Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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A design of teaching units for experiencing mathematising of elementary gifted students: inquiry into the isoperimetric problem of triangle and quadrilateral

초등영재 학생의 수학화 학습을 위한 교수단원 설계: 삼·사각형의 등주문제 탐구

  • Choi, Keunbae (Dept. of Math. Edu., Teachers College, Jeju National University)
  • Received : 2017.01.05
  • Accepted : 2017.04.03
  • Published : 2017.05.15
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Abstract

In this paper, it is aimed to design the teaching units 'Inquiry into the isoperimetric problem of triangle and quadrilateral' to give elementary gifted students experience of mathematization. For this purpose, the teacher and the class observer (researcher) made a discussion about the design of the teaching unit through the analysis of the class based on the thought processes appearing during the problem solving process of each group of students. The following is a summary of the discussions that can give educational implications. First, it is necessary to use mathematical materials to reduce students' cognitive gap. Second, it is necessary to deeply study the relationship between the concept of side, which is an attribute of the triangle, and the abstract concept of height, which is not an attribute of the triangle. Third, we need a low-level deductive logic to justify reasoning, starting from inductive reasoning. Finally, there is a need to examine conceptual images related to geometric figure.

이 논문에서는 초등 영재학생들에게 수학화의 경험을 주기 위한 교수단원 <삼 사각형의 등주문제>를 설계하는 것이 목적이다. 이를 위해서, 각 조별 학생들의 문제 해결과정 중에 나타나는 사고과정을 바탕으로 교사와 수업관찰자(연구자)가 수업분석을 통하여 교수단원 설계와 관련된 논의를 하였다. 교육적 시사점을 줄 수 있는 논의 내용을 요약하면 다음과 같다. 첫째, 학생들의 인지적인 간극을 줄이기 위한 교구활용을 고려해야한다. 둘째, 삼각형에서 삼각형이 지닌 속성인 변의 개념과 추상적인 속성인 높이 개념과의 관계를 심도 있게 다룰 필요가 있다. 셋째, 귀납적인 추론으로부터 시작하여 추론을 정당화하는 낮은 수준의 연역적인 논리가 필요하다. 끝으로, 도형을 보는 직관(spatial sense)에 영향을 줄 수 있는 도형의 개념이미지를 조사할 필요성이 있다.

Keywords

References

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