Research On The Problem Solving Teaching Of Conic Curve By Integrating The Subject Of Arts And Science

In 2014,the State Council clearly puts forward the reform requirements of integrating the subject of Arts and Science in college entrance examination,which is a hot issue of education in recent years.Therefore,in the perspective of this background,how to teach for teachers effectively and how to learn for students actively are concerned by every high school mathematics teacher and each student.Because of the strong comprehensiveness of analytic geometry,the logical reasoning ability,mathematical operation ability,intuitive imagination ability and so on are required to be higher for students.Conic curve is also an important part of plane analytic geometry in senior high school,and some knowledge points of ellipse,hyperbola and parabola are relatively close,which makes it easy to get confused for students.Therefore,this thesis will study the problem solving teaching of conic curve in the view of integrating the subject of Arts and Science,summarize relevant knowledge points,and give some suggestions for the representative teaching design of problem solving.This thesis mainly uses literature research,investigation research and comparative research and other research methods.The main body is divided into six parts.The first part introduces the theoretical basis,including difference teaching theory,Polya’s problem solving theory and constructivism learning theory.Secondly,it discusses the research status of integrating the subject of Arts and Science,mathematics problem solving teaching and conic curve.Through literature analysis,combining with the current college entrance examination policy and previous research,the direction and content of research are determined.The second part,through the questionnaire survey of students and teachers,the learning situation of students on conic curve and the difference of students between Arts and Science are viewed.Combined with the questionnaire survey,individual interviews with teachers are made,it is concluded that the overall differences of conic problem solving among Arts and Science students are as follows,(1)the mathematics foundation of Arts students is not as good as that of Science students;(2)the computing ability of Arts students is not as good as that of Science students;(3)the thinking ability of Arts students is not as good as that of Science students.The third part sums up the definition,standard equation and properties of ellipse,parabola,hyperbola,then gives a summary of common questions and corresponding examples of conic curve,making the foundation for problem solving teaching.The fourth part compares the requirements of new and old curriculum standards in macro and micro aspects,and concludes that the conic curve part of the new curriculum standards is closer to the requirements of the old curriculum standards(liberal Arts).Then,the thesis compares the structure,score and difficulty of the new and old college entrance examination papers.This thesis takes the Zhejiang and Shanghai papers of 2018 and 2019 years as the new college entrance examination,and the national Arts and Science college entrance examination volume I as the old one.It is found that proportion of the scores in the test paper is relatively high,and the difficulty is also large,especially the high demand for the operation ability.According to the requirements of the course standard and the comparison results of the college entrance examination paper,the corresponding teaching suggestions are put forward respectively.In the fifth part,the teaching design of the ellipse focus triangle problem,the hyperbola exploration problem,the parabola focus chord problem and the conic comprehensive problem are given,and the specific teaching strategies are put forward.The last part is the summary and prospect of the thesis.It reviews and reflects the research,sums up the shortcomings,and makes the prospect of future research.