Abstract :

Mathematics education has a significant role in developing students’ critical thinking skills, especially in dealing with complex problems. In an effort to support this, this study aims to evaluate the effectiveness of applying the Problem-Based Learning (PBL) learning model combined with the Realistic Mathematics Education (RME) approach to learning the concept of Power Dominating Set (PDS). The PDS concept, which is part of graph theory, is used to solve power network optimization problems by minimising the number of control points. This is expected to improve the efficiency of resource use and the overall performance of the power grid. This research method involves the application of the PBL model, where students are actively involved in the learning process through real context-based problem solving, as well as the RME approach that connects abstract mathematical concepts with realistic situations. The learning process is focused on mastering the concept of PDS both from the theoretical side and its application in power network optimisation. The results showed that the combination of the PBL model and the RME approach significantly improved students’ understanding of the PDS concept, both in terms of mathematical abstraction and its application in practical contexts. In addition, this approach proved effective in developing students’ critical thinking skills, especially in analysing and solving complex power network optimisation problems. The discussion of the results of this study highlights that learning strategies that integrate PBL and RME are able to provide deeper and more relevant learning experiences for students. This approach not only helps students understand complex mathematical concepts, but also trains them to apply the knowledge in real situations. The implications of this research provide important insights for educators to adopt innovative learning methods that can improve the quality of mathematics learning, especially in teaching applicable concepts such as Power Dominating Set.

---

Keywords :

Critical Thinking Skills, Electricity network optimization, Power Dominating Set, Problem based learning., Realistic Mathematics Education.

---

References :

1. Alikhani, S., Bakhshesh, D., & Golmohammadi, H. (2024). Total coalitions in graphs. Quaestiones Mathematicae, 47(11), 2283-2294. doi: https://doi.org/10.2989/16073606.2024.2365365
2. Arif, D. S. F., Zaenuri, Z., & Cahyono, A. N. (2020). Analisis kemampuan berpikir kritis matematis pada model problem based learning (PBL) berbantu media pembelajaran interaktif dan google classroom. In Prosiding Seminar Nasional Pascasarjana (Vol. 3, No. 1, pp. 323-328).
3. Arviana, R., & Dewi, M. P. (2018). Problem based learning in mathematics education and its effect on student’s critical thinking. Advanced Science Letters, 24(1), 211-213. doi: https://doi.org/10.1166/asl.2018.11962
4. Chellali, M., Jafari Rad, N., Sheikholeslami, S. M., & Volkmann, L. (2020). Roman domination in graphs. Topics in domination in graphs, 365-409. doi: https://doi.org/10.1007/978-3-030-51117-3_11
5. Dahl, B. (2018). What is the problem in problem-based learning in higher education mathematics. European Journal of Engineering Education, 43(1), 112-125. doi: https://doi.org/10.1080/03043797.2017.1320354
6. Dorbec, P., Mollard, M., Klavžar, S., & Špacapan, S. (2008). Power domination in product graphs. SIAM journal on discrete mathematics, 22(2), 554-567. doi: https://doi.org/10.1137/060661879
7. Haynes, T. W., Hedetniemi, S. M., Hedetniemi, S. T., & Henning, M. A. (2002). Domination in graphs applied to electric power networks. SIAM journal on discrete mathematics, 15(4), 519-529. doi: https://doi.org/10.1137/S0895480100375831
8. Haynes, T. W., Hedetniemi, S. T., & Henning, M. A. (Eds.). (2020). Topics in domination in graphs (Vol. 64). Cham: Springer. doi: https://doi.org/10.1007/978-3-030-51117-3
9. Haynes, T. W., Hedetniemi, S. T., & Henning, M. A. (2023). Domination in graphs: Core concepts. Cham: Springer. doi: https://doi.org/10.1007/978-3-031-09496-5
10. Kurniawati, A., Wardani, S., Asikin, M., & Dewi, N. R. (2023). The Effectiveness of the Problem Based Learning Model with a Realistic Mathematics Education Approach to Problem Solving Ability. International Journal of Research and Review, 10(1), 491-497. doi: https://doi.org/10.52403/ijrr.20230156
11. Mandasari, N. (2021). Problem-based learning model to improve mathematical reasoning ability. In Journal of Physics: Conference Series (Vol. 1731, No. 1, p. 012041). IOP Publishing. doi: https://doi.org/10.1088/1742-6596/1731/1/012041
12. Mariani, S. (2019, October). Problem based learning with Indonesian realistic mathematics education approach assisted e-schoology to improve student mathematization. In Journal of Physics: Conference Series (Vol. 1321, No. 3, p. 032094). IOP Publishing. doi: https://doi.org/10.1088/1742-6596/1321/3/032094
13. Maslihah, S., Waluya, S. B., Karomah, N., & Iqbal, K. (2021, June). Increasing mathematical literacy ability and learning independence through problem-based learning model with realistic mathematic education approach. In Journal of Physics: Conference Series (Vol. 1918, No. 4, p. 042123). IOP Publishing. doi: https://doi.org/10.1088/1742-6596/1918/4/042123
14. Prabhu, S., Arulmozhi, A. K., Henning, M. A., & Arulperumjothi, M. (2024). Power Domination and Resolving Power Domination of Fractal Cubic Network. arXiv preprint arXiv:2407.01935.
15. Rewah, V., Sulangi, V., & Salajang, S. (2021, July). Development of learning devices with the PBL model using the Pythagoras theorem of RME approach. In Journal Of Physics: Conference Series (Vol. 1968, No. 1, p. 012050). IOP Publishing. doi: https://doi.org/10.1088/1742-6596/1968/1/012050
16. Umar, U. P. S., & Zakaria, Z. (2022). The effectiveness of the realistic math education (RME) learning method based on manipulative media in improving the problem-solving abilities of elementary school students. Ekspose: Jurnal Penelitian Hukum dan Pendidikan, 21(1), 1369-1376. doi: http://dx.doi.org/10.30863/ekspose.v21i1.3405
17. Saibavani, T. N. P., & Parvathi, N. (2023). Power Domination in Different Graphs with Applications. Mathematical Modelling of Engineering Problems, 10(2). doi: https://doi.org/10.18280/mmep.100222
18. Susanti, G., & Rustam, A. (2018). The effectiveness of learning models realistic mathematics education and problem based learning toward mathematical reasoning skills at students of junior high school. Journal of Mathematics Education, 3(1), 33-39. doi: https://doi.org/10.31327/jme.v3i1.534
19. Yuanita, P., Zulnaidi, H., & Zakaria, E. (2018). The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as mediator between mathematical belief and problem solving. PloS one, 13(9), e0204847. doi: https://doi.org/10.1371/journal.pone.0204847
20. Waluya, S. B., & Mariani, S. (2016, February). Mathematics literacy on problem based learning with indonesian realistic mathematics education approach assisted e-learning edmodo. In Journal of Physics: Conference Series (Vol. 693, No. 1, p. 012014). IOP Publishing. doi: https://doi.org/10.1088/1742-6596/693/1/012014
21. Zhao, M., Kang, L., & Chang, G. J. (2006). Power domination in graphs. Discrete mathematics, 306(15), 1812-1816. doi: https://doi.org/10.1016/j.disc.2006.03.037