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大家知道在坐标平面内,用代数知识解、证几何题的方法叫坐标法。如果把这个思维过程称作坐标法的正向思维的话,那么就把与之相反的思维过程——即在坐标平面内,用几何知识解、证代数题的思维过程称作坐标法的逆向思维。解析几何教材系统地阐明了坐标法的正向思维而对坐标法的逆向思维只字未提。对学生长期进行这种单向思维训练,势必造成他们思想方法上的缺陷。他们只会用坐标法解证几何题而不会(也未必有这种企图)用坐标法解证代数题。85年高考理科第八题就是一个最有说服力的证据。
We all know that in the coordinate plane, the method of using algebraic knowledge to solve geometric problems is called coordinate method. If this thinking process is called the forward thinking of the coordinate method, then the opposite thinking process - that is, in the coordinate plane, the thinking process of solving and verifying algebraic problems with geometric knowledge is called reverse thinking of the coordinate method. . The analytical geometry textbook systematically illustrates the positive thinking of the coordinate method and does not mention the reverse thinking of the coordinate method. The long-term training of students in such one-way thinking will inevitably cause defects in their methods of thinking. They will only use the coordinate method to solve the geometry problem and will not (and may not have such an attempt) use the coordinate method to solve the algebra problem. The eighth question of the 85th college entrance examination science is the most convincing evidence.