Discovery Learning as a Diagnostic Framework for Analyzing Conceptual, Procedural, and Technical Errors in Function Graph Interpretation - Sumargiyani Sumargiyani; Siti Nur Rohmah; Fariz Setyawan (Universitas Papua, 2025)
Understanding functions and their graphical representations constitutes a fundamental component of introductory calculus learning; however, many first-year university students continue to experience substantial difficulties in interpreting graphs and relating mathematical functions to authentic real-world situations. Although previous studies have extensively examined students’ procedural performance in calculus, limited attention has been devoted to diagnosing the underlying conceptual obstacles through instructional approaches that simultaneously function as learning and assessment instruments, thereby establishing the novelty of this study through the integration of Discovery Learning-based worksheets as both diagnostic and pedagogical tools. This study aims to identify, classify, and reduce students’ errors in understanding functions and graph representations among 21 first-semester students in the Mathematics Education Program at Universitas Ahmad Dahlan using a qualitative descriptive design. Data were collected from students’ worksheet responses and analyzed through iterative processes of data reduction, data display, and conclusion drawing. The findings revealed three categories of errors, namely conceptual, procedural, and technical errors, with conceptual errors emerging as the most dominant, particularly in distinguishing functions from relations, interpreting discrete and continuous domains, and contextualizing functions in real-life applications. Furthermore, the Discovery Learning worksheets promoted active concept construction through exploration, reflection, and guided problem-solving activities while revealing persistent misconceptions and reasoning patterns. These findings provide a meaningful pedagogical contribution to mathematics education by offering a systematic framework for diagnosing learning obstacles and strengthening students’ conceptual understanding of functions in introductory calculus courses.