Learning Activities in Mathematics Education: Application of the PBL Model and RME Approach in the Power Dominating Set for Solving Electricity Network Optimization Problems to Enhance Students' Critical Thinking Skills

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.