Kemampuan Penalaran Matematis Siswa dalam Pembelajaran Berbasis Masalah: Studi Kasus di Sekolah Menengah Pertama

Achmad Damar; Julya Ananta

doi:10.66031/smarth.v2i1.300

Authors

Achmad Damar Universitas Sembilanbelas November Kolaka Author
Julya Ananta Universitas Sembilanbelas November Kolaka Author

DOI:

https://doi.org/10.66031/smarth.v2i1.300

Keywords:

Penalaran Matematis, Problem-Based Learning, Geometri, Siswa SMP

Abstract

Penelitian ini bertujuan mendeskripsikan kemampuan penalaran matematis siswa dalam pembelajaran berbasis masalah pada materi geometri di sekolah menengah pertama. Penelitian menggunakan pendekatan kuantitatif dengan desain pretest–posttest yang diperkaya data kualitatif melalui observasi dan wawancara. Subjek penelitian adalah siswa kelas VIII yang mengikuti pembelajaran Problem-Based Learning (PBL). Hasil menunjukkan peningkatan signifikan kemampuan penalaran matematis, ditunjukkan oleh kenaikan skor rata-rata dari 36,8 (pretest) menjadi 73,6 (posttest) dengan nilai normalized gain 0,59 pada kategori sedang–tinggi serta korelasi tinggi antara pretest dan posttest (r = 0,87; p < 0,001). Peningkatan terjadi pada seluruh indikator penalaran, terutama kemampuan menarik kesimpulan dan memberikan justifikasi logis. Data kualitatif menunjukkan peningkatan keterlibatan siswa dalam diskusi, pemodelan masalah, dan refleksi. Temuan ini menegaskan bahwa PBL efektif mengembangkan kemampuan berpikir logis, analitis, dan reflektif siswa. Penelitian merekomendasikan penerapan PBL pada materi matematika lain dengan mempertimbangkan karakteristik individual siswa.

Downloads

Download data is not yet available.

References

Adeyemi, O. F., Xaviel, A. M., Fatqurhohman, F., & Bustanul, R. (2025). Machine learning evaluation of junior high student’s math representations in complex problem-solving tasks. SMARTH: Journal of Mathematics Education and Learning, 1(2), 91–106.

Amirudin, A., Muzaki, I. A., & Nurhayati, S. (2025). Problem-based learning as a pedagogical innovation for transforming higher education students' Islamic religious comprehension. Educational Process: International Journal, 18, e2025412. https://doi.org/10.22521/edupij.2025.18.412

Anggraeni, N., & Sofhan, I. K. (2025). Transformative of problem-based learning model to enhance learning outcomes of Muhammadiyah high school students. JINEA: Journal of Innovation in Education and Learning, 1(2), 51–62. https://doi.org/10.66031/jinea.v1i2.9

Aslan, A. (2021). Problem-based learning in live online classes: Learning achievement, problem-solving skill, communication skill, and interaction. Computers & Education, 171, 1–15. https://doi.org/10.1016/j.compedu.2021.104237

Astriani, N., & Al Dhana, M. B. (2024). Kemampuan penalaran matematis siswa melalui pendekatan contextual teaching and learning. Jurnal THEOREMS (The Original Research of Mathematics), 8(2), 263–271. https://doi.org/10.31949/th.v8i2.7404

Aulya, R., & Purwaningrum, J. P. (2021). Pengaruh model pembelajaran PBL berbantuan alat peraga dalam peningkatan kemampuan penalaran matematis. Jurnal MathEdu (Mathematic Education Journal, 4(3), 401–406. https://doi.org/10.37081/mathedu.v4i3.3103

Bahri, S., Santosa, F. H., Kurniawati, K. R. A., & Negara, H. R. P. (2022). Kemampuan penalaran matematis mahasiswa berdasarkan variasi gender dan self-efficacy matematis. Journal of Didactic Mathematics, 2(3), 134–141. https://doi.org/10.34007/jdm.v2i3.1047

Basid, A., Sutrisno, E., & Aliyeva, L. R. (2024). Analysis of the effect of contextual problem solving on students’ mathematical reasoning ability. International Journal of Science and Mathematics Education, 1(3), 24–33. https://doi.org/10.62951/ijsme.v1i3.258

Cahyani, N. D., & Sritresna, T. (2023). Kemampuan penalaran matematis siswa dalam menyelesaikan soal cerita. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu (PME), 2(1), 103–112. https://doi.org/10.31980/powermathedu.v2i1.2720

Díaz, V., & Aravena, M. (2021). Solving problem types and levels of proportional reasoning in initial training of mathematics teachers. Journal of Research in Mathematics Education, 10(3), 296–317. https://doi.org/10.17583/redimat.7125

Fatqurhohman, F., Malini, A. N., & Mendyas, F. (2025). Mathematical representations of students with dyscalculia in differentiated learning environments: A conceptual review. SMARTH: Journal of Mathematics Education and Learning, 1(1), 37–50.

Fatqurhohman, F., Murniasih, T. R., Anwar, R. B., & Halim, F. A. (2025). The role of UbD in developing students’ mathematical problem-solving skills: A literature review. RESET: Review of Education, Science, and Technology, 1(1), 29–42. https://doi.org/10.66031/reset.v1i1.18

Hadi, S., Rahman, A., & Gafur, A. (2024). Students’ mathematical reasoning ability in junior high school mathematics learning with contextual reasoning. Journal of Education and Social Science, 1(1), 6–11. https://doi.org/10.70716/jess.v1i1.57

Hamdani, A., & Romadhoni. (2025). Digital-based learning innovation of health psychology and physical activity to promote healthy lifestyles among high school students. JINEA: Journal of Innovation in Education and Learning, 1(1), 29–36. https://doi.org/10.66031/jinea.v1i1.7

Hardianti, A., Fatqurhohman, F., & Juliastuti, I. A. (2025). Penerapan model problem-based learning berbantuan Geogebra untuk meningkatkan hasil belajar peserta didik. Media Pendidikan Matematika, 13(1), 75–84. https://doi.org/10.33394/mpm.v13i1.15439

Hasanah, S. U., Suryaningrum, C. W., & Fatqurhohman, F. (2023). Penalaran matematis siswa dalam mengonstruksi konsep luas daerah persegi panjang. Jurnal Silogisme: Kajian Ilmu Matematika dan Pembelajarannya, 8(1), 14–22. https://doi.org/10.24269/silogisme.v8i1.4941

Hastuti, I. D., Fuster-Guill, D., Paola, J., Garay, P., Hern, R. M., & Namaziandost, E. (2022). The effect of problem-based learning on metacognitive ability in the conjecturing process of junior high school students. Hindawi Education Research International, 2022(1), 1–10. https://doi.org/10.1155/2022/2313448

Herbert, S. (2021). Overcoming challenges in assessing mathematical reasoning. Australian Journal of Teacher Education (Online), 46(8), 17–30. https://doi.org/10.14221/ajte.2021v46n8.2

Husniah, A., & Azka, R. (2022). Modul matematika dengan model pembelajaran problem-based learning untuk memfasilitasi kemampuan penalaran matematis siswa. Mosharafa: Jurnal Pendidikan Matematika, 11(2), 328. https://doi.org/10.31980/mosharafa.v11i2.724

Kharisma, D. N., & Hidayatulloh, M. K. Y. (2025). Penerapan model problem-based learning terhadap kemampuan berpikir kritis siswa SMK. RESET: Review of Education, Science, and Technology, 1(2), 93–100. https://doi.org/10.66031/reset.v1i2.44

Kladchuen, R., & Srisomphan, J. (2021). The synthesis of a model of problem-based learning with the gamification concept to enhance the problem-solving skills for high vocational certificate. International Journal of Emerging Technologies in Learning, 16(4), 4–21. https://doi.org/10.3991/ijet.v16i14.20439

Kurniawan, D. A., Astalini, Darmaji, T., Tanti, & Maryani, S. (2022). Innovative learning: Gender perception of e-module linear equations in mathematics and physics. Indonesian Journal on Learning and Advanced Education (IJOLAE), 4(2), 92–106. https://doi.org/10.23917/ijolae.v4i2.16610

Kusasih, I. H., & Satria, D. (2024). Strategi pembelajaran berbasis masalah (problem-based learning) dalam meningkatkan kemampuan berpikir kritis peserta didik. Jurnal Teknologi Pendidikan dan Pembelajaran, 2(2), 562–568. https://jurnal.kopusindo.com/index.php/jtpp/article/view/344

Latifah, U., Fatqurhohman, F., & Sugiyantoro, E. (2025). Peningkatan kemampuan representasi matematis peserta didik melalui problem-based learning berbantuan Google Sheets. Mandalika Mathematics and Educations Journal, 7(2), 874–890. https://doi.org/10.29303/jm.v7i2.8986

Lin, J. W., Zhao, S. L., Darmawan, P., & Fatqurhohman, F. (2025). Evaluation of Junior High School Students’ Representation Skills in Differentiated Learning. SMARTH: Journal of Mathematics Education and Learning, 1(2), 63-76.

Muhamed, H., Syuhada, I. N., Noor, R., & Fatqurhohman, F. (2026). Digital distraction in university students: A critical analysis for higher education instructional design. JINEA: Journal of Innovation in Education and Learning, 2(1), 41–54. https://doi.org/10.66031/jinea.v21i.162

Nurlinda, E., Azis, Z., & Nasution, M. D. (2024). Students’ mathematical reasoning ability and self-efficacy viewed from the application of problem-based learning and contextual teaching and learning models assisted. Journal of Mathematics Education and Application, 3(2). https://doi.org/10.30596/jmea.v3i2.20329

Nurwita, F., Kusumah, Y. S., & Priatna, N. (2022). Exploring students’ mathematical computational thinking ability in solving Pythagorean theorem problems. Al-Jabar: Jurnal Pendidikan Matematika, 13(2), 273–287. https://doi.org/10.24042/ajpm.v13i2.12496

Prayekti, N. (2025). Improving mathematical reasoning ability through project-based learning in middle school classrooms. Jurnal Konseling dan Pendidikan, 13(2), 89–98. https://doi.org/10.29210/1150400

Putty, I. A. D., Fatqurhohman, F., & Imamah, N. (2025). The effectiveness of problem-based learning on the development of spatial skills among junior high school students: A systematic literature review. Jurnal Math-UMB.EDU, 13(1), 88–98. https://doi.org/10.36085/mathumbedu.v13i1.9339

Sofiana, K., Suryaningrum, C. W., & Fatqurhohman, F. (2025). Implementing problem-based learning with differentiated learning styles to improve higher-order thinking skills. JTMT: Journal Tadris Matematika, 6(2), 54–61. https://doi.org/10.47435/jtmt.v6i2.4184

Usman, U., Juniati, D., & Khabibah, S. (2026). Analysis of students’ mathematical reasoning ability on junior high school. JIML, 9(1), 138–148. https://dx.doi.org/10.22460/jiml.v9i1.p30533

Wijaya, T., Chen, X., & Purnama, S. (2026). Evaluating design thinking in mathematics students: The impact of AI utilization and digital literacy. JINEA: Journal of Innovation in Education and Learning, 2(1), 27–40. https://doi.org/10.66031/jinea.v2i1.161

Wicaksono, S., Saputra, I., & Hamzah, S. N. (2025). Profile of junior high school students’ critical thinking skills in solving geometric problems based on cognitive styles. SMARTH: Journal of Mathematics Education and Learning, 1(1), 29–36