Developing a Hypothetical Learning Trajectory with Problem-Based Learning and a Learning Medium for Middle School

A teacher must consider the learning trajectory that will emerge during the learning process while designing an instructional plan. In mathematics, the degree to which students comprehend the learning context the teacher applies indicates the teacher's ability to construct a learning framework. This study aims to design the Hypothetical Learning Trajectory (HLT) for learning linear equations in two variables using the graphical method, problem-based learning, and the WolframAlpha application (as a learning medium). The design research methodology was used to construct the HLT design. This study begins with interviews with teachers who have taught similar material and students who have received this learning material. The findings from these interviews serve as the foundation for this research. As a result, this study provided an HLT design employing the graphical method for teaching mathematics in middle schools. It was discovered that the order in which students solved problems on the HLT corresponded to their cognitive states. Using the proposed learning trajectory design, students will find it less scary to advance through the current mathematical learning stages. Students might follow each procedural step without teacher pressure using this method. The developed learning strategy is expected to be able to solve the provided mathematical problem. Moreover, this HLT design indicates that the contextual qualities of the problem-based learning model make it best suited for relevant material.