Teaching Research On Conical Curve In High School From HPM Perspective

Under the new mathematics curriculum concept,mathematics education in China is constantly exploring and practicing mathematics culture and mathematics history into mathematics education,and has achieved certain results.The completion of this paper,in the study of the mathematical history related to the conical curve,the corresponding teaching design theory and the literature on the related fields,the conical curve is rerecognized.The teaching design based on the teaching of the history of mathematics is given.Finally,according to the results of the experiment,the conclusion is given.Finally,the whole research data of the truth is completed.The main body of this thesis consists of seven parts.The first part is the introduction of this study,which is introduced from the significance of the topic,the background of the research,the content of the research and the structure of the paper.The significance of this study and the expectation of this study are introduced in the practice and exploration of the mathematics teaching under the concept of the new curriculum.Mainly introduces the background of conic curve in the middle school mathematics education value,middle school conic teaching situation,teaching materials and the conic,on Freudenthal conic teaching view.The experimental system of students' mathematical ability of the reference Krute J Ki set three survey volume,three papers are divided into different levels.In order to understand the teaching status of the conical curve in the middle school,the senior sophomores from a school were randomly selected to take part in the questionnaire survey.Through the literature analysis and the previous investigation,the main research content and the main structure of this study are determined.The second part is the literature review,which mainly introduces the research on HPM and the research status of conical curves.Through the literature analysis,to find the breakthrough point of this study.The third part is the research ideas and methods,and introduces the main research ideas and the main three methods of research in this study.The main research methods of this study are: literature analysis,questionnaire survey,case analysis.For the questionnaire survey,this study was used two times.The first is the early stage of experimental research,which is used to investigate the current situation of teaching.The object of investigation is not the following experimental subjects,but the last student of the follow-up experiment.The second time is to test the effect of experiment.In addition,the interview method and test paper test method are also added to assist the study.The fourth part is the history of conic curves,and concludes that conic curves have experienced four important periods.From the historical research,we have found the reference method for subsequent teaching design and the mathematical historical data into Mathematics Teaching--the focal radius property of Apollonius,the definition of conic section of Papows,and the mechanical drawing method.The fifth part is the teaching design from the perspective of HPM,and the teaching design of ellipse,hyperbola,parabola and the standard equation is given.The sixth part is the experimental study.It introduces the specific object,method and result analysis of the experiment.The seventh part is the study of evaluation and reflection,mainly to the objective evaluation and reflection of this study,and the teaching inspiration of research.