Mapping errors in solving linear equations: A hermeneutic phenomenological study

Many students struggle with solving linear equations, especially in translating word problems into algebraic expressions. While previous studies have focused on identifying procedural errors, they often overlook deeper cognitive and interpretative factors that influence students' problem-solving capabilities. This study addresses that gap through a hermeneutic phenomenological approach to examine how students' perceptions and experiences shape their understanding and approach to linear equations. Data were collected from 37 seventh-grade students at a public junior high school in West Sumatra, Indonesia, through written tests and semi-structured interviews. As a qualitative phenomenological study, the participants were selected based on the relevance of their experiences. Analysis revealed that students primarily committed conceptual, procedural, and resultant errors. Conceptual errors stemmed from misunderstandings of mathematical concepts, procedural errors incorrect application of mathematical operations, and resultant errors occurred in the final solutions due to earlier mistakes. The findings emphasize the importance of addressing both cognitive and interpretative challenges in teaching linear equations. This study contributes to the existing literature by offering insights into factors influencing students' learning processes and highlighting teaching strategies that go beyond merely correcting technical errors. These findings can inform educators in designing more effective approaches that consider students' cognitive and interpretative needs, ultimately improving problem-solving skills and mathematical understanding.