TRANSFORMATION OF PRE-SERVICE MATHEMATICS STUDENT'S ALGEBRA AND CALCULUS THINKING IN SOLVING DIFFERENTIAL EQUATION PROBLEMS
TRANSFORMASI BERPIKIR ALJABAR DAN KALKULUS MAHASISWA MATEMATIKA DALAM MENYELESAIKAN MASALAH PERSAMAAN DIFERENSIAL
Abstract
This study aims to analyze the transformation of algebraic thinking and calculus of preservice the mathematics students based on SOLO taxonomy in solving differential equations problems. The research subjects were 86 students in the mathematics education study program. Subject selection uses purposive sampling (students who take courses in differential equations). Data were collected using problem-solving tests and interviews which were then analyzed using the descriptive qualitative method with the following stages: (1) transcribing test and interview data, (2) coding segmentation, (3) analyzing student thinking transformations, and (4) concluding. The results showed that the transformation of algebraic and calculus thinking was used by students at each level of thinking to solve problems. The higher the level of thinking achieved, the better and the maximum transformation of algebraic and calculus thinking used by students. These results indicate that students need to be well supported and facilitated in problem-solving to achieve higher levels of thinking, such as the relational and extended abstract levels.
Downloads
References
Afriyani, D., Sa’dijah, C., Subanji, S., & Muksar, M. (2018). Characteristics of students’ mathematical understanding in solving multiple representation task based on SOLO taxonomy. International Electronic Journal of Mathematics Education, 13(3), 281–287. https://doi.org/10.12973/iejme/3920.
Arslan, S. (2010). Do students really understand what an ordinary differential equation is? International Journal of Mathematical Education in Science and Technology, 41(7), 873–888. https://doi.org/10.1080/0020739X.2010.486448.
Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75. https://doi.org/10.1007/s10649-005-0808-x.
Chick, H. (1998). Cognition in the formal modes: Research mathematics and the SOLO taxonomy. Mathematics Education Research Journal, 10(2), 4–26. https://doi.org/10.1007/BF03217340.
Claudia, L. F., Kusmayadi, T. A., & Fitriana, L. (2020a). High school students’ responses in solving linear program problems based on SOLO taxonomy viewed from mathematical disposition. Journal of Physics: Conference Series, 1539(1), 012087. https://doi.org/10.1088/1742-6596/1539/1/012087.
Claudia, L. F., Kusmayadi, T. A., & Fitriana, L. (2020b). The SOLO taxonomy: Classify students’ responses in solving linear program problems. Journal of Physics: Conference Series, 1538(1), 012107. https://doi.org/10.1088/1742-6596/1538/1/012107.
Czocher, J. A., Tague, J., & Baker, G. (2013). Where does the calculus go? An investigation of how calculus ideas are used in later coursework. International Journal of Mathematical Education in Science and Technology, 44(5), 673–684. https://doi.org/10.1080/0020739X.2013.780215.
Faradiba, S. S., Andriani, P., Alifiani, A., Walida, S. E., Daryono, D., Hasana, S. N., Angriani, A. D., Chamidah, D., Defitriani, E., & Qurohman, M. T. (2018). The inconsistency of level critical thinking in solving differential equation problem. Universitas Pendidikan Indonesia, 3, 842–847. Retrieved from http://science.conference.upi.edu/proceeding/index.php/ICMScE/article/view/93.
Johnson, R. B., & Larry, C. (2004). Educational research: Quantitative, qualitative, and mixed approaches second edition (Second edi). Library of Congress Cataloging-in-Publicatiom Data.
Knapp, M., Adelman, N., Marder, C., McCoHum, H., Needels, C., Padilla, C., Shields, P., Turnbull, B., & Zucker, A. (1982). Teaching for meaning in high-poverty classrooms. In Teachers College Press. Teachers College Press. https://doi.org/10.1177/000494418302700311.
Lapp, D. A., Nyman, M. A., & Berry, J. S. (2010). Student connections of linear algebra concepts: An analysis of concept maps. International Journal of Mathematical Education in Science and Technology, 41(1), 1–18. https://doi.org/10.1080/00207390903236665.
Lian, L. H., & Yew, W. T. (2012). Assessing algebraic solving ability: A theoretical framework. International Education Studies, 5(6), 177–188. https://doi.org/10.5539/ies.v5n6p177.
McDowell, Y. L. (2021). Calculus misconceptions of undergraduate students. [Theses Doctoral]. Columbia University.
Miles, M. B., & Huberman, A. M. (1994). Qualitatif data analysis: An expand sourcebook second edition (R. Holland (ed.); Second Edi). United States: SAGE Publication Ltd.
Novitasari, D., Triutami, T. W., Wulandari, N. P., Rahman, A., & Alimuddin. (2020). Students’ creative thinking in solving mathematical problems using various representations. Advances in Social Science, Education and Humanities Research (ASSEHR), Proceedings of the 1st Annual Conference on Education and Social Sciences (ACCESS 2019), 465(Access 2019), 99–102. https://doi.org/10.2991/assehr.k.200827.026.
Putri, U. H., Mardiyana, M., & Saputro, D. R. S. (2017). How to analyze the students’ thinking levels based on solo taxonomy? Journal of Physics: Conference Series, 895(1), 012031. https://doi.org/10.1088/1742-6596/895/1/012031.
Raychaudhuri, D. (2014). Adaptation and extension of the framework of reducing abstraction in the case of differential equations. International Journal of Mathematical Education in Science and Technology, 45(1), 35–57. https://doi.org/10.1080/0020739X.2013.790503.
Rustika, P., & Rohaeti, T. (2020). Algebraic thinking ability and learning interesr through social media-based pictorial puzzle in new normal era. MaPan: Jurnal Matematika Dan Pembelajaran, 8(2), 329–342. https://doi.org/10.24252/mapan.2020v8n2a11.
Sangwin, C. J. (2019). The mathematical apprentice: an organising principle for teaching calculus in the 21st century. Calculus in Upper Secondary and Beginning University Mathematics, 94–97. Retrieved from https://math.ou.edu/events/talks?3022.
Saputra, D. C., Nurjanah, A., & Retnawati, H. (2019). Students’ ability of mathematical problem-solving based on SOLO taxonomy. Journal of Physics: Conference Series, 1320(1), 012070. https://doi.org/10.1088/1742-6596/1320/1/012070.
Socas, M., & Hernandez, J. (2013). Mathematical problem solving in training elementary teachers from a semiotic logical approach. Mathematics Enthusiast, 10(1–2), 191–218. https://doi.org/10.54870/1551-3440.1265.
Swastika, G. T., Nusantara, T., Subanji, & Irawati, S. (2019). Differential problems with different type solutions of mathematics education’s students. Journal of Physics: Conference Series, 1175(1). https://doi.org/10.1088/1742-6596/1175/1/012144.
Upu, H., & Bangatau, N. S. (2019). The profile of problem-solving in algebra based on SOLO taxonomy in terms of cognitive style. Advances in Social Science, Education and Humanities Research (ASSEHR), 227(Icamr 2018), 372–376. https://doi.org/10.2991/icamr-18.2019.91.
Yantz, J. (2013). Connected representations of knowledge: Do undergraduate students relate algebraic rational expressions to rational numbers? Mid-Western Educational Researcher, 25(4), 47–61. Retrieved from https://eric.ed.gov/?id=EJ1022565.
Copyright (c) 2022 Arjudin, Sripatmi, Muhammad Turmuzi, Dwi Novitasari, Ratih Ayu Apsari
This work is licensed under a Creative Commons Attribution 4.0 International License.
