图形变换与中国初中几何课程的自然融合

On Integration Of The Three Basic Isometric Transformations (Translation,Reflection And Rotation) with Euclidean Plane Geometry in Chinese Junior Middle School’s Traditional Plane Geometry Courses

图形变换是欧氏几何的核心内容之一,但中国传统初中几何课程并不包含这些核心内容.《全日制义务教育数学课程标准（实验稿及2011年版）》都规定了图形的轴对称、图形的旋转、图形的平移等＂图形与变换＂的内容.根据中国初中几何的特点及教学的实际进展来看,线段的垂直平分线、平行四边形和圆可以分别作为图形的轴对称、图形平移和图形旋转的知识生长点,实现图形变化与初中几何课程二者的自然融合.

According to Felix Klein＇s transformation group theory, transformations of geometric figure are one of the important contents in Euclidean plane geometry. However, they are not included in Chinese Junior Middle School＇s plane geometry courses. This thesis discusses the way of naturally integrating the three basic isometric transformations （symmetry, translation and rotation） into our Chinese traditional courses as well as explores their nature and properties, thus constructing geometry courses under the guidance of geometric figure transformations.