Design of Learning Activities using Rigorous Mathematical Thinking (RMT) Approach in Application of Derivatives
Learning design is one of the factors that support the learning process in order to achieve learning objectives in all subjects including mathematics. Many approaches can be employed by a teacher in making learning design, one of which is rigorous mathematical thinking (RMT) approach. The RMT approach puts forward students actively in constructing their knowledge through the use of psychological tools and mediation. This article reports a set of learning activities designed through a developmental study using the RMT approach in the topic of application of derivatives. Participants of this research were twenty-six of 11th grade students from a private secondary school. Data were collected through written test and classroom observation. The research instruments were student worksheet and observation sheet. In the learning process, students use psychological tools to connect their previous knowledge to the material being studied. This makes students able to construct their own knowledge more thoroughly. On the other hand, with the mediation carried out by the teacher, students can focus more and understand each material well and bridge the conceptual errors. Based on the results of the study and some literature, Design of learning activities using Rigorous Mathematical Thinking (RMT) on application of derivative can be an alternative as effective learning.
Abstract View : 25, PDF Download : 20
Adu-Gyamfi, K., Bossé, M. J., & Chandler, K. (2017). Student connections between algebraic and graphical polynomial representations in the context of a polynomial relation. International Journal of Science and Mathematics Education, 15(5). https://doi.org/10.1007/s10763-016-9730-1.
Firmasari, S., Sulaiman, H., Hartono, W., & Noto, M. S. (2019). Rigorous mathematical thinking based on gender in the real analysis course. Journal of Physics: Conference Series. 11574 (042106). https://doi.org/10.1088/1742-6596/1157/4/042106.
Francisco, J. M. (2013). The mathematical beliefs and behavior of high school students: Insights from a longitudinal study. The Journal of Mathematical Behavior, 32(3), 481-493. https://doi.org/10.1016/j.jmathb.2013.02.012.
García-García, J., & Dolores-Flores, C. (2019). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 1-22. https://doi.org/10.1007/s13394-019-00286-x.
Hashemi, N., Abu, M. S., Kashefi, H., & Rahimi, K. (2014). Undergraduate students’ difficulties in conceptual understanding of derivation. Procedia-Social and Behavioral Sciences, 143, 358-366. https://doi.org/10.1016/j.sbspro.2014.07.495.
Hendrayana, A. (2017). Pengaruh pembelajaran pendekatan rigorous mathematical thinking (RMT) terhadap pemahaman konseptual matematis siswa SMP. Jurnal Riset Pendidikan Matematika, 4(2), 186-199. https://doi.org/10.21831/jrpm.v4i2.15385.
Hidayat, D., Nurlaelah, E., & Dahlan, J. A. (2017). Rigorous mathematical thinking approach to enhance students’ mathematical creative and critical thinking abilities. In Journal of Physics: Conference Series, 895 (012087). https://doi.org/10.1088/1742-6596/895/1/012087.
Kinard, J. (2007). U.S. Patent Application No. 11/584,367.
Kinard, J. T., & Kozulin, A. (2006). Creating rigorous mathematical thinking: a dynamic that drives mathematics and science conceptual development. Transsylvanian Journal of Psychology-Erdély Pszichológiai Szemle, 2, 251-266.
Kozulin, A., & Kinard Sr, J. T. (2008). Rigorous mathematical thinking: Conceptual formation in the mathematics classroom. New York: Cambridge University Press. https://doi.org/10.1017/cbo9780511814655.
Kwakman, K. (2003). Factors affecting teachers’ participation in professional learning activities. Teaching and Teacher Education, 19(2), 149-170. https://doi.org/10.1016/s0742-051x(02)00101-4.
McLaughlin, M. W. (1997). Rebuilding teacher professionalism in the United States. Beyond educational reform: Bringing teachers back in, 77-93. https://doi.org/10.1108/ijem.19188.8.131.52.1.
Mielicki, M. K., & Wiley, J. (2016). Alternative representations in algebraic problem solving: When are graphs better than equations? The Journal of Problem Solving, 9(1), 3-12. https://doi.org/10.7771/1932-6246.1181.
Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. (2013). Calculus students’ and instructors’ conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11(6), 1491-1515. https://doi.org/10.1007/s10763-013-9411-2.
Nugraheni, Z., Budiyono, B., & Slamet, I. (2018). The impact of rigorous mathematical thinking as learning method toward geometry understanding. Journal of Physics, Conference Series, 1013(012121). https://doi.org/10.1088/1742-6596/1013/1/012121.
Resmi, R. A. (2020, June). Implementation of lesson study with rigorous mathematical thinking based on student worksheet to enhance the students’ mathematical critical thinking. Journal of Physics: Conference Series, 1563 (012059) https://doi.org/10.1088/1742-6596/1563/1/012059.
Sahin, Z., Yenmez, A. A., & Erbas, A. K. (2015). Relational understanding of the derivative concept through mathematical modeling: A case study. Eurasia Journal of Mathematics, Science & Technology Education, 11(1). https://doi.org/10.12973/eurasia.2015.1149a.
Tall, D. A. V. I. D. (2011). Looking for the bigger picture. For the Learning of Mathematics, 31(2), 17-18.
Van Garderen, D., & Montague, M. (2003). Visual‐spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246-254. https://doi.org/10.1111/1540-5826.00079.
Yunita, D. R., Maharani, A., & Sulaiman, H. (2019, April). Identifying of rigorous mathematical thinking on olympic students in solving non-routine problems on geometry topics. In 3rd Asian Education Symposium (AES 2018). Atlantis Press. https://doi.org/10.2991/aes-18.2019.111.
Copyright (c) 2021 IJORER : International Journal of Recent Educational Research
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
The copyright of the received article once accepted for publication shall be assigned to the journal as the publisher of the journal. The intended copyright includes the right to publish the article in various forms (including reprints). The journal maintains the publishing rights to the published articles.