중등교육과정에서의 도형의 변환에 대한 연구 = (A) Study on the tranformation of figures in the middle-high school mathematics education

다국어 초록 (Multilingual Abstract)

It doest's recently begin for us to use the idea of transformation in the studying direction of a figure. If we examine the directive content of the figure used till now, the most part of it is the static of the Euclid. Although it is a kinetic content like the movement in the instructive content of a figure, ire doesn't think of it as a kinetic content, but treat only a static drawing.
However, we can't say that the Euclidean method mentioned before is not good. Obviously, it has its oirn good way. However we must firmatively introduce a kinetic movement and transformation into the instructive system of a figure, and newly need to treat it in a different view of arguments, and do need to study the instructive method to harmony both sides.
And the goal of this thesis is to analyze the educational process of mathematics in milldle-high school, connected with the theoretical background of figure transformation after examined an Euclid, an Affine, a projective, and a topological transformation and to develope an effective instruction method for students to have the interest and courage.

목차 (Table of Contents)

• 목차
• Ⅰ. 서론 = 3
• 1. 연구의 필요성과 목적 = 3
• 2. 연구방법 = 4
• Ⅱ. 본론 = 5
• 1. Euclid공간과 변환 = 8
• (1) 평행이동 = 12
• (2) 대칭이동 = 13
• (3) 회전이동 = 14
• 2. Affine공간과 변환 = 15
• (1) 확대도,축도(Extended, Reduced figure) = 17
• (2) 닮음변환(Similar Transformation) = 18
• (3) 정사영(Orthogonal Projection) = 18
• 3. 사영공간과 변환 = 19
• 4. 위상공간과 변환 = 23
• (1) 위상기하(Topology) = 24
• (2) 위상변환 = 24
• 5. 지도상의 유의점 = 28
• Ⅲ. 교육과정의 분석(도형의 변환) = 31
• 1. 중학교 교육과정 = 31
• 2. 고등학교 교육과정 = 35
• 3. 교육과정분석 = 47
• (1) 중학교 도형의 변환 = 47
• (2) 지도내용의 요소분석 = 48
• (3) 고등학교 도형의 변환 = 49
• (4) 지도내용의 요소분석 = 50
• Ⅳ. 교과서 지도의 실제 = 51
• Ⅴ. 결론 = 61
• 참고문헌 = 63
• ABSTRACT = 65