Journal of the Korean School Mathematics Society (한국학교수학회논문집)

The Korean School Mathematics Society (한국학교수학회)
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An analysis on the perception of resemblance and difference between parallelogram and rhombus in middle and high school students

중·고등학생의 평행사변형과 마름모의 유사성과 차이에 대한 인식 분석

  • Chang, Hyun Suk (University of Ulsan) ;
  • Kim, Myung Chang (Gyeongsan Girls' Middle School)
  • 장현석 (울산대학교 ) ;
  • 김명창 (경산 여자중학교 )
  • Received : 2024.01.04
  • Accepted : 2024.03.07
  • Published : 2024.03.30
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Abstract

In this study, the perception of the resemblance and difference between the parallelogram and rhombus of middle and high school students was analyzed. To this end, a test tool was developed, a total of 191 middle and high school students were tested, and some students were interviewed. The results of the study are as follows. In common with resemblances and differences, the response rate to the type of parallelogram and rhombus was the highest, and the quantitative response rate such as length was the lowest. In the case of resemblances, first, the response rate was high in the order of the definition of parallelogram and rhombus, the edge and angle, and the lower value of the diagonal. Second, the response rate from the perspective of transformation was relatively lowest. Third, in general, female students responded based on quantitative information based on the shape of the figure, and male students responded based on the definition of parallelogram and rhombus. Fourth, in the case of manipulation, there was no difference between male and female students in frequency and ratio, but it increased as the grade went up. In the case of differences, the response rate to the length of the diagonal was higher than that of the overall length. However, there was no response to diagonals relating to the properties of parallelogram and rhombus.

이 연구에서는 중·고등학생의 평행사변형과 마름모의 유사성과 차이에 대한 인식을 분석하였다. 이를 위해 검사 도구를 개발하고 중·고등학생 총 191명을 대상으로 검사하고, 일부의 학생을 면담하였다. 연구 결과는 다음과 같다. 유사점과 차이점에서 공통으로 평행사변형과 마름모의 종류에 대한 응답 비율이 가장 높았고, 길이와 같은 양적인 응답 비율이 가장 낮았다. 유사점의 경우 첫째, 평행사변형과 마름모의 정의, 변과 각 그리고 대각선의 내림차순으로 응답 비율이 높았다. 둘째, 변환 관점의 응답 비율은 다른 범주와 비교해서 상대적으로 가장 낮았다. 셋째, 대체로 여학생은 도형의 형태에 기반 한 양적인 정보를 토대로 응답하고 남학생은 평행사변형과 마름모의 정의에 기반 해서 응답하였다. 넷째, 조작의 경우 빈도와 비율에서 남학생과 여학생의 차이는 없었지만 학년이 올라감에 따라 증가하였다. 차이점의 경우는 전체적인 길이에 대한 응답에 비해 대각선의 길이에 대한 응답 비율이 높았다. 그러나 대각선을 평행사변형과 마름모의 성질과 관련 지은 응답은 없었다. 마지막으로 개념 정의와 개념 이미지의 관점에서 중·고등학생은 평행사변형과 마름모의 개념 정의에 대한 기억 또는 이름을 이용하거나 개념 이미지 및 각 등을 부분적으로 주목하고 이를 시각적으로 변환하거나 넓이와 같은 양적인 정보를 이용하여 평행사변형과 마름모의 유사성과 차이에 대해 응답하였다.

Keywords

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