The Fraction Magnitude Knowledge through Representations at Students with Mathematics Difficulties

Elementary school students’ knowledge of fraction magnitude may predict their mathematics achievement. Students’ mathematics achievement is influenced by their mathematics difficulties. This study exposes students’ representations in estimating fractions to indicate their fraction magnitude knowledge. This study is conducted on the 4th grade of elementary students in Surabaya. A class which consists of 10 girls and 18 boys, had chosen purposively from 3 available classes. All students had to answer two tests, namely the diagnostic test and the fraction magnitude test. Four volunteer students were selected as research subjects which have different and interesting mathematics difficulty in fraction. Semistructured interview was conducted to all subjects to reveal students’ thinking process when solving diagnostic and fractions magnitude tests. Results suggest that 46% of 26 students who have bad score (low ability) have mathematics difficulties in representing and estimating simple fraction because they considered nominator and denominator as independent numbers (i.e. 1/3 is represented as a bar model which is divided by 4 equally parts and a part is in shaded). More than 20% of 26 students had mathematics difficulties which were not able to estimate non-simple fraction but they were able to represent it. Their ability is influenced by difficulties in fraction magnitude. Keywords—fraction magnitude knowledge, representation, students’ difficulties