Newman’s Error Analysis of Common Errors in Solving Convergence of Power Series Using Ratio Test

Abstract

In mathematics, the students are urged to answer the questions correctly. Answers with complete sets of solutions shows a certain level of understanding of students. However, it is undeniable that some student had difficulty in answering the questions correctly. The students may not have certain understanding on a particular topic and that does not mean that they are poor in mathematics. Some errors that students do in doing mathematics may due to misunderstanding of questions, incorrect concepts, careless mistakes or skip of required answer steps. The purpose of this study was to give insight to the instructors on the common errors done by the students in solving question with long sets of solution. This research method is a descriptive study, with the aim of finding out the number of percentage and the level of students' mistakes using Newman's Error Analysis. This study focused on year two student that undertook Further Calculus in Engineering emphasised on convergent test of power series using ratio test topic. The data were collected from their final examination answer papers, focused only on related questions. The results show the most common error made by the students were transformation error (38%) and encoding error (38%) and did less in comprehension error (2%). While reading error (5%) and process skill error (17%) could also had been considered low. Instructors must guide the students more on correct transformation (solve fraction and factorisation) and encoding (interval of convergence) in order to solve convergence of power series using ratio test.

Using Newman Error Analysis to Detect Students’ Error in Solving Junior High School Mathematics Problem

“…From figure 6(a), (b), and (c) it is found that errors made at the process skill phase result in encoding error. Mansor et al (2021) also stated the same thing that the fourth phase, that is process skill. They stated that most students who make error in process skills tend to make error in incoding, that is the students record their result inappropriately.…”