Research On The Teaching Of Conic Curve In High School Under Freidenthal Theory

According to the requirements of the new curriculum standard,high school mathematics teaching should be core quality oriented,pay attention to the students’ position,and cultivate students’ ability to solve problems.In high school mathematics,the contents of conic curves connect algebra and geometry.And it is very important,highly abstract and comprehensive.Freidenthal’s theory emphasizes that mathematics teaching should take students’ “mathematical reality” as the growth point and “re-creation” as the teaching method,so as to cultivate students’ mathematical ability.This is not only coherent with the requirement of mathematics teaching in the new curriculum standard,but also can provide guidance for the class teaching of the conic curves.Firstly,this thesis analyzes the existing research results of the theory and the conic curves.We found that the researches on the combinations are not comprehensive,and most of the literature focuses on the research of a certain idea in Freidental’s theory in the teaching of a certain type of questions.Secondly,combining with the teaching practice,it analyzes the contents of the Freidental’s theory and the current new curriculum standard and the history of conic curves.Based on the relevant research of Freidenthal’s theory and the knowledge of conical curve,the questionnaires of students and teachers are designed from five aspects.According to the statistics of the results,we found that:(1)there are still deficiencies in conic curve teaching in some senior high schools,which are mainly manifested in that it is difficult for teachers to arouse students’ enthusiasm by the lead-in activities,the frequency and time of students’ independent inquiry need to be optimized,and the summary methods are in single form;(2)High school students are looking forward to a more life-style and independent inquiry class;(3)Although high school mathematics teachers hold a positive attitude towards integrating educational theories into classroom teaching,the understanding and application of the theory still need to be strengthened.According to above findings,some suggestions are put forward for students’ learning and teachers’ teaching.Specifically,the thesis provides the following suggestions of conic curves teaching:(1)The teaching of conic curves can be introduced from the classroom combining students’ mathematical reality and mathematical history;(2)High school students’ mathematical level training can be based on life problems;(3)The lead-in can consider problem-driven independent inquiry activities.As application of above teaching strategy,the thesis gives the teaching design on the first sections of hyperbola.Based on Freidenthal’s theory,this thesis proposes suggestions on teaching of conic curve,and gives an example of the teaching design.In addition,we hope to help students participating in the class,and lay a solid foundation for conical curves learning through the improvement of the teaching methods and ideas.