Survey Study On The Current Situation Of High School Students' Derivative And Its Application

As we all know,calculus is an important mathematical discipline.Undoubtedly,it will be very beneficial for high school students to know and master a little preliminary knowledge of calculus.They will not only appreciate the convenience of calculus in studying the properties of various functions and solving real-reality problems,but also learn the idea of dialectic unity in calculus.Moreover,students can learn to analyze and solve problems using a calculus perspective which will expand their vision and improve their mathematical accomplishment,laying a solid foundation for them to study calculus in the future.New curriculum proposes goals and requests in teaching the chapter of derivative: Calculus teaching should focus on the essence of the concept of the derivative and avoid learning it as a few calculation rules and steps with its fundamental idea and value ignored.Calculus teaching should help students to understand the values of calculus in science,application and promotion of the human culture development through studying calculus.However,some unsatisfying phenomena have been found in teaching reality.On one hand,students simply rote what they learn with ambiguous understanding and cannot truly perceive the essence of the concepts of limit and derivative.The transfer ability of acquired knowledge is very limited.On the other hand,teachers feel the scarcity of their knowledge reservoir,but face the conflicts in continuing education and teaching tasks which cause teaching simply focuses on training students with the skills of solving specific problems to cope with exams and ignore their long-term development.These phenomena are the main motivation of conducting this study.This study was conducted through multiple perspectives and “trinity” questionnaire surveys and interviews(high school students,high school teachers as well as college teachers)after doing a comprehensive literature review.This is the main novelty of our study.Previous studies only focus on surveying and interviewing students and teachers in high schools,and few involve college teachers.Through questionnaire surveys and interviews,we mainly aim to understand:(1)Students: students' mastery status of the idea of limit and comprehension of the concept of derivative;the ability of students in correctly interpreting the practical meaning of derivative in solving real-world problems;the depth of their understanding of the geometric meaning of derivative;as well as their mastery status of derivative calculation and derivative application.(2)High school teachers: How math teachers in high schools deal with the content closely related to derivative,such as the concept of limit and the development history of calculus;whether there are phenomena of book worship and limited vision in teachers;their experience and feeling in teaching the content related to derivative and their good suggestions for educational reform of mathematics.(3)College teachers: the experience and feeling of college teachers in teaching the students who have already mastered preliminary knowledge of calculus;their reasonable and feasible suggestions for educational reform of high school mathematics.Based on the statistical analysis of the survey data we acquired,we made the following conclusions: Students' mastery of the concept of limit is not satisfying;Their understanding of the essence of derivative is not deep enough.Their understanding of the geometric meaning of derivative is no not comprehensive.We found that students have a good mastery of derivative formula and calculation rules and have a preliminary ability to solve practical problems using derivative.We also found that teachers barely touched "the history of mathematics" in their teaching and did very little to emphasize the importance of the concept of limit.Teachers pay more attention to calculation than to the comprehension of basic concepts,and most of them just maintain their teaching ability at the same level without much improvement.Based on the problems found in survey and the interviews of college teachers,we provide corresponding teaching suggestions.Teachers should devote much attention to the introduction of limit theory and concepts and emphasize students comprehend the essence of derivative in classrooms.Teachers should change their philosophy,expand their understanding and vision,and have a sense of times and urgency.We hope these teaching suggestions will provide students and teachers valuable information and reference.