Journal of Science Education (과학교육연구지)

Science Education Research Institute Kyungpook National University (경북대학교 과학교육연구소)
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The Analysis of 5th Graders' Visual Representation in Mathematical Problem Solving

수학 문제해결에서 초등학교 5학년 학생들의 시각적 표현 분석

  • Received : 2021.06.29
  • Accepted : 2021.08.13
  • Published : 2021.08.31
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Abstract

Visual representation has been a useful tool in mathematical problem solving because it vividly express and structure the variables in the problem. But its effects may vary according to the types of problems. So, this study analyzes the survey results on the 5th graders' visual representations using questionnaire consisting of the routine problems and the non-routine problems. The results are follows: The rate of correct answers in routine problems was higher than that of the non-routine problems. Even though the subjects were asked to solve the problem using visual representations, the ratio of solving the problem using the numerical expression was high in the routine problems. On the other hand, the rate of solving the problem using visual representation was high in the non-routine problems. The number of respondents who used visual representation in the non-routine problems was twice as many as that of the routine problems. But, among the subjects who used visual representation in the non-routine problems, the proportion of incorrect answers was also high, which resulted in using visual pictures. So, it is necessary to provide an experience that can use various types of the visual representations for problem solving and pay attention to the process of converting problems into visual representations.

수학 문제해결에서 시각적 표현은 문제 이해와 해결에 유용한 수학적 표현으로 인식되고 있다. 그렇지만 그 효과는 문제 내용이나 유형, 또는 이용되는 시각적 표현 유형에 따라 다를 수 있다. 본 연구에서는 정형화된 문제와 비정형화된 문제해결에 이용된 시각적 표현의 양상을 살펴보기 위해 초등학교 5학년 학생들을 대상으로 조사연구를 실시하였다. 분석 결과, 정답률에서는 정형화된 문제가 비정형화된 문제보다 높게 나타났다. 정형화된 문제에서는 시각적 표현을 이용하여 문제를 해결하도록 하였음도 불구하고 수식을 이용하여 해결한 비율이 높게 나타났다. 반면에 비정형화된 문제에서는 시각적 표현을 이용하여 해결한 비율이 높게 나타났다. 그렇지만 비정형화된 문제에서 시각적 표현을 이용한 대상자 중에 오답자의 비율도 높게 나타났는데, 이것은 문제 상황을 묘사하는 수준의 시각적 표현에 그친 경우였다. 따라서 다양한 유형의 시각적 표현을 문제해결에 이용할 수 있는 경험을 제공하도록 하고, 시각적 표현으로의 변환 과정에도 주의를 기울일 필요가 있다.

Keywords

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