An Analysis of Students’ Errors Based on Newman’s Error Analysis in Solving Partial Derivative Problems in Calculus

Abstract

Understanding student errors in calculus is crucial for improving the quality of mathematics learning. This study analyzes students’ errors in solving partial derivative problems in a calculus course based on the Newman Error Analysis framework. A quantitative descriptive approach was employed. The participants were 20 students from the Mathematics Education Study Program at Universitas Timor enrolled in a calculus course. Data was collected through written tests and unstructured interviews and then analyzed using error categorization and percentage distribution. The findings reveal that the most frequent errors occur at the comprehension, transformation, and process skills stages. Comprehension errors are indicated by students’ difficulties in interpreting the meaning and structure of mathematical expressions. Transformation errors are characterized by students’ inability to convert problems into appropriate mathematical forms or procedures, particularly in selecting suitable strategies. Process skills errors arise when students make computational mistakes despite correctly understanding the problem. In contrast, errors at the reading and encoding stages are relatively infrequent. These results suggest that students’ main difficulties lie in the intermediate stages of problem-solving, where conceptual understanding and procedural fluency are required simultaneously. Therefore, calculus instruction should emphasize conceptual strengthening and incorporate non-routine, higher-order thinking skills-based problems to enhance students’ problem-solving abilities.