常用的数学思想有:等价变换思想、函数思想、方程思想、数形结合思想、分类讨论思想、对称思想、组合思想等.在日常教学或高三复习过程中不失时机的培养学生用数学思想解题的意识和能力,可以大大开阔学生的思路,提高以数学思维能力为核心的数学能力,有利于培养学生思维的严密性和敏捷性.下面着重介绍前四种数学思想.一、用等价变换思想解题人们在解决问题时,对未解决的问题作等价或非等价变换,使之逐步转化为已解决的问题,达到化繁为简,化难为易,这样我们容易看出新意,理出思路.所谓等价变换是指两个数学命题 A 和 B,如果 A和 B 互为充要条件,那么由 A 变到 B 就是等价变换,如方程和不等式中的同解变换就是等价变换.否则就 Common mathematical ideas include: equivalent transformation ideas, function ideas, equations, combined ideas of number and shape, classification and discussion ideas, symmetry ideas, combination of ideas, etc. In the daily teaching or third-year review process, the opportunity to cultivate students to solve problems with mathematical thinking Consciousness and ability can greatly broaden the students’ thinking, improve mathematics ability with mathematics thinking ability as the core, and help develop the rigor and agility of students’ thinking. The following focuses on the first four mathematical ideas. First, use equivalent transformation. In solving problems, people solve unsolved problems by making equivalent or non-equivalent changes to unsolved problems, so that they can be gradually transformed into solved problems, and they can be simplified and simplified, and it is difficult to change them. This way we can easily see new ideas. Rationalize the idea. The so-called equivalent transformation refers to two mathematical propositions A and B. If A and B are mutually sufficient and necessary conditions, then changing from A to B is an equivalent transformation, such as equations and inequalities in the same solution transformation is Price transformation. Otherwise