THE EFFECTIVENESS OF PROBLEM-BASED AND DISCOVERY LEARNING MODELS ON STUDENTS' MATHEMATICAL CRITICAL THINKING ABILITIES
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Abstract
Critical thinking skills are essential for addressing 21st-century challenges, which requires a learning model that can optimally engage students' cognitive abilities. This study aims to examine the improvement of students' critical mathematical thinking skills (KBKM) through learning that utilizes the Problem-Based Learning (PBL) and Discovery Learning models, based on the students' skill levels. The method used in this study is a mixed-method approach with a sequential explanatory design. In the quantitative phase, quasi-experimental research was conducted with a one-group pretest-posttest design, ANOVA, and a 3x2 factorial design. In the qualitative phase, an embedded concurrent strategy was applied. The sample consisted of 72 grade VII students from State Junior High Schools in Cimahi City. The results revealed that the criteria had a significant effect on the critical mathematical thinking skills scores. The learning model also had a direct impact on improving these skills. Additionally, the study found that the average score of the high group was higher than that of the medium and low groups. In terms of learning models, Discovery Learning proved to be more effective in the learning process.
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Nurjaman, A., Sari, I. P., & Hidayat, W. (2025). THE EFFECTIVENESS OF PROBLEM-BASED AND DISCOVERY LEARNING MODELS ON STUDENTS’ MATHEMATICAL CRITICAL THINKING ABILITIES. Kalamatika: Jurnal Pendidikan Matematika, 10(1), 113-124. https://doi.org/10.22236/KALAMATIKA.vol10no1.2025pp113-124
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References
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Dewi, N. R., & Maulida, N. F. (2023). The Development of STEM-nuanced Mathematics Teaching Materials to Enhance Students’ Mathematical Literacy Ability Through Information and Communication Technology-Assisted Preprospec Learning Model. International Journal of Educational Methodology, 9(2), 409–421. https://doi.org/10.12973/IJEM.9.2.409
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Hidayati, K., & Listyani, E. (2010). Pengembangan Instrumen Kemandirian Belajar Mahasiswa. Jurnal Penelitian Dan Evaluasi Pendidikan, 14(1). https://doi.org/10.21831/pep.v14i1.1977
Hung, W. (2009). The 9-step problem design process for problem-based learning: Application of the 3C3R model. Educational Research Review, 4(2), 118–141. https://doi.org/10.1016/j.edurev.2008.12.001
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Palinussa, A. L., Lakusa, J. S., & Moma, L. (2023). Comparison of Problem-Based Learning and Discovery Learning To Improve Students’ Mathematical Critical Thinking Skills. Formatif: Jurnal Ilmiah Pendidikan MIPA, 13(1), 109–122. https://doi.org/10.30998/formatif.v13i1.15205
Rahayu, F. D., Mawarsari, V. D., & Suprapto, R. (2023). Development of PBL e-modules on polyhedron constructions for geometrical thinking ability. Kalamatika: Jurnal Pendidikan Matematika, 8(1), 107-118.
Rahman, A., Andri Nugroho, A., Roshayanti, F., Dasar, P., & PGRI Semarang, U. (2022). Pengaruh Model Problem Based Learning Berbasis Kontekstual Berbantuan Audio Visual Terhadap Berpikir Kritis Dan Hasil Belajar Pada Materi Magnet Kelas Vi. 7(2), 2022.
Safitri, T., Hidayat, W., & Sari, I. P. (2022). Problem based learning (PBL) pada materi teorema pythagoras: Suatu action research. JPMI (Jurnal Pembelajaran Matematika Inovatif), 5(3), 885-896.
Septian, A., & Komala, E. (2019). Kemampuan Koneksi Matematik Dan Motivasi Belajar Siswa Dengan Mengunakan Model Problem-Based Learning (Pbl) Berbantuan Geogebra Di Smp. Prisma, 8(1), 1. https://doi.org/10.35194/jp.v8i1.438
Shahrill, M., Putri, R. I. I., Zulkardi, & Prahmana, R. C. I. (2018). Processes involved in solving mathematical problems. AIP Conference Proceedings, 1952. https://doi.org/10.1063/1.5031981
Slavin, R. (2012). Educational Psychology (Theori and Practice) Tenth Edition. Pearson.
Soden, R. (1994). Teaching Problem Solving in Vocational Education. Routledge.
Sulistyawati, D., Hadi, W., Hidayat, A., & Muhammad, R. R. (2023). The impact of problem-based learning augmented with hots problems on students’ mathematical problem-solving abilities. Kalamatika: Jurnal Pendidikan Matematika, 8(2), 219-236.
Sung, Y. T., Chang, K. E., & Liu, T. C. (2016). The effects of integrating mobile devices with teaching and learning on students’ learning performance: A meta-analysis and research synthesis. Computers and Education, 94, 252–275. https://doi.org/10.1016/j.compedu.2015.11.008
Suparman, Juandi, D., & Tamur, M. (2021). Review of problem-based learning trends in 2010-2020: A meta-analysis study of the effect of problem-based learning in enhancing mathematical problem-solving skills of Indonesian students. Journal of Physics: Conference Series, 1722(1). https://doi.org/10.1088/1742-6596/1722/1/012103
Suryawan, I. P. P., Sudiarta, I. G. P., & Suharta, I. G. P. (2023). Students’ Critical Thinking Skills in Solving Mathematical Problems: Systematic Literature Review. Indonesian Journal Of Educational Research and Review, 6(1), 120–133. https://doi.org/10.23887/ijerr.v6i1.56462
Suteja, S., & Setiawan, D. (2022). Students’ Critical Thinking and Writing Skills in Project-Based Learning. International Journal of Educational Qualitative Quantitative Research, 1(1), 16–22. https://doi.org/10.58418/ijeqqr.v1i1.5
Warsah, I., Morganna, R., Uyun, M., Hamengkubuwono, H., & Afandi, M. (2021). The Impact of Collaborative Learning on Learners’ Critical Thinking Skills. International Journal of Instruction, 14(2), 443–460. https://doi.org/10.29333/iji.2021.14225a
Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1.
Angraini, L. M., & Nurmaliza, N. (2022). The Effect of Interactive Multimedia-Based Learning on Students’ Mathematical Critical Thinking Ability in the Course of Structure Algebra. Jurnal Didaktik Matematika, 9(2), 217–229. https://doi.org/10.24815/jdm.v9i2.26839
Arsih, F., Ferdian, R., & Fadilah, M. (2023). Effectiveness of Digital-Based COVID-19 Prevention Supplement Books to Empower High School Students’ Scientific Literacy and Critical Thinking Skills. Jurnal Penelitian Pendidikan IPA, 9(4), 2244–2251. https://doi.org/10.29303/jppipa.v9i4.3474
Awang, H., & Ramly, I. (2008). Through Problem-Based Learning : Pedagogy and Practice in the Engineering Classroom. World Academy of Science, Engineering and Technology International Journal of Educational and Pedagogical Sciences, 2(4), 334–339.
Benyamin, Qohar, A., & Made Sulandra, I. (2021). Analisis Kemampuan Berpikir Kritis Siswa SMA Kelas X IPA Dalam Memecahkan Soal Cerita Ditinjau Dari Gender dan Kemampuan Matematika. Jurnal Pendidikan Matematika, 11(1), 28–41.
Bloom, B. S. (1976). Human characteristics and school learning. McGraw-Hill.
Bruner, J. S. (1961). The act of discovery. Harvard Educational Review.
Demir, E. (2022). An examination of high school students’ critical thinking dispositions and analytical thinking skills. Journal of Pedagogical Research, 6(4), 190–200. https://doi.org/10.33902/JPR.202217357
Dewi, N. R., & Maulida, N. F. (2023). The Development of STEM-nuanced Mathematics Teaching Materials to Enhance Students’ Mathematical Literacy Ability Through Information and Communication Technology-Assisted Preprospec Learning Model. International Journal of Educational Methodology, 9(2), 409–421. https://doi.org/10.12973/IJEM.9.2.409
Dharma, B. A., Tasrikah, N., & Churiyah, M. (2020). Effectiveness of Problem Based Learning (PBL) Towards Learning Outcomes Through Critical Thinking Skills. Jurnal Ad’ministrare, 7(2), 235. https://doi.org/10.26858/ja.v7i2.15343
Elliott, B., Oty, K., McArthur, J., & Clark, B. (2001). The effect of an interdisciplinary algebra/science course on students’ problem solving skills, critical thinking skills and attitudes towards mathematics. International Journal of Mathematical Education in Science and Technology, 32(6), 811–816. https://doi.org/10.1080/00207390110053784
Farib, P. M., Ikhsan, M., & Subianto, M. (2019). Proses berpikir kritis matematis siswa sekolah menengah pertama melalui discovery learning. Jurnal Riset Pendidikan Matematika, 6(1), 99–117. https://doi.org/10.21831/jrpm.v6i1.21396
Ghifari, M. T., Nurjanah, N., Herman, T., & Rahmah, H. (2024). Challenges in developing junior high school students' computational thinking skills in mathematics through problem-based learning. Kalamatika: Jurnal Pendidikan Matematika, 9(2), 135-146.
Hidayati, K., & Listyani, E. (2010). Pengembangan Instrumen Kemandirian Belajar Mahasiswa. Jurnal Penelitian Dan Evaluasi Pendidikan, 14(1). https://doi.org/10.21831/pep.v14i1.1977
Hung, W. (2009). The 9-step problem design process for problem-based learning: Application of the 3C3R model. Educational Research Review, 4(2), 118–141. https://doi.org/10.1016/j.edurev.2008.12.001
Joyce, B., & Weil, M. (n.d.). dan Calhoun E. 2011 Models Of Teaching. Yogyakarta: Percetakan Pustaka Belajar.
Kids, B. for. (2019). Framework for 21st century learning definitions. Battelle for Kids.
Kilpatrick, J., Swafford, J., & Findell, B. (2002). Helping Children Learn Mathematics. In Helping Children Learn Mathematics. https://doi.org/10.17226/10434
Lestari, K. E. (2013). Implementasi Brain-Based Learning Untuk Meningkatkan Kemampuan Koneksi dan Berpikir Kritis Matematis Siswa SMP. Universitas Pendidikan Indonesia.
Palinussa, A. L., Lakusa, J. S., & Moma, L. (2023). Comparison of Problem-Based Learning and Discovery Learning To Improve Students’ Mathematical Critical Thinking Skills. Formatif: Jurnal Ilmiah Pendidikan MIPA, 13(1), 109–122. https://doi.org/10.30998/formatif.v13i1.15205
Rahayu, F. D., Mawarsari, V. D., & Suprapto, R. (2023). Development of PBL e-modules on polyhedron constructions for geometrical thinking ability. Kalamatika: Jurnal Pendidikan Matematika, 8(1), 107-118.
Rahman, A., Andri Nugroho, A., Roshayanti, F., Dasar, P., & PGRI Semarang, U. (2022). Pengaruh Model Problem Based Learning Berbasis Kontekstual Berbantuan Audio Visual Terhadap Berpikir Kritis Dan Hasil Belajar Pada Materi Magnet Kelas Vi. 7(2), 2022.
Safitri, T., Hidayat, W., & Sari, I. P. (2022). Problem based learning (PBL) pada materi teorema pythagoras: Suatu action research. JPMI (Jurnal Pembelajaran Matematika Inovatif), 5(3), 885-896.
Septian, A., & Komala, E. (2019). Kemampuan Koneksi Matematik Dan Motivasi Belajar Siswa Dengan Mengunakan Model Problem-Based Learning (Pbl) Berbantuan Geogebra Di Smp. Prisma, 8(1), 1. https://doi.org/10.35194/jp.v8i1.438
Shahrill, M., Putri, R. I. I., Zulkardi, & Prahmana, R. C. I. (2018). Processes involved in solving mathematical problems. AIP Conference Proceedings, 1952. https://doi.org/10.1063/1.5031981
Slavin, R. (2012). Educational Psychology (Theori and Practice) Tenth Edition. Pearson.
Soden, R. (1994). Teaching Problem Solving in Vocational Education. Routledge.
Sulistyawati, D., Hadi, W., Hidayat, A., & Muhammad, R. R. (2023). The impact of problem-based learning augmented with hots problems on students’ mathematical problem-solving abilities. Kalamatika: Jurnal Pendidikan Matematika, 8(2), 219-236.
Sung, Y. T., Chang, K. E., & Liu, T. C. (2016). The effects of integrating mobile devices with teaching and learning on students’ learning performance: A meta-analysis and research synthesis. Computers and Education, 94, 252–275. https://doi.org/10.1016/j.compedu.2015.11.008
Suparman, Juandi, D., & Tamur, M. (2021). Review of problem-based learning trends in 2010-2020: A meta-analysis study of the effect of problem-based learning in enhancing mathematical problem-solving skills of Indonesian students. Journal of Physics: Conference Series, 1722(1). https://doi.org/10.1088/1742-6596/1722/1/012103
Suryawan, I. P. P., Sudiarta, I. G. P., & Suharta, I. G. P. (2023). Students’ Critical Thinking Skills in Solving Mathematical Problems: Systematic Literature Review. Indonesian Journal Of Educational Research and Review, 6(1), 120–133. https://doi.org/10.23887/ijerr.v6i1.56462
Suteja, S., & Setiawan, D. (2022). Students’ Critical Thinking and Writing Skills in Project-Based Learning. International Journal of Educational Qualitative Quantitative Research, 1(1), 16–22. https://doi.org/10.58418/ijeqqr.v1i1.5
Warsah, I., Morganna, R., Uyun, M., Hamengkubuwono, H., & Afandi, M. (2021). The Impact of Collaborative Learning on Learners’ Critical Thinking Skills. International Journal of Instruction, 14(2), 443–460. https://doi.org/10.29333/iji.2021.14225a