Search For The Teaching Of The Concept Of Limit In The High School

Both the mathematical teaching in the high school and the university, the concept of Limit is one of the most important concepts, and is also one of the most difficult concepts to the students. Since 2004, the current teaching material has been promoted in the high school in Sichuan Province, from which we can see that the teaching of the concept of Limit has already been attenuated. The concept describes its definition with the non-formalized language, so the author holds the opinion that it is necessary to discuss how to design the teaching of Limit, especially how to deal with the relation of the two different teaching methods about the non-formalized language and the formalized language. This article reviews the process of the concept of Limit teaching, makes some comparison between China and the West, analyzes the requirements of Limit in the new program and the test explanation, and then makes some discussion about the Teaching strategy and Teaching design in the high school. On the one hand, it advocates we should carry out teaching according to the teaching material instructed by non-formalized concept of Limit; on the other hand, we should supplement the formalized definition of Limitε- Language Definition Teaching, based on the non-formalized teaching. To contrast these two kinds of teaching designs, after class, I made some comparison on the differences and similarities through some surveys to the students, such as the methods of examinations and questionnaires and so on. To those who have the psychological barrier during the learning of Limit, I made some detailed analysis, hoping to enable the students to deepen the understanding of Limit and construct their own knowledge system initiatively based on their own experience of life and knowledge, and trying to study the different influence of the teaching of Limit on Derivative from the macroscopic angle during the high school. To sum up, I have got the following conclusions and enlightenments:1. The concept of sequence of number Limit is one of the most difficult points. In order to enable the students to understand and grasp this concept well, we should strengthen the intuitive teaching, by analyzing some basic sequences.2. Through experiments and studies, during the present high school teaching material, learning Limit does not influence the derivative study greatly.3. The teaching of Calculus should be avoided being tought only by memorizing some formulas and conclusions.4. During the process of teaching in middle school, we should not pursue the formalized definition excessively but should let the students construct their own knowledge structure willingly.