Sebuah Tinjauan Commognitive: Apakah Matriks Singular?

Authors

  • Endrayana Putut Laksminto Emanuel Universitas Wijaya Kusuma Surabaya
  • Fatkul Anam Universitas Wijaya Kusuma Surabaya

DOI:

https://doi.org/10.28926/briliant.v7i4.1073

Keywords:

commognitive, aljabar matriks, singular

Abstract

Penelitian ini bertujuan untuk mendeskripsikan konflik commognitive mahasiswa mengenai istilah “singular†pada matriks 3x3. Metode penelitian terdiri atas tahapan persiapan, pengumpulan data, transkrip data, analisis data. Sebanyak 10 mahasiswa diberi lembar soal matematika, berisi dua nomor mengenai matriks singular. Dua mahasiswa terpilih sebagai subjek penelitian karena terindikasi mengalami konflik commognitive, meliputi komponen words use, visual mediators, narratives, routines. Subjek penelitian diwawancarai secara semi tersruktur dan mendalam untuk menggali informasi lebih lanjut adanya konflik commognitive. Hasil wawancara dianalisis menggunakan kerangka kerja commognitive komponen narratives. Hasil penelitian menunjukkan bahwa konflik commognitive terjadi pada saat subyek menentukan apakah suatu matriks singular atau tidak menggunakan nilai determinan. Peneliti menawarkan konsep baru tentang “singular†pada matriks dan subjek penelitian menerima konsep baru tersebut. Perbedaan konsep antara subjek dan peneliti ini yang menimbulkan adanya konflik commognitive yang pada akhirnya subjek menerima konsep baru yang ditawarkan oleh peneliti tentang “singular†pada matriks.

Author Biographies

Endrayana Putut Laksminto Emanuel, Universitas Wijaya Kusuma Surabaya

Department of Mathematics Education

Fatkul Anam, Universitas Wijaya Kusuma Surabaya

Department of Teacher Professional Education

References

Cresswel, J. (2013). Qualitative, quantitative, and mixed methods approaches. In Research design. https://doi.org/10.2307/3152153

Emanuel, E. P. L., & Meilantifa. (2022). Dimanakah Nilai Ekstrim Fungsi Kuadrat Ditinjau dari Lensa Commognitive ? BRILIANT Jurnal Riset Dan Konseptual, 7(54), 269–279.

Febiharsa, D., & Djuniadi, D. (2018). Pengembangan Media Pembelajaran Interaktif 3 Dimensi untuk Pembelajaran Materi Pengenalan Lingkungan Pada Anak Usia Dini di Indonesia. Journal of Studies in Early Childhood Education (J-SECE). https://doi.org/10.31331/sece.v1i1.590

Heyd-Metzuyanim, E., & Graven, M. (2019). Rituals and explorations in mathematical teaching and learning: introduction to the special issue. Educational Studies in Mathematics, 101(2). https://doi.org/10.1007/s10649-019-09890-x

Ho, W. K., Hong, L. S., Tay, E. G., Leong, Y. H., & Ming, K. (2019). Passing a Proof Message : Student-Teacher Communication Through A Commognitive Lens. 42nd Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (MERGA 2019) on “Mathematics Education Research: Impacting Practice†(Pp. 700–706), Adelaide, Australia.

Ioannou, M. (2018). Commognitive analysis of undergraduate mathematics students’ first encounter with the subgroup test. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-017-0222-6

Kahu, E., Nelson, K., & Picton, C. (2017). Student interest as a key driver of engagement for first year students. Student Success. https://doi.org/10.5204/ssj.v8i2.379

Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics.

Lefrida, R., Siswono, T. Y. E., & Lukito, A. (2021). A commognitive Study on Field-dependent students’ Understanding of Derivative. Journal of Physics: Conference Series, 1747(1). https://doi.org/10.1088/1742-6596/1747/1/012025

Mpofu, S., & Pournara, C. (2018). Learner Participation in the Functions Discourse: A Focus on Asymptotes of the Hyperbola. African Journal of Research in Mathematics, Science and Technology Education, 22(1). https://doi.org/10.1080/18117295.2017.1409170

Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus. Research in Mathematics Education. https://doi.org/10.1080/14794802.2014.918338

Ngin, C. S. (2018). Examining a teacher ’ s use of multiple re presentations in the teaching of percentages : A commognitive perspective A Commognitive Perspective of Learning and Teaching. Mathematics Education Research Group of Australasia.

Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2020). Textual and contextual commognitive conflict students in solving an improper fraction. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.678528

Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. Journal of the Learning Sciences. https://doi.org/10.1080/10508400701525253

Sfard, A. (2008). Thinking as Communicating. In Thinking as Communicating. https://doi.org/10.1017/cbo9780511499944

Sfard, A. (2018). Commognition. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-3-319-77487-9_100031-1

Sudarsana, I. K., Nakayanti, A. R., Sapta, A., Haimah, Satria, E., Saddhono, K., … Mursalin, M. (2019). Technology Application in Education and Learning Process. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1363/1/012061

Susanto, A. (2017). Pemanfaatan ICT (Informations and Communication Technologies) dalam Pembelajaran Anak Usia Dini. Tarbawy : Jurnal Pendidikan Islam. https://doi.org/10.32923/tarbawy.v4i2.820

Thoma, A., & Nardi, E. (2016). Routines in the didactical and mathematical discourses of closed-book examination tasks A commognitive analysis of closed-book examination tasks and lecturers’ perspectives. First Conference of International Network for Didactic Research in University Mathematics.

Thoma, A., & Nardi, E. (2018). Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students’ Examination Scripts. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-017-0064-3

Ulfa, S. (2016). Pemanfaatan teknologi bergerak sebagai media pembelajaran bagi anak usia dini. Edcomtech.

van Rooij, E. C. M., Jansen, E. P. W. A., & van de Grift, W. J. C. M. (2018). First-year university students’ academic success: the importance of academic adjustment. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-017-0347-8

Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers’ pedagogical discourse: a commognitive analysis. International Journal of Mathematical Education in Science and Technology, 46(8), 1165–1181. https://doi.org/10.1080/0020739X.2015.1034206

Windasari, Suci & Sofyan, H. (2018). Pengaruh Penggunaan Media Audio Visual Terhadap. Jurnal Pendidikan Dasar.

ZAYYADÄ°, M. (2020). Content and Pedagogical Knowledge of Prospective Teachers in Mathematics Learning: Commognitive Framework. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.642131

Zayyadi, M., Nusantara, T., Subanji, Hidayanto, E., & Sulandra, I. M. (2019). A commognitive framework: The process of solving mathematical problems of middle school students. International Journal of Learning, Teaching and Educational Research. https://doi.org/10.26803/ijlter.18.2.7

Published

2022-11-19

Issue

Section

Education and Social Science