Abstract
Translation among forms of representation defines as changing process one form of representation to other representations. Translation activities from one representation (source) to another (target) are very important in expressing mathematical ideas. In translating among representations, students are not only interact with the basic concepts contained in the information, but also they must be able to connect parts of these basic concepts with different things related to the intended representation. The purpose of this qualitative research is: 1) to analyze the tendency of mathematical representations to be used in solving mathematical problems given in verbal representations, and 2) to analyze the translational structure of the target representations made. The research subjects were 3rd year students of Mathematics Education at Universitas PGRI Semarang. The research data were taken by means of tests and interviews immediately after solving the math problems given in the form of verbal representations. The results showed that the group students who were solving the verbal questions indicated that they tended to translate from the verbal representations to symbolic representations in presenting definitions and in proof. However, this symbolic representation still contained verbal representations such as in the source problems. The stages of representation in this research followed the translation stages: unpacking the source, preliminary coordination, constructing the target, but left for determinant of equivalence. High-ability group of students in solving the questions tend to translate from verbal representation to symbolic representation. Further, some of them translate verbal to visual representation to increase understanding. The translation stages are unpacking the source, preliminary coordination, constructing symbol representation, constructing visual representation, determining the equivalence of the visual representation to verbal representation, and determining the equivalence of the symbol representation form to verbal representation.
Highlights
Representation is creativity that involves expressing or exposing someone's ideas to present mathematical answers or ideas for their work [1][2][3]
The tendency of using representations in understanding definitions and in providing proof, as well as the structure of the translation of the form of representation carried out by dividing the results of problem solving into two groups, namely the medium and high groups are as follows: 1) Students with the classified into moderate show that they tend to translate from verbal representations to symbolic representations in presenting definitions and in proof, but still contain verbal representations such as the problems given
The translation stage of unpacking the source is seen when unpacking the two questions, the subject knows the information from the source well and knows he is asked to present it in the form of a symbol representation
Summary
Representation is creativity that involves expressing or exposing someone's ideas to present mathematical answers or ideas for their work [1][2][3]. Second opinion about representation is that representation plays a significant role in understanding mathematical concepts, namely by interpreting representations as a tool in representing mathematical ideas [8][11][12]. This is in accordance with the results obtained by Gagatsis & Elia [7], Michaelidou et al [11]. Another opinion is expressed by Harries & Barmby [8] that mathematics is accepted if its thougtful representations are element of a structure of portrayels.
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