有向线段数量公式是解析几何的理论基础 ,让学生掌握这个公式的证明是这部分教学的基本要求 ,然而 ,现行课本中介绍的那种分六种不同情况逐一推证的做法 ,高二学生较难理解和接受 ,实践证明 ,绝大多数的同学学完中学平面解析几何以后仍然只能停留在知其然而不能真正知其所以然 The formula for the number of directed segments is the theoretical basis for analytic geometry. The proof that students can master this formula is the basic requirement for this part of the teaching. However, the current textbook describes the practice of classifying each of the six different situations. Difficult to understand and accept, practice has proved that the vast majority of students still can only stay in the know after learning the plane of analytical geometry but cannot really know why