层次性在数列极限教学的应用

Application of hierarchy in the limit of a sequence of teaching

微积分是以极限为基础的，极限概念又由函数概念与哲学观点所形成。在对极限的教学中，总是在放弃讲解或花大量的时间来讲解之间选择。以函数的视角来看待数列，结合层次性的观点，将整个极限的概念分为两个层次，将自变量与因变量的趋势分开来讲解。理解自变量的“越来越大”与因变量到常值距离“越来越小”的这两种趋势其中的一个，整个数列极限的概念便建立起来。为了加深理解，结合一个具体的例子进行讲解。这对于一个初学者来说，懂得用数学语言来精确描述日常用语，已经是很大的进步。将这种方法应用在教学过程中，一个学时便可以建立极限过程。

The basis of calculus is the limit, the concept of function and philosophical point of view constitute the concept of limit. We explain the concept of limit, or by means of giving up to explain either spending a lot of time to explain. Function with a view to recognize the sequence, combined with the level view, the whole concept of limit will be divided into two levels. The independent variable and dependent variable are separated to explain the trend. Understanding the trend of one of＇More and more＂ independent variables and dependent variables to the constant distance ＂smaller and smaller＂, the whole concept of limit of a sequence is established. To further understanding the abstract concepts, we combine with a specific example to explain. For a beginner, learning to use mathematical language to describe precisely the everyday language, is a big progress. The application of this method in the teaching process, a school can establish the limit process.