<![CDATA[This study aims to uncover and analyze hidden misconceptions in algebraic understanding among first-year students in the Mathematics Education Department at a private university in Malang. Conducted from January to March 2024, the research involves two first-year students as subjects. The first subject exhibits the misconception known as "illegal canceling," while the second subject demonstrates the "assumption of distributivity of exponents." Utilizing a qualitative research methodology, diagnostic interviews and problem-solving tasks were employed to identify and understand these misconceptions. Our findings indicate that these hidden misconceptions significantly hinder the students' ability to correctly solve algebraic problems and understand underlying concepts. For the first subject, the error in illegal canceling often led to incorrect simplifications, while the second subject's erroneous application of exponent rules resulted in fundamentally flawed solutions. By systematically categorizing these misconceptions, the study offers tailored instructional strategies to effectively address and correct them. This research highlights the critical need for early detection and targeted intervention in mathematical education. By providing a deeper insight into specific algebraic misunderstandings, the study suggests practical approaches for educators to enhance their teaching methodologies, ultimately improving students' overall algebra comprehension. The novelty of this research lies in its detailed focus on hidden misconceptions and the provision of actionable solutions, offering a fresh perspective on improving algebra education for first year university students.]]>
