Development of RBL-STEM learning tools to improve students' combinatorial thinking skills in solving QRIS watermarking problems using local metric dimension

The advancement of digital technology highlights the importance of enhancing students’ combinatorial thinking skills, particularly in addressing mathematical problems related to data security. One effective model that can be applied is Research-Based Learning (RBL) integrated with Science, Technology, Engineering, and Mathematics (STEM). This study aims to identify RBL-STEM activities, describe the development process of RBL-STEM learning tools, and analyze their effectiveness in improving students’ combinatorial thinking skills in solving QRIS watermarking problems using the local metric dimension. The research employed a Research and Development (R&D) method based on the 4D model, consisting of Define, Design, Develop, and Disseminate stages. The developed products included the Student Task Design (RTM), Student Worksheet (LKM), and Learning Outcome Test (THB). The learning tools obtained a validity score of 93.61%, indicating very high validity. The trial, conducted with 36 students, demonstrated that the RBL-STEM tools were practical (95.25%) and effective (94%) in improving learning outcomes. Students showed positive responses and high engagement during learning. The post-test results revealed that 58% of students achieved a high level of combinatorial thinking, 36% were in the moderate category, and 6% were in the low category. Statistical analysis using the paired samples t-test (Sig. = 0.000 < 0.05) confirmed a significant improvement between pre-test and post-test scores. Therefore, the RBL-STEM learning tools are effective in enhancing students’ combinatorial thinking and their ability to apply mathematical reasoning to QRIS digital watermarking problems.