Research On The Conceptual Learning Difficulties And Causes Of Derivatives Of High School Students

It is inevitable that students have mathematical learning difficulties in the process of mathematics learning,but how to reduce or even solve students’ mathematical learning difficulties is the focus of our attention.Therefore,investigating and exploring the root causes of mathematics learning difficulties among high school students and discovering effective solutions so that students can master mathematics more easily are of great significance to both the theory and practice of mathematics education.The concept of derivative,as one of the very important concepts in high school mathematics,not only affects students’ learning at the high school mathematics course level,but also has an important impact on students who enter university to study advanced mathematics.In addition,when students learn the content of derivative concepts,they show many problems,such as not knowing the concept of derivative,not being able to appreciate the mathematical ideas of the concept of derivative,and so on.Therefore,based on the content of the derivative concept,it is of positive significance to study the mathematical learning difficulties of high school students and analyze the causes of their difficulties in learning the derivative concept so that teachers can understand students better and then teach in a targeted way,so that teachers’ teaching and students’ learning can be full of efficiency.In this paper,the concept of derivative in high school mathematics of the Northern Normal University edition is used as the carrier,and the students in the second year of senior high school in a school in Ganzhou City are used as the investigation and research subjects.The correlation analysis as well as the difference analysis are used to explore the difficulty points and causes of high school students in learning the concept of derivative by means of student and teacher questionnaires and student test papers.The questionnaire mainly explores students’ learning attitudes,learning habits,learning methods and teachers’ teaching styles.The test paper was based on the doctoral dissertation of D.S.Qin on the level of students’ understanding of derivatives and its development pattern,and the suggestions of mathematics teachers in the author’s internship school.The test paper was divided into four levels by SOLO classification evaluation theory on students’ test paper responses,including rate of change,derivative meaning,derivative function and derivative application,and interviews with students and teachers were added to make the The research analysis reflects the problem more.From the students’ test papers,the main types of errors were conceptual confusion,calculation errors,graphing errors,and errors in the actual interpretation of derivative concepts.Finally,the analysis analyzed the causes of high school students’ difficulties in learning derivative concepts from the perspectives of male and female students,literature and science subjects.Through research and analysis,it is found that students have a vague understanding of the concept of instantaneous rate of change,a low level of understanding of the physical and formal meaning of the derivative,a lack of ability to launch the image of the derivative function from the original function,and difficulties in the practical application of the concept of the derivative.The difficulties of learning the concept of derivative for high school students are:(1)the difficulty of understanding abstract concepts;(2)the difficulty of mastering symbolic operations;(3)the difficulty of transforming the idea of derivative(4)the difficulty of using mathematical ideas and methods flexibly.According to the students’ difficulties in learning the concept of derivative,the author analyzes both from the students and teachers,and puts forward some practical strategies and suggestions to cope with them.Teachers should create a situation,contact with the actual life of the concept of derivative teaching,the use of information technology to let students intuitively understand the essence of the concept of derivative;students should develop a good learning attitude and method,face the problem to solve in time,more summary and more thinking.