Unraveling Misconceptions: A Study of First-Year University Students’ Understanding of Basic Mathematical Concepts

Abstract

This study investigated the misconceptions held by first-year university students regarding basic mathematical concepts, with a focus on integer operations, fractions, and elementary algebra. Conducted at a private university in Aceh, Indonesia, the research involved 26 students enrolled in the Elementary Algebra course. A diagnostic test consisting of five open-ended questions was administered, followed by structured interviews with 6 students who exhibited notable errors. The findings revealed persistent misconceptions, including misapplication of integer rules, incorrect fraction operations (e.g., adding numerators and denominators directly), and flawed algebraic reasoning. These issues indicate a reliance on procedural knowledge rather than conceptual understanding, often rooted in prior learning experiences. The results highlight the importance of early diagnostic assessments and concept-focused instruction in bridging the gap between school and university mathematics. Addressing these misconceptions is essential to support students’ mathematical development and academic success in higher education.