Exploring secondary students’ reflective thinking skills in statistics based on mathematical ability
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Abstract
Reflective thinking plays a vital role in mathematics learning, particularly in solving complex problems. Understanding students’ reflective thinking abilities across its aspects—technique, monitoring, insight, and conceptualization—is essential for selecting appropriate instructional methods. This study aims to describe junior high school students’ reflective thinking abilities in learning statistics based on their initial mathematical ability. A qualitative approach with a case study design was used to explore reflective thinking skills in the four aspects: technique, monitoring, insight, and conceptualization. The research participants consisted of 30 seventh-grade students from a junior high school in Boyolali, Indonesia, who were grouped into three categories based on their mathematical ability: high, medium, and low. Data were collected through reflective thinking tests, observations, and interviews, and analyzed using the constant comparative analysis method. The results reveal a hierarchical relationship between mathematical ability and reflective thinking. Students with high mathematical ability demonstrated complete reflective thinking, fulfilling all indicators across the four aspects. Students with moderate ability exhibited partial reflective thinking, meeting some indicators but not fully optimizing others. Students with low mathematical ability showed the weakest reflective thinking skills, meeting indicators only partially in technique, monitoring, and insight, while failing to achieve the conceptualization indicators optimally. These findings confirm that foundational mathematical knowledge is a critical determinant of students’ capacity for deep reflective problem solving in statistics and provide important implications for the development of targeted instructional methods.
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Masduki, M., Mahmudah, M. H., & Hastuti, W. (2026). Exploring secondary students’ reflective thinking skills in statistics based on mathematical ability. Kalamatika: Jurnal Pendidikan Matematika, 11(1), 146-177. https://doi.org/10.22236/KALAMATIKA.vol11no1.2026pp146-177
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Angkotasan, N., Suharna, H., Abdullah, I. H., & Dahlan, S. (2024). The Difficulty of Students’ Reflective Thinking in Problems Solving of Linear Program. International Education Studies, 17(1), 18. https://doi.org/10.5539/ies.v17n1p18
Ardani, D. A. P.. (2021). Profile Of High School Students Reflective Thinking In Solving Algebra Problems Viewed From Mathematical Ability. MATHEdunesa: Jurnal Ilmiah Pendidikan Matematika, 10(1), 59–68. https://doi.org/10.26740/mathedunesa.v10n1.p59-68
Broza, O., Lifshitz, A., & Atzmon, S. (2021). Exploring a Model to Develop Critical Reflective Thought Among Elementary School Math Preservice Teachers. Elementary School Math Preservice Teachers, 202(4). https://doi.org/10.1177/0022057421998336
Casanellas, M., Petrović, S., & Uhler, C. (2020). Algebraic statistics in practice: Applications to networks. Annual Review of Statistics and Its Application, 7, 227–250. https://doi.org/10.1146/annurev-statistics-031017-100053
Coppersmith, J. G., & Star, J. R. (2022). A Complicated Relationship: Examining the Relationship Between Flexible Strategy Use and Accuracy. Journal of Numerical Cognition, 8(3), 382–397. https://doi.org/10.5964/jnc.7601
Cresswell, J. W. (2014). Research design: Qualitative, Quantitative, and Mixed Methods Approaches. Sage Publication.
Damastuti, A. S., Triyanto, T., & Nurhasanah, F. (2023). Reflective Thinking Students with Different Adversity Quotients in Solving Mathematics Problems. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(4), 1128. https://doi.org/10.31764/jtam.v7i4.16552
Deringöl, Y. (2019). The Relationship Between Reflective Thinking Skills and Academic Achievement in Mathematics in Fourth-Grade Primary School Students. International Online Journal of Education and Teaching (IOJET), 2019(3), 613–622.
Erdogan, F. (2019). Effect of cooperative learning supported by reflective thinking activities on students’ critical thinking skills. Eurasian Journal of Educational Research, 2019(80), 89–112. https://doi.org/10.14689/ejer.2019.80.5
Erdoğan, F. (2020). The relationship between prospective middle school mathematics teachers’ critical thinking skills and reflective thinking skills. Participatory Educational Research, 7(1), 220–241. https://doi.org/10.17275/per.20.13.7.1
Glass, G. V., & Hopkins, K. D. (1996). Statistical Methods in Education and Psychology. Allyn and Bacon.
Hendryadi, Tricahyadinata, I., & Zannati, R. (2019). Metode Penelitian: Pedoman Penelitian Bisnis dan Akademik (Research Methods: A Guide to Business and Academic Research). LPMP Imperium.
Howley, P., & Roberts, T. (2020). Engaging school students and educators with the practice of statistics. Statistics Education Research Journal, 19(1), 29–38. https://doi.org/10.52041/serj.v19i1.117
Junaedi, Y., & Wahyudin, W. (2020). Improving Student’s Reflective Thinking Skills Through Realistic Mathematics Education Approach. Proceedings of the 4th Asian Education Symposium (AES 2019), 438, 196–202. https://doi.org/10.2991/assehr.k.200513.044
Karaoglan Yilmaz, F. G., Ustun, A. B., Zhang, K., & Yilmaz, R. (2023). Metacognitive Awareness, Reflective Thinking, Problem Solving, and Community of Inquiry As Predictors of Academic Self-Efficacy in Blended Learning: a Correlational Study. Turkish Online Journal of Distance Education, 24(1), 20–36. https://doi.org/10.17718/tojde.989874
Kholid, M. N., Sa’dijah, C., Hidayanto, E., & Permadi, H. (2020). How are students’ reflective thinking for problem solving? Journal for the Education of Gifted Young Scientists, 8(3), 1135–1146. https://doi.org/10.17478/JEGYS.688210
Kholid, M. N., Sa’Dijah, C., Hidayanto, E., & Permadi, H. (2022). Students’ reflective thinking pattern changes and characteristics of problem solving. Reflective Practice, 23(3), 319–341. https://doi.org/10.1080/14623943.2021.2025353
Kholid, M. N., Santosa, Y. T., Toh, T., Wijaya, A. P., Sujadi, I., & Hendriana, H. (2024). Defragmenting students’ reflective thinking levels for mathematical problem solving: does it work?. Reflective Practice, 25(3), 319-351. https://doi.org/10.1080/14623943.2024.2320140
Kholid, M. N., Telasih, S., Pradana, L. N., & Maharani, S. (2021). Reflective Thinking of Mathematics Prospective Teachers’ for Problem Solving. Journal of Physics: Conference Series, 1783(1). https://doi.org/10.1088/1742-6596/1783/1/012102
Khotimah, R. P., Adnan, M., Che Ahmad, C. N., & Murtiyasa, B. (2023). The effectiveness of the STEMDISLEARN module in improving students’ critical thinking skills in the differential equations course. Cogent Education, 10(2). https://doi.org/10.1080/2331186X.2023.2220233
Koga, S. (2022). Characteristics of statistical literacy skills from the perspective of critical thinking. Teaching Statistics, 44(2), 59–67. https://doi.org/10.1111/test.12302
Kuncoro, K. S., Hidayat, A., Nadzeri, M. B., Hendriyanto, A., Meirani, F., & Juandi, D. (2025). Thinking Beyond the Equations: A Deep Dive into Reflective Thinking for Mathematics Learning. Participatory Educational Research, 12(5), 310–334. https://doi.org/10.17275/per.25.75.12.5
Kurnia, A. B., Lowrie, T., & Patahuddin, S. M. (2024). The development of high school students’ statistical literacy across grade level. Mathematics Education Research Journal, 36(Suppl 1), 7–35. https://doi.org/10.1007/s13394-023-00449-x
Kvasz, L. (2019). How Can Abstract Objects of Mathematics Be Known? Philosophia Mathematica, 27(3), 316–334. https://doi.org/10.1093/philmat/nkz011
Lestari, J., Rohman, A. A., & Norasia, Y. (2023). Examining the Influence of the WEE (Wondering, Exploring, and Explaining) Learning Model on Students’ Mathematical Reflective Thinking Proficiency. Kontinu: Jurnal Penelitian Didaktik Matematika, 7(2), 36. https://doi.org/10.30659/kontinu.7.2.36-48
Merriam., S. B., & Tisdell., E. J. (2015). Qualitative Research: A Guide to Design and Implementation. John Wiley & Sons.
Moleong, L. . (2007). Qualitative Research Methodology. PT Remaja Rosdakarya Offset.
Morkoyunlu, Z., & Altun, S. D. (2022). The Effect of Error-Based Activities on the Reflective Thinking Skills of Pre-service Elementary Education Mathematics Teachers. Acta Didactica Napocensia, 15(1), 156–168. https://doi.org/10.24193/adn.15.1.13
Mukti, F. Z., & Permatasari, D. (2023). Kemampuan Berpikir Reflektif dalam Menyelesaikan Soal PISA-Like Ditinjau dari Disposisi Matematis Siswa SMP. JTMT: Journal Tadris Matematika, 4(1), 9–22. https://doi.org/10.47435/jtmt.v4i1.1670
OECD. (2022). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD.
Özbek, G., & Cho, S. (2022). Effects of Mathematical Modelling Based Project Production and Management Program on Gifted Students’ Mathematical Modelling and Reflective Thinking for Real-Life Problem Solving. Gifted Education International, 39(3). https://doi.org/https://doi.org/10.1177/02614294221118005
Rahmadhani, E., Wahyuni, S., Mandasari, L., & Setiawan, Y. (2020). Reflective Thinking Ability of Teacher Candidate Students Based on Ability Level and Gender. Conference: 7th South East Asia Design Research International Conference. https://doi.org/http://dx.doi.org/10.24071/seadr.2019.23
Ratnaningsih, N., & Hidayat, E. (2020). Reflective mathematical thinking process and student errors: An analysis in learning style. Journal of Physics: Conference Series, 1613(1). https://doi.org/10.1088/1742-6596/1613/1/012037
Salido, A., & Dasari, D. (2019). The analysis of students’ reflective thinking ability viewed by students’ mathematical ability at senior high school. Journal of Physics: Conference Series, 1157(2), 1–6. https://doi.org/10.1088/1742-6596/1157/2/022121
Saracoglu, M. (2022). Reflective thinking and inquiry skills as predictors of self-efficacy in teaching mathematics. Problems of Education in the 21st Century, 80(1), 213-231. https://doi.org/10.33225/pec/22.80.213
Scheibe, D. A., Was, C. A., Dunlosky, J., & Thompson, C. A. (2023). Metacognitive Cues , Working Memory , and Math Anxiety : The Regulated Attention in Mathematical Problem Solving ( RAMPS ) Framework. Journal of Intelligence, 11(6), 117. https://doi.org/10.3390/jintelligence11060117
Setiyani, Waluya, S. B., Sukestiyarno, Y. L., & Cahyono, A. N. (2022). International Journal of Educational Methodology Mathematical Reflective Thinking Process of Prospective Elementary Teachers Review from the Disposition in Numerical Literacy Problems. International Journal of Educational Methodology, 8(3), 405–420. https://doi.org/10.12973/ijem.8.3.405
Setiyani, Waluya, S. B., Sukestiyarno, Y. L., & Cahyono, A. N. (2024). Construction of reflective thinking: A field independent student in numerical problems. Journal on Mathematics Education, 15(1), 151–172. https://doi.org/10.22342/jme.v15i1.pp151-172. https://doi.org/10.22342/jme.v15i1.pp151-172
Setyaningsih, N., & Ghufron, M. (2024). Game development “GETAK” based on RPG maker MV on statistics material. AIP Conference Proceedings, 2629(1). https://doi.org/https://doi.org/10.1063/5.0183698
Sumitro, N. K., Sa’dijah, C., Raharjo, S., & Rahardi, R. (2019). The emergence of metacognitive activities through the scaffolding interaction. International Journal of Recent Technology and Engineering, 8(1), 665–671. Retrieved from https://www.ijrte.org/wp-content/uploads/papers/v8i1C2/A11110581C219.pdf
Tisngati, U., & Genarsih, T. (2021). Reflective thinking process of students in completing mathematical problems based on mathematical reasoning ability. Journal of Physics: Conference Series, 1776(1), 1–9. https://doi.org/10.1088/1742-6596/1776/1/012035
Toraman, Ç., Orakcı, Ş., & Aktan, O. (2020). Analysis of the Relationships between Mathematics Achievement, Reflective Thinking of Problem Solving and Metacognitive Awareness. International Journal of Progressive Education, 16(2), 72–90. https://doi.org/10.29329/ijpe.2020.241.6
Ugur, N., & Çakiroglu, Ü. (2024). Implementing Reflective Thinking in Computer Science Unplugged to Enhance Computational Thinking. International Journal of Technology in Education and Science, 8(2), 196–218. https://doi.org/10.46328/ijtes.515
Yan, S., Sun, D., Zhou, Q., Yang, Y., & Tian, P. (2025). Exploring the Impact of Virtual Laboratory with KWL Reflective Thinking Approach on Students’ Science Learning in Higher Education. Computing in Higher Education, 37(1), 89–110. https://doi.org/10.1007/s12528-023-09385-y
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