A Study On The Common Mistakes Of Senior High School Students In "Derivative Application"

Derivatives are the limits of the increment of the dependent variable and the increment of the independent variable when the increment of the independent variable approaches zero.In high school mathematics courses,the derivative is an effective tool for solving problems such as function,inequality,analytic geometry,sequence and life optimization.The use of derivative problem solving,the complexity of the problem is simple,can quickly and accurately solve the problem,but high school students in the "derivative application" often made many mistakes have seriously affected the smooth settlement of related issues.The purpose of this study is to understand the common errors and causes of the knowledge of the third part of the student's learning derivative,especially the derivative application of the derivative application,to provide teachers with simple and effective teaching suggestions,to improve the score of the comprehensive problem of derivative application,and to improve the students' self-confidence,For students to enter a higher level of learning to prepare.This paper studies the post-homework and test paper of "derivative application" of senior high school students by means of works analysis and test paper analysis,and draws the common errors and their causes in the application of "derivative application" of senior high school students.Mainly for the performance:(1)Knowledge error.Including the concept of ambiguity,meaning to understand the error,the algorithm is not accurate memory,ignoring the implied conditions.(2)Logical errors.Including false proof,necessary and sufficient conditions.(3)Strategic errors.Including the classification standard is not uniform,the conversion problem is not equivalent,difficult to construct function,the combination of inaccurate figures.(4)Psychological errors.Including fear of hardship,local sense of accomplishment caused by the error.Through the literature research and interview analysis of the reasons for the students have the wrong,put forward the following teaching suggestions:(1)attention to basic knowledge to explain and learn,focusing on the distinction between individual concepts(at a certain point of the tangent and a point of the tangent,extreme points andcan not be guided,seeking the monotonic interval and the function of the monotone function Value range as an example);(2)attention to summed up a comprehensive review,the main corresponding conditions(to arbitrary,the existence of the problem as an example to do so.);(3)in-depth analysis of the problem,pay attention to method selection(to constructor,classification discussion as an example to focus on);(4)concerned about the mental health of students.