Metacognitive Skills Profiles of Students in Solving Higher-Order Differential Equation Problems: A Qualitative Case Study
Keywords:
Metacognitive Skills, Higher-Order Differential Equations, Mathematical Problem Solving, Mathematical Ability, Qualitative Study
Abstract
Metacognitive skills is essential for solving complex mathematical problems, particularly in higher-order ordinary differential equations that require structured reasoning and reflection. This study aimed to describe university students’ metacognitive skilss profiles in solving higher-order differential equation problems based on their mathematical ability levels. A qualitative case study approach was employed. The population consisted of 43 students from Universitas Negeri Makassar who had enrolled in the Ordinary Differential Equations course. Three students were purposively selected to represent high, moderate, and low mathematical ability levels. Data were collected through problem-solving tests and semi-structured interviews. The data were analyzed qualitatively using the stages of data collection, data reduction, data display, and conclusion drawing, guided by three metacognitive indicators: planning, monitoring, and evaluation. The results showed that students with high mathematical ability demonstrated strong metacognitive awareness by effectively planning, monitoring, and evaluating their problem-solving processes. Students with moderate mathematical ability were able to plan and monitoting their solutions but experienced difficulties in evaluating their work. In contrast, Students with low mathematical ability can maximally fulfill one metacognitive indicator; Planning indicators. Students make a calculation error in the strategy that has been designed so it results in the final result of the answer. These findings highlight the need for instructional strategies that explicitly foster metacognitive awareness to support students in solving advanced differential equation problems.
References
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Oz, H. (2016). The Importance of Personality Traits in Students Perceptions of Metacognitive Awareness. Procedia - Social and Behavioral Sciences, 232, 655–667. https://doi.org/10.1016/j.sbspro.2016.10.090
Pramono, A. J. (2017). Aktivitas Metakognitif Siswa SMP Dalam Pemecahan Masalah Matematika Berdasarkan Kemampuan Matematika. Kreano, Jurnal Matematika Kreatif-Inovatif, 8(2), 133–142. https://doi.org/10.15294/kreano.v8i2.6703
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Schraw, G., & Dennison, R. S. (1994). Assessing Metacognitive Awareness. Contemporary Educational Psychology, 19(4), 460–475. https://doi.org/10.1006/CEPS.1994.1033
Schraw, G., & Moshman, D. (1995). Metacognitive Theories. Educational Psychology Review , 7(4), 351–371. https://digitalcommons.unl.edu/edpsychpapers/40
Setyaningsih, N., & Rahmawati, E. Z. (2022). Metacognitive skills of student in solving problems of two-variable linear equation systems in terms of self-regulated learning. Jurnal Riset Pendidikan Matematika, 9(1), 8. https://doi.org/10.21831/jrpm.v9i1.49163
Sukiyanto, S. (2020). MUNCULNYA KESADARAN METAKOGNISI DALAM MENYELESAIKAN MASALAH MATEMATIKA. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(1), 126–132. https://doi.org/10.24127/AJPM.V9I1.2654
Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal 2004 16:2, 16(2), 25–48. https://doi.org/10.1007/BF03217394
Young, A., & Fry, J. (2008). Metacognitive Awareness and Academic Achievement in College Students. Journal of the Scholarship of Teaching and Learning, 8(2), 1–10. https://doi.org/10.3109/0142159X.2010.487711
Ahmad, H., Febryanti, F., Fatimah, fatimah, & Muthmainnah, M. (2018). Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem. IOP Conference Series: Materials Science and Engineering, 300(1), 012048. https://doi.org/10.1088/1757-899X/300/1/012048
Arsyad, N. (2016). Model Pembelajaran Menumbuhkembangkan Kemampuan Metakognitif. Makassar: Pustaka Refleksi.
Asmaun, A., & Baharuddin, B. (2024). Thinking Process Analysis Reflective Student in Solve Problem Non-routine on Probability Material. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 4(3). https://doi.org/10.51574/kognitif.v4i3.2079
Aulia, L. I., & Murtiyasa, B. (2023). Analisis Profil Metakognisi Siswa dalam Pemecahan Masalah Matematis Ditinjau dari Gender pada Pembelajaran Matematika. Jurnal Cendekia : Jurnal Pendidikan Matematika, 7(2), 1545–1557. https://doi.org/10.31004/CENDEKIA.V7I2.2302
Ayazgök, B., & Aslan, H. (2014). The Review of Academic Perception, Level of Metacognitive Awareness and Reflective Thinking Skills of Science and Mathematic University Students. Procedia - Social and Behavioral Sciences, 141, 781–790. https://doi.org/10.1016/J.SBSPRO.2014.05.137
Blakey, E., & Spence, S. (1990). Developing Metacognition. ERIC Custom Transformations Team. www.eric.ed.gov
Cihanoglu, M. O. (2012). Metacognitive Awareness of Teacher Candidates. Procedia - Social and Behavioral Sciences, 46, 4529–4533. https://doi.org/10.1016/J.SBSPRO.2012.06.290
Creswell, J. W. (2016). Research design: Pendekatan metode kualitatif, kuantitatif dan campuran. Yogyakarta: Pustaka pelajar.
Dirkes, M. A. (1985). Metacognition: Students in charge of their thinking. Roeper Review, 8(2), 96–100. https://doi.org/10.1080/02783198509552944
Fatmawati, B., Hunaepi, H., & Asy’ari, M. (2025). The moderating role of cognitive style on the relationship between critical thinking disposition, metacognitive awareness, and metacognitive strategies. Social Sciences & Humanities Open, 12, 102006. https://doi.org/10.1016/J.SSAHO.2025.102006
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906–911. https://doi.org/10.1037/0003-066X.34.10.906
Güner, P., & Erbay, H. N. (2021). Metacognitive Skills and Problem-Solving. International Journal of Research in Education and Science, 7(3), 715–734. https://doi.org/10.46328/IJRES.1594
Hamda, H., Ahmad, A. E. N. A. A., & Ja’faruddin, J. (2024). Analisis Metakognitif Siswa dalam Menyelesaikan Soal Asesmen Kompetensi Minimum ditinjau dari Kecerdasan Emosional dan Gaya Belajar Siswa. IMED: Issues in Mathematics Education, 8(2), 188–206. https://doi.org/10.35580/imed.v8i2.5195
Huda, N., Sutawidjaja, A., Subanji, Subanji., & Rahardjo, S. (2018). The errors of metacognitive evaluation on metacognitive failure of students in mathematical problem solving. Journal of Physics: Conference Series, 1008(1). https://doi.org/10.1088/1742-6596/1008/1/012073
Huda, N., Syaiful, S., Gustiningsi, T., & Novferma, N. (2025). Students’ Metacognitive Ability in Solving Mathematical Problems Based on Information Processing Theory in Discrete Mathematics Course. Edumatica : Jurnal Pendidikan Matematika, 15(2), 283–295. https://doi.org/10.22437/EDUMATICA.V15I2.44689
Jaleel, S., & P, Premachandran. (2016). A Study on the Metacognitive Awareness of Secondary School Students. Universal Journal of Educational Research, 4(1), 165–172. https://doi.org/10.13189/ujer.2016.040121
Kassimi, I. El. (2025). Assessing Metacognition: An Overview. Journal of English Language Teaching and Applied Linguistics, 7(2), 222–230. https://doi.org/10.32996/JELTAL.2025.7.2.21
Kaya, Z. B., & Kepceoglu, I. (2022). Metacognitive Failures of Preservice Mathematics Teachers ın Problem Solving. Athens Journal of Sciences, 9(4), 273–290. https://doi.org/10.30958/AJS.9-4-4
Magiera, M. T., & Zawojewski, J. S. (2011). Characterizations of social-based and self-based contexts associated with students’awareness, evaluation,and regulation of their thinking during small-group mathematical modeling. Journal for Research in Mathematics Education, 42(5), 486–520. https://doi.org/10.5951/jresematheduc.42.5.0486
Oz, H. (2016). The Importance of Personality Traits in Students Perceptions of Metacognitive Awareness. Procedia - Social and Behavioral Sciences, 232, 655–667. https://doi.org/10.1016/j.sbspro.2016.10.090
Pramono, A. J. (2017). Aktivitas Metakognitif Siswa SMP Dalam Pemecahan Masalah Matematika Berdasarkan Kemampuan Matematika. Kreano, Jurnal Matematika Kreatif-Inovatif, 8(2), 133–142. https://doi.org/10.15294/kreano.v8i2.6703
Putera, D. B. R. A., Hidayah, R., Suarningtyas, S., & Mitasari, R. A. (2021). Profil Kesadaran Metakognisi Mahasiswa di Universitas Trunojoyo Madura pada Program Studi Pendidikan IPA. JURNAL PENELITIAN PENDIDIKAN MATEMATIKA DAN SAINS, 5(2), 84–91. https://doi.org/10.26740/JPPMS.V5N2.P84-91
Schraw, G., & Dennison, R. S. (1994). Assessing Metacognitive Awareness. Contemporary Educational Psychology, 19(4), 460–475. https://doi.org/10.1006/CEPS.1994.1033
Schraw, G., & Moshman, D. (1995). Metacognitive Theories. Educational Psychology Review , 7(4), 351–371. https://digitalcommons.unl.edu/edpsychpapers/40
Setyaningsih, N., & Rahmawati, E. Z. (2022). Metacognitive skills of student in solving problems of two-variable linear equation systems in terms of self-regulated learning. Jurnal Riset Pendidikan Matematika, 9(1), 8. https://doi.org/10.21831/jrpm.v9i1.49163
Sukiyanto, S. (2020). MUNCULNYA KESADARAN METAKOGNISI DALAM MENYELESAIKAN MASALAH MATEMATIKA. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(1), 126–132. https://doi.org/10.24127/AJPM.V9I1.2654
Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal 2004 16:2, 16(2), 25–48. https://doi.org/10.1007/BF03217394
Young, A., & Fry, J. (2008). Metacognitive Awareness and Academic Achievement in College Students. Journal of the Scholarship of Teaching and Learning, 8(2), 1–10. https://doi.org/10.3109/0142159X.2010.487711
Published
2026-02-16
How to Cite
Asmaun, A., & Liani, A. M. (2026). Metacognitive Skills Profiles of Students in Solving Higher-Order Differential Equation Problems: A Qualitative Case Study. International Journal of Education, Vocational and Social Science , 5(01), 777-801. https://doi.org/10.63922/ijevss.v5i01.2980
Contact Person +6282139474255
Email : ijevss@citakonsultindo.or.id / editor.ijevss@gmail.com
