Analysis of The Critical Thinking Skills of Mathematics Education Students in Solving Differential Calculus Problems

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Published: Oct 31, 2026
DOI: https://doi.org/10.21067/pmej.v9i2.13841
Keywords:
critical thinking; differential calculus; Polya indicators; problem solving, mathematics education.

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Aq’sya Azalia Azzahra
Universitas Muhammadiyah Sorong
Marlinda Indah Eka Budiarti
Universitas Muhammadiyah Sorong

Abstract

This study uses a descriptive qualitative approach with the aim of analyzing the critical thinking skills of 15 first-semester Mathematics Education students at Muhammadiyah University Sorong in solving problems in differential calculus material. The focus of this study stems from initial findings that indicate students' difficulties in understanding the concept of derivatives in story problems, which are thought to be caused by procedural errors and a lack of reflective skills in the thinking process. Specifically, this study aims to describe the profile of students' critical thinking skills based on Polya's indicators. The research used a descriptive qualitative approach with a written test consisting of three-story problems on December 17, 2025, and semi-structured interviews with six subjects (two high, two medium, two low), supported by a 1-4 scale assessment and Miles and Huberman's data analysis model with triangulation. The results reveal variations in ability: high-ability students consistently meet all four indicators; medium-ability students meet some indicators but are hampered by procedural problems; low-ability students have fundamental difficulties starting from understanding the problem. These findings emphasize the importance of differential calculus learning based on conceptual understanding, reflection, and contextual questions in Southwest Papua to improve students' critical thinking skills.

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How to Cite
Aq’sya Azalia Azzahra, & Budiarti, M. I. E. (2026). Analysis of The Critical Thinking Skills of Mathematics Education Students in Solving Differential Calculus Problems. Pi: Mathematics Education Journal, 9(2), 69–82. https://doi.org/10.21067/pmej.v9i2.13841
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Vol. 9 No. 2 (2026): Oktober
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Articles
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References

] Oktariani and E. Ekadiansyah, “Peran Literasi dalam Pengembangan Kemampuan Berpikir Kritis,” J. Penelit. Pendidikan, Psikol. Dan Kesehat., vol. 1, no. 1, pp. 23–33, 2020, doi: 10.51849/j-p3k.v1i1.11.

[2] A. F. Hakiki, A. Livina, I. Selvianti, S. M. Febrianti, and U. Hernaeny, “Kesulitan Mahasiswa pada Kalkulus Diferensial dengan Meningkatkan Kemampuan Berpikir Kritis,” J. Pendidik. Mat., vol. 2, no. 2, pp. 1–12, 2025, doi: 10.47134/ppm.v2i2.1187.

[3] W. Mataheru, N. C. Huwaa, and C. Matitaputty, “Analisis kesalahan mahasiswa dalam perkuliahan matematika dasar secara daring,” J. Magister Pendidik. Mat., vol. 3, no. 1, pp. 45–50, 2021.

[4] T. Supriyatin and Syafa’atun, “ANALYSIS OF STUDENT ERRORS IN SOLVING DIFFERENTIAL CALCULUS PROBLEMS ON ABSOLUTE INEQUALITIES AND FUNCTIONS CONTINUITY,” vol. 8, no. 1, pp. 16–27, 2025, doi: 10.32665/james.v8i1.4095.

[5] Y. Sulistyorini and S. Napfiah, “ANALISIS KEMAMPUAN BERPIKIR KRITIS MAHASISWA DALAM MEMECAHKAN MASALAH KALKULUS,” AKSIOMA J. Progr. Stud. Pendidik. Mat., vol. 8, no. 2, pp. 279–287, 2019, doi: 10.24127/ajpm.v8i2.1947.

[6] S. S. Adawiyah, Z. U. Auliya, and M. D. Pamungkas, “Analisis Kemampuan Berpikir Kritis Mahasiswa dalam Menyelesaikan Soal Persamaan Diferensial Ditinjau dari Perbedaan Gender,” MATH LOCUS J. Ris. dan Inov. Pendidik. Mat., vol. 2, no. 2, pp. 57–66, 2021, doi: 10.31002/mathlocus.v2i2.1933.

[7] Zetriuslita and R. Ariawan, “STUDENTS’ MATHEMATICAL THINKING SKILL VIEWED FROM CURIOSITY THROUGH PROBLEM- BASED LEARNING MODEL ON INTEGRAL CALCULUS,” Infin. J., vol. 10, no. 1, pp. 31–40, 2021, doi: 10.22460/infinity.v10i1.p31-40.

[8] N. Azzahra, P. Isnaini, S. N. K. Nst, and C. Natalia, “Analisis Miskonsepsi Turunan Fungsi pada Buku Matematika SMA : Definisi Turunan, Visual Grafik, dan Contoh Soal,” Pendas J. Ilm. Pendidik. Dasar, vol. 10, no. 3, pp. 260–271, 2025, doi: 10.23969/jp.v10i03.33292.

[9] T. Siahaan and H. F. Sianipar, “PENINGKATAN KEMAMPUAN PEMECAHAN MASALAH MAHASISWA PADA MATAKULIAH KALKULUS DIFERENSIAL MELALUI MODEL PROBLEM BASED LEARNING,” Maju, vol. 7, no. 2, pp. 150–155, 2020.

[10] A. R. Rahmawati, S. Sudirman, and R. Rahardi, “Kesalahan Mahasiswa Pendidikan Matematika dalam Menyelesaikan Masalah Fungsi dan Persamaan Polinomial,” J. Cendekia J. Pendidik. Mat., vol. 5, no. 3, pp. 2548–2559, 2021, doi: 10.31004/cendekia.v5i3.893.

[11] E. Astika, F. Fitriati, and Rahmatullah, “ANALISIS KEMAMPUAN PEMECAHAN MASALAH MATEMATIKA SISWA PADA MATERI SISTEM PERSAMAAN LINIER DUA VARIABEL KELAS X IA-1 MAN 2 ACEH BESAR,” J. Ilm. Mhs., vol. 2, no. 2, pp. 1–13, 2021.

[12] A. Riyanto and N. Ishartono, “Kemampuan Berpikir Kritis Siswa dalam Menyelesaikan Artimatika Sosial Ditinjau dari Kemampuan Matematis dan Gender,” J. Cendekia J. Pendidik. Mat., vol. 06, no. 03, pp. 2552–2568, 2022, doi: 10.35141/jie.v5i2.363.

[13] S. S. Dewanti, “PROFIL BERPIKIR KRITIS MAHASISWA PGMI DALAM MEMECAHKAN MASALAH MATEMATIKA DASAR,” J. Mat. dan Pembelajaran, vol. 6, no. 1, pp. 11–22, 2018, doi: 10.33477/mp.v6i1.451.

[14] Y. I. Sari, Sumarmi, D. H. Utomo, and I. K. Astina, “The Effect of Problem Based Learning on Problem Solving and Scientific Writing Skills,” Int. J. Instr., vol. 14, no. 2, pp. 11–26, 2021, doi: 10.4324/9781315585697-27.

[15] L. Lea, T. S. Mantili, and E. Christin, “Analisis Kemampuan Pemahaman Matematis Siswa pada Materi Turunan Fungsi Kelas XI SMA,” Juwara J. Wawasan dan Aksara, vol. 2, no. 1, pp. 15–24, 2022, doi: 10.58740/juwara.v2i1.35.

[16] W. Ismayanti, C. A. H. F. Santosa, and I. Rafianti, “Minat Belajar, Efikasi Diri, dan Kemampuan Berpikir Kritis Berpengaruh Terhadap Hasil Belajar Matematika Siswa,” J. Educ. FKIP UNMA, vol. 8, no. 3, pp. 943–952, 2022, doi: 10.31949/educatio.v8i3.2847.

[17] S. Rejeki, Riyadi, and Siswanto, “Students’ Critical Thinking Skill in Solving Geometry Problems Viewed from Their Emotional Intelligence,” J. Phys. Conf. Ser., vol. 1796, no. 1, 2021, doi: 10.1088/1742-6596/1796/1/012012.

[18] S. Mukarromah, N. D. Rahmawati, L. Ariyanto, and S. R. Al Ashari, “Kemampuan Pemecahan Masalah Matematis Ditinjau dari Belief in Mathematics Siswa dalam Menyelesaikan Soal Turunan Fungsi,” J. Pendidik. dan Pembelajaran Indones., vol. 4, no. 2, pp. 733–745, 2024, doi: 10.53299/jppi.v4i2.539.

[19] A. Mirza, D. Fitriawan, Z. R, and A. Nursangaji, “Prospective mathematics teachers’ understanding of proof in mathematics for high school,” Al-Jabar J. Pendidik. Mat., vol. 13, no. 1, pp. 1–11, 2022, doi: 10.24042/ajpm.v13i1.10089.

[20] T. Andayani, Y. Fuad, and E. B. Rahaju, “Proses Pemecahan Masalah Matematika High Order Thinking Skills Siswa SMA Materi Trigonometri,” EDUKASIA J. Pendidik. dan Pembelajaran, vol. 5, no. 1, pp. 1361–1370, 2024, doi: 10.62775/edukasia.v5i1.1035.

[21] Hajerina, I. Suciati, and H. W. Mailili, “Analisis Kesalahan Mahasiswa pada Mata Kuliah Kalkulus Diferensial Materi Turunan,” Equal. J. Ilm. Pendidik. Mat., vol. 5, no. 1, pp. 24–33, 2022, doi: 10.46918/equals.v5i1.1238.

[22] Y. Ariyana, A. Pudjiastuti, R. Bestary, and Zamroni, Buku Pegangan Pembelajaran Berorientasi Pada Keteramilan Berpikir Tingkat Tinggi. 2018.

[23] D. Sulistyaningsih, S. B. Waluya, Isnarto, and Sugiman, “Students’ Problem-Solving Behavior in Differential Calculus Based on Mathematical Prior Knowledge,” Educ. Process Int. J., vol. 19, 2025, doi: 10.22521/edupij.2025.19.565.

[24] I. Fitriana, U. Kosasih, S. Saputra, and A. Wahid, “Analisis Terhadap Kemampuan Berpikir Kritis Peserta Didik melalui Pembelajaran Papan Permainan Evaluasi Trigonometri,” J. Dimens. Mat., vol. 5, no. 1, pp. 422–434, 2022, doi: 10.33059/jdm.v5i02.5723.

[25] D. R. Nuraini, T. A. Kusmayadi, and L. Fitriana, “Mathematics problem solving based on Schoenfeld in senior high school students,” J. Phys. Conf. Ser., vol. 1318, no. 1, 2019, doi: 10.1088/1742-6596/1318/1/012093.

[26] W. Xiong, H. Zhang, C. Ye, L. Chen, N. Jiang, and T. Zhang, “Self-rewarding correction for mathematical reasoning,” arXiv Prepr. arXiv2502.19613, 2025.

[27] H. Hasanah, “ANALISIS KESULITAN MAHASISWA DALAM MENYELESAIKAN SOAL TURUNAN FUNGSI ALJABAR,” J. InTent, vol. 2, no. 1, pp. 76–84, 2019, doi: 10.47080/intent.v2i1.520.

[28] R. Lusiana, “Analisis Kesalahan Mahasiswa Dalam Memecahkan Masalah Pada Materi Himpunan Ditinjau Dari Gaya Kognitif,” J. Penelit. dan Pembelajaran Mat., vol. 10, no. 1, pp. 24–29, 2017, doi: 10.30870/jppm.v10i1.1290.

[29] L. V. Hari, L. S. Zanthy, and H. Hendriana, “Hasil analisis menunjukkan bahwa terdapat hubungan yang signifikan antara self-efficacy siswa dengan kemampuan berpikir kritis matematis siswa dan pengaruh self- efficacy terhadap kemampuan berpikir kritis siswa SMK kelas XI negatif yaitu sebesar 19,89% s,” J. Pembelajaran Mat. Inov., vol. 1, no. 3, pp. 435–444, 2018, doi: 10.22460/jpmi.v1i3.435-444.

[30] S. S. Hidayah, S. B. Waluya, and Sugiman, “Critical thinking ability reviewed from self efficacy in the problem based learning model based on differentiation,” Turots J. Pendidik. Islam, vol. 7, no. 2, pp. 1635–1644, 2025, doi: 10.51468/jpi.v7i2.996.