<![CDATA[This study investigates the difficulties experienced by first-year calculus students when interpreting function graphs and linking them to real-world contexts. Previous observations indicated that around 71.4% of students had difficulty accurately reading and representing functions graphically. To address this, the study used Discovery Learning-based worksheets for diagnosis and instruction to identify, categorise and reduce errors in students’ understanding of functions and their graphical representations. A qualitative descriptive research design involving 21 first-semester students from the Mathematics Education Programme at Universitas Ahmad Dahlan was applied. Data were collected from the students’ responses to the worksheets and analysed through iterative processes of data reduction, display and drawing conclusions. Student errors were classified into three categories: conceptual, procedural and technical. The findings revealed that conceptual errors were the most prevalent, particularly when distinguishing functions from general relations, interpreting discrete and continuous domains, and understanding the meaning and application of functions in real-life situations. The Discovery Learning worksheets encouraged students to actively construct concepts through exploration, reflection, and guided problem solving, while simultaneously providing insight into their reasoning processes and persistent misconceptions. This study concludes that Discovery Learning worksheets are effective in diagnosing errors and reinforcing concepts in calculus learning. These findings offer mathematics educators a practical pedagogical framework for identifying learning obstacles and strengthening students’ foundational understanding of functions and graphical representations in introductory calculus courses.]]>
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