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统编教材第三册,以一节书的篇幅介绍了数学归纳法,这是因为数学归纳法是一种重要的推理方法,它在初等数学和高等数学中都有广泛的应用。让学生在中学学习阶段就懂得数学归纳法的原理,掌握它的证题方法是十分必要的。这对于提高他们的逻辑推理能力、解题能力和进一步学习都有很大的好处。鉴于中学生的基础知识不宽和教学时间有限,在学生初次接触数学归纳法时,不宜将数学归纳法证题的各种“变着”(如反向归纳法、翘翘板归纳法等)和盘托出,讲得过深过难。而只能使学生懂得数学归纳法的基本原理,掌握它的一般证题方法。要实现这一教学目的,笔者认为在教学过程中必须抓好三环。即讲清数学归纳法的形成过程(即数学归纳法是怎样总结出来的),熟练三类基本题(即恒等式、数列的通项公式和整除问题)的证法,以及在后续的教学中适当的引伸和经常应用。
The third volume of textbooks was compiled and the mathematical induction was introduced in the length of a section of the book. This is because mathematical induction is an important method of reasoning. It has extensive applications in both elementary and advanced mathematics. It is very necessary for students to understand the principles of mathematical induction at the stage of secondary school and to master its method of testifying. This has great benefits for improving their logical reasoning ability, problem-solving ability and further learning. Given that the basic knowledge of middle school students is not wide and teaching time is limited, when students first come into contact with the mathematical induction method, it is not appropriate to include all kinds of “variation” (such as inverse induction, seesaw induction, etc.) of mathematical induction test questions. It’s too hard to tell. Only students can understand the basic principles of mathematics induction and master its general method of certification. To achieve this teaching goal, I believe that we must do a good job in the teaching process. That is, to clarify the formation process of mathematical induction (that is, how mathematics induction is summarized), to be proficient in the verification of three basic problems (ie, identity, general term formulas for series, and integer divisibility issues), and appropriate in subsequent teaching. Extensions and often applied.