Students' cognitive processes in understanding the application of derivatives
DOI:
https://doi.org/10.33292/amm.v2i1.16Keywords:
Cognitive processes, application of derivatives, trans level, APOSAbstract
Derivatives are one of the objects of calculus that is difficult for students to learn. The purpose of this study was to describe the cognitive processes of students in understanding the application of derivatives. This is a qualitative research involving one subject with the initials L. The main instrument of this research is the researcher who is guided by an assignment sheet and an interview guide. Data collection was carried out through task-based interviews. To get complete and accurate data recorded through audiovisual. Data were analyzed descriptively through genetic decomposition based on APOS (action-process-object-schema) theory. The results of this study are that L can coordinate the process-object of all the properties of a given function, with adjacent or overlapping intervals in all h domains so that a mature scheme of function graph sketches is formed. So that an accurate function graph sketch is obtained. The conclusion is that L's cognitive process of applying derivatives is at a high level. It's a trance level.
References
A, R., Masriyah, M., & Manuharawati, M. (2019). Difficulties of Undergraduate Students to Understand of 2nd Calculus. International Journal of Trends in Mathematics Education Research, 2(1), 26. https://doi.org/10.33122/ijtmer.v2i1.35
Andriani, D., Widada, W., Herawaty, D., Ardy, H., Nugroho, K. U. Z., Ma’rifah, N., … Anggoro, A. F. D. (2020). Understanding the number concepts through learning Connected Mathematics (CM): A local cultural approach. Universal Journal of Educational Research, 8(3), 1055–1061. https://doi.org/10.13189/ujer.2020.080340
Baker, B., Cooley, L., & Trigueros, M. (2000). A Calculus Graphing Schema. Journal for Research in Mathematical Education, 31(5).
Baker, B., Cooley, L., Trigueros, M., & Trigueros, M. (2000). A Calculus Graphing Schema. Journal for Research in Mathematics Education, 31(5), 557=578. https://doi.org/10.2307/749887
Dorier, J.-L. (2002). Teaching linear algebra at university. ICM, III(1–3). Retrieved from http://arxiv.org/abs/math/0305018
Dubinsky, E. (2000). Using a Theory of Learning in College Mathematics Courses. MSOR Connections, 1(2), 10–15. https://doi.org/10.11120/msor.2001.01020010
Dubinsky, E. (2010). Using a Theory of Learning in College Mathematics Courses. MSOR Connections, 1(2), 10–15. https://doi.org/10.11120/msor.2001.01020010
Dubinsky, E., Dautermann, J., Leron, U., & Zazkis, R. (1994). On learning fundamental concepts of group theory. Educational Studies in Mathematics, 2–38.
Dubinsky, E., & McDonald, M. A. (2000). APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research. USA: Georgia State University.
Fatimah, S., & Yerizon. (2019). Analysis of difficulty learning calculus subject for mathematical education students. International Journal of Scientific and Technology Research, 8(3), 80–84.
Herawaty, D., Khrisnawati, D., Widada, W., & Mun anda, P. (2020). The cognitive process of students in understanding the parallels axiom through ethnomathematics learning. IOP Conf. Series: Journal of Physics: Conf. Series 1470 (2020) 012077 Doi:10.1088/1742- 6596/1470/1/012077, 1470, 1–8. https://doi.org/10.1088/1742-6596/1470/1/012077
Nugroho, K. U. Z., Widada, W., & Herawaty, D. (2019). The Ability To Solve Mathematical Problems Through Youtube Based Ethnomathematics Learning. International Journal of Scientific & Technology Research, 8(10), 1232–1237.
Raj Acharya, B. (2017). Factors Affecting Difficulties in Learning Mathematics by Mathematics Learners. International Journal of Elementary Education, 6(2), 8. https://doi.org/10.11648/j.ijeedu.20170602.11
Tall, D. (1993). Students’ Difficulties in Calculus. Proceedings of Working Group 3 on Students’ Difficulties in Calculus, ICME-7 , (Proceedings of Working Group 3 on Students’ Difficulties in Calculus, ICME-7), 13–28. https://doi.org/Canada
Tarmizi, R. A. (2010). Visualizing students’ difficulties in learning calculus. Procedia - Social and Behavioral Sciences, 8(February), 377–383. https://doi.org/10.1016/j.sbspro.2010.12.053
Tsamir, P., & Dreyfus, T. (2002). Comparing Infinite Sets - a process of abstraction. TheCase of Ben. The Journal of Mathematical Behavior, 21(1).
Widada, W. (2015). THE EXISTENCE OF STUDENTS IN TRANS EXTENDED COGNITIVE
DEVELOPMENT ON LEARNING OF GRAPH THEORY. Jurnal Math Educator Nusantara, 1(1), 1–20.
Widada, W. (2016). Profile Of Cognitive Structure Of Students In Understanding The Concept Of
Real Analysis. Journal of Mathematics Education (Infinity), 5(2), 83–98. https://doi.org/10.22460/infinity.v5i2.215
Widada, W. (2017). Beberapa Dekomposisi Genetik Siswa dalam Memahami Matematika. Jurnal Pendidikan Matematika Raflesia, 1(1), 44–54.
Widada, W., & Herawaty, D. (2017). Dekomposisi Genetik tentang Hambatan Mahasiswa dalam Menerapkan Sifat-sifat Turunan. Jurnal Didaktik Matematika, 4(2), 136–151. https://doi.org/10.24815/jdm.v4i2.9216
Widada, W., & Herawaty, D. (2018). The Effects of the Extended Triad Model and Cognitive Style on the Abilities of Mathematical Representation and Proving of Theorem. Advances in Social Science, Education and Humanities Research, 218(ICoMSE 2017), 89–95. https://doi.org/10.2991/icomse-17.2018.16
Widada, W., Herawaty, D., Ma’rifah, N., & Yunita, D. (2019). Characteristics of Students Thinking in Understanding Geometry in Learning Ethnomathematics. International Journal of Scientific & Technology Research, 8(11), 3496–3503.
Widada, W., Herawaty, D., Nugroho, K. U. Z., & Anggoro, A. F. D. (2019a). The Scheme Characteristics for Students at the Level of Trans in Understanding Mathematics during Etno- Mathematics Learning. Advances in Social Science, Education and Humanities Research, 253(Aes 2018), 417–421.
Widada, W., Herawaty, D., Nugroho, K. U. Z., & Anggoro, A. F. D. (2019b). The Scheme Characteristics for Students at the Level of Trans in Understanding Mathematics During Etno-Mathematics Learning. 3rd Asian Education Symposium, 8(Aes 2018). https://doi.org/10.2991/aes-18.2019.95
Widada, W., Nugroho, K. U. Z., & Sari, W. (2018). The Ability of Mathematical Representation through Realistic Mathematics Learning Based on Ethnomathematics Teori APOS sebagai suatu alat analisis dekomposisi genetik terhadap perkembangan konsep matematika seseorang The Scheme Characteristics for Student. Semin. Adv. Math. Sci. Eng. Elem. Sch. Mercur. Hotel Yogyakarta, 16.
