无穷小概念教学的5个强化

Five Reinforcements on Teaching Concepts of Infinitesimal

在研究"无穷小教学问题"的基础上,提出了"无穷小"教学的5个"强化":在概念产生过程强化概念;从几何的角度强化概念;在后续的学习中强化概念;在无穷小的比较中强化概念;在符号"o"和"O"的运算中强化概念.

All forms of function limit can be expressed by infinitesimals, and the concept of infinitesimal and function limit are actually two equivalent concepts. For this reason, we can eliminate the character of limit and transform a function question into a question of ＂number＂ by using an infinitesimal to express an function limit, which makes the question much easier and more specific, and get twice the result with half the effort. However, the concept of ＂infinitesimal＂ is a highly abstract math concept, which is involved with both ＂number＂ and ＂variation trend＂ that makes teaching and learning more difficult, consequently how to solve the teaching problem of infinitesimal is of great importance. Five ＂reinforcements＂ are proposed on the basis of the investigating of ＂the teaching probiem of infinitesimal＂ ： reinforcing the concept during the generation of it ; reinforcing the concept from the perspective of geometry ; reinforcing the concept in the following study; reinforcing the concept in the comparison between two infinitesimals; and reinforcing the concept in the operation of ＂o＂ and ＂O.＂