# 수학 문제 해결에서 학업성취도에 따른 표상 활용 능력과 특징 분석

• Kim, Min-Kyung (Dept. of Curriculum and Instruction, Graduate School of Korea University) ;
• Kwean, Hyuk-Jin (Dept. of Math. Education, Korea University)
• Accepted : 2010.04.14
• Published : 2010.05.15

#### 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.

본 연구에서는 고등학교 1학년 113명을 대상으로 수학 문제 해결에서 표상 활용 능력을 학업성취도에 따라 분석하고, 학업성취도에 따른 표상 활용의 특징에 대하여 알아보았다. 이를 위해서 학생들에게 다양한 표상을 사용하여 해결할 수 있는 문제를 제시하고, 이를 최대 세 가지방법을 이용하여 풀도록 하였다. 또한 지필 평가의 비교분석 결과를 토대로 6명의 학생을 선발하여 인터뷰를 실시하고 학업성취도에 따라 표상 활용에 차이가 나는 원인을 분석해 보았다. 그 결과 상위권 학생들은 50%이상이 모든 문항에서 두 가지 이상의 표상을 활용해 문제를 해결하였지만, 중위권 학생들은 문항의 난이도에 따라 편차가 있었고, 하위권 학생들은 문제 해결에 표상을 다양하게 활용하지 못하였다. 표상 활용의 특징으로, 상위권 학생들은 수식사용을 선호하였고 문제 해결과정에서 수학적 기호를 효율적으로 사용하였다. 이에 반해 중 하위권 학생들은 표나 그림을 이용하는 경우가 대다수였고, 같은 표상 양식이라 할지라도 상위권 학생이 중 하위권 학생보다 더 구조적이고 세련되게 표현하고 있었다.

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