| Conic curve includes ellipse(special case is "circle"),hyperbola,parabola three kinds of curve,is the focus of high school.Conic curve is an important part of analytic geometry,which has been taught in middle school for more than one hundred years.The history of mathematics involved in the conic curve is numerous,from apollonius in ancient Greece to Kepler in the astronomy in the 16 th century and the cartesian coordinate system in modern times.The conic curve also involves two proofs of pure geometry such as Dandelin double sphere to explore the nature of conic curve and analytic geometry.The drawing of conic curve involves the drawing of ruler and The Geometric Sketchpad.Through the comparative analysis of the content of conic curve in Chinese the Peoplel's Education Press A and Japanese the Tokyo Edition,the author hopes to provide some references for the rewriting of textbooks and the teaching of conic curve in senior high schools under the new curriculum reform in China.This paper applies four methods: comparative method,content analysis method,literature research method and model method.Firstly,it compares the curriculum standards of Chinese and Japanese high schools and the teaching requirements of "conic curve".Secondly,it makes a comparative analysis of the conic curve contents in Chinese and Japanese textbooks from a macro perspective(Chinese textbooks choose 2-1,4-1 and 4-4 as electives),including curriculum arrangement,"Conic curve definition",mathematical history,content setting,eccentricity and comparison of example exercises and their comprehensive difficulty.Once again,the three parts of Chinese and Japanese conic curves--ellipse,hyperbola and parabola are compared and analyzed respectively from the micro perspective(only elective 2-1 is selected in this part of Chinese textbook),and the three dimensions of concept introduction and nature,specific content setting and course difficulty are compared and analyzed respectively.Finally,this paper analyzes the similarities and differences between Chinese and Japanese textbooks on conic curve content,draws conclusions and puts forward Suggestions.Through comparison,the following conclusions are drawn: the curriculum standards of the two countries both pay attention to the characteristics of The Times and the introduction of mathematical history;In China,the teaching requirement is to explore the source of conic curve property through Dandelin double sphere pure geometry and analytic geometry,while in Japan,the teaching requirement is to learn in stages: memorization,understanding,understanding(flexible application)and mastery.In terms of macro and overall comparison,the curriculum arrangement of the two countries is different.In addition to using analytic geometry to define conic curve,the definition of conic curve by demonstration geometry was also added.Both countries pay attention to the integration of mathematical history,but the content of the integration is different.In terms of content setting,the number of knowledge points in the Tokyo Version is more than that in the Peoplel's Education Press A,and there is no content of "parallel movement of conic curve" in the the Peoplel's Education Press A.There is only one form of "example" in the the Peoplel's Education Press A,and the Tokyo edition is divided into two kinds of "examples" and "examples" with different degrees of difficulty.Problem arrangement on the Tokyo edition set up more "question" form;It is difficult to set the sample question type of A version in the dongjing version.The difficulty of setting the sample question type in the two editions of the textbook is the same.The number of sample questions in the two editions is almost the same.The number of exercises taught by people in the Peoplel's Education Press A is relatively low;The comprehensive difficulty of the Tokyo sample problems is higher,but the Tokyo sample problems are not combined with the "background".In the aspect of microscopic comparison of ellipse,hyperbola and parabola,the introduction of concept was mainly "instance import".Tokyo is dominated by "give it directly";Geometrically,the two textbooks are roughly the same.Specific content Settings,Chinese and Japanese textbooks are slightly different;The time of the two versions of courses is similar,the depth of courses in Tokyo version is greater than that in renjiao the Peoplel's Education Press A,and the breadth and difficulty of courses in renjiao A version are greater than that in Tokyo version.Based on the comparison of conic content between Chinese and Japanese textbooks,some Suggestions are put forward for the compilation and first-line teaching of Chinese textbooks :(1)Optimize the readability of textbooks to ensure the implementable content.(2)Optimize the content arrangement of textbooks to increase the consistency of knowledge.(3)Optimize the structure system of the example exercises and expand the open questions.(4)Optimize the content of conic curve and reduce the difficulty of textbook courses. |
