Unveiling students’ cognitive patterns in word problem solving: The case of single-variable linear equations

Abstract

Students often struggle to transfer their procedural knowledge of linear equations into meaningful solutions when faced with word problems, revealing a persistent gap in integrating conceptual understanding, strategic reasoning, and metacognitive evaluation. This study investigates students’ cognitive profiles in solving mathematical word problems involving single-variable linear equations. Grounded in a synthesized framework from Polya’s heuristic model and the NCTM problem-solving process, the research focuses on five cognitive stages: understanding, analyzing, strategizing, executing, and evaluating. Using a qualitative descriptive method, data were collected from 30 eighth-grade students through written tasks and semi-structured interviews. The findings indicate strong performance in problem comprehension; however, there was a notable decline in evaluation and reflection stages. Interview data revealed that low-performing students often lacked conceptual understanding and demonstrated limited metacognitive awareness, whereas high performers integrated conceptual, procedural, and reflective thinking. This study highlights the gap between procedural fluency and strategic reasoning across performance levels, emphasizing the need for instructional approaches that integrate metacognitive scaffolding to enhance problem-solving competence. A diagnostic framework is proposed to support teachers in identifying and addressing students' cognitive needs.