Derivative Teaching Research Based On Polya's Problem-solving Theory

Derivative plays an important role in senior high school teaching.It plays a great role in the development of students' thinking,intelligence and learning in the future.This study aims to develop students' thinking ability and problem-solving ability and improve their mathematics accomplishment,as well as comprehensive quality through the application of the educational thought of mathematician and mathematics educator Polya in the derivative teaching of mathematics in senior high school in order to cultivate the students' thinking ability and problem-solving ability.In this thesis,with the help of literature researches,investigations and case analyses,combined with teaching experience and observation practice,under the background of the new curriculum reform,the present situation of derivative and its application teaching in senior and second grade are investigated and analyzed.It is known that derivative and its application teaching is one of the difficult points and important points in high school mathematics,and the content of derivative and its application teaching has a large proportion in the examination paper of college entrance examination.High school students generally feel having obstacles in the process of derivative learning,understanding of the concept is not so deep.They can not flexibly use derivatives to solve related problems.In order to overcome the difficulties that students encounter in learning derivative and its application,this thesis puts forward the teaching and solution of derivative in combination with Polya's problem-solving theory.Some strategies on the subject are proposed:1.Properly inserting knowledge of the history of mathematics to cultivate students' interest in learning;2.Clarify the function of derivative in mathematics to attract students' attention;3.Pay attention to guide students to participate in derivative and related concept formation process;4.Encourage cooperation and independent inquiry,check and fill gaps,so that students can integrate the knowledge learned;5.Help students master Polya's problem solving strategies and so on.At the same time,to the student and the teacher two aspects put forward many teaching suggestions.In order to explain the concrete applications of the teaching strategies and measures,we also give some teaching cases based on Polya's problem-solving theory,and investigate the effect of the new teaching methods.The results show that the teachers and students agree with the new teaching method and think the effect is good,and hope to further develop and promote it.The strategies,methods and suggestions put forward by us have certain reference value for the teaching and learning of derivative and its application.It is helpful to cultivate students' creative thinking,stimulate students' consciousness of exploring knowledge,and gradually improve their ability to solve problems.The structure of this thesis is divided into three parts:the first part mainly introduces Polya's problem-solving theory,focusing on the analysis of the process of solving the problem and Polia's thought of solving the problem.The second part is the investigation and analysis of the current situation of derivative teaching in senior high school.The third part is to study the application cases,analyses and teaching effect investigation of Polya's problem-solving theory in senior high school teaching.