Abstract
The purpose of this research was to reveal how the construction process of symbolic representation and verbal representation made by students in problem solving. The construction process in this study referred to the problem-solving stage by Polya covering; 1) understanding the problem, 2) devising a plan, 3) carrying outthe plan, and 4) looking back. This research was qualitative research by getting involved 4 students of Junior High School class VIII. This study obtained results that the construction process of symbolic representation made by students since in the process of understanding the problem. In understanding the problem, students were able to identify the problem well. Then students could make the symbol used as a variable that the value was not known. By using the symbol students could perform a series of calculation to obtain the value of the symbol. Symbols created by students were very helpful and facilitated students in solving problems. While in the construction process, verbal representation was done by students since the process of understanding the problem. The form of verbal representation was manifested by writing down all information known from a slightly changed problem because they used a language that they understood more. Based on the known information, students could plan and performed a series of calculations using written sentences so that the problems could be solved properly.
Highlights
National Council of Teachers of Mathematics (2000) set five standard processes that must be mastered by students such as representation
It was in accordance with the opinion of Lesh et al (1987) that the skill of symbolic representation is characterized by the skill in transforming mathematical problems into the representation of arithmetic formulas
The symbol simplified the problem solving process. This finding was in accordance with the opinion of Dahlan and Juandi (2016) that in high school students, representations are useful for solving problems or clarifying, or expanding mathematical ideas starting from the process of collecting facts, arranging tables or graphs, until the development of symbolic representation
Summary
National Council of Teachers of Mathematics (2000) set five standard processes that must be mastered by students such as representation. Through representation students can make mathematical ideas to be more concrete and facilitate to do reflection (NCTM, 2000). The mathematical problem solving using representation is strongly recommended because it can be used as a tool to facilitate during the problem solving process (Stylianou 2008). Schoenfeld (in Stylianou, 2010) calls representation as a means to understand the information obtained in problem situations. Newell and Simon (1972) see that representations can be as a means of recording while Stylianou and Silver (2004) call representation as a tool that facilitates the exploration of concepts or problems. In addition Gibson (1998) and Izsak (2003) view representation as a means of monitoring and evaluation to assess progress in solving problems
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