Study On The Conic Section Comprehensive Example Teaching

Conic section is one of the important knowledge points in high school mathematics,and plays an important role in high school mathematics curriculum.Its comprehensive problems cover many knowledge points,flexible solutions and complicated calculation,which bring many obstacles to students' study.In order to help students solve difficulties and learn how to resolve problems,the author launch a research of the conic section comprehensive example teaching.The premise of teaching is to select good examples,so there are two main problems in this paper:(1)good selection criteria for comprehensive examples of conic section;(2)how to teach the comprehensive example of conic section.In this paper,130 Senior High School mathematics teachers who from the NO.1 Middle School attached to Center China Normal University,Middle School attached to Wuhan University,Hankou Railway High School in Wuhan,Middle School attached to Huazhong University of Science and Technology,and 100 students from the sophomore(15)class(experimental class)and sophomore(16)class(control class)in the NO.1 Middle School attached to Center China Normal University are studied.Mainly using literature research,questionnaire survey,interview,classroom observation and testing method.First of all,through the study of the scholar' standards on good problems and the analysis of the results of the teacher questionnaire survey,interview survey,classroom observation and the actual selection of teachers and students,the selection standards of the good conic section comprehensive examples are worked out,and according to the standards some good examples of conic section comprehensive problems are selected;Then,according to the problems existing in the process of the students' problem solving and the teachers' example teaching of the conic section comprehensive problems,this paper puts forward some strategies to improve the example teaching,in order to verify the effectiveness of the proposed strategies,contrast teaching experiments are designed,and the experimental class has carried on the example teaching practice for two months based on the strategies;Finally,after the contrast experimental teaching,the two classes of students are tested and the results of the two classes are analyzed to explain the effect of the proposed strategies.Through the research the following main conclusions are obtained:(1)Teachers generally recognize the importance of the example teaching of conic section comprehensive problems,and often apply in the actual teaching process,they pay attention to guide students to analyze the questions,explore the ideas,but the exploration process of problem-solving is not clear,and the writing of the problem-solving steps is also not normative;(2)The selection standards for good examples of the conic comprehensive problems:contacting the knowledge points closely;with strong representativeness;can variant and generalize;the structure is relatively simple;(3)According to the problems existing in the process of the students' problem solving and the teachers' example teaching of the conic section comprehensive problems,the teaching strategy that based on mind map to teach the conic section comprehensive examples are proposed;(4)The conic section comprehensive example teaching strategy based on mind map can promote the improvement of students' achievement,and the impact on different levels of students is different,among them,the influence on the middle students is obvious,and the effect on the outstanding students and the poor students is not significant.