Analysing pupils' errors in operations of integers among form 1 pupils

Abstract

Previous studies have shown that pupils have difficulties and errors in dealing with many areas of mathematics including in various topics of the number system such as integers. Pupils’ difficulty with the concept of integers causes them to struggle in solving mathematical problems, especially those involving the four basic operations. This study aims to diagnose pupils’ errors in the operations of integers, subsequent to validating the Errors Identification Integers Test (EIIT) which can identify the types of errors that pupils possess in dealing with the operations of integers. The EIIT which consists of multiple-choice questions involving different combinations of positive and negative numbers was adapted to suit the Malaysian context. The population of this study is all Form One pupils from selected public schools in Peninsular Malaysia. A total of eight schools were involved in the data collection as samples. Cluster sampling was employed in order to ensure that the selected schools represented the population. The Rasch Model was used to improve and validate the instrument used in this study. In addition, teachers’ and pupils’ interviews were conducted to find and confirm the errors of the operations of integers. Then, a teaching intervention that was designed to remedy and improve pupils’ understanding of the operations of integers was implemented. Sixty pupils who were involved at this stage of the quasi-experimental study were selected using purposive sampling. The pre and post tests were given to the pupils to determine the effectiveness of the algebraic tiles method in improving their performance in the operations of integers. Carelessness, rule mix-up, inability to assimilate concepts and surface understanding/poor knowledge were identified as the types of errors in this study. Meanwhile, this study found that parenthesis misapprehension, poor mathematical language, calculator hooking, superficial understanding and external limitation were the possible causes that led to the errors. The results also showed that the intervention using algebraic tiles as a strategy for teaching operations of integers was successful. The ANCOVA used to calculate the difference between the post-test as compared to the pre-test further returned a statistically significant result.