Types of Student Errors in Mathematical Symbols, Graphs and Problem-Solving

Abstract

This study aims to identify the level of difficulty, discrimination and errors based on symbols, graphs and problem-solving in mathematics achievement. The participants consisted of 315 grade 10 students randomly selected from eight secondary day schools situated in the state of Kedah, Malaysia. The mathematics written test consisted of 15 open-ended items with five items each for symbols, graphs and problem-solving and all the items were analyzed using the difficulty and discrimination index. Semi-structured clinical interviews were also carried out among 20 selected students to identify the errors they had made in mathematics. In the content analysis, the descriptor code key was used to identify conceptual, careless, problem-solving and value errors. The findings showed that item 4 (Standard Form) of the symbols, item 6 (Linear Equation) of the graphs, and item 15 (Line & Plane in 3 Dimension) of the problem-solving was the most difficult item in mathematics. All of these items had a good discrimination as well as difficulty index. Content analysis showed that 52 (57%) students made conceptual errors, 22 (24%) made careless errors, 12 (13%) made problem-solving errors and 5 (6%) made value errors. The major reasons given for errors made were a lack of understanding, procedures being forgotten, negligence in transcribing information from the question, carelessness and guesswork. This study has implications for the student learning process and understanding graphs because graphs are widely used in daily life to manage, communicate and analyze information.

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