Abstract
A deep understanding of Green’s Theorem (GT) requires students to construct coherent mental representations that connect line integrals and double integrals within a unified conceptual framework. However, many students struggle to develop such integrated understanding when solving advanced calculus problems. This study aims to analyze students’ mental construction processes and identify the types of errors they make when solving GT problems. A descriptive qualitative approach was employed involving 23 fourth-semester mathematics students from the FMIPA, Universitas Negeri Padang. Data were collected through written tests, semi-structured interviews and documentation to capture students’ reasoning and problem-solving processes. The analysis of mental construction was guided by APOS (Action–Process–Object–Schema) theory, while students’ errors were examined using the Newman’s Error Analysis (NEA) framework. Although most students were able to perform actions such as recalling formulas and identifying given information, many encountered difficulties at the process and object stages, particularly in transforming line integrals into double integrals and determining the correct orientation of the curve. In addition, the most dominant errors were transformation errors and process skill errors, reflecting students’ difficulties in translating problems into appropriate mathematical representations and executing solution procedures accurately. The study highlights the need for instructional strategies that emphasize conceptual mental construction, visual reasoning and reflective error analysis to enhance students’ conceptual understanding and problem-solving competence in advanced calculus.
Keywords: APOS Theory, Green’s Theorem, Mental Construction, Newman’s Error Analysis.