Design of the Learning Trajectory of One-Variable Linear Equations in Junior High School Through a Realistic Mathematical Approach to Generative Models
DOI:
https://doi.org/10.61132/ijed.v2i3.376Keywords:
Epistemological Obstacles, Hypothetical Learning Trajectory, Junior High School, Learning Obstacles, Trajectory DesignAbstract
This study aims to identify students' learning obstacles in the process of understanding one-variable linear equations in grade VII, develop an appropriate learning trajectory using a Realistic Mathematical Education (RME) approach, and produce an effective learning design to reduce these obstacles through generative models. The research adopts a design research methodology consisting of three main stages. The first stage, preparation for the experiment, includes a literature review and analysis of teachers’ instructional practices to develop a Hypothetical Learning Trajectory (HLT) for one-variable linear equations. The second stage, design experiment, involves testing the designed learning activities through a pilot experiment and teaching experiment. The third stage, retrospective analysis, compares actual classroom observations with the initial HLT to refine and validate the learning trajectory. The research subjects include seven grade VII students in the pilot experiment and 44 students from SMP Negeri 2 Mataram in the teaching experiment. Data collection methods include tests, observations, interviews, and documentation, with retrospective analysis used to generate a validated Local Learning Trajectory (LLT). The findings reveal several epistemological obstacles experienced by students, such as difficulties in applying fundamental arithmetic concepts (addition, subtraction, multiplication, division) within the context of linear equations. Students also struggled with concept recognition, representation, and interpretation of linear equations in various forms. The developed LLT proved effective, as students demonstrated improved understanding and were able to follow the learning sequence meaningfully. Retrospective analysis confirmed that the LLT successfully addressed and reduced students’ learning obstacles in mastering one-variable linear equations.
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