Learning, 18(3), 233–238. https://doi.org/10.1080/10986065.2016.1184953

Reinholz, D. L. (2016). Developing mathematical practices through reflection cycles. Mathematics Education Research Journal, 28(3), 441–455. https://doi.org/10.1007/s13394-016-0175-1

Rodgers, C. (2002). Defining Reflection: Another Look at John Dewey and Reflective Thinking. Teachers College Record,104, 104(4), 842–866.

Román-González, M., Pérez-González, J. C., & Jiménez-Fernández, C. (2017). Which cognitive abilities underlie computational thinking? Criterion validity of the Computational Thinking Test. Computers in Human Behavior, 72, 678–691. https://doi.org/10.1016/j.chb.2016.08.047

Rusdiana, R., Samsuddin, A. F., Muhtadin, A., & Fendiyanto, P. (2023). Development of Mathematical Literacy Problems in the Context of East Kalimantan. Jurnal Cendekia : Jurnal Pendidikan Matematika, 7(1), 197–210. https://doi.org/10.31004/cendekia.v7i1.1885

Rusdin, R. (2023). Transformasi Pendidikan Islam di Banten Melalui Program Unggulan. An-Nuha: Jurnal Sosial & Humaniora, 1(1), 31–43. https://doi.org/10.63005/annuha.v1i1.1

Simatupang, H. W., Riskiana, R. R., Widowati, S., & Alitu, A. F. (2022). Evaluasi Usability Website dengan Website Usability Evaluation tool dan Importance-Performance Analysis. Techno.Com, 21(1), 103–114. https://doi.org/10.33633/tc.v21i1.5584

Siregar, S. M., Utomo, B., & Marlina, L. (2020). Perancangan Buku Interaktif untuk Memperkenalkan Ragam Profesi Sebagai Sarana Pengembangan Minat Pelajar Usia Dini. Prosiding Konferensi Nasional Pengabdian Kepada Masyarakat dan Corporate Social Responsibility (PKM-CSR), 3, 828–834. https://doi.org/10.37695/pkmcsr.v3i0.881

Stufflebeam, D. L., & Zhang, G. (2017). The CIPP Evaluation Model: How to Evaluate for Improvement and Accountability. Guilford Publications.

Suharna, H., Hairun, Y., Abdullah, I. H., Alhaddad, I., Afandi, A., Ardiana, & Sari, D. P. (2020). The Reflective Thinking Elementary Student in Solving Problems Based on Mathematic Ability. International Journal of Advanced Science and Technology, 29(6), 3880–3891.

Syamsudin, S. (2020). Problem Based Learning dalam Mengembangkan Kemampuan Berpikir Kritis dan Keterampilan Sosial. ELSE (Elementary School Education Journal) : Jurnal Pendidikan dan Pembelajaran Sekolah Dasar, 4(2), 81. https://doi.org/10.30651/else.v4i2.4610

Syazwani, S. A. H., & Voutama, A. (2025). ANALISIS PENGGUNAAN SISTEM INFORMASI DALAM PENGAMBILAN KEPUTUSAN PEMASARAN PADA TOKO ONLINE DI SHOPEE (STUDI KASUS: TOKO LINAZENSHOP OFFICIAL). Jurnal Informatika Dan Teknik Elektro Terapan, 13(2). https://doi.org/10.23960/jitet.v13i2.6358

Trimawati, K., Kirana, T., & Raharjo, R. (2020). Pengembangan Instrumen Penilaian IPA Terpadu dalam Pembelajaran Model Project Based Learning (PjBL) untuk Meningkatkan Kemampuan Berpikir Kritis dan Kreatif Siswa SMP. Quantum: Jurnal Inovasi Pendidikan Sains, 11(1), 36. https://doi.org/10.20527/quantum.v11i1.7606

Weintrop, D., Rutstein, D. W., Bienkowski, M., Mcgee, S., Weintrop, D., Rutstein, D. W., Bienkowski, M., & Mcgee, S. (2021). Assessing computational thinking: An overview of the field. Computer Science Education, 31(2), 113–116. https://doi.org/10.1080/08993408.2021.1918380

Widiya, A. W., & Radia, E. H. (2023). Pengaruh Model Pembelajaran Inkuiri Terbimbing Terhadap Kemampuan Berpikir Kritis dan Hasil Belajar IPS. Aulad: Journal on Early Childhood, 6(2), 127–136. https://doi.org/10.31004/aulad.v6i2.477

Yildiz, A., & Baltaci, S. (2016). Reflections From the Analytic Geometry Courses Based on Contextual Teaching and Learning. The Online Journal of New Horizons in Education, 6(4), 155–166.

Zayyadi, M., Nusantara, T., Subanji, Hidayanto, E., & Sulandra, I. M. (2019). A Cognitive Framework: The Process of Solving Mathematical Problems for Middle School Students. International Journal of Learning, Teaching and Educational Research, 18(2), 89–102. https://doi.org/10.26803/ijlter.18.2.7