Analisis Kesulitan Belajar Mahasiswa pada Materi Teori Kebebasan Lintasan dalam Mata Kuliah Kalkulus Vektor

Abstract

This study aims to analyze the forms of learning difficulties experienced by students in understanding the path independence theorem in the Vector Calculus course. The focus of the research is a group of students who had previously presented this material in class. Data were collected through a questionnaire containing both open- and close-ended questions to explore conceptual understanding, difficulties in distinguishing between conservative and non-conservative fields, and challenges in solving application problems. The analysis revealed that although students reported having a fair grasp of the basic concepts, they still expressed uncertainty in understanding the relationship between path independence and the conditions for conservative fields. Difficulties were also found in spatial visualization and in connecting concepts with the fundamental theorem of calculus. In addition, students showed a preference for worked example problem sets and visual learning media as the most effective learning supports. These findings indicate the need for an interactive, contextual, and visually supported instructional approach to enhance students’ conceptual understanding and application skills related to this topic.