Analysis of Students' Errors in Solving Multivariable Calculus Optimization Problems Using Newman's Error Analysis

Abstract

This study aims to describe the types of errors made by students when solving optimization problems in the Multivariable Calculus course based on Newman Error Analysis (NEA). The study employs a qualitative descriptive approach with simple quantitative analysis in the form of percentages to illustrate the frequency of errors. The research subjects were 34 students in the Mathematics Education program who had taken the Multivariable Calculus course. Data were collected through essay tests and semi-structured interviews. Data analysis was conducted using the Miles and Huberman model, while error classification was based on Newman’s five stages: reading, comprehension, transformation, process skills, and encoding. This study identified three types of errors made by students in multivariable calculus optimization problems: (1) transformation errors 58,83%), characterized by an inability to construct a mathematical model and relate the objective function to the constraints; (2) process skills errors (26,47%), characterized by errors in differentiation, algebraic manipulation, and incomplete procedures; and (3) encoding errors (14,70%), characterized by a failure to communicate the final answer. These findings indicate that students’ difficulties lie not only in conceptual and procedural skills, but also in mathematical communication. These results can serve as a basis for instructors in designing more effective instruction and diagnostic assessments.