A Survey Of Senior High School Students' Understanding Of Derivative Concepts

Derivative is an important content of high school mathematics curriculum, and is closely related to the university to learn knowledge of differential and integral calculus, and considering the demands of high school students cognitive level and age, high school students study derivative knowledge has certain feasibility. Teaching is the foundation of learning new knowledge and concept, a concept to grasp firmly is not strong, weak, direct have a significant impact on the later calculation and application, so a lot of the math teachers reflect, concept of high school students is a serious mistake.This paper based teaching research in high school calculus at home and abroad, combined with the derivative of this section the content of the new curriculum standard of senior high school on the rate of change, through the method of literature survey, questionnaire and interview the three methods with A second middle school(two class school in a district of the city of A grade) 420 students as the research object, according to the research objective, considering the actual situation of the study on the dimensions of the questionnaire survey to determine the adjustment around the students' cognition on the concept of derivative problems, whether the students for the different circumstances of the derivative concept is clear, whether the actual situation of the students clearly identify the derivative concept, students using definition of the derivative operation whether skilled design of the "test" questionnaire for the mastery of the derivative concept, the questionnaire reliability was 0.815.Through the analysis of the questionnaire and summary, the following conclusions:(1) the student to the derivative concept understanding is not thorough, the student does not understand the essence of the concept of derivative is increment ratio, but the partial derivative is instantaneous velocity, etc.;(2) students can't accurately tell different circumstances, the concept of derivative, just on the surface that is physical movement problem of instantaneous velocity, the curve tangent slope, rather than the instantaneous rate of change in mathematics problems. Student's understanding of derivative is mechanical, not from the Angle of the infinite approach to understand. Students generally just as the definition of the derivative of the formula to memory, with the title of the same type are directly according to the fixed models in the mind to do it, do not understand the true meaning of the concept of derivative problems in different situation, it is difficult to abstract the derivative concept;(3) students can't accurately understand the actual situation of derivative, the concept of life in specific situations, students of derivative concept confusion, the application of in familiar circumstances, such as rainfall, students can more easily understand the concept of derivative, and in the case of the stranger, as in the work of the physical problems, students are more easy to understand the concept of the derivative error. And the students' mathematics generalization ability is low also makes them can't sum up the essence of mathematics in from real life background, and so cannot be applied to;(4) students without enough skills in derivative calculation of situation;According to the survey results, combined with teachers to interview survey, find out the high school students in learning derivative concept, the main reasons for the difficulties, at ordinary times in the process of test comparison pay attention to the use of the elementary function derivation formula, neglected the student to the understanding of the concept of derivative; Teachers' teaching content more from real life, is not conducive to the students understand the concepts of derivative. Thus need to strengthen the cultivation of the student to study the derivative concept habits, improve teachers' teaching level, and reasonable arrange materials reduce the students form a junior high school teaching in three aspects: the derivative error concept.