An Investigation Of Students’ Understanding Of Derivative

In order to investigate students’ understanding of derivative from the perspective of multiple representation.This paper intends to answer two questions.First,what are the categories of students’ representations of derivative? What kind of representation do students use most? Second,how do students perform in the four representations(Symbolic,Graphical,Verbal,Physical)? In order to answer the above questions,this paper uses Zandieh’s theoretical framework based on derivative,and adopts the survey method,text content analysis and interview method.After investigation,we got these conclusions.First,There are nine categories of students’ representations of derivative:definition,graphical,verbal,symbolic,applied,thought method,association,nature,and emotional attitude.Among them,students use the verbal representation most,followed by the definition,the symbol representation and the applied representation.Second,students performed best in symbolic representation,followed by graphical representation,and inferior in verbal and physical representation.Students tend to confuse the concepts of slope,rate of change,and velocity.There are no sex differences at all three levels of these four representations.Third,for symbolic representation,Students performed no differently in the ratio layer than in the limit layer,and performed the worst in the function layer.The students in honors class are better than the regular class at the limit layer.For image representation,there are no difference in the ratio and limit layers,with the function layer performing the worst.Students in honors class performed better than the regular class in the ratio level.For verbal and physical representations,students performed better than the ratio layer at the limit layer and worse at the function layer.The students in honors class are better than the regular class students in the ratio class.Last but not least,the author summarizes some typical problems by analyzing students’ questionnaires and interviews,and puts forward some suggestions for derivative teaching based on the above conclusions.