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An Analysis of Representation Usage Ability and Characteristics in Solving Math Problems According to Students' Academic Achievement  

Kim, Min-Kyung (Dept. of Curriculum and Instruction, Graduate School of Korea University)
Kwean, Hyuk-Jin (Dept. of Math. Education, Korea University)
Publication Information
Communications of Mathematical Education / v.24, no.2, 2010 , pp. 475-502 More about this Journal
Abstract
In this paper, the ability to use mathematical representations in solving math problem was analyzed according to student assessment levels using 113 first-year high school students, and the characteristics of their representation usage according to student assessment levels were also examined. For this purpose, problems were presented that could be solved using various mathematical representations, and the students were asked to solve them using a maximum of three different methods. Also, based on the comparative analysis results of a paper evaluation, six students were selected and interviewed, and the reasons for their representation usage differences were analyzed according to their student assessment levels. The results of the analysis show that over 50% of high ranking students used two or more representations in all questions to solve problems, but with middle ranking students, there were deviations depending on the difficulty of the questions. Low ranking students failed to use representation in diverse ways when solving problems. As for characteristics of symbol usage, high ranking students preferred using formulas and used mathematical representations efficiently while solving problems. In contrast, middle and low ranking students mostly used tables or pictures. Even when using the same representations, high ranking students' representations were expressed in a more structurally refined manner than those by middle and low ranking students.
Keywords
mathematical representation; mathematical problem solving;
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