A Survey Of Pre-Concept For School Students In Changshu

The survey is for the Senior Three students who will attend the 2007 College Entrance Examination in Jiangsu Province and those new students who went into Senior Two last September. We choose 1242 students from four schools, include eleven Senior Two classes and twelve Senior Three classes. We mainly use the way of doing questionnaire and talking with the students. The things we observed are:( I ) The idea about limit among middle school students. (II) The use of limit when the middle school students solve their problems. (III) Their knowledge of infinite. (IV) The conception of one-to-one corresponding.The results show that: ( I ) Their ideas about limit are:(1)In their mind, the idea about limit in daily life is the number that refers to the maximum or close to but cannot surpass it. But when we use the concept of limit in our everyday language, sometimes, we cannot make sure whether it exits or not.(2) Students can understand the simple change of number series, but they cannot understand the meaning of these words correctly: n is big enough, tend to, go on doing, finally, etc.(3) The middle school students have not got a good combination about the two sides of the concept on limit. When they meet with the limit, sometimes, they only pay attention to its?infinite process, but cannot understand that it is a stable result ( 0.9 );sometimes, it is in theopposite way.( II ) We do not make the use of limit be widely accepted and spread in our teaching process. Students are not familiar with the idea. They have difficulty in solving the infinitely small about algebra problems.(III) Their knowledge of infinite are as follows:(1) In their mind, almost everyone thinks that ∞ is an infinitely great real number, and it can be used as the real number to have the four fundamental rules.(2) When they do the exercises on infinite, they will use the way of finite set to deal with them unconsciously. When solving infinite problems, they usually depend on their feeling or logical judgement and do not have further understanding about its real meaning.(3) If we use infinite set as a whole in solving problems, many students can accept it. At this time, they will pay more attention to the whole and neglect the infinite of the set itself.(IV) Students do not have a deep understanding of one-to-one corresponding.At last, from the results of this survey, I'd like to say something about the course of infinitesimal calculus. But because of my limited ability and the shortage of time, there are still some problems to be discussed. For example, are there any differences between boys and girls when they are talking about the fore-concept of limit, how to correct students' misunderstanding about limit, etc.