Students' Problem-Solving Strategies in Solving Equation and Linear Inequality Problems of One Variable

Abstract

Background - Students’ ability to solve mathematical problems reflects their mastery of mathematical concepts, their thinking processes, and the strategies they use when facing cognitive challenges. Examining these strategies helps clarify how students interpret problems, organize information, and develop solutions. 
Purpose - This study aimed to identify and describe students’ problem-solving strategies when solving linear equations and inequalities with one variable, focusing on students with different mathematical ability levels. 
Method/approach - The study employed a qualitative approach with a single instrumental case study design and an evaluative method. Three students representing high, moderate, and low mathematical ability levels were selected from 29 potential participants. Data collection involved written task sheets on one-variable linear equations and inequalities and semi-structured interviews. The analysis followed three stages: data condensation, data display, and conclusion drawing. 
Findings - The three selected students demonstrated different problem-solving strategies. The student with high mathematical ability predominantly used logical reasoning to develop systematic solutions. The student with moderate ability organized data to understand the available information and structure the solution process. The student with low ability relied on trial-and-error strategies. Written responses and interview explanations provided complementary insights into how each student approached the tasks.
Conclusion – The study identified three problem-solving strategies: logical reasoning, data organization, and trial and error. Each strategy involved a different approach to interpreting information and developing solutions. These findings describe variations across the three selected cases. 
Novelty/Originality/Value - The study integrates written solutions with interview explanations to describe contrasting strategy profiles among three students working on one-variable linear equations and inequalities. This combination provides a more detailed account of students’ solution processes than written answers alone.