ANALISIS KEGAGALAN PENALARAN KOVARIASIONAL MAHASISWA DALAM MENGONSTRUKSI GRAFIK FUNGSI
Abstract
This research aims to identify failures in covariational reasoning of mathematics education students in the Numerical Methods course. This research is descriptive qualitative type with the researcher as the main instrument and supporting instruments in the form of assignment sheets, interview guides and documentation. The research subjects were 18 students from the Mathematics Education study program, FMIPA, PGRI Banyuwangi University. The work results are grouped into 5 based on the type of function graph created, namely subjects without function graphs (4 students), graphing linear functions (5 students), graphing quadratic functions (6 students), graphing polynomial functions (1 student), and graphing circle functions (2 students). Covariational reasoning failures are identified based on the 5 mental actions that Carlos has compiled. The results showed that there was failure of mental action 1 in groups 1 subjects; 2nd mental failure in subjects groups 1 and 5; 3rd mental failure in subjects groups 1 and 4; 4th mental failure in subjects groups 1 subjects and 3, and mental failure 5 in subjects groups 1 and 2. Research can be continued by exploring aspects of the causes of failure in covariational reasoning.
References
Fuad, Y., Ekawati, R., Sofro, A., & Fitriana, L. D. (2019). Investigating Covariational Reasoning: What Do Students Show when Solving Mathematical Problems? Journal of Physics: Conference Series (MISEIC 2019), 1417(1), 1–8. https://doi.org/10.1088/1742-6596/1417/1/012061
Harini, N. V., Fuad, Y., & Ekawati, R. (2018). Students’ Covariational Reasoning in Solving Integrals’ Problems. Journal of Physics: Conference Series, 947(1), 1–7. https://doi.org/10.1088/1742-6596/947/1/012017
Hidayanto, T., Zulkarnain, I., Kamaliyah, & Ismail. (2020). Penalaran Kovariasional Mahasiswa dalam Memodelkan Grafik Hubungan Antara Waktu dan Kecepatan. Jurnal Penelitian Pembelajaran Matematika, 13(2), 298–319. http://dx.doi.org/10.30870/jppm.v13i2.8380
Jaenudin, A. (2022). Students’ Covariational Reasoning Reviewed From Cognitive Styles. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(3), 2511–2522. https://doi.org/10.24127/ajpm.v11i3.5854
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis, A Me-thods Sourcebook (3rd ed.). Sage Publications.
NCTM. (2010). Executive Summary Principles and Standarts For School Mathematics. Journal of Equine Veterinary Science, 18(11), 719. https://doi.org/10.1016/s0737-0806(98)80482-6
Ningrum, R. W., Fuad, Y., & Ekawati, R. (2018). Students’ Covariational Reasoning in Fraction Compare Problem. Journal of Physics: Conference Series (MISEIC 2018), 1108(1), 1–6. https://doi.org/10.1088/1742-6596/1108/1/012108
Paoletti, T., Vishnubhotla, M., & Mohamed, M. (2019). Inequalitien and Systems Of Relationships: Reasoning Covariationally To Develop Productive Meanings. Proceedings of the 41st Annual Meeting of PME-NA, 157–166.
Rahman, F., Juniati, D., & Siswono, T. Y. E. (2023). Covariational Reasoning Profile Of Prospective Mathematics Teacher Students With Field-Independent Cognitive Style In Solving Covariation Problems. PROXIMAL: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 6(1), 305–312. https://doi.org/10.30605/proximal.v5i2.2300
Sandie, Purwanto, Subanji, & Hidayanto, E. (2019). Student difficulties in solving covariational problems. International Journal of Humanities and Innovation (IJHI), 2(2), 42–47. https://doi.org/10.33750/ijhi.v2i2.38
Sandie, & Susiaty, U. D. (2020). Student’s Covariational Reasoning In Solving Covari-ational Problems Of Dynamic Events. Journal of Education, Teaching, and Learning, 5(2), 375–382. http://dx.doi.org/10.26737/jetl.v5i2.2092
Subanji. (2015). Teori Kesalahan Konstruksi Konsep dan Pemecahan Masalah Mate-matika. Universitas Negeri Malang.
Subanji, R., & Supratman, A. M. (2015). The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dy-namics Based on Assimilation and Accommodation Frameworks. Research in Mathematical Education, 19(1), 61–79. https://doi.org/10.7468/jksmed.2015.19.1.61
Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. Compendium for Research in Mathematics Education, 421–456. https://www.researchgate.net/publication/302581485_Variation_covariation_and_functions_Foundational_ways_of_thinking_mathematically.
Thompson, P. W., Hatfield, N. J., Yoon, H., & Joshua, S. (2017). Covariational reasoning among U.S. and South Korean secondary mathematics teachers. Journal of Mathematical Behavior, 48(1), 1–44. https://doi.org/10.1016/j.jmathb.2017.08.001
Tyburski, B. A., Drimalla, J., Byerley, C., & Moore, K. C. (2021). From theory to me-thodology: Guidance for analyzing students’ covariational reasoning. Proceed-ings of the 43rd Annual Meeting of PME-NA, 1839–1849. https://www.researchgate.net/publication/360261915
Umah, U., As’ari, A. R., & Sulandra, I. M. (2014). Penalaran Kovariasional Siswa Kelas VIIIB MTs Negeri Kediri 1 Dalam Mengostruksi Grafik Fungsi. https://www.researchgate.net/publication/294259258
Yohanes, B., & Yusuf, F. I. (2021a). Intrinsic Cognitive Load in Online Learning Model of School Mathematics 1 in Covid-19 Pandemic Period. JIPM (Jurnal Ilmiah Pen-didikan Matematika), 9(2), 59-69. https://doi.org/10.25273/jipm.v9i2.7292
Yohanes, B., & Yusuf, F. I. (2021b). Teori Beban Kognitif: Peta Kognitif dalam Peme-cahan Masalah pada Matematika Sekolah. AKSIOMA: Jurnal Program Studi Pen-didikan Matematika, 10(4), 2215-2224. https://doi.org/10.24127/ajpm.v10i4.4033
Yohanes, B., Darmawan, P., & Nugroho, P. B. (2023). Penalaran Induktif Siswa Sekolah Dasar Dalam Menyelesaikan Masalah Keterbagian Bilangan Bulat. SIGMA, 8(2), 84–93. http://ejournal.unira.ac.id/index.php/jurnal_sigma/article/view/1735