Mathematics errors in fractions work: a longitudinal study of primary level pupils in Brunei

Abstract

This study examined the different types of mathematical errors exhibited by primary level pupils in Brunei when working with fractions. In addition, the study examined pupils' attitudes towards the learning of fractions and investigated if there were gender differences among Bruneian pupils' performances with fractions and with their attitudes towards fractions. The study was longitudinal in nature and its two phases involved a single cohort of Primary 5 pupils followed through a full year period in four government-funded primary schools in Brunei Darussalam. Pupils' mathematical errors were assessed by means of researcher-developed paper-and-pencil tests, while pupils' attitudes towards the learning of fractions were measured by means of an adapted version of attitude questionnaire that has been used previously with Bruneian pupils. Guided by six research questions, a number of statistical analyses were carried out to ensure the validity and reliability of the instruments used. These included piloting and revising the instruments, the use of Cronbach's alpha with the items in the attitude questionnaire, and the calculation of the Pearson Product Correlation Coefficient between scales of the questionnaire. The data was analysed by calculating the percentages and means of occurrences of each type of error. Paired and independent sample t-tests were carried out in order to investigate gender differences in pupils' errors and the impact of further instruction on fraction at the P6 level, while the GLM test was administered in order to investigate if there were significant change in pupils' attitudes towards fractions from the pre- to the posttests. Qualitative information obtained through pupils' interviews, field notes and lesson observations was used to support the quantitative data.The study revealed that though pupils' achievement in the post-test improved, their performances on fraction work remained generally unsatisfactory. Many pupils in the study continued to have difficulty with the basic operations on fractions and resorted to the use of keyword strategies in dealing with word problems. Despite the pupils' unsatisfactory performance in the diagnostic tests, they generally held very positive attitudes towards the learning of fractions. No significant gender differences were observed either in pupils' performance in working with fractions tasks nor with their attitudes towards the learning of fractions. The findings of this study also highlight a number of issues for mathematics teachers to consider when dealing with fractions, and the findings also have implications for the quality of the instructional activities provided by the teachers, for the impact of language transfer in the medium of instruction - that is, from Bahasa Melayu to English at the pupils' Primary 4 level- and for the quality of the teacher training program in Brunei.