<![CDATA[This study explores students' conceptual understanding and problem-solving approaches in algebra, specifically focusing on the interpretation and manipulation of algebraic expressions and equations. The research was conducted at SMK Negeri 1 Sragen with first-year students as informants. Using a qualitative descriptive method, the study analyzes students' responses to algebraic problems that involve symbolic reasoning, operations with variables, and rational expressions. Data collection involved observation, problem-solving tests, and interviews, with data validity ensured through triangulation techniques. Two informants employed different cognitive strategies in solving equivalent algebraic problems. While both demonstrated some logical consistency, their solutions revealed common misconceptions, such as misapplying the distributive property and misunderstanding the implications of dividing by zero. In particular, the study identified that assuming division by zero in expressions like y/z - z led to invalid conclusions. However, when solving the equation xy = x/y = x-y both informants eventually arrived at the consistent solution x=−1/2, y=−1 confirming the validity of their algebraic reasoning under guided support.The results highlight the need for deeper conceptual instruction in algebra, especially in understanding symbolic manipulation and domain restrictions. The findings also underscore the importance of implementing cognitive-based learning strategies in mathematics education to enhance students' critical thinking and problem-solving skills.]]>
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