PENALARAN KOVARIASIONAL MAHASISWA DALAM MEMODELKAN GRAFIK HUBUNGAN ANTARA WAKTU DAN KECEPATAN

Taufiq Hidayanto, Iskandar Zulkarnain, Kamaliyah Kamaliyah, Ismail Ismail

Abstract


 

Penalaran kovariasional merupakan salah satu bentuk penalarana matematis yang perlu dimiliki seseorang baik untuk memahami konsep maupun menyelesaikan masalah yang berkenaan dengan kehidupan sehari-hari. Realitanya bahwa penalaran kovariasional mahasiswa tergolong rendah. Tujuan dari penelitian ini adalah untuk mengetahui penalaran kovariasional mahasiswa dalam memodelkan hubungan antara waktu dan kecepatan. Penelitian ini menggunakan pendekatan kualitatif dengan subjek sebanyak 87 mahasiswa semester 3. Analisis data yang dilakukan yaitu pengumpulan data, kondensasi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa penalaran kovariasional mahasiswa terbagi menjadi 5 kategori, yaitu mahasiswa memodelkan grafik namun tidak bermakna, Mahasiswa memodelkan grafik dengan menggeneralisasi masalah, mahasiswa memodelkan grafik yang terus naik sehingga tidak sesuai konteks, mahasiswa memodelkan grafik yang perubahan bentuknya tidak sesuai konteks, dan mahasiswa memodelkan grafik dengan rinci dan sesuai konteks.

 

Kata kunci: penalaran kovariasional, memodelkan grafik, waktu dan kecepatan

Full Text:

PDF

References


Adamura, F., & Susanti, V. D. (2018). Penalaran Matematis Mahasiswa dengan Kemampuan Berpikir Intuitif Sedang dalam Memecahkan Masalah Analisis Real. Jurnal Edukasi Matematika Dan Sains, 6(2), 77–92. https://doi.org/10.25273/jems.v6i2.5366

Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378. https://doi.org/10.2307/4149958

Carlson, M., Larsen, S., & Jacobs, S. (2001). An Investigation of Covariational Reasoning and Its Role in Learning the Concepts of Limit and Accumulation. Proceedings of the 23rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Educatio, (Table 1), 145–453.

Gibbs, A. L., & Gil, E. (2017). Promoting Modeling and Covariational Reasoning Among Secondary School Students in the Context of Big Data. Statistics Education Research Journal, 16(2), 163–190. Retrieved from https://iase-web.org/documents/SERJ/SERJ16(2)_Gil.pdf?1512143282

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

Johnson, Heather L. (2012). Reasoning about variation in the intensity of change in covarying quantities involved in rate of change. Journal of Mathematical Behavior, 31(3), 313–330. https://doi.org/10.1016/j.jmathb.2012.01.001

Johnson, Heather Lynn, McClintock, E., & Hornbein, P. (2017). Ferris wheels and filling bottles: a case of a student’s transfer of covariational reasoning across tasks with different backgrounds and features. ZDM - Mathematics Education, 49(6), 851–864. https://doi.org/10.1007/s11858-017-0866-4

Kertil, M., Erbas, A. K., & Cetinkaya, B. (2019). Developing prospective teachers’ covariational reasoning through a model development sequence. Mathematical Thinking and Learning, 21(3), 207–233. https://doi.org/10.1080/10986065.2019.1576001

Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Zac. Journal for Research in Mathematics Education, 45(1), 102–138.

Nagle, C., Tracy, T., Adams, G., & Scutella, D. (2017). The notion of motion: covariational reasoning and the limit concept. International Journal of Mathematical Education in Science and Technology, 48(4), 573–586. https://doi.org/10.1080/0020739X.2016.1262469

Oehrtman, M., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. Making the Connection: Research and Teaching in Undergraduate Mathematics Education, 27–42. https://doi.org/10.5948/UPO9780883859759.004

Saldanha, L. A., & Thompson, P. W. (1998). Re-thinking Covariation from a Quantitative Perspective: Simultaneous Continuous Variation. Proceedings of the Annual Meeting of the Psychology of Mathematics Education - North America, 1(1), 298–304.

Sandie, Purwanto, Subanji, & Hidayanto, E. (2019a). Process thinking of students in translating representation of covariational dynamic events problems. International Journal of Scientific and Technology Research, 8(10), 1405–1408.

Sandie, S., Purwanto, P., Subanji, S., & Hidayanto, E. (2019b). Student difficulties in solving covariational problems. International Journal of Humanities and Innovation (IJHI), 2(2), 25–30. https://doi.org/10.33750/ijhi.v2i2.38

Şen Zeytun, A., Çetinkaya, B., & Erbaş, A. K. (2010). Mathematics teachers’ covariational reasoning levels and predictions about students’ covariational reasoning abilities. Educational Sciences: Theory & Practice, 10(3), 1601–1612.

Subanji. (2011). Teori Berpikir Pseudo Penalaran Kovariasi. Malang: UM Press.

Subanji, R., & Supratman, A. M. (2015). The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dynamics Based on Assimilation and Accommodation Frameworks. Research in Mathematical Education, 19(1), 61–79. https://doi.org/10.7468/jksmed.2015.19.1.61

Sugiyono. (2017). Metode Penelitian Kualitatif. Bandung: Alfabeta.

Thompson, P. W., & Carlson, M. (2017). Variation, covariation and functions: Foundational ways of mathematical thinking. Compendium for Research in Mathematics Education, (January), 421–456.

Umah, U., Asari, A. R., & Sulandra, I. M. (2016). Struktur Argumentasi Penalaran Kovariasional Siswa Kelas VIIIB MTsN 1 Kediri. JMPM: Jurnal Matematika Dan Pendidikan Matematika, 1(1), 1–12. https://doi.org/10.26594/jmpm.v1i1.498

Yemen-Karpuzcu, S., Ulusoy, F., & Işıksal-Bostan, M. (2017). Prospective Middle School Mathematics Teachers’ Covariational Reasoning for Interpreting Dynamic Events During Peer Interactions. International Journal of Science and Mathematics Education, 15(1), 89–108. https://doi.org/10.1007/s10763-015-9668-8




DOI: http://dx.doi.org/10.30870/jppm.v13i2.8380

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 JPPM (Jurnal Penelitian dan Pembelajaran Matematika)

Ciptaan disebarluaskan di bawah Lisensi Creative Commons Atribusi 4.0 Internasional .

JPPM (Jurnal Penelitian dan Pembelajaran Matematika). Jurnal ini diterbitkan oleh Jurusan Pendidikan Matematika FKIP Universitas Sultan Ageng Tirtayasa (cetak) dan Jurnal Untirta (eprint).

Alamat Penerbit: Jl. Raya Ciwaru No 25 Kota Serang Banten, Jurusan Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Sultan Ageng Tirtayasa, Kampus Ciwaru, Serang, Banten, Indonesia. Telepon / Faks: (0254) 280330 Ext 111, Email: jppm@untirta.ac.id |Klik untuk mengakses: Jurnal Penelitian dan Pembelajaran Matematika