An investigation of sixth grade students' skills of using multiple representations in addition and subtraction of fractions

The aim of this study is to determine the representation preferences of the sixth-year students for the addition and subtraction of fractions, to reveal their successes in their preferences, and to analyze students' skills to construct each representation by examining the transitions between the representations involved in addition and subtraction operations (algebraic, model, number line and verbal). This research has been conducted as a case study. The study group consists of 59 students, 31 of whom are boys and 28 of whom are girls, who are in the sixth grade of three junior high schools affiliated to MoNE in the city of Kastamonu in the academic year 2015-2016.A purposeful sampling selection method was used to select participants. In determining the schools to be studied, the provincial general achievement average was taken into account and three schools with average level of achievement were included in the study. The data were collected by "MultiRepresentation Test in Addition-Subtraction of Fractions" and analyzed in accordance with predefined transition criteria. Representation preferences of students and interpretations of their success in their preferences were presented through descriptive statistics (percentage and frequency).While algebraic representation takes second place in preferences, verbal representations are the least preferred type of representation. When students' performances in the representations are examined, the most successful representations of students in addition and subtraction of fractions are algebraic and model representations. On the other hand, it has been seen that the achievement status of students in the verbal and numerical representation types is considerably low. Analysis of students' representation skills turns out that students make mistakes at every step in their representation transitions. It has been determined that students make more mistakes in the steps of determining numerator of the appropriate whole from the given set of model representations. In the case of creating algebraic representation, the execution of the operation is a more frequently determined mistake. While students face problems with the number line model including the steps expressing the fractions in the number line and showing the result, in the process of forming a verbal representation, the mistakes made in the process of forming the question rooting are noteworthy