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对于广大中学数学学习者,一定无法避免对于解题方法的研究,一题多解,一解对应多题,都是十分常见的现象。如何在更短的时间内找到一道题的最优解,或是将同类型题目归纳在一起,亦或是解决一道竞赛题,理解主要的几类数学思想一定可以让你事半功倍。广义上的数学思想大概包括这几类;符号思想,映射思想,化归思想,分解思想,转换思想,参数思想,归纳思想,类比思想,分解思想,模型思想。其中,转换,化归与映射又可以归为一类,在这里我们暂且称它为转化与化归思想,而符号思想与模型思想可以统称为模型思想,对于这些思想在解题上的运用,我们将结合具体实例来分析。
For the majority of middle school mathematics learners, we must not be able to avoid the study of the problem-solving method, which is a very common phenomenon. How to find the optimal solution of a question in a shorter period of time, or to summarize the same type of questions together, or to solve a competition question? Understanding some major types of mathematical thinking can definitely help you to do more with less. The generalized mathematical thought probably includes these kinds; the symbolic thinking, the mapping ideology, the transformation of thought, the decomposition of thought, the transformation of thought, the argument of thought, the inductive thought, the analogous thought, the decomposition of thought and the model thought. Among them, conversion, conversion and mapping can be grouped into a category, here we call it conversion and conversion for the time being thinking, and symbolic thinking and model ideas can be collectively referred to as the model idea, for these ideas in the use of problem solving, We will combine the specific examples to analyze.