毕业论文：不等式证明问题的若干解题方法教学研究.docxVIP

第 PAGE 3页 PAGE 不等式证明问题的若干解题方法教学研究 中文提要 不等式的教学是高中数学教学的一个重点问题，也是历年高考的考核重点。可以独立出题作为大题的第一或第二题，也可与数列函数综合在最后两题中出现。与其他知识点联系密切。不等式的教学可大致分为两种，一是解不等式的教学，一是不等式证明的教学。本文就不等式的证明进行教学研究。通过对五种不等式证明的典型技巧性方法的研究，设计教学方案，希望能够通过专题教学的方式加深同学们对不等式的理解，并能够灵活运用各种技巧解决较为复杂的不等式证明问题。主要论文设计内容分为两步，一，挑选出高中不等式证明的五种典型方法：公式法，放缩法，数学归纳法，导数法以及变量代换法。加以介绍。二，进行教学研究，研究成果通过制作教学设计展现，分为两课时进行教学，教学内容主要是方法讲解，方法的使用条件，方法运用（配以例题），以及最后通过总结，归纳出方法的选取原则。 关键词：不等式证明 方法 高中教学 Abstract The teaching of inequality is a key issue in high school mathematics education and it is also the highlight in the College Entrance Examination every year. The inequality problem could either occur independently in the first two problem-solving questions, or integrate with sequence and function in the last two questions. The inequality is related closely with other knowledge and its teaching can be broadly divided into two parts: one is inequality-solution and the other is inequality-proving. The article is committed to research the teaching method on inequality-proving problems. Designing the teaching plan by researching five kinds of typical skills on inequality-proving approaches, and the aim is to deepen the students understanding on inequality related problems by the way of thematic teaching method as well as could use various techniques to solve more complex problems flexibly on it. The main content includes two steps. The first step is introducing five kinds of typical methods selected from high school inequality-proving knowledge; they are formula method, scaling method, mathematical induction method, derivative method and the variable substitution method. The second step is carrying out teaching research. The production of research is shown by the teaching plan and it will takes two periods of teaching to explain the methods, conditions of using the methods, the applying of the methods (together with examples) as well as how to choose a suitable method to the certain problem by summing up the key points. Key Words: the proof of