Earticle

This study explores how high school students demonstrate instrumental understanding in the context of integer operations. Using a qualitative case study approach, semi-structured interview data from a second-year student were analyzed through the lens of Skemp’s (1976) distinction between instrumental and relational understanding and Sfard’s (1991) theory of mathematical discourse. The analysis revealed five key characteristics: reliance on memorized rules, difficulties in connecting operations with real-life contexts, dominant natural number-based strategies, conceptual errors, and lack of metacognitive strategies to avoid mistakes. The student often interpreted operations procedurally, applied rules mechanically, and showed limited structural understanding of integers. Attempts to contextualize problems with real-world scenarios frequently resulted in mismatches between the symbolic and narrative representations. These findings underscore the persistence of rule-based reasoning in mathematical learning and highlight the challenges students face when transitioning from procedural fluency to conceptual understanding. The study concludes with implications for mathematics education, emphasizing the need for instruction that supports relational understanding, fosters representational connections, and scaffolds the development of algebraic thinking through meaningful discourse.