### REPRESENTASI MATEMATIS SISWA KELAS VII DI SMP N 9 YOGYAKARTA DALAM MEMBANGUN KONSEP SISTEM PERSAMAAN LINEAR DUA VARIABEL

#### Abstract

**Abstract:** The purpose of this study was to describe the preference of using of mathematical representations form of the seventh grade students of SMP 9 Yogyakarta who have high ability in developing the concept of a Systems of Linear Equations in Two Variables (SLETV) and describing the characteristics of the use of such mathematical representations form. This research was categorized as a qualitative case study approach. The subjects of this study were 6 (six) students of seventh grade of SMP Negeri 9 Yogyakarta who have high ability. Data in this study were the use of mathematical representation forms in developing concepts of SLETV that obtained from observation and interview-based tasks. The data were analyzed into three categories of SLETV developing concepts: 1) stating SLETV definition and SLETV’s solution definition; 2) using the concept SLETV in everyday life; and 3) solving the problem of SLETV. The use of students’ mathematical representation that includes a symbolic representation, a verbal representation, and a visual representation were be seen by each category. The validity of the data being used in this study was triangulation time, through the first observational data and task-based interview, and the second observational data and task-based interviews. The same consistent data were categorized as valid data that illustrate the use of students’ mathematical representation in developing concepts of SLETV. The results of this study are as follows. 1) The preference of the use of students’ representation forms in stating SLETV definition and solution sets by using verbal representation. Characteristics of using this representation are by mentioning SLETV’ characteristics (for SLETV definition), and by mentioning the characteristics SLETV solution (for solution sets); 2) Preference of the use of students representation forms in using SLETV concept in the daily life is by using symbolic representation. The characteristics of the use of representation are: a) by changing the description of the conditions that are known to be an equation form; b) by making a conjecture to find the right answer; c) by clarifying the rightness of the conjecture that has been made to determine the correct answer; d) by performing algebra arithmetic operations, and arithmetic operations to determine the right answer. 3) The preference of the use of students’ representation forms in finishing SLETV problem is by using symbolic representation. The characteristics of using this representation are: a) by changing the shape that was known as an equation form; b) by manipulating the form of the equations that have been made to get the right answer easier; c) by making a conjecture to find the right answer; d) by clarifying the rightness of the conjecture that has been made to determine the correct answer; e) by doing algebra arithmetic operations and arithmetic operations to determine the right answer.

**Keywords :** Developing of concepts, Systems of Linear Equations in Two Variables (SLETV), mathematical representation.

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