化归思想在中学数学解题中的应用  

The Application of Naturalization in Middle School Mathematics Problem Solving

作　　者：韩佳航 刘君[1] 

机构地区：[1]北华大学数学与统计学院,吉林 吉林

出　　处：《理论数学》2024年第3期9-18,共10页Pure Mathematics

摘　　要：“化归”思想在数学解题中有多种形式,其主要作用是将问题的解决由复杂变为简单,由抽象变为具体。化归思想在数学教学中的应用也很广泛,如利用化归思想解决数列问题、不等式问题、方程问题等,尤其是在一些综合性较强的问题中,常常会把若干个相关的知识综合在一起,通过各种转化把它们统一到一个整体上来分析研究。本文首先介绍了研究的背景和意义,说明了研究的重要性。其次阐述了化归思想的概念和基本原理,以及化归思想方法在数学解题中的原则,同时提出了化归思想的一般模式。接着从中学数学中的不同领域出发,分别探讨化归思想在函数、数列、不等式等方面的应用。The idea of naturalization has many forms in mathematical problem solving, and its main function is to change the solution of the problem from complex to simple, from abstract to concrete. The application of naturalization thought in mathematics teaching is also very wide, such as the use of naturalization thought to solve the problem of number series, inequality, equation, especially in some comprehensive problems, which often will synthesize several related knowledge together, through a variety of transformation to unify them into a whole on the analysis and research. This paper first introduces the background and significance of the study, explains the importance of the study;then elaborates the concept and basic principle of naturalization thought, as well as the principle of naturalization thought method in mathematical problem solving, and puts forward the general mode of naturalization thought;next from the different fields of middle school mathematics, respectively explore the naturalization thought in the function, series, inequalities and other aspects of the response use.

关 键 词：数学教学 化归思想 解题应用 

分 类 号：G63[文化科学—教育学]