Research On The Understanding Level And Influencing Factors Of Derivative About High School Students

In recent years, the slogan of "teaching for understanding" gradually became a basic task of classroom teaching, people more and more attention to the cultivation of students' ability of mathematical understanding. Although the understanding of general meaning is not abstract, the comprehension of a certain knowledge is vary between people, we are puzzled about comprehension which depends on the degree of acquiring knowledge,especially the degree of obtaining a certain knowlege by students,obviously,we are lack of clear cognition. The creating of Calculus provides important method and means for the study of variables and functions, the concept of derivative is one of the core concepts of calculus, it has abundant practical background and extensive application. Meanwhile, as the great changed content which have taken place in the curriculum reform, derivative has widely caused the attention of the mathematics education workers. So in this paper, the derivative will be a breakthrough point for exploration about students' understanding of the content of the derivative level and influencing factors.Through the analysis of previous research and the university entrance exam questions, The study designed derivative test, students' non-intelligence factors questionnaire and teacher questionnaires, about400 students and more than 30 teachers had participate in these field test and the survey; According to the survey data of quantitative and qualitative analysis, we have got the following conclusions:One is the students' understanding of the derivative level. Through the application phase, object, scheme of derivative understanding situation and comprehensive comparison or analysis of three stages,we show the following conclusions:(1) the students' understanding of the derivative geometric meaning level is higher, but have the lowest levels of the average rate of change and concept of derivative;(2)For students,the difficulty in understanding the concepts of average rate of change and derivative is know the relationship between derivative and the instantaneous rate of change;(3)the student's understanding of derivative geometric meaning the difficulty is that the geometric meaning of derivative intuitiveunderstanding;(4) the students understanding of derivative application level at the lowest level;(5) the students' understanding of the derivative geometric meaning and derivative application is not built on understanding of the concept of derivative, but merely to derivative fixed program to solve the problem of the function of memory.The other one is the factors influencing understanding level of students about derivative:(1) the students understanding of the average rate of change of knowledge and student non-intelligence factors such as self-confidence on its derivative understanding level;(2) the teachers' knowledge level, teaching method and teaching material processing ability and so on;(3) the order of teaching materials, presentation and the influence of column setup;(4) the derivative of the influence of the content itself is abstract.Based on the conclusion of this study as well as the problems found during the process of data analysis, we have some concrete suggestions for the standard setters,textbook writers and teachers. In the end,there are some reflection of problems existed in this research.