递推数列通项公式的教学设计.pdfVIP

递推数列通项公式的教学设计 目录 1 引言2 2 相关理论基础3 2.1 弗赖登塔尔的“数学化”理论 3 2.2 布鲁纳归类理论4 2.3 皮亚杰的建构主义理论 4 2.4 奥苏贝尔的有意义学习理论 4 3 常用方法概述5 4 常见递推数列通项公式的推导及使用 6 4.1 作差求和法6 4.2 作商求和法6 4.3 换元法6 4.4 积差相消法7 4.5 取倒数法7 4.6 取对数法8 4.7 平方（开方）法8 4.8 待定系数法8 4.9 猜想法10 5 教学设计 12 6 总结15 参考文献16 致谢17 递推数列通项公式的教学设计 专业：数学与应用数学 学号：201413008188 学生姓名：肖祥彬 指导老师：钟祥贵 职称：教授 【内容摘要】在课本《数列》的整个篇章中，学生学习的难点就是如何求得整个 数列的通项公式，同时这也是本章的一个十分重要的知识点。在实际遇到的题型 中，有些数列，再给出首项和递推的公式后，发现他们不是等差或等比数列，这 时候怎么样求得数列的通项公式就是问题的关键了。在这里，我们教导大家如何 使数列明确化，并且就大多数递推数列的种类及各种类间的通项公式求解方法做 一一谈论，让同学们能够熟悉了解并能解决类似的问题，通过所掌握的一些常规 方法，把各种递推关系往等差或等比关系上靠，体会从特殊到一般和化归两种思 想方法。 【关键词】 递推数列;教学设计;数学方法;通项公式 【Abstract 】In this chapter, how to find the general terms of series is an important problem, and it is also a difficult point for students to learn. In practice, some series are neither equal nor equal. After giving the first term and the recurrence formula of the sequence, how to find the general term formula of the sequence is often the key. This paper makes an analysis of the common recurrence sequence type and the calculation method of the general term formula of each type in order to make the sequence clear. In order to solve the related problems, this paper mainly let students use the recurrence relation of the series to solve the general formula of the recursive series, master some commonly used mathematical methods, experience from the special to the general thinking method, let the Students learn how all kinds of recurrence relations change in the relationship of equal difference or equal ratio , and realize the thought method of normalization . 【Key words 】Recursive sequence; instructional de