Kemampuan Pemecahan Masalah Matematis dalam Menyelesaikan Operasi Baris Elementer pada Mata Kuliah Aljabar Matriks
DOI:
https://doi.org/10.28918/circle.v6i1.2606Abstract
Mathematical problem-solving ability plays a crucial role in enabling students to understand mathematical concepts and solve complex problems, particularly in matrix algebra courses at the university level. This study aims to describe students’ mathematical problem-solving abilities in solving problems related to elementary row operations in the matrix algebra course. This research employed a descriptive qualitative approach. The study was conducted at Sekolah Tinggi Agama Islam Al-Bahjah Cirebon involving second-semester students of the Mathematics Education program who were enrolled in the matrix algebra course. The research subjects consisted of three students representing high, medium, and low categories based on their test scores. Data were collected using a written test on elementary row operations. The data analysis was carried out using the Miles and Huberman model, which includes data collection, data reduction, and data presentation. Students’ problem-solving abilities were analyzed based on Polya’s problem-solving indicators, namely understanding the problem, devising a plan, carrying out the plan, and looking back. The results showed that high-level students were able to meet all indicators of mathematical problem-solving skills, medium-level students were able to meet two indicators of mathematical problem-solving skills, namely understanding problems and planning problem-solving strategies, and low-level students were only able to meet one indicator of mathematical problem-solving skills, namely understanding problems.
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References
Damayanti, N., & Kartini, K. (2022). Analisis Kemampuan Pemecahan Masalah Matematis Siswa SMA pada Materi Barisan dan Deret Geometri. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 107-118. https://doi.org/10.31980/mosharafa.v11i1.691
Dorimana, A., Uworwabayeho., A, & Nizeyimana, G. (2022). Enhancing upper secondary learners’ problem-solving abilities using problem-based learning in mathematics. International Journal of Learning, Teaching and Educational Research, 21(8), 235-252. https://doi.org/10.26803/ijlter.21.8.14
Dulun, Ö., & Lane, J. F. (2023). Supporting critical thinking skills needed for the International Baccalaureate Diploma Programme: A content analysis of a national and two international education programs in Turkey. Thinking Skills and Creativity, 47, 101211. https://doi.org/10.1016/j.tsc.2022.101211
Fadilah, N. S., & Hakim, D. L. (2022). Analisis kemampuan pemecahan masalah matematis siswa SMA pada Materi Fungsi. Jurnal THEOREMS (The Original Research of Mathematics), 7(1), 64-73. https://unma.ac.id/ju rnal/index.php/th/article/view/3824
Firda, N., Suryadi, D., & Dahlan, J. A. (2023). Mathematical Problem-Solving Ability of Junior High School Students Based on Polya. Edumatica: Jurnal Pendidikan Matematika, 13(3), 273-284. https://doi.org/10.22437/edumatica.v13i03.29287
Göktaş, O., & Yazıcı, E. (2020). Effectiveness of teaching mathematical problem-solving strategies to students with mild intellectual disabilities. Turkish Journal of Computer and Mathematics Education, 11(2), 361-85. https://doi. org/10.16949/turkbilmat.662461
Handayani, I., & Noviana, W. (2022). Analisis Kesalahan Mahasiswa dalam Menyelesaikan Soal Aljabar Linear dan Matriks pada Materi Sistem Persamaan Linear. Jurnal Pendidikan Glasser, 6(1), 63-69. https://doi.org/10.32529/glasser.v6i1.1353
Hanggara, Y., Aisyah, S. H., & Amelia, F. (2022). Analisis kemampuan pemecahan masalah matematis siswa ditinjau dari perbedaan gender. Pythagoras J. Progr. Stud. Pendidik. Mat, 11(2), 189-201. https://doi.org/10.33373/pythagoras.v11i2.4490
Hanifah, A. I. (2022). Kemampuan pemahaman matematis pada mata kuliah aljabar linear elementer. J-PiMat, 4(1), 437-442. https://doi.org/10.31932/j-pimat.v4i1.1625
Hidayati, D. W., & Junaedi, I. (2025). Studi Perbandingan Kurikulum Finlandia dan Indonesia: Upaya Peningkatan Kemampuan Pemecahan Masalah Matematika Siswa SMA. Circle: Jurnal Pendidikan Matematika, 5(1), 1-21. https://doi.org/10.28918/circle.v5i1.9812
Kaitera, S., & Harmoinen, S. (2022). Developing Mathematical Problem-Solving Skills in Primary School by Using Visual Representations on Heuristics. LUMAT: International Journal on Math, Science and Technology Education, 10(2), 111-146. https://doi.org/10.31129/LUMAT.10.2.1696
Kousloglou, M., Petridou, E., Molohidis, A., & Hatzikraniotis, E. (2023). Assessing students’ awareness of 4cs skills after mobile-technology-supported inquiry-based learning. Sustainability, 15(8), 6725. https://doi.org/10.3390/su15086725
Kusuma, D. A., Ruchjana, B. N., Widodo, S. A., & Dwipriyoko, E. (2024). Combination of ethnomathematics and the mozart effect to improve problem-solving skills and mathematical disposition. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 18(2), 1155-1166. https://doi.org/10.30598/barekengvol18iss2pp1155-1166
La'ia, H. T., & Harefa, D. (2021). Hubungan kemampuan pemecahan masalah matematis dengan kemampuan komunikasi matematik siswa. Aksara: Jurnal Ilmu Pendidikan Nonformal, 7(2), 463-474. http://dx.doi.org/10.37905/aksara.7.2.463-474.2021
Li, L., & Disney, L. (2021). Young children’s mathematical problem solving and thinking in a playworld. Mathematics Education Research Journal, 35(1), 23-44. https://doi.org/10.1007/ s13394-021-00373-y
Lusiana, L., Armiati, A., & Yerizon, Y. (2022). Kemandirian Belajar dan Persepsi Siswa Mengenai Guru Terhadap Kemampuan Pemecahan Masalah Matematis Siswa SMK. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 155-166. https://doi.org/10.31980/mosharafa.v11i1.1074
Luzano, J. F. (2024). Assessment in mathematics education in the sphere of artificial intelligence: A systematic review on its threats and opportunities. International Journal of Academic Multidisciplinary Research, 8(2), 100-104. http://dx.doi.org/10.2139/ssrn.5221121
Masfufah, R., & Afriansyah, E. A. (2021). Analisis kemampuan literasi matematis siswa melalui soal PISA. Mosharafa: Jurnal Pendidikan Matematika, 10(2), 291-300. https://doi.org/10.31980/mosharafa.v10i2.662
Nawafilah, N. Q. (2019). Analisis kesalahan mahasiswa dalam menyelesaikan soal sistem persamaan linear menggunakan operasi baris elementer. Reforma: Jurnal Pendidikan dan Pembelajaran, 8(1), 167-172. https://doi.org/10.30736/rfma.v8i1.112
Nindiasari, H., Pranata, M. F., Sukirwan, S., Sugiman, S., Fathurrohman, M., Ruhimat, A., & Yuhana, Y. (2024). The use of augmented reality to improve students' geometry concept problem-solving skills through the STEAM approach. Infinity Journal, 13(1), 119-138. https://doi.org/10.22460/infinity.v13i1.p119-138
Novitasari, P., & Aisyah, A. S. (2024). Kemampuan Pemecahan Masalah Mahasiswa dalam Menyelesaikan Masalah Matematika pada Mata Kuliah Aljabar Matriks. Journal of Contemporary Issues in Primary Education, 2(1), 25-30. https://doi.org/10.61476/an6bbs04
Özcan, Z. Ç., & Eren Gümüş, A. (2019). A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety. Australian Journal of Education, 63(1), 116-134. https://doi.org/10.1177/0004944119840073
Piñeiro, J. L., Castro-Rodríguez, E., & Castro, E. (2021). Mathematical problem-solving in two teachers’ knowledge models: A critical analysis. Mathematics Teaching-Research Journal, 13(1), 71-93
Pratami, S. R., Sundayana, R., & Sofyan, D. (2023). Kesalahan kemampuan pemecahan masalah matematis siswa berdasarkan prosedur newman pada materi sistem persamaan linear dua variabel. Jurnal Inovasi Pembelajaran Matematika: Power MathEdu, 2(2), 165-174. https://doi.org/10.31980/pme.v2i2.1418
Pratiwi, D. T., & Alyani, F. (2022). Kemampuan pemecahan masalah matematika siswa kelas V SD pada materi pecahan. Journal for Lesson and Learning Studies, 5(1), 136-142. https://doi.org/10.23887/jlls.v5i1.49100
Rahmawati, D., & Afriansyah, E. A. (2023). Kemampuan pemecahan masalah matematis melalui proses planning, execution, dan revision ditinjau dari kemampuan awal matematis siswa. Plusminus: Jurnal Pendidikan Matematika, 3(2), 191-208. https://doi.org/10.31980/plusminus.v3i2.3130
Rahmawati, A., Warmi, A., & Marlina, R. (2022). Analisis kemampuan pemecahan masalah matematis siswa SMP pada materi teorema pythagoras. Jurnal Cendekia: Jurnal Pendidikan Matematika, 6(1), 365-374. https://doi.org/10.31004/cendekia.v6i1.1012
Rosyidi, A. H., Sari, Y. M., Fardah, D. K., & Masriyah, M. (2024). Designing mathematics problem-solving assessment with GeoGebra Classroom: proving the instrument validity. Journal of Education and Learning (EduLearn), 18(3), 1038-1046. https://doi.org/10.11591/edulearn.v18i3.21191
Rumiati, L., & Novitasari, P. (2025). Analisis Kemampuan Pemahaman Matematis Aljabar Linear Mahasiswa. Jurnal Jendela Matematika, 3(02), 127-133. https://doi.org/10.57008/jjm.v3i02.1628
Ruswana, A. M. (2019). Analisis kemampuan pemahaman matematis pada mata kuliah aljabar linier elementer. Jurnal Cendekia, 3(2), 293-299. https://doi.org/10.31004/cendekia.v3i2.111
Sagita, D. K., Ermawati, D., & Riswari, L. A. (2023). Kemampuan pemecahan masalah matematis siswa sekolah dasar. Jurnal Educatio Fkip Unma, 9(2), 431-439. https://doi.org/10.31949/educatio.v9i2.4609
Santos-Trigo, M. (2024). Problem solving in mathematics education: tracing its foundations and current research-practice trends. ZDM–Mathematics Education, 56(2), 211-222. https://doi.org/10.1007/s11858-024-01578-8
Saputra, R. J., Sofyan, D., & Mardiani, D. (2023). Kemampuan pemecahan masalah matematis siswa ditinjau dari self-confidence siswa pada materi bangun ruang sisi datar. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu, 2(1), 79-92. https://doi.org/10.31980/pme.v2i1.1402
Siskawati, E., Zaenuri, Z., Waluya, S. B., & Junaedi, I. (2022). Mathematical error patterns to facilitate solving math problems for junior high school students. Journal of Higher Education Theory & Practice, 22(9), 112-117. https://doi.org/10.33423/jhetp.v22i9.5368
Sitopu, J. W., Khairani, M., Roza, M., Judijanto, L., & Aslan, A. (2024). The importance of integrating mathematical literacy in the primary education curriculum: A literature review. International Journal of Teaching and Learning, 2(1), 121–134.
Sriwahyuni, K., & Maryati, I. (2022). Kemampuan pemecahan masalah matematis siswa pada materi statistika. Plusminus: Jurnal Pendidikan Matematika, 2(2), 335-344. https://doi.org/10.31980/plusminus.v2i2.1109
Stewart, S., Axler, S., Beezer, R., Boman, E., Catral, M., Harel, G., ... & Wawro, M. (2022). The linear algebra curriculum study group (LACSG 2.0) recommendations. Notices of the American Mathematical Society, 69(5). https://dx.doi.org/10.1090/noti2479
Udmah, S., Purwaningrum, J. P., & Ermawati, D. (2024). Penggunaan Media KOKUBA untuk Meningkatkan Kemampuan Pemecahan Masalah Matematis Siswa SD. Jurnal Pendidikan Dan Kewirausahaan, 12(1), 59-74. https://doi.org/10.47668/pkwu.v12i1.1016
Ulya, H., Sugiman, R. R., & Retnawati, H. (2024). Technology-based learning interventions on mathematical problem-solving: a meta-analysis of research in Indonesia. Int J Eval & Res Educ ISSN, 2252(8822), 8822. http://doi.org/10.11591/ijere.v13i1.26380
Usman, P. M., Tintis, I., & Nihayah, E. F. K. (2022). Analisis Kemampuan Pemecahan Masalah Matematika Siswa dalam Menyelesaikan Sistem Persamaan Linear Tiga Variabel. Jurnal Basicedu, 6(1), 664-674. https://doi.org/10.31004/basicedu.v6i1.1990
Widyastuti, R. T., & Airlanda, G. S. (2021). Efektivitas Model Problem Based Learning terhadap Kemampuan Pemecahan Masalah Matematika Siswa Sekolah Dasar. Jurnal Basicedu, 5(3), 1120–1129. https://doi.org/10.31004/basicedu.v5i3.896
Wulandari, N., Riswari, L., A., & Ermawati, D. (2024). Analisis kemampuan pemecahan masalah matematis siswa SD pada materi kecepatan dan debit. Prismatika: Jurnal Pendidikan Dan Riset Matematika, 6(2), 275-291. https://doi.org/10.33503/prismatika.v6i2.3460
Xu, C., Lafay, A., Douglas, H., Di Lonardo Burr, S., LeFevre, J. A., Osana, H. P., ... & Maloney, E. A. (2022). The role of mathematical language skills in arithmetic fluency and word-problem solving for first-and second-language learners. Journal of Educational Psychology, 114(3), 513. https://doi.org/10.1037/edu0000673
Yuliany, N., Halimah, A., Manzila, F., & Ichiana, N. N. (2021). Analisis kemampuan penalaran matematis pada mata kuliah aljabar linear elementer mahasiswa pendidikan matematika fakultas tarbiyah dan keguruan UIN Alauddin Makassar. Al Asma: Journal of Islamic Education, 3(2), 275-286.
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