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解析几何的本质是用代数方法研究几何问题,在灵活运用代数知识解题的同时,充分抓住问题的“几何本质”往往是解决问题的关键。长期以来,解析几何教学重模式化的代数运算,而忽视了隐藏于问题中的几何背景,使解题陷入“过程冗长,运算烦琐”的境地,导致学生“望而生畏,知难而退”。鉴于此,笔者认为,解析几何的教学要转变重代数运算、轻几何本质的现象,通过紧扣定义、揭示问题的几何本质来优化运算,回归解析几何的本源。
The essence of analytic geometry is to use algebraic methods to study the geometric problems. While using the algebraic knowledge flexibly, it is often the key to solve the problem to fully grasp the “geometric essence” of the problem. For a long time, the analysis of geometry teaching re-patterning algebraic operations, while ignoring the geometric background hidden in the problem, the problem-solving into the “long process, cumbersome computing,” the situation, leading students “daunting, ”. In view of this, I believe that the analysis of geometry teaching to change the heavy algebra operations, light geometric nature of the phenomenon, through close definition, reveal the geometric nature of the problem to optimize the operation, regression analysis of the origin of the geometry.