Analysis of students' misunderstandings in comparing fractions as part-whole comparisons through students' representation

Abstract

Fractions is one of the essential topics in mathematics learning at school that is often considered difficult to understand by students. Students in Indonesia generally learn fractions in the part-whole comparisons construct. This study aims to describe students' misunderstandings in comparing fractions in fraction constructs as part-whole comparisons through representations presented by students. This research is descriptive qualitative research and the data collection was collected by test, interview, and video documentation. The subjects of this study were seven elementary school students at the fifth grade, one of the schools in Bandung. The result of this study show that students who correctly answer the problem of comparing fractions and can represent the fractions that are given in fraction constructs as PartWhole Comparisons evidently have a misunderstanding of comparing two fractions. The types of mistakes made by students are 1) Students compare the numerator of the two fractions given, 2) Students compare the denominator of the fractions given, and 3) Student do not divide the unit into equal-sized shares. Based on the result, we conclude that students' understanding of the definition and representation of fractions as part-whole comparisons is still limited to memorization, not to the good meaning.