Kemampuan penalaran matematis siswa dalam aktivitas problem posing
DOI:
https://doi.org/10.61291/jpi.v7i1.62Keywords:
effect, problem posing, mathematical reasoning ability, kemampuan penalaran matematisAbstract
Mathematical reasoning is essential for understanding concepts, constructing arguments, and solving mathematical problems, yet classroom observations indicate that many students remain passive and have difficulty expressing conjectures, performing mathematical manipulations, and drawing conclusions. Learning activities that require students to formulate and solve their own problems may provide more opportunities to develop these abilities. This study aimed to examine the effect of the problem-posing learning model on students' mathematical reasoning ability. The population comprised all 263 eighth-grade students of SMP Negeri 29 Bandar Lampung in the 2024/2025 academic year, distributed across nine classes (VIII.1–VIII.9). Two classes taught by the same teacher were selected through cluster random sampling. Class VIII.4, consisting of 28 students, served as the experimental group and received problem-posing instruction, whereas class VIII.2, consisting of 30 students, served as the control group and received conventional instruction. The study used a pretest–posttest control-group design. Data were collected through essay tests developed to measure four indicators of mathematical reasoning: presenting mathematical statements, proposing conjectures, performing mathematical manipulations, and drawing conclusions. Students' gain scores were analyzed using the Mann–Whitney U test. The results showed that the mean gain in mathematical reasoning scores of students taught through problem posing was higher than that of students taught conventionally. The experimental group also demonstrated stronger achievement across the measured reasoning indicators. These findings indicate that the problem-posing learning model affects students' mathematical reasoning ability. Requiring students to formulate questions, discuss possible strategies, solve the problems they create, and evaluate their solutions can promote active participation and provide meaningful practice in mathematical reasoning.
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Alani, N. (2024). Pengaruh pendekatan pembelajaran problem posing terhadap kemampuan berpikir kritis matematis siswa. Jurnal Penelitian Pendidikan, 16(1), 50–63. https://doi.org/10.21137/jpp.2024.16.1.5
Amir, M. Z., Urrohmah, A., & Andriani, L. (2021). The effect of application of realistic mathematics education (RME) approach to mathematical reasoning ability based on mathematics self efficacy of junior high school students in Pekanbaru. Journal of Physics: Conference Series, 1776(1), 012039. IOP Publishing. https://doi.org/10.1088/1742-6596/1776/1/012039
Andriono, R., & Pradipta, T. R. (2022). Analisis penalaran matematis siswa ditinjau dari motivasi belajar. ANARGYA: Jurnal Ilmiah Pendidikan Matematika, 5(1), 106–114. https://doi.org/10.24176/anargya.v5i1.8016
Anggraini, A., Syofiana, M., & Ramadianti, W. (2023). Analisis kemampuan penalaran matematis siswa berbasis masalah pada materi bilangan pecahan. Range: Jurnal Pendidikan Matematika, 4(2), 267–277. https://doi.org/10.32938/jpm.v4i2.3156
Ayuni, N., Maryana, M., Marhami, M., Nufus, H., & Mursalin, M. (2021). Peningkatan kemampuan penalaran matematis siswa melalui model pembelajaran problem posing berbantuan software Autograph pada siswa MTsS Al-Madinatuddiniyah Syamsuddhuha. Jurnal Pendidikan Matematika Malikussaleh, 1(2), 65–74. https://doi.org/10.29103/jpmm.v1i2.5588
Blegur, I. K. S. (2022). Problem posing: Strategi yang memfasilitasi keterampilan berpikir tingkat tinggi matematika siswa. FRAKTAL: Jurnal Matematika dan Pendidikan Matematika, 3(1), 97–106. https://doi.org/10.35508/fractal.v3i1.7292
Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521–1540. https://doi.org/10.1007/s10763-016-9758-2
Hidayatullah, M. S., Sulianto, J., & Azizah, M. (2019). Analisis kemampuan penalaran ditinjau dari kemampuan pemecahan masalah matematis. Thinking Skills and Creativity Journal, 2(2), 93–102. https://doi.org/10.23887/tscj.v2i2.21198
Himmah, W. I., & Istiqlal, M. (2019). Keefektifan pembelajaran problem posing tipe post-solution posing terhadap kemampuan pemecahan masalah matematik. Kreano: Jurnal Matematika Kreatif-Inovatif, 10(1), 78–85. https://doi.org/10.15294/kreano.v10i1.12695
Irham, M., & Maulidyawati, D. (2023). Penerapan model pembelajaran problem posing untuk meningkatkan kemampuan pemecahan masalah siswa di SMP Negeri 2 Sumbawa. REALISTIC: Journal of Education Mathematics and Science, 1(1), 30–40. https://journal.pcn.ac.id/index.php/real/article/view/33
Kosasih, U., Shekhawati, N. N., Aqilah, N., Sulastri, Y. L., Prasetyo, E., & Mulia, S. (2023). Penerapan model problem posing untuk meningkatkan kemampuan penalaran matematis peserta didik SMP. UJMES (Uninus Journal of Mathematics Education and Science), 8(2), 118–127. https://doi.org/10.30999/ujmes.v8i2.2605
Kwon, H., & Capraro, M. M. (2021). Nurturing problem posing in young children: Using multiple representation within students’ real-world interest. International Electronic Journal of Mathematics Education, 16(3), em0648. https://doi.org/10.29333/iejme/11066
Schoevers, E. M., Leseman, P. P. M., & Kroesbergen, E. H. (2020). Enriching mathematics education with visual arts: Effects on elementary school students’ ability in geometry and visual arts. International Journal of Science and Mathematics Education, 18, 1613–1634. https://doi.org/10.1007/s10763-019-10018-z
Meltzer, D. E. (2002). The relationship between mathematics preparation and conceptual learning gains in physics: A possible hidden variable in diagnostic pretest scores. American Journal of Physics, 70(12), 1259–1268. https://doi.org/10.1119/1.1514215
Mukuka, A., Mutarutinya, V., & Balimuttajjo, S. (2021). Mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Journal on Mathematics Education, 12(1), 73–92. https://doi.org/10.22342/jme.12.1.12508.73-92
Muniroh, L., & Buchori, A. (2024). Analisis kemampuan penalaran matematis peserta didik dalam menyelesaikan masalah kontekstual pada materi sistem persamaan linear tiga variabel (SPLTV). FARABI: Jurnal Matematika dan Pendidikan Matematika, 7(1), 49–58. https://doi.org/10.47662/farabi.v7i1.704
Narpila, S. D., Tarwiyah, Purba, O. N., Purba, A., & Lestari, I. (2025). A systematic literature review: Self-efficacy toward mathematical reasoning ability. Jurnal Absis: Jurnal Pendidikan Matematika dan Matematika, 8(2), 291–302. https://doi.org/10.30606/absis.v8i2.3450
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM. https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf
Negara, H. R. P., Santosa, F. H., & Siagian, M. D. (2024). Overview of student’s mathematics reasoning ability based on social cognitive learning and mathematical self-efficacy. Mathematics Teaching Research Journal, 16(1), 121–142. https://eric.ed.gov/?id=EJ1427397
Nuridayanti, Akil, M., & Darmawan, F. A. (2020). Penerapan model pembelajaran problem posing terhadap hasil belajar. Jurnal MediaTIK: Jurnal Media Pendidikan Teknik Informatika dan Komputer, 3(2), 39. https://doi.org/10.26858/jmtik.v3i2.14361
OECD. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en
Oktaviana, V., & Aini, I. N. (2021). Deskripsi kemampuan penalaran matematis siswa SMP pada materi aritmatika sosial. Delta: Jurnal Ilmiah Pendidikan Matematika, 9(2), 157–170. https://doi.org/10.31941/delta.v9i2.1334
Putri, R. C., Husna, A., & Amelia, F. (2021). Analisis kemampuan penalaran matematis siswa dalam menyelesaikan soal cerita aljabar ditinjau dari gender di kelas VIII SMP IT El-Yasin Batam. Cahaya Pendidikan, 7(2), 115–122. https://doi.org/10.33373/chypend.v7i2.3795
Samosir, K. (2022). Penerapan model kooperatif problem posing dalam meningkatkan aktivitas dan hasil belajar Bahasa Indonesia siswa SMA Negeri 5 Tebo. PAEDAGOGY: Jurnal Ilmu Pendidikan dan Psikologi, 2(1), 45–50. https://doi.org/10.51878/paedagogy.v2i1.1058
Sari, S. K. N., Muchtadi, & Prihatin, I. (2023). Pengaruh pembelajaran problem posing terhadap hasil belajar matematika siswa pada materi pecahan kelas VII. Jurnal Riset Rumpun Matematika dan Ilmu Pengetahuan Alam (JURRIMIPA), 2(1), 167–173. https://doi.org/10.55606/jurrimipa.v2i1.757
Sasmita, R. S., & Harjono, N. (2021). Efektivitas model Problem Based Learning dan problem posing dalam meningkatkan kemampuan berpikir kritis siswa sekolah dasar. Jurnal Basicedu, 5(5), 3472–3481. https://doi.org/10.31004/basicedu.v5i5.1313
Shufa, N. F., & Khumaedi. (2023). Penerapan model pembelajaran problem posing untuk meningkatkan berpikir kritis siswa kelas VIII MTs Al-Islam Sumurrejo. Unnes Physics Education Journal, 12(1), 50–56. https://doi.org/10.15294/upej.v12i1.67461
Siregar, R. N., Suryadi, D., Prabawanto, S., & Mujib, A. (2022). Improving student learning: Mathematical reasoning ability through a realistic mathematic education. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 2698–2713. https://doi.org/10.24127/ajpm.v11i4.6250
Sumartini, T. S., & Utami, I. E. (2023). Analisis kemampuan penalaran matematis siswa pada materi relasi dan fungsi. PRISMA, 12(2), 333–341. https://doi.org/10.35194/jp.v12i2.3062
Supriadi, N., Jamaluddin Z, W., & Suherman, S. (2024). The role of learning anxiety and mathematical reasoning as predictor of promoting learning motivation: The mediating role of mathematical problem solving. Thinking Skills and Creativity, 52, 101497. https://doi.org/10.1016/j.tsc.2024.101497
Syamsuddin, S., Tayeb, T., Rasyid, M. R., Abrar, A. I. P., & Amin, B. (2022). Efektivitas pendekatan pembelajaran problem posing terhadap hasil belajar matematika siswa. Al Asma: Journal of Islamic Education, 4(2), 84–94. https://doi.org/10.24252/asma.v4i2.30638
Ulpa, F., Marifah, S., Maharani, S. A., & Ratnaningsih, N. (2021). Analisis kesalahan siswa dalam menyelesaikan soal kontekstual pada materi bangun ruang sisi datar ditinjau dari teori Nolting. Square: Journal of Mathematics and Mathematics Education, 3(2), 67–80. https://doi.org/10.21580/square.2021.3.2.8651
Vebrian, R., Putra, Y. Y., Saraswati, S., & Wijaya, T. T. (2021). Kemampuan penalaran matematis siswa dalam menyelesaikan soal literasi matematika kontekstual. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(4), 2602–2614. https://doi.org/10.24127/ajpm.v10i4.4369
Wau, H. A., Harefa, D., & Sarumaha, R. (2022). Analisis kemampuan penalaran matematis pada materi barisan dan deret siswa kelas XI SMK Negeri 1 Toma tahun pembelajaran 2020/2021. AFORE: Jurnal Pendidikan Matematika, 1(1), 41–49. https://doi.org/10.57094/afore.v1i1.435
Wijaya, T. T., Ying, Z., & Purnama, A. (2020). Using Hawgent dynamic mathematic software in teaching trigonometry. International Journal of Emerging Technologies in Learning (iJET), 15(10), 215–222. https://doi.org/10.3991/ijet.v15i10.13099
Wulandari, D. A. (2020). Strategi pembelajaran problem posing dalam menentukan panjang satuan baku pada sekolah dasar. Universitas Nusantara PGRI Kediri. https://repository.unpkediri.ac.id/996/
Zhang, C., Zhou, Y., Wijaya, T. T., Chen, J., & Ning, Y. (2024). Effects of a problem posing instructional intervention on student learning outcomes: A three-level meta-analysis. Thinking Skills and Creativity, 53, 101587. https://doi.org/10.1016/j.tsc.2024.101587
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