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习题是对本章节所学知识的巩同、消化与运用。做完习题之后,应该作好习题的总结,才不致于陷入一片汪洋的题海之中。下面以高中数学第三册不等式证明一章为例,谈谈如何引导学生作好习题的总结。一、纵贯全局,总结开拓:做完习题后,首先引导学生认真回顾本章节所学内容,按照习题类型,小结解题方法,着重探求知识的运用范围,启发学生进行开拓。笔者在不等式证明一章引导学生作了如下的总结提纲。 1.不等式的概念与性质是解不等式、证明不等式的理论依据。 2.证明不等式的基本方法是比较法。分析法和综合法,遇有特殊情况,便于利用,有时可采取直接运用基本不等式、放缩法、反证法、几何法等进行变通。 3.不等式的应用: (1)求函数定义域、值域、单调区间,以及最值、极值。并用于三角、
The exercises are the concurrence, digestion, and use of the knowledge learned in this chapter. After completing the exercises, you should make a summary of the exercises so that you will not fall into a sea of questions. In the following, we will use the example of the proof of the third grade inequality of high school mathematics as an example to talk about how to guide students to make a summary of exercises. First, through the overall situation, summarize and open up: After the exercises, first guide students to carefully review the contents of this chapter, according to the types of exercises, summary method of solving problems, focusing on exploring the scope of application of knowledge, inspire students to open up. The author in the inequality proof chapter guides students to make the following summary. 1. The concept and nature of inequality is the theoretical basis for solving inequalities and proving inequalities. 2. The basic method of proving inequalities is the comparative method. Analytical methods and comprehensive methods are often used in cases where special circumstances are encountered and they can be easily used. Sometimes, basic inequalities, contractions, anti-evidence methods, geometric methods, etc. can be used for adaptation. 3. The application of inequality: (1) Find the function definition domain, value domain, monotonic interval, and the maximum and extreme values. And for triangles,