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一一映射的概念和后面将要学的逆映射、反函数、互为反函数的函数图象间的关系在内容上是连成一体的,其重点内容是反函数。反函数的实质是逆映射,而只有一一映射才有逆映射,因此,让学生正确理解一一映射的概念,是学好这四节教材的关键。由于课本编写得比较简炼,概念的引入比较突然,对一一映射的定义只是从文字上加以描述,另外,配备的例题及练习较少。对教学造成了一些困难,为此我设计了如下的教学过程。一、引出课题 1.设置情境,提出问题。“劣孤AB上的点和弦AB上的点哪个“多”?”有人说:“AB上的点多。理由是AB的长度大于弦AB的长度。”而数学家却说:“AB上的点与弦AB上的点一样多”。到底谁是谁非,如果数学家说得对的话,又该如何解释呢?要搞清这个问
The concept of one-to-one mapping is related to the inverse mapping, inverse function, and inverse function function image that will be learned in the following. The key content is the inverse function. The essence of the inverse function is the inverse mapping, and only the one-to-one mapping has the inverse mapping. Therefore, allowing students to correctly understand the concept of one-to-one mapping is the key to learning these four materials. Because the textbooks are written more succinctly, the introduction of concepts is more abrupt. The definition of the one-to-one mapping is only described in words. In addition, there are fewer examples and exercises. The teaching has caused some difficulties. For this reason, I designed the following teaching process. First, lead the subject 1. Set the situation, ask questions. “Where is the point on the point chord AB on the inferior orphan AB?” Someone said: “There are more points on the AB. The reason is that the length of the AB is longer than the length of the string AB.” And the mathematician said: “The point on the AB As many points as on string AB”. Who is right and wrong, if the mathematician is right, how should he explain it?