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常用的数学思想有函数与方程思想、数形结合思想、分类讨论思想、转化(化归)思想等,在运用这些思想解题时要注意以下问题。一、函数与方程思想所谓函数的思想,就是运用运动变化的观点分析和研究具体问题中的数量关系,剔除问题中的非数学因素,抽象其数学特征,用函数的形式把这种数量关系表示出来,并加以研究,运用函数的性质使问题获得解决的思想。这种思想方法通过对具体问题的变量的动态研究,从变量的运动变化、联系和发展的角度拓宽解题思
Commonly used mathematical thinking has the function and the idea of the equation, the number-shape combination of thinking, classification of thinking, transformation (conversion) thought, in the use of these ideas to solve the problem should pay attention to the following questions. First, the function and the idea of the equation The so-called function of the idea is to use the viewpoint of changes in the movement to analyze and study the relationship between the number of specific issues, excluding non-mathematical factors in the problem, abstraction of its mathematical characteristics, the function of this form of quantitative relationship Come out and study it, using the nature of the function to get the problem solved. This method of thinking through the dynamic study of variables of specific problems, broaden the problem-solving thinking from the perspective of the changes of the variables, the connection and the development