Teaching Research On The Concept Of Derivative About High Students

With the development of curriculum reform, some of the university curriculum content inSenior High School. Considering the students understanding of the development of law,learning calculus in high school is not only necessary but also feasible. High school studentsstudy calculus can feel the idea and method of variable mathematics again, form the rationalthinking and lay a solid foundation for the future study. The new curriculum standard points out:calculus teaching should highlight of the concept of derivative essence; pay attention to thepenetration of mathematical way of thinking; value the cultivation of students’ applicationconsciousness; improve the students’ mathematical thinking ability; reflect the Mathematicseducation value and cultural value.This paper, based on the analysis of the calculus teaching in middle schools of China andsome other countries, through the combination of literature investigation、questionnaire andinterview survey method, carry out the research to the learning of derivative and its applicationof high school students, which includes the following three aspects:(1)teacher and students’point of the adjusted teaching material.(2)high school students’ cognizing on derivative concept.(3)students’ ability of solving practical problems of derivative.Through the analysis of questionnaire survey data and the summary of interviews survey,we get the following results:(1) High school students are not clear to the cognizing onderivative concept. Students don’t understand instantaneous variation is the limit of the averagerate, can’t tell the meaning of the geometrical significance of derivative in different background,have no idea about the essence of the derivative definition, can’t transform the image of originalfunction and derived function vividly.(2) High school students are not enough clear about thelimit thought.(3) Students’ ability to solve practical problems with derivative is low.According to the survey results, and connecting with the teacher’s interview survey, wefind on the main reason. To the teaching of derivative, this proposes five suggestions forimprovement: pay attention to the formation process of derivative concept, highlight theconcept of derivative;pay attention to the creation of the limit thought; emphasize the trainingof students’ ability of solving practical problems with derivative; attach importance to the history of calculus, excavate the cultural value, stimulate students’ interesting in learning;enhance the ability of teacher, change the point of view about teaching, improve the teachingreform. In the end, we put forward the new teaching design to the teaching of derivative.