Performance of Understanding Students’ Construction In The Naming Fraction of The Three Representation

Abstract

The purpose of this study is to describe students’ thinking processes in constructing the names of the fraction in circular, rectangular and number line representations by using APOS Theory (Action, Process, Object, and Scheme). For that purpose, the researcher used qualitative research approach. The subject of this research is the students of class XI in Malang. The process of collecting data begins with giving the questions to the subject to be completed. Then the students are interviewed to reinforce the answers that have given. From the performance of the subject and results of the interview, the data are analyzed using indicators of APOS Theory is action, process, object, and scheme. The results of this study indicate that for the thinking process students with circle representation S1 reached the stage of the scheme, while for S2 and S3 only reached the stage of the process. With the rectangular representation, S1 and S2 reach the stage of the scheme, but different with S3, S3 that reached the stage of the process. Moreover, the thinking process by using the number line representation S1, S2 and S3 can reach the stage of the scheme. To construct the name of the fraction with a circle and rectangular representation the subject is using the whole-part concept and area model of the fraction. As for the representation that uses the number line the subject using the concept of measurement and associates it with the length model in constructing the name of the fraction.