Students’ mathematical critical thinking during project-based probability learning: A repeated-measures study
DOI:
https://doi.org/10.33474/jpm.v12i2.25861Keywords:
Project-Based Learning, Mathematical Critical Thinking, Probability, FRISCO Framework, Repeated Measurement DesignAbstract
In the 21st century, mathematical critical thinking is a core competency that students must master. However, high school students still struggle to analyze word problems in mathematics. This study examines how students’ mathematical critical thinking skills develop over three Project-Based Learning (PjBL) sessions on probability. The study employs a quantitative approach with a pre-experimental, single-group repeated measures (time-series) design, involving 35 10th-grade students at SMAN 3 Kediri (Public Senior High School 3 Kediri). Data were collected through essay-based word-problem tests at the end of each session and assessed using a rubric based on the six FRISCO indicators (Focus, Reasoning, Inference, Situation, Clarity, and Overview), adapted from Ennis. The data were analyzed using the nonparametric Friedman and Wilcoxon Signed-Rank tests because the distributions of Test 2 and Test 3 scores deviated from normality. Average scores increased gradually from 59.86 (Test 1) to 61.61 (Test 2) and 69.04 (Test 3), with a statistically significant increase only observed from Test 2 to Test 3. At the indicator level, “Focus” and “Situation” increased sharply in the third session; “Reason” remained the strongest indicator, while “Inference” and “Overview” remained the weakest. These findings suggest that students’ mathematical critical thinking skills developed gradually throughout the PjBL sequence, although the single-group design without a control group limits causal claims regarding PjBL’s contribution. Teachers are advised to supplement PjBL with explicit scaffolding during the inference and answer evaluation stages.
References
Aini, M., Ridianingsih, D. S., & Yunitasari, I. (2022). Efektivitas model pembelajaran project based learning (PJBL) berbasis stem terhadap keterampilan berpikir kritis siswa. [The effectiveness of stem-based project based learning (PJBL) learning model on critical thinking]. Jurnal Kiprah Pendidikan, 1(4), 247–253.
https://doi.org/10.33578/kpd.v1i4.118
Aizah, D. L., & Dewi, H. L. (2024). Efektivitas project based learning dalam kurikulum merdeka terhadap kemampuan berpikir kritis matematis siswa smp negeri 1 karangdadap. [The effectiveness of project-based learning in the merdeka curriculum on the mathematical critical thinking skills of students at karangdadap public junior high school 1]. Circle: Jurnal Pendidikan Matematika, 4 (2), 175–185. https://doi.org/10.28918/circle.v4i2.8714
Amir, A., & Solida, A. (2022). Penerapan pembelajaran berbasis proyek dan hasil belajar mahasiswa [The implementation of project-based learning and student learning outcomes]. Jurnal Ilmiah Universitas Batanghari Jambi, 22(3), 2112. https://doi.org/10.33087/jiubj.v22i3.3018
Anantasia, G., & Rindrayani, S. R. (2025). Metodologi penelitian quasi eksperimen [Quasi-experimental research methodology]. Adiba: Journal of Education, 5(2), 183–192. https://jutepe-joln.net/index.php/JURPERU/article/view/811/800
Anisa, W. N. & Prasetyo, A. K. (2023). Peningkatan kemampuan menyelesaikan soal cerita melalui model problem based learning pada pembelajaran matematika di kelas v sd negeri blotongan 02 [Improving the ability to solve workshops through the problem-based learning model in mathematics instruction in grade 5 at blotongan 02 public elementary school]. Didaktik : Jurnal Ilmiah PGSD STKIP Subang, 9(4), 2550–2562. https://doi.org/10.36989/didaktik.v9i04.1832
Ansya, Y. A., & Salsabilla, T. (2025). Keterampilan guru abad 21 dalam pembelajaran ipa di sekolah dasar [21st-century teacher skills in science instruction in elementary school]. Jurnal Dunia Pendidikan, 6(2), 498–512. https://doi.org/10.55081/jurdip.v6i2.4579
Azizah, R. (2022). Project based learning dalam pembelajaran matematika [Project-based learning in mathematics education]. J-PiMat Jurnal Pendidikan Matematika, 4(2), 539–550. https://doi.org/10.31932/j-pimat.v4i2.2026
Difinubun, F. A., Makmuri, M., & Flavia Aurelia, H. (2022). Analisis kebutuhan modul ajar matematika untuk meningkatkan kemampuan pemecahan masalah siswa smk kelas x [Analysis of the needs for mathematics instructional modules to improve problem-solving skills among 10th-grade vocational high school students]. Griya Journal of Mathematics Education and Application, 2(4), 853–864. https://doi.org/10.29303/griya.v2i4.244
Fisher, D., Kusumah, Y. S., & Dahlan, J. A. (2020). Project-based learning in mathematics: A literatur review. Journal of Physics: Conference Series, 1657(1). https://doi.org/10.1088/1742-6596/1657/1/012032
Inayah, S., Safitri, Y., Zurweni, Sarmada, N., Andriani, N., Maison, Anindita, M., Mardhotillah, B., Multahadah, C., Gusmanely, Z., Muhammad, D., & Karmanto, B. (2025). Statistika non parametrik. U ME Publishing. https://umepublishing.com/statistika-non-parametrik/
Khasanah, U. N., Rejeki, S., & Sugiyanti, S. (2024). Efektivitas pembelajaran project-based learning berbasis steam terhadap kemampuan berpikir kritis pada siswa smp [The effectiveness of steam-based project-based learning on critical thinking skills among middle school students]. Jurnal Cendekia : Jurnal Pendidikan Matematika, 8(3), 2225–2242. https://doi.org/10.31004/cendekia.v8i3.3529
Kristiyanto, D. (2020). Peningkatan kemampuan berpikir kritis dan hasil belajar matematika dengan model project based learning (PJBL) [Improving critical thinking skills and mathematics learning outcomes using the project-based learning (PJBL) model]. Mimbar Ilmu, 25(1), 1-10. https://doi.org/10.23887/mi.v25i1.24468
Lapase, M. H. (2021). Implementasi pembelajaran berbasis proyek untuk meningkatkan hasil belajar siswa pada mata pelajaran matematika di sd negeri pinedapa [Implementation of project-based learning to improve student learning outcomes in mathematics at pinedapa public elementary school]. Jurnal Paedagogy, 8(2), 134. https://doi.org/https://doi.org/10.33394/jp.v8i2.3492
Lestari, R., & Lubis, A. (2023). Pengaruh model project based learning dengan media visual terhadap keterampilan berpikir kritis [The effect of project-based learning with visual media on critical thinking skills]. JMPM: Jurnal Matematika dan Pendidikan Matematika, 8(1), 15–27. https://doi.org/https://doi.org/10.26594/jmpm.v8i1.3631
Maesaroh, S. (2021). Kemampuan berpikir kritis matematis siswa smp pada materi bangun ruang sisi datar [Middle school students’ mathematical critical thinking skills in the topology of flat-sided three-dimensional shapes]. Jurnal Riset Intervensi Pendidikan (JRIP), 3(2), 99–105. https://journal.rekarta.co.id/index.php/jrip/article/view/164
Muhajirin, Risnita, & Asrulla. (2024). Pendekatan penelitian kuantitatif dan kualitatif serta tahapan penelitian [Quantitative and qualitative research approaches and research phases]. Journal Genta Mulia, 15(1), 82–92. https://ejournal.uncm.ac.id/index.php/gm/article/view/903
Rafik M., Febrianti V. P., Nurhasanah A., & Muhajir S. N. (2022). Telaah literatur: pengaruh model pembelajaran project based learning (pjbl) terhadap kreativitas siswa guna mendukung pembelajaran abad 21 [Literature review: the effect of the project-based learning (PJBL) model on student creativity to support 21st-century learning]. Jurnal Pembelajaran Inovatif, 5(1), 80–85. https://doi.org/https://doi.org/10.21009/JPI.051.10
OECD. (2023). PISA 2022 results (volume I and ii) – country notes: Indonesia. OECD Publishing. https://www.oecd.org/en/publications/pisa-2022-results-volume-i-and-ii-country-notes_ed6fbcc5-en/indonesia_c2e1ae0e-en.html
Benyamin, B., Qohar, A., & Sulandra, I. M. (2021). Analisis kemampuan berpikir kritis siswa sma kelas x dalam memecahkan masalah spltv [An analysis of the critical thinking skills of 10th-grade high school students in solving spltv problems]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 5(2), 909–922. https://doi.org/https://doi.org/10.31004/cendekia.v5i2.574
Rosa, E., Destian, R., Agustian, A., & Wahyudin, W. (2024). Inovasi model dan strategi pembelajaran dalam implementasi kurikulum merdeka [Innovations in learning models and strategies in the implementation of the merdeka curriculum]. Journal of Education Research, 5(3), 2608–2617. https://doi.org/10.37985/jer.v5i3.1153
Setiana, D. S., Nuryadi, N., & Santosa, R. H. (2020). Analisis kemampuan berpikir kritis matematis ditinjau dari aspek overview [Analysis of mathematical critical thinking skills from an overview perspective]. JKPM (Jurnal Kajian Pendidikan Matematika), 6(1), 1-12. https://doi.org/10.30998/jkpm.v6i1.6483
Sherly, D. F., Hadi, F. Rahmatika, & Pradana, L. N. (2020). Efektivitas model pembelajaran project based learning (PJBL) terhadap keterampilan menyelesaikan soal cerita matematika [The effectiveness of the project-based learning (PJBL) model on students’ skills in solving mathematics workshops]. Prosiding Konferensi Ilmiah Dasar, 4(1). http://prosiding.unipma.ac.id/index.php/KID
Sugiyono. (2019). Metode Penelitian Kuantitatif, Kualitatif, dan R&D (Bandung). Alfabeta.
Triani Putri, M., Sagala, V., & Listiana, Y. (2022). Profil berpikir kritis siswa dalam memecahkan soal higher order thinking berdasarkan gaya berpikir sternberg menurut fungsinya [Profile of students’ critical thinking in solving higher-order thinking problems based on sternberg’s thinking styles according to their functions]. GAUSS: Jurnal Pendidikan Matematika, 5(1), 50–59. https://doi.org/10.30656/gauss.v5i1.4741
Tunu, D. J. I., Daniel, F., & Gella, N. J. M. (2022). Analisis kemampuan menyelesaikan soal cerita matematika siswa ditinjau dari gender [An analysis of students’ ability to solve math word problems by gender]. Jurnal Cendekia : Jurnal Pendidikan Matematika, 6(2), 1499–1510. https://doi.org/10.31004/cendekia.v6i2.1366
Widiana, D. R., Syafiuddin, Sriwijayasih, I., Aju, I. R., Praharsi, Y., & Novianarenty, E. (2025). The use of the Wilcoxon signed-rank test in analyzing the difference in test scores before and after digital marketing training. Jurnal Teknologi Maritim, 8(2), 23-32. https://doi.org/10.35991/jtm.v8i2.73
Zahra, F. A., & Hakim, D. L. (2022). Kesulitan siswa kelas vii smp dalam berpikir kritis matematis pada materi garis dan sudut [Difficulties faced by seventh-grade middle school students in mathematical critical thinking regarding lines and angles]. PHI: Jurnal Pendidikan Matematika, 6(2), 208. https://doi.org/10.33087/phi.v6i2.244
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