Hypothetical Learning Trajectory Based on Realistic Mathematics Education in SPLDV Material: Implementation to Accommodate Differences in Junior High School Students' Initial Abilities

This study stems from the challenge of understanding the concept of SPLDV, which is generally still procedural and lacks meaning, as well as the diversity of students' initial abilities that influence their thinking processes and problem-solving strategies. The research method used was qualitative descriptive within the framework of Didactical Design Research (DDR) at SMP Muhammadiyah 5 Surakarta with three ninth-grade students representing high, medium, and low initial abilities as subjects. Data were collected through SPLDV concept comprehension tests and in-depth interviews. The results showed that the application of RME-based HLT helped students understand concepts gradually, starting from real contexts, situational models, mathematical models, to formal representations. Students with high initial abilities were able to fulfill all of Polya's problem-solving indicators, including the evaluation stage. Students with medium initial abilities were able to understand the problem and develop a plan but were not consistent in evaluating the results. Meanwhile, students with low initial abilities were only able to identify basic information without being able to model or implement a solution strategy. Overall, RME-based HLT proved to be effective in facilitating differences in students' initial abilities and improving their understanding of SPLDV concepts through a structured and contextual learning path.