Rigorous Mathematical Thinking Aprroach for Support Relational Understanding: Designing a Learning Trajectory on Linear Equation

Abstract

The linear equation is a fundamental mathematics topic that often poses significant challenges for students. These difficulties are primarily due to traditional teaching methods that emphasize memorization of formulas over deep understanding, coupled with insufficient focus on developing reasoning and problem-solving skills. This study seeks to develop a learning trajectory for teaching linear equations using the Rigorous Mathematical Thinking (RMT) approach, aiming to enhance students' relational understanding. The research was conducted using a design research method, which involved creating and refining a learning trajectory through preliminary design, experimental implementation, and retrospective analysis, all conducted over two cycles. Participants included 8th-grade students from a junior high school in Palembang, with 32 students in class 8.2 participating in the pilot experiment and 36 students in class 8.1 in the teaching experiment, selected through purposive sampling. Data collection methods included observations, written tests, and interviews, with qualitative analysis used to present the findings in a narrative format. The study resulted in the development of a learning trajectory that effectively supports students' relational understanding of linear equations. The learning process encouraged students to draw on their existing knowledge, identify the most efficient and effective strategies, provide detailed solutions, and gain confidence in the accuracy of their answers while solving problems related to the equation of a line through two points and the equation of a line perpendicular to another line.