Abstract

Mathematical critical thinking is a fundamental competency that students must develop to solve complex problems effectively; however, empirical evidence consistently indicates that this ability remains underdeveloped among junior high school students in Indonesia, particularly in the domain of set theory. This study aims to describe and analyze the mathematical critical thinking skills of seventh-grade students at a public junior high school located in a rural district of West Kalimantan, Indonesia, in solving set theory problems, based on four Facione indicators: interpretation, analysis, evaluation, and inference. A descriptive qualitative design was employed, involving six students selected through purposive sampling from a class of 29 students in the 2025/2026 academic year, categorized into high, medium, and low ability groups. Data were collected through a written essay test and semi-structured interviews, then analyzed using an interactive model comprising data reduction, data display, and conclusion drawing. Results show that high-ability students fulfilled all four critical thinking indicators optimally but demonstrated a consistent limitation in verbal mathematical justification. Medium-ability students performed adequately on interpretation and analysis but encountered difficulties in evaluation and systematic inference. Low-ability students failed to meet most indicators, with the most pronounced deficits in evaluation and inference. This study contributes to the field by investigating the distribution of critical thinking profiles within a unified classroom environment. Crucially, it highlights that verbal mathematical justification represents a fundamental developmental barrier that transcends procedural competence, offering specific implications for the refinement of mathematics instruction.

There is no Figure or data content available for this article

References

• Aisyah, A., & Juandi, D. (2022). The Description of Indonesian Student Mathematics Literacy in the Last Decade. International Journal of Trends in Mathematics Education Research, 5(1), 105–110. https://doi.org/10.33122/ijtmer.v5i1.114
• Aizikovitsh-Udi, E., & Cheng, D. (2015). Developing Critical Thinking Skills from Dispositions to Abilities: Mathematics Education from Early Childhood to High School. Creative Education, 6(4), 455–462. https://doi.org/10.4236/ce.2015.64045
• Alhowail, A. M., & Albaqami, S. E. (2024). Evaluation of the Critical Thinking Skills of Secondary School Students in Saudi Arabia. Problems of Education in the 21st Century, 82(1), 7–28. https://doi.org/10.33225/pec/24.82.07
• Azmi, Z. L., Marlina, L., Fathurohman, A., Putri, R. I. I., Zulkardi, Z., Sari, D., Gustiningsih, T., Rawani, D., Lisnani, L., Sari, A., & Septimiranti, D. (2022). Study of Critical Thinking Skills for Junior High School Students In the Era Industial Revolution 4.0. JIPFRI (Jurnal Inovasi Pendidikan Fisika Dan Riset Ilmiah), 6(1), 19–23. https://doi.org/10.30599/jipfri.v6i1.1255
• Bagni, G. T. (2006). Some historical and epistemological notes on set theory in mathematics education. The Mathematics Enthusiast, 3(1), 117–132. https://scholarworks.umt.edu/tme/vol3/iss1/7/
• Baran, A. A., & Kabael, T. (2021). An investigation of eighth grade students’ mathematical communication competency and affective characteristics. The Journal of Educational Research, 114(4), 367–380. https://doi.org/10.1080/00220671.2021.1948382
• Basri, H., Purwanto, P., As’ari, A. R., & Sisworo, S. (2019). Investigating Critical Thinking Skill of Junior High School in Solving Mathematical Problem. International Journal of Instruction, 12(3), 745–758. https://doi.org/10.29333/iji.2019.12345a
• Chasanah, C., Riyadi, R., & Usodo, B. (2020). Analysis of Written Mathematical Communication Skills of Elementary School Students. Proceedings of the 3rd International Conference on Learning Innovation and Quality Education (ICLIQE 2019). https://doi.org/10.2991/assehr.k.200129.082
• Chimoni, M., & Pitta‐Pantazi, D. (2015). Connections between algebraic thinking and reasoning processes. HAL (Le Centre Pour La Communication Scientifique Directe). https://hal.science/hal-01286897
• Cohen, L., Manion, L., & Morrison, K. (2007). Research Methods in Education (6th ed.). Routledge.
• Damayanti, H. T., & Sumardi, S. (2018). Mathematical Creative Thinking Ability of Junior High School Students in Solving Open-Ended Problem. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 36. https://doi.org/10.23917/jramathedu.v3i1.5869
• Dorner, C., Ableitinger, C., & Krammer, G. (2025). Revealing the nature of mathematical procedural knowledge by analysing students’ deficiencies and errors. International Journal of Mathematical Education in Science and Technology, 57(3), 413–434. https://doi.org/10.1080/0020739x.2024.2445666
• Elicer, R., & Neto, V. F. (2018). Statistics as a tool for decision-making : Two countries and one pattern. Research Portal Denmark, 150.
• Facione, P. A. (1990). Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction (The Delphi Report). PhilPapers (PhilPapers Foundation). https://philarchive.org/rec/FACCTA
• Facione, P. A., Sánchez, C. A., Facione, N. C., & Gainen, J. (1995). The Disposition Toward Critical Thinking. The Journal of General Education, 44(1), 1–25. http://www.jstor.org/stable/27797240
• Facione, P. A. (2011). Critical thinking: What it is and why it counts. Insight assessment, 1(1), 1-23.
• Facione, P. A., & Facione, N. C. (1993). Profiling critical thinking dispositions. Assessment Update, 5(2), 1–4. https://doi.org/10.1002/au.3650050202
• Falloon, G. (2023). Investigating pedagogical, technological and school factors underpinning effective ‘critical thinking curricula’ in K-6 education. Thinking Skills and Creativity, 51, 101447. https://doi.org/10.1016/j.tsc.2023.101447
• Firdaus, F., Aras, L., & Mahmud, R. (2024). Students’ Critical Thinking Ability in Solving Geometry Problems. In Advances in Social Science, Education and Humanities Research/Advances in social science, education and humanities research (pp. 71–81). https://doi.org/10.2991/978-2-38476-210-1_6
• Jamil, M., Bokhari, T. B., & Iqbal, J. (2024). Incorporation of Critical Thinking Skills Development: A Case of Mathematics Curriculum for Grades I-XII. Deleted Journal, 13(1), 375–382. https://doi.org/10.62345/jads.2024.13.1.32
• Junarti, Zainudin, M., & Utami, A. D. (2022). The sequence of algebraic problem-solving paths: Evidence from structure sense of Indonesian student. Journal on Mathematics Education, 13(3), 437–464. https://doi.org/10.22342/jme.v13i3.pp437-464
• Ketaren, M. A., Armanto, D., & Simbolon, N. (2022). Development of Numeration Literacy Module Based on Realistic Approach for Elementary School. Elementary School Journal PGSD FIP UNIMED, 12(4), 340-347. https://doi.org/10.24114/esjpgsd.v12i4.40722
• Khusna, A. H., Siswono, T. Y. E., & Wijayanti, P. (2023). Research trends in critical thinking skills in mathematics: a bibliometric study. International Journal of Evaluation and Research in Education (IJERE), 13(1), 18. https://doi.org/10.11591/ijere.v13i1.26013
• Lämsä, J., Virtanen, A., Tynjälä, P., Maunuksela, J., & Koskinen, P. (2023). Exploring students’ perceptions of self-assessment in the context of problem solving in STEM. LUMAT International Journal on Math Science and Technology Education, 11(2). https://doi.org/10.31129/lumat.11.2.2028
• Lestari, I. L., Sari, M., Uripno, G., & Hariyanti, F. (2026). Unveiling AI ’ s Transformative Power in Mathematical Induction Proofs : Overcoming Challenges to Revolutionize Education. 12(1), 199–207. https://doi.org/https://doi.org/10.26638/
• Lestari, I. L., Sari, M., Uripno, G., Suprihatiningsih, S., & Hariyanti, F. (2025). Analysis of Artificial Intelligence Assisted Proof Process Through Principle of Mathematical Induction in Real Analysis Course. 6(2), 94–102. https://doi.org /10.26740/jomp.v6n2.p94-102
• Li, S., Tang, S., Geng, X., & Liu, Q. (2022). Constructing a critical thinking evaluation framework for college students majoring in the humanities. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.1017885
• Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.
• Mirtasari, A. (2024). Analysis ff Junior High School Student’s Mathematical Literacy Ability in Rme-Based Mathematics Learning in View of Self-Efficacy. Prima Jurnal Pendidikan Matematika, 8(1), 173. https://doi.org/10.31000/prima.v8i1.9832
• Moukhliss, M., Ennassiri, B., Abouhanifa, S., Achtaich, N., & Alkhozai, E. (2022). Analysis of Students’ Reasoning in Solving Comparison Problems. Journal of Educational and Social Research, 12(5), 63. https://doi.org/10.36941/jesr-2022-0123
• Napitupulu, E. E. (2017). Analyzing the Teaching and Learning of Mathematical Reasoning Skills in Secondary School. Asian Social Science, 13(12), 167. https://doi.org/10.5539/ass.v13n12p167
• Netti, S., Khairul, K., & Amelia, P. (2019). Student’s Mathematical Communication Skill Based on The Assimilation and Accommodation Framework. International Journal of Trends in Mathematics Education Research, 2(3), 133–137. https://doi.org/10.33122/ijtmer.v2i3.79
• Nguyen, H. T. M., Nguyen, G. T. C., Nguyen, B. N. T., Truong, D. T. T., & Thai, L. T. H. (2025). Mathematical Communication Skills for High School Students: A Comprehensive Review of Present Practices, Challenges, and Prospective Advancements. TEM Journal, 2349–2360. https://doi.org/10.18421/tem143-40
• Rahmawati, A. N. L., Sa’dijah, C., & Sudirman, S. (2025). Exploring High School Students’ Mathematical Representation Abilities: Translation from Verbal to Symbolic Using Higher-Order Thinking Skills. TEM Journal, 2442–2453. https://doi.org/10.18421/tem143-48
• Sachdeva, S., & Eggen, P.-O. (2021). Learners’ Critical Thinking About Learning Mathematics. International Electronic Journal of Mathematics Education, 16(3). https://doi.org/10.29333/iejme/11003
• Santoso, T., Cholily, Y. M., & Syaifuddin, M. (2021). An Analysis of Students’ Errors in Completing Essay HOTS Questions Based On Watson’s Criteria Viewed From The Cognitive Style Perspective. JTAM (Jurnal Teori Dan Aplikasi Matematika), 5(1), 121. https://doi.org/10.31764/jtam.v5i1.3776
• Sezgin, A., Kökçü, H., & Atagün, A. O. (2025). A Comprehensive Study on Restricted and Extended Intersection Operations of Soft Sets. Natural and Applied Sciences Journal, 8(1), 44–111. https://doi.org/10.38061/idunas.1613387
• Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36. https://doi.org/10.1007/BF00302715
• Siswono, T. Y. E. (2019). Paradigma Penelitian Pendidikan : Pengembangan Teori dan Aplikasi Pendidikan Matematika. Remaja Rosyda Karya.
• Syahlan, S., & Simamora, R. (2022). Improve Students’ Mathematical Critical Thinking Skills Sumatera Utara Islam: Using Models for Problem-Based Learning. AKSIOMA Jurnal Program Studi Pendidikan Matematika, 11(4), 3040-3051. https://doi.org/10.24127/ajpm.v11i4.5503
• Tall, D. (2013). How Humans Learn to Think Mathematically. Cambridge University Press. https://doi.org/10.1017/CBO9781139565202
• Theabthueng, P., Khamsong, J., & Worapun, W. (2022). The Development of Grade 8 Student Analytical Thinking and Learning Achievement Using the Integrated Problem-Based Learning and Think-Pair-Share Technique. Journal of Educational Issues, 8(1), 420. https://doi.org/10.5296/jei.v8i1.19711
• Uripno, G., & Nurfalah, E. (2025). Leveraging Contextual Worksheet to Reveal Students’ Proofing in Counting Rules. Riemann: Research of Mathematics and Mathematics Education, 7(2), 189–203. https://doi.org/10.38114/riemann.v7i2.114
• Vinner, S. (2002). The Role of Definitions in the Teaching and Learning of Mathematics. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 65–81). Springer Netherlands. https://doi.org/10.1007/0-306-47203-1_5
• Yang, S. (2024). Research on Application of Artificial Intelligence in Higher Education Management. Education Journal, 7(1), 120-126. https://doi.org/10.31058/j.edu.2023.71014
• Yohannes, Y., Juandi, D., & Tamur, M. (2021). The Effect of Problem-Based Learning Model on Mathematical Critical Thinking Skills of Junior High School Students: A Meta-Analysis Study. JP3I (Jurnal Pengukuran Psikologi Dan Pendidikan Indonesia), 10(2), 142–157. https://doi.org/10.15408/jp3i.v10i2.17893
• Zhu, H. (2023). Transforming Mathematics Education: Fostering Critical Thinkers. In Advances in Social Science, Education and Humanities Research/Advances in social science, education and humanities research (pp. 108–114). https://doi.org/10.2991/978-2-38476-158-6_16

How to Cite This

Article Metrics

Download Statistics

Other Statistics

Copyright and Permissions

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors published in this journal agree to the following terms:

• The copyright of each article is retained by the author (s) without restrictions
• The journal allows the author(s) to retain publishing rights without restrictions
• The author grants the journal the first publication rights with the work simultaneously licensed under the Creative Commons Attribution License, allowing others to share the work with an acknowledgement of authorship and the initial publication in this journal.
• Authors may enter into separate additional contractual agreements for the non-exclusive distribution of published journal versions of the work (for example, posting them to institutional repositories or publishing them in a book), with acknowledgement of their initial publication in this journal
• Authors are permitted and encouraged to post their work online (For example in the Institutional Repository or on their website) before and during the submission process, as this can lead to productive exchanges, as well as earlier and larger citations of published work
• Articles and all related material published are distributed under a Creative Commons Attribution-4.0 International Public License (CC - BY 4.0).

License

AlphaMath: Journal of Mathematics Education is licensed under a Creative Commons Attribution- 4.0 International Public License (CC - BY 4.0).

You are free to :

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially

Data Availability