A Study of Learning Obstacles: Determining Solutions of a System of Linear Equation Using Gauss-Jordan Method
DOI:
https://doi.org/10.31980/mosharafa.v12i1.748Keywords:
Hambatan belajar, Metode Gauss-Jordan, Penelitian didaktis, Sistem Persamaan Linier, Learning obstacles, Gauss-Jordan Method, Didactical Design Research, System of Linear EquationsAbstract
Salah satu metode pencarian solusi SPL yang dipelajari di pendidikan tinggi adalah metode Gauss-Jordan. Berdasarkan data penelitian, mahasiswa melakukan kesalahan dalam melakukan operasi baris elementer (OBE), membentuk ke dalam matriks yang diperbesar, dan bahkan pemahaman mendasar mengenai reduksi baris dan ini berpengaruh dalam menentukan solusi suatu SPL. Untuk itu perlu dianalisis hambatan belajar yang terjadi dalam menentukan solusi SPL menggunakan metode Gauss-Jordan. Peneitian ini merupakan penelitian kualitatif dan merupakan bagian dari Didactical Design Research (DDR). Penelitian ini dilaksanakan di salah satu universitas di Nusa Tenggara Timur (NTT) dengan subjek penelitian merupakan 20 mahasiswa calon guru matematika. Teknik penelitian ini adalah tes diagnostik dan wawancara. Hasil penelitian menunjukkan beberapa hambatan yang dialami mahasiswa adalah keterbatasan pemahaman pada OBE, pengklasifikasian MEBT, dan merepresentasikan MEBT ke dalam solusi SPL. Rekomendasi dari penelitian ini adalah pengajar hendaknya membuat suatu bahan ajar yang dapat meminimalisir hambatan belajar yang dialami mahasiswa.
One of many methods of finding solution of a system of linear equations (SLE) studied in higher education is the Gauss-Jordan method. Based on the research, students made mistakes in performing elementary row operations (ERO), forming into augmented matrices, and even basic understanding of row subtraction and this has an effect on determining the solution of an SLE. For this reason, it is necessary to analyze the learning obstacles that occur in determining the solution of LES using the Gauss-Jordan method. This qualitative research is part of the Didactical Design Research (DDR). This research was conducted at a university in East Nusa Tenggara (NTT) involving 20 students as preservice mathematics teacher. The technique of this research is diagnostic test and interview. The results show that some of the obstacles faced by students are insufficient understanding of ERO, classifying reduced row-echelon form (RREF), and representing MEBT into SPL solutions. This study recommends that teachers create teaching materials that minimizes learning obstacles experienced by students.
References
Anton, H., Rorres, Chris., & Black, Christine. (2005). Elementary linear algebra, with applications. Student solutions manual. J. Wiley.
Brouseau, G. (1997). Theory of Didactical Situation in Mathematics. Dordrecht: Kluwer Academic Publisher.
Brown, G., & Quinn, R. (2006). Algebra students’ difficulty with fractions. Australian Mathematics Teacher, 62(4), 28–40.
Doyumgaç, I., Tanhan, A., & Kiymaz, M. S. (2021). Understanding the most important facilitators and obstacles for online education during COVID-19 through online photovoice methodology. International Journal of Higher Education, 10(1), 166-190.
Funny, R. A. (2017). Using Matlab To Help Students Understanding Gauss-Jordan Methods. Angkasa: Jurnal Ilmiah Bidang Teknologi, 9(2), 75. https://doi.org/10.28989/angkasa.v9i2.176
Hariati, A., & Septiadi, D. D. (2019). Analysis of students’ mistakes in solving system of linear equation in three variables: A case on HOTS problems. International Journal on Teaching and Learning Mathematics, 2(1), 29. https://doi.org/10.18860/ijtlm.v2i1.7616
Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of Student Learning Obstacles in Solving Fraction Problems in Elementary School. International Journal of Educational Methodology, 8(3), 505-515.
Klau, K. Y., Siahaan, M. M. L., & Simarmata, J. E. (2020). An Identification of Conceptual and Procedural Understanding : Study on Preservice Secondary Mathematics Teacher. 11(2), 339–350.
Mahyudi, Ariani, N. M., & Ramadianti, W. (2017). Desain bahan ajar aljabar linier. Kalamatika, 2(1), 1–14.
Mahyudi, & Endaryono. (2020). Learning Obstacles Konsep Operasi Baris Elementer Ditinjau Dari Hambatan Epistemologi. Inovasi Pendidikan Matematika Desember Jurnal, 3(1), 48–59.
Muharomi, L. T., & Afriansyah, E. A. (2022). Kemampuan Koneksi Matematis dan Kemandirian Belajar Siswa pada Materi Sistem Persamaan Linear Dua Variabel. Leibniz: Jurnal Matematika, 2(2), 45-64.
Nurhanifah, N. (2022). Kemampuan berpikir kreatif matematis siswa kelas viii smp pada materi geometri. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu, 1(2), 161-172. https://doi.org/10.31980/powermathedu.v1i2.2228
Raj, L. L. (2011). Focusing Learning on Concepts of Introductory Linear Algebra using MAPLE Interactive Tutors. Integration of Technology Into Mathematics Education: Past, Present and Future, 439–448.
Salamah, S., Susiaty, U. D., & Ardiawan, Y. (2022). Instrumen Three-Tier Test Berbasis Kemampuan Representasi Matematis untuk Mengetahui Miskonsepsi Siswa. Plusminus: Jurnal Pendidikan Matematika, 2(3), 391-404. https://doi.org/10.31980/plusminus.v2i3.2205
Setiadji, B. H., Supriyono, & Indriastuti, A. K. (2022). The Use of Gauss-Jordan Elimination Method in Determining the Proportion of Aggregate Gradation. Lecture Notes in Civil Engineering, 216, 431–440. https://doi.org/10.1007/978-981-16-7949-0_38
Silvi, K. L., & Auliya, N. N. F. (2022). Bahan Ajar E-LKS Berbasis Realistic Mathematics Education Materi Sistem Persamaan Linear Dua Variabel. Plusminus: Jurnal Pendidikan Matematika, 2(3), 381-390. https://doi.org/10.31980/plusminus.v2i3.2223
Smith, L., & Powell, J. (2011). An Alternative Method to Gauss-Jordan Elimination : Minimizing Fraction Arithmetic. The Mathematics Educator, 20(2), 44–50.
Sugiarti, L. (2018). Kesulitan Siswa Dalam Menyelesaikan Soal Operasi Bentuk Aljabar. Prosiding Seminar Nasional Etnomatnesia Yogyakarta. Hal. 325-329.
Sumarni, T. (2021). Analisis Kesalahan Mahasiswa Menyelesaikan Sistem Persamaan Linier dengan Menggunakan Metode Gauss Jordan pada Mata Kuliah Aljabar Linier Elementer. MENARA Ilmu, XV(02), 102–109.
Suryadi, D. (2010). Metapedadidaktik dan Didactical Design Research (DDR): Sintesis Hasil Pemikiran Berdasarkan Lesson Study. Bandung: FPMIPA Universitas Pendidikan Indonesia.
Ulfa, N. C. A., & Sundayana, R. (2022). Kemampuan representasi matematis siswa pada materi bilangan berdasarkan self-confidence. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu, 1(2), 193-200. https://doi.org/10.31980/powermathedu.v1i2.2231
Yudi, M., Ariani, N. M., & Ramadianti, W. (2017). Desain Bahan Ajar Mata Kuliah Alajabar Linear Untuk Mengembangkan Kemampuan Berfikir Kreatif Matematis. KALAMATIKA Jurnal Pendidikan Matematika, 2(1), 1. https://doi.org/10.22236/kalamatika.vol2no1.2017pp1-14
Yusuf, Y., Titat, N., & Yuliawati, T. (2017). Analisis Hambatan Belajar (Learning Obstacle) Siswa SMP Pada Materi Statistika. AKSIOMA, 8(1), 76. https://doi.org/10.26877/aks.v8i1.1509
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