The development of hypothetical learning trajectory (HLT) based on problem-based learning (PBL) in the concept of relations and functions

<p class="Afiliasi">This study aims to develop a learning process that aligns with the diverse thinking processes of students in Grade VIII at MTsN 9 Padang Pariaman. This is a developmental research study using the Gravemeijer and Cobb model. This development model consists of three stages: 1) Preparing for the experiment, which involves conducting a needs analysis (such as analyzing students and educators, syllabus analysis, literature review, and concept analysis), designing the HLT, and assessing the HLT (self-evaluation and expert review); 2) Conducting the experiment, which includes product trials with students at MTsN 9 Padang Pariaman through one-to-one evaluation and small group evaluation; 3) The retrospective analysis, which involves analyzing data obtained from the previous stages. The results of this analysis are used to plan activities and refine the design of future learning activities. The results of this study indicate that the developed HLT is highly valid, with an average validity score of 89.71%. This research demonstrates that an HLT based on Problem-Based Learning can be validly used in mathematics learning, specifically in the topic of relations and functions.</p>