Comparative Study On The Difficulty Of Conic Sections Between Chinese And American Senior Middle School Mathematics Textbooks

Mathematics teaching material is an important course resource to realize the goal of mathematics curriculum resources and develop students' core accomplishment of mathematics discipline.The compilation of mathematics teaching material should be improved continuously.The comparison of teaching materials can provide teachers with a broader vision and provide reference for the improvement of teaching materials.Difficulty comparison is an important field of textbook comparison.The textbook is too difficult,which does not conform to the cognitive development level of students.Students cannot fully understand it,which is likely to make students weary of learning.The difficulty of the textbook is too small to achieve the purpose of cultivating students' mathematical thinking,and students are not satisfied with food,which is not conducive to the improvement of core mathematical literacy.Conic sections are the important content of mathematics course in senior high school,the core test point of college entrance examination,and the important content of analytic geometry.Based on the literature research,this research adopts the methods of content analysis,comparative study,questionnaire survey,statistical analysis and so on.Starting with the conic sections,this paper studies the difficulty of teaching materials in A edition and Glencoe edition.This study makes a comparative study on the conic sections part of the two editions of People's Education Press A and Glencoe Press from the four dimensions of content breadth,content depth,example difficulty and exercise difficulty,and analyzes the similarities and differences between the two editions by statistical data,and comprehensively considered the four dimensions to obtain the textbook difficulty of the conic part of textbooks from the two editions.Finally,the author puts forward some suggestions on the compilation of the teaching materials of People's Education Press A.Finally,the author draws the following conclusions:(?)content breadth.There is no significant difference in the scope of the conic part between People's Education Press A and Glencoe Press.There are two more knowledgepoints in People's Education Press A than in Glencoe Press.Most of the same knowledge points in the two editions of textbooks are the same,but the curves and equations,the equation of the curve,the eccentricity of the ellipse,the eccentricity of the hyperbolic curve,the eccentricity of the parabola,the isobaric hyperbolic,etc.,are not covered in the text of the Glencoe edition.The standard equations of the three conic sections in the Glencoe version are not covered in the text of Glencoe.For example,in the Glencoe version,the standard equations of the ellipse can represent all the levels of the axis of symmetry.The path of parabola in Glencoe version,the general equation of three kinds of conic curves into A standard equation,and the use of graphs to solve quadratic inequalities are not mentioned in the version A taught by people.(?)depth of content.The chi-square test shows that there is no significant difference in the percentage distribution of the presentation of knowledge points between the A edition and the Glencoe edition.The depth-weighted average for People's Education Press A is1.5405 higher than the Glencoe Press 1.3714.In terms of the presentation of knowledge points,the two editions of the textbooks are mainly intuitive description,intuitively presenting the concept or proposition contained in the knowledge point to the students,simple and clear.However,it can be seen from the details of the presentation of the knowledge points that the teaching materials of People's Education Press A are more clear and logical,and the explanation of the knowledge is more profound,which is It is helpful to improve students' mathematical literacy.(?)the difficulty of examples and exercises.(1)In terms of the level of demand for examples and exercises,the two editions of the teaching materials of People's Education Press A and Glencoe Press mainly focus on the non-related and related procedural level,and mainly examine the basis of the students.Focus on the development of students' basic knowledge,basic skills and basic ideas.Glencoe Press has topics at the mathematical level,not for inquiry,but for the real discovery of students,to explore and study mathematical problems in life.(2)In terms of the number of examples and exercises,the number of examples and exercises in People's Education Press A is higher than that in Glencoe Press.People's Education Press A pays more attention to the comprehensive application of knowledge points.(3)In the background of examples and exercises,the background of Glencoe edition is rich and diverse,involvingmany aspects such as sports,architecture,astronomy and so on.The data are detailed and reliable,and the real sense is increased.Not only that,Glencoe Press of the textbook is also in the real background of the example with a color picture,to increase the students' knowledge of life,pictures and texts,avoid the boring of pure text.(4)Considering the level of requirement,the number of knowledge points,the background,and the difficulty value 2.1322 higher than that of Glencoe Press 1.873,which is not close to the life of the students.Taking into account the requirement level,the number of knowledge points,the background,and the difficulty value of the A edition of the Human Education textbook is much higher than that of the English version.The difficulty value of the A edition exercises is 1.9188 higher than that of the Glencoe Press 1.7552.(?)the difficulty of teaching materials.Considering the breadth of content,the depth of content,the difficulty of example and the difficulty of exercises,the overall difficulty of the conic part of A textbook is higher than that of Glencoe Press.The content of People's Education Press A shows wide and deep characteristics,involving more knowledge points,deeper contents and more difficult to study.Based on the above conclusions,the author in teaching taught A version of the conic section puts forward the following Suggestions:(1)Pay attention to the integrity of the conic knowledge and intuitive.(2)The main body of the conic section increased examples and exercises in the real life of color images,avoid boring plain text.(3)To maintain the hierarchy of conic section problem sets,properly increasing the topic of spiral review.(4)Do the math from the life level of examples and exercises,and let students experience the information and data of the process of collecting,sorting and expression.(5)To increase personal life background of the subject,pay attention to the diverse background of examples and exercises.