A Research On The Situation Of Senior High School Students' Cognition Of The Concept Of Limit

The Limit cognition has an extensive application in modern mathematics, as well as physics etc, which is determined by its inherent function of reasoning. It revealed the connection between opposing and consolidation, variable and invariable, infinitude and finitude, and it is the application of the rule of the universal principle in mathematics, with which, we can explore the infinitude. from finitude, change from settlement, curve from line, quality change to quantity change, accuracy from similarity.Limit is the base and core of Modem Mathematics, the concept of Limit is also the keystone for senior high students, according to the teaching practice, Limit concept is the nodules for the students as well as teaching. It is just because of this, the thesis carries out a tentative research on the cognizing status of the senior high students so as to find a solution to a more suitable way for teaching the students, and put forward some constructive suggestion for conducting the teaching material.As the limitation of region and experimental condition, the author just chose two senior schools in Hubei province as the research object, one is a demonstrative school in Hubei province, and the other one is a demonstrative school in Jingmen city. To guarantee the comparativeness for different grades, students of the same levels are chosen, in this research, the top students are chosen.In this research, a sample class will be chosen in each school, so this research is not universal theoretically, and can't be applied to all the students. However, while considering the students of the same age or grade have the similar cognizing ability and knowledge structure, which makes them form the same cognizmg ability in mathematical theory, so, the misunderstanding in the concept shares some similarities. So we are confident that this research is to be the embodiment for the students' understanding on Limit concept and be of great value.The method to carry out the research is examining and conversation, after which the results is to be summed to make statistics.This thesis is to carry out the tentative research on the following two aspects:Problem I: the status of senior high students' cognizing on limit concept.In senior middle school, Whether we should use the definition of depicting or" ε - N "?" ε - N "definition is abstract and strange to students, should the dialecticrelation be understood by the students? Which one is more suitable? The thesis carries out the investigation and research on the cognizing ability of senior students, we need to find out the cognizing ability of the students to define Limit properly.Problem II: preliminary research on the difficulties and the reasons of the students' cognizing on the concept of Limit.The thesis begins with the make out the difficulties for the students in understanding the concept of limit, then it analyzes the reason form the perspectives of cognizing psychology, the formation and the essence of the concept of limit so as to put forward the corresponding suggestion for the class organization and teaching strategy.In the first part, the thesis introduces the study background and the practical purport, surveys the actuality and puts forwards the research method.In the second part, the thesis tells the definition and history of Limit and briefly introduces the current regulation on Limit.In the third part, the thesis summarizes the characteristics and forming of mathematical definition.In the forth part, the thesis analyzes the students' cognizing on the concept of Limit.In the fifth part, the thesis focuses on the students' difficulties in understanding the concept of Limit and then analyzes the reasons.In the sixth part, the thesis puts forwards the proposals on teaching the concept of Limit and even the mathematical teaching objectives and materials for senior high students through analyzing the difficulties and mistakes while they are learning the concept of Limit.Last but not the least, this thesis is only a tentative research on the problem and it must be very superficial, many problems needs further research:For example, what are really necessary to be mastered in senior high school? What need to be set to learn which is relevant to limit is still a question for us to research and study;How to control the stringency of the concept of limit more suitably, and the difficulties in combining teaching contents and research on the teaching software etc.