Exploring 8th Grade Students’ Skills and Knowledge on Irrational Numbers

Abstract

This study has aimed to determine 8th grade middle school students’ skills and knowledge on irrational numbers. A total of ten 8th grade students from a public school in Polatlı District of Ankara were participated. In the study, a basic qualitative research design was used, and data were collected by means of clinical interviews. Interview questions were developed based on a review of the relevant literature, and the final versions of the questions were determined in accordance with expert opinions. Analyses of the resultant data revealed that students experienced some difficulties when defining irrational numbers. They were relatively good at classifying numbers as irrational or not and explaining the reason for this classification. Nevertheless, it was concluded that they had difficulty identifying the relationships among sets of numbers, explaining the difference between rational and irrational numbers and performing operations with irrational/rational numbers. A set of recommendations were developed for overcoming those challenges. Among them were using different types of representations during the instruction process, making use of non-routine problems, making connections to the history of mathematics and using calculators.