The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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A study on the performance of sixth-grade elementary school students about the perimeter and area of plane figure and the surface area and volume of solid figure

평면도형의 둘레와 넓이, 입체도형의 겉넓이와 부피에 대한 초등학교 6학년 학생들의 수행 능력 조사

  • Received : 2019.03.22
  • Accepted : 2019.05.21
  • Published : 2019.05.31
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Abstract

Among the measurement attributes included in the elementary school mathematics curriculum, perimeter, area, volume and surface area are intensively covered in fifth and sixth graders. However, not much is known about the level of student performance and difficulties in this area. The purpose of this study is to examine the understanding and performance of sixth-grade elementary school students on some ideas of measurement and ultimately to give some suggestions for teaching measurement and the development of mathematics textbooks. For this, diagnosis questions were developed in relation to the following parts: measurement of perimeter and area of plane figure, measurement of surface area and volume of solid figure, and the relationships between perimeter and area, and the relationships between surface area and volume. The performances of 95 sixth graders were analyzed for this study. The results showed children's low performance in the measurement area, especially measurement of perimeter and surface area, and relationship of the measurement concepts. Finally, we proposed the introduction order of the measurement concepts and what should be put more emphasis on teaching measurement. Specifically, it suggested that we consider placing a less demanding concept first, such as the area and volume, and dealing more heavily with burdensome tasks such as the perimeter and surface area.

초등학교 교육과정에 포함된 측정 속성 가운데 둘레와 넓이, 겉넓이와 부피는 5, 6학년에서 집중적으로 다루어진다. 그러나 이 영역에서 학생들의 수행능력이 어느 정도가 되며 어떤 문제가 있는지에 대해서는 알려진 바가 많지 않다. 이 연구는 평면도형의 둘레와 넓이, 입체도형의 겉넓이와 부피에 대한 초등학교 6학년 학생들의 이해 정도를 진단하고, 각 요소별 수행 능력을 비교 분석하여 차후 수학 교과서 개발 및 측정 영역 지도를 위한 시사점을 도출하고자 하였다. 이를 위해 둘레, 넓이, 겉넓이, 부피, 둘레와 넓이의 관계, 겉넓이와 부피의 관계에 관련된 문항을 구성하여 6학년 학생 95명을 대상으로 수행 능력을 분석하였다. 분석결과 초등학교 6학년들의 수행능력이 둘레, 겉넓이, 둘레와 넓이의 관계, 겉넓이와 부피의 관계 영역에서 특히 낮은 것으로 드러났다. 이러한 연구 결과를 바탕으로 둘레와 넓이, 겉넓이와 부피 개념의 도입 순서와 지도 방법, 지도 순서 등에 대한 몇 가지 아이디어를 제안하였다.

Keywords

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[Fig. 1] Introduction of rectangular perimeter (Ministry of Education, 2015a, p.130)

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[Fig. 2] Introduction of rectangular area (Ministry of Education, 2015a, p.134)

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[Fig. 3] Introduction of rectangular parallelepiped surface area (Ministry of Education, 2015b, p.176)

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[Fig. 4]I introduction of rectangular parallelepiped volume (Ministry of Education, 2015b, p.180)

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[Fig. 6] An example of determining an area based on the perimeter of a figure(Lee, 2002)

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[Fig. 7] a comparison problem of areas of two figures with same widths but different perimeters(Lee, 2002)

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[Fig. 8] An example of the information processing error

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[Fig. 5] Volume measurement of irregular space figures in Japanese elementary school textbooks(東京書籍, 2013)

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[Fig. 9] An example of volume comparison error

[Table 3] Types of incorrect answers adopted by this research

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[Table 4] Percentages of correct answers of perimeter and area, and volume and surface area

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[Table 5] Percentages of correct answers of the relationship between perimeter and area, and the relationship between volume and surface area

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[Table 7] Percentages of correct answers of perimeter measurement according to the presence or absence of a picture

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[Table 8] Percentages of correct answers of the stair type’s perimeter measurement

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[Table 12] Percentages of correct answers of the stair type’s area measurement

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[Table 14] Percentages of correct answers of relationships between perimeter and area

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[Table 16] Percentages of correct answers of surface area measurement according to the presence or absence of a picture

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[Table 17] Percentages of correct answers of the stair type’s surface area measurement

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[Table 18] Percentages of correct answers of composing rectangular parallelepiped with a given surface area

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[Table 19] Percentages of correct answers of each volume question

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[Table 21] Percentages of correct answers of volume measurement for a stair type’s space figure

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[Table 1] Problems on perimeters and areas of plane figures

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[Table 2] Problems on surface areas and volumes of solid figures

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[Table 6] Percentages of correct answers of each perimeter question

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[Table 9] Percentages of correct answers of composing rectangles with a given perimeter

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[Table 10] Percentages of correct answers of area measurement

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[Table 11] Percentages of correct answers of area measurement according to the presence or absence of a picture

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[Table 13] Percentages of correct answers of composing rectangles with a given area

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[Table 15] Percentages of correct answers of each surface area question

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[Table 20] Percentages of correct answers of volume measurement according to the presence or absence of a picture

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[Table 22] Percentages of correct answers of composing rectangular parallelepiped with a given volume

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[Table 23] Percentages of correct answers of relationships between volume and surface area

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