Error Analysis of Students in Implementing the Newton-Raphson and Bisection Methods on Nonlinear Equation Root Problems Based on Newman's Error

Abstract

This study aims to describe students' errors in solving nonlinear equation root problems using the Bisection and Newton-Raphson methods based on Newman's Error Analysis (NEA). This study uses a qualitative approach with descriptive methods. The research subjects consisted of 33 students of the Mathematics Education Study Program who had taken the Numerical Analysis course. The research instrument was a Mid-Semester Exam question on the material of nonlinear equation roots covering the Bisection and Newton-Raphson methods. Data collection techniques were carried out through written tests and semi-structured interviews, then analyzed based on Newman's error categories, namely reading, comprehension, transformation, process skills, and encoding. The results showed that the most dominant errors made by students were in the process skills category. In the Bisection method, student errors mostly occurred in the process of evaluating functions and determining new intervals during iteration, while in the Newton-Raphson method, dominant errors occurred in determining function derivatives and substituting iteration values ​​into the Newton-Raphson formula. In addition, it was found that some students experienced transformation errors due to the inability to connect mathematical concepts with algorithmic procedures of numerical methods. Interview results indicate that student errors are influenced by a lack of understanding of basic concepts, low accuracy in numerical operations, and a lack of habit of double checking calculation results. This research is expected to serve as a basis for designing Numerical Analysis learning strategies that emphasize students' conceptual understanding and procedural accuracy.