<![CDATA[This study originates from the gap between students’ conceptual understanding and procedural ability in solving linear function problems in calculus courses. Many students struggle to connect the symbolic representations, graphical interpretations, and applications of linear functions. The purpose of this study is to analyze students’ understanding of linear function concepts based on Van Hiele’s theory, classify students according to Van Hiele’s levels of thinking, and determine the relationship between their thinking levels and learning outcomes. The research employed a quantitative descriptive approach involving 59 first-year university students from East Java Province as participants. Data were collected through a diagnostic test structured around Van Hiele’s thinking levels and analyzed using the Item Response Theory (IRT) model to identify item characteristics and students’ ability levels. The results revealed that most students were at the levels of analysis and informal deduction, while only a small proportion reached the formal deduction and rigor levels. The findings indicate that students’ understanding of linear functions remains largely operational and not fully abstract. The implications of this study highlight the importance of applying Van Hiele’s thinking level framework and IRT analysis in designing instructional strategies that enhance students’ abstract thinking skills in understanding linear function concepts.]]>
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