Research On The Level Of Understanding Of Derivative And Its Applications In High School

Derivative and its application is one of the important parts of mathematics learning in high school.Students spend a lot of time and effort to practice,but it is still difficult for them to reach a high level of understanding of the derivative knowledge,resulting in serious loss of scores in the college entrance examination.Therefore,this study explores the understanding level of derivative and its application of high school students based on the Pirie-Kieren model for the dynamical growth of mathematical understanding.This paper uses the questionnaire survey and interviews method to carry research,the understanding level of derivative and its application of high school students is tested,which is based on the Pirie-Kieren model for the dynamical growth of mathematical understanding.With the help of SPSS25.0 statistical software for data analysis,and combined with interviews with teachers and students,this paper analyzes students' understanding of derivative knowledge and its influencing factors,and further understands high school students' understanding of derivative and its application,the following conclusions are drawn:One is the students' understanding level of derivative and its application :1.Students have a low overall understanding of the concept of derivative.Most of the students are not clear about the relationship between the average rate of change,instantaneous rate of change and the concept of derivative,the students' understanding of the limit is wrong,and they don't understand the development of the concept of derivative.2.Students have a high level of overall understanding of the derivative application.More than 40% of the students have reached the understanding level of the derivative application,and mastered the relevant knowledge of the derivative.students' understanding of the derivative application has reached the requirements of the curriculum standard.3.The students' understanding of the concept of derivative is not deep enough,or there are some errors,which have little influence on the problems related to the application of derivative;Students better understand the situation in the derivative applications,it does not mean they have a real understanding of the concept of derivative.Second,factors that affect students' understanding level of derivative and its application:1.The concept of derivative itself is difficult to understand.Due to the complexity of the concept of derivative,students cannot view correctly the formation process and results of the concept of derivative,therefore,it is difficult for students to form a correct understanding.2.The teacher's teaching schedule.The teacher's teaching process of the concept of derivative is too fast,and students' needs are not fully considered.As a result,students don't fully understand the concept of derivatives,which affects their learning of the application of derivative.3.Test emphasis on the application of derivative.Both teachers and students take the college entrance examination as the guide,take the derivative application as the important content and neglect the learning of the derivative concept,which makes it difficult for students to form a correct view of the derivative.Based on the conclusions of this study and the problems found in the process of data analysis,this paper puts forward some specific suggestions for teachers' teaching.