A Survey Of Senior High School Students’ Understanding Of Derivative Concept

With the deepening of function application,calculus emerged as the times require.It is another great creation after European geometry and can be called a milestone in the history of mathematics.Derivative is one of the core concepts of calculus.It is the most powerful tool to study the nature of functions and solve practical problems.As the focus of derivative teaching,mastering the essence of derivative can effectively reduce the difficulty of students’ learning function and enhance their ability to build derivative model.Mathematics comprehension is a topic that educators pay more attention to after problem solving.In order to understand the high school students’ understanding of the concept of derivative,I have compiled a questionnaire suitable for this study through the analysis of literature and chooses three parallel classes of senior high school students in Gu’an County of Langfang City for collective test.After the test,three students with different learning performance and four front-line teachers were interviewed.The questionnaire is mainly designed from one essence(the essence of derivative),two dimensions(change rate and derivative meaning),six knowledge points(average change rate,instantaneous change rate,limit thought,physical meaning,geometric meaning and formal meaning of derivative).It mainly investigates the following two questions: 1.What problems do senior high school students have in understanding the concept of derivative.2.What are the main reasons why senior high school students have difficulty in understanding the concept of derivative.Based on SOLO classification theory,the data of the questionnaire are sorted out and analyzed.The conclusions are as follows: 1.The students’ understanding of the essence of derivatives is low,only 23.1% of the students understand that the essence of derivative is the instantaneous change rate,and most of the students misinterpret them as slope;2.The students have a higher understanding of the average change rate,a lower understanding of the instantaneous change rate,students are more inclined to use derivative calculation to deal with the problem of instantaneous change rate;3.Students know little about the limit thought;4.Students have a low understanding of the physical and practical significance of derivatives;5.Students do not understand the formal meaning of derivatives thoroughly,most students cannot understand the consistency of formula increments,and cannot flexibly transform them;6.Students have a good grasp of the geometric meaning of derivatives.Combining with interview records,the reasons for these problems are analyzed: 1.The limitation of examination content;2.The problem situation is not rich enough;3.The students’ high-level thinking ability is weak;4.The teachers’ lack of infiltration of extreme thinking;5.Students’ knowledge reserve is limited and their participation in class is low.In view of the above problems and the causes of the problems,some teaching suggestions are put forward: 1.Strengthening the infiltration of mathematical thinking and methods;2.Enriching problem situations;3.Strengthening the connection between derivative concept learning and life practice;4.Give full play to the main role of students;5.Introduce the development history of calculus appropriately;6.Teaching derivative concept based on APOS theory.Finally,based on APOS theory,this paper designs three teaching cases of derivative concept.