Conceptual Knowledge of Seventh Graders with High-Mathematics Ability in Solving Linear Equation Problems

Abstract

Conceptual knowledge is a crucial foundation for learning more advanced mathematics, especially when students begin to explore algebraic concepts such as linear equations. However, even students with high mathematical ability may encounter challenges in articulating and transferring conceptual understanding to new contexts. This study aims to describe a seventh-grade student's conceptual knowledge of solving linear equation problems. A qualitative descriptive method was used, involving one student selected based on mathematics ability and communication skill. Data were collected through a conceptual knowledge task and a semi-structured interview. The results indicate that the student demonstrated a solid understanding of unit conversion and the structure of the problem, applied procedures accurately, and showed awareness of relationships among concepts. However, the student struggled to express formal mathematical terminology and encountered difficulty transferring concepts when the problem context was slightly altered. These findings emphasize that even high-performing students may benefit from instructional support that increases flexibility and the depth of conceptual knowledge.