Students’ mathematical critical thinking skills and difficulties in solving geometry problems: An analysis

Authors

  • Rahmawati Universiti Teknologi MARA (UiTM)
  • Lalu Wahyu Rizaldi Universitas Negeri Yogyakarta

DOI:

https://doi.org/10.33474/jpm.v11i2.24423

Keywords:

Mathematics Education, Geometry, Probelm Solving, Mathematical Critical Thinking

Abstract

Critical thinking is widely recognized as a key competence in mathematics education; however, many students still struggle to apply it when solving problems. This suggests that the role of critical thinking in mathematics learning needs to be examined more closely. This study describes the overall level of students’ mathematical critical thinking skills and investigates the challenges they experience in utilizing these skills during the process of solving geometry problems. A mixed-methods research design was employed involving 76 junior high school students aged 13–14 years. The quantitative phase utilized a paper-and-pencil test to provide an overview of students’ mathematical critical thinking levels, while the qualitative phase explored the specific difficulties students encountered in applying these skills during problem solving. The findings indicate that students’ mathematical critical thinking skills were at a moderate level, with an overall mean score of 65.62. Of the 76 students involved in the study, 13 students (17.1%) were classified in the low category, 50 students (65.8%) were in the medium category, and 13 students (17.1%) were categorized at the high level. The main difficulties identified were related to reasoning coherence, unit representation, and conclusion formulation. The results of this study are expected to provide valuable insights for mathematics teachers in designing more effective instructional strategies to foster students’ critical thinking in geometry learning.

References

Anastia, A., Nurcahyono, N. A., & Setiani, A. (2024). Students’ Critical Thinking in Solving Geometric Problems. Prisma, 13(1), 149. https://doi.org/10.35194/jp.v13i1.4006
Angkotasan, N., Suharna, H., Abdullah, I. H., & Dahlan, S. (2024). The Difficulty of Students ’ Reflective Thinking in Problems Solving o f Linear Program. International Education Studies, 17(1), 18–24. https://doi.org/10.5539/ies.v17n1p18
Creswell, J. W. (2012). Educational Research : Planning, Conducting, and Evaluating Quantitative and Qualitative Research (4th Editio). Pearson
Ennis, R. H. (1989). Critical Thinking and Subject Specificity: Clarification and Needed Research. Educational Researcher, 18(3), 4–10. https://doi.org/10.3102/0013189X018003004
Fachrudin, A. D., & Juniati, D. (2023). Kinds of Mathematical Thinking Addressed in Geometry Research in School : A Systematic Review. Jurnal Riset Pendidikan Dan Inovasi Pembelajaran Matematika, 6(2), 154–165. https://doi.org/https://doi.org/10.26740/jrpipm.v6n2.p154-165
Febriyanti, W., Wahyuddin, & Mutaminnah. (2024). Analysis of Student Errors in Solving Problems on Three-Dimensional Shapes with Flat Surfaces : A Qualitative Study on Eighth-Grade Students. Journal of Geometry Research and Innovation in Education, 1(2), 58–66. https://doi.org/10.56855/gradient.v1i2.1198
Fineldi, R. J. (2023). Students ’ Difficulties : Mathematical Creative Thinking Skill Questions Based on Habits of Mind. Jurnal Riset Pendidikan Matematika, 10(1), 16–19. https://doi.org/http://dx.doi.org/10.21831/jrpm.v10i1.60001
Mei, A., Sa’o, S., & Naja, F. Y. (2021). Profil Berpikir Kritis Mahasiswa dalam Memecahkan Masalah Geometri Ditinjau dari Adversity Quotient dan Learning Style [University Students’ Critical-Thinking Profiles in Solving Geometry Problems Viewed from Adversity Quotient and Learning Style]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(3), 1709–1721. https://doi.org/https://doi.org/10.24127/ajpm.v10i3.3882
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third edit). SAGE Publications Ltd.
Monteleone, C., Miller, J., & Warren, E. (2023). Conceptualising Critical Mathematical Thinking in Young Students. Mathematics Education Research Journal, 35(2), 339–359. https://doi.org/10.1007/s13394-023-00445-1
Nu’man, M., & Azka, R. (2023). Kesulitan Siswa dalam Menyelesaikan Masalah Geometri [Students’ Difficulties in Solving Geometry Problems]. Polynom: Journal in Mathematics Education, 3(2), 49–55. https://doi.org/https://doi.org/10.14421/polynom.2023.32.49-55
OECD. (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing. https://doi.org/10.1787/53f23881-en
Rahmaini, N., & Chandra, S. O. (2024). Pentingnya Berpikir Kritis dalam Pembelajaran Matematika [The Importance of Critical Thinking in Mathematics Learning]. Griya Journal of Mathematics Education and Application, 4(1), 1–8. https://doi.org/https://doi.org/10.29303/griya.v4i1.420
Rahmawati, L., Juandi, D., & Nurlaelah, E. (2022). Implementasi STEM dalam Meningkatkan Kemampuan Berpikir Kritis dan Kreatif Matematis [Implementing STEM to Improve Mathematical Critical and Creative Thinking Abilities]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(3), 2002–2014. https://doi.org/https://doi.org/10.24127/ajpm.v11i3.5490
Ramdjid, N. R., Sukestiyarno, S., Rochmad, R., & Mulyono, M. (2022). Students ’ Difficulties in Solving Geometry Problems. Cypriot Journal of Educational Sciences, 17(12), 4628–4640. https://doi.org/https://un-pub.eu/ojs/index.php/cjes/article/view/7039
Romero-Ariza, M., Quesada-Armenteros, A., & Estepa-Castro, A. (2024). Promoting Critical Thinking Through Mathematics and Science Teacher Education: The Case of Argumentation and Graphs Interpretation about Climate Change. European Journal of Teacher Education, 47(1), 41–59. https://doi.org/10.1080/02619768.2021.1961736
Sari, D. R., & Caswita. (2020). The Analysis of Mathematical Critical Thinking Skills of Students in Junior High School. Advances in Social Science, Education and Humanities Research, 422(Icope 2019), 123–126. https://doi.org/10.2991/assehr.k.200323.103
Sodik, R., Hendriana, H., Supriatna, T., & Putra, H. D. (2025). Analysis Of Students ’ Errors in Solving Mathematical Critical Thinking Problems On. (JIML) Journal of Innovatıve Mathematıcs Learnıng, 8(2), 212–220. https://doi.org/https://dx.doi.org/10.22460/jiml.v8i2.p23858
Sujero, C. V. S., & Alcuizar, R. A. (2025). Teaching Approaches and Students ’ Conceptual Understanding in Geometry. International Journal of Multidisciplinary Research and Analysis, 08(07), 4210–4219. https://doi.org/10.47191/ijmra/v8-i07-56
Syafril, S., Aini, N. R., Netriwati, Pahrudin, A., Yaumas, N. E., & Engkizar. (2020). Spirit of Mathematics Critical Thinking Skills (CTS). Journal of Physics: Conference Series, 1467(1). https://doi.org/10.1088/1742-6596/1467/1/012069
Syaiful, Huda, N., Mukminin, A., & Kamid. (2022). Using a Metacognitive Learning Approach to Enhance Students’ Critical Thinking Skills Through Mathematics Education. SN Social Sciences, 2(4), 1–26. https://doi.org/10.1007/s43545-022-00325-8
Tasya Aprilla Trisna, Ikhsan, M., & Elizar, E. (2022). Abilities and Difficulties of Ninth-Grade Students in Solving Geometry Transformation Problems. Jurnal Pendidikan MIPA, 23(October), 1724–1737. https://doi.org/http://dx.doi.org/10.23960/jpmipa/v23i4.pp1724-1737
Wijaya, A., & Dewayani, S. (2021). Framework Asesmen Kompetensi Minimum (AKM) [Minimum Competency Assessment Framework]. Badan Penelitian Dan Pengembangan Dan Perbukuan Kementerian Pendidikan Dan Kebudayaan, 1–108.

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Published

2025-12-31

How to Cite

Rahmawati, & Rizaldi, L. W. (2025). Students’ mathematical critical thinking skills and difficulties in solving geometry problems: An analysis. Jurnal Pendidikan Matematika (JPM), 11(2), 191–201. https://doi.org/10.33474/jpm.v11i2.24423