Mathematical Reasoning in Solving Linear Equation Problems: A Case Study of Junior High School Students

Abstract

This study aims to describe the mathematical reasoning abilities of students at Bina Utama Junior High School, Pontianak, in solving word problems on the system of linear equations in one variable. The approach used is descriptive qualitative with a case study format. The research subjects consisted of three eighth-grade students selected through purposive sampling technique based on high, medium, and low ability categories. Data collection was carried out through written tests in the form of essay questions and semi-structured interviews. Data analysis refers to the Miles and Huberman interactive analysis model which includes data reduction, data presentation, and conclusion drawing. Data validity was obtained through triangulation techniques. The results show that students' mathematical reasoning abilities vary across categories. High-ability students are able to understand problems and obtain correct answers, but have not yet used systematic solution steps and have not developed formal mathematical models. Medium-ability students show visible progress in reasoning, but still make errors in mathematical modeling and have not verified their answers. Meanwhile, low-ability students have not met the indicators of mathematical reasoning, which is characterized by difficulty understanding problems, developing mathematical models, and drawing logical conclusions. Overall, students' mathematical reasoning abilities still need to be improved through learning that emphasizes mathematical modeling and systematic problem solving.