Comparative Study On Geometry Exercises Of Junior Middle School Mathematical Textbooks In China And The United States

With the curriculum and education reform,comparative study is a hotspot of research on education and teaching all the time.Geometry is one of the main content of the mathematics teaching content,all walks of life's attention to it increase every day.As an important part of the teaching material content,the textbook exercises guide students to understand knowledge,to construct knowledge structure,to understanding knowledge deeply,to improve the problem solving ability,to develop mathematical thinking,to enhance mathematical literacy.Therefore,the international comparative study of geometry exercises have important meaning and function to draw on the advantages of other countries.In the current studies,specifically for comparative study of the geometry exercises are few,there is a need for Chinese and foreign contrast research,o provide support for the compilation of geometry exercises in our junior middle school mathematics teaching material,to indicate the direction for the our geometry development.The article selected the teaching materials of CM version and PEP version,to make a comparison on the exercises of geometrical part,and select “the Pythagorean theorem” chapter as an example.Firstly,adopt the methods of documentary analysis to summarized “The related researches of mathematics textbook exercises” and “The comparative studies of geometric exercises in mathematics teaching material”,understood the existing research,and got key revelation that the surface research of exercises approaching completed,the deep comparative dimension of geometry exercises should be explored,Van Hiele's theory of geometric thinking is increasingly prominent,etc,ay a foundation for the comparative study of this article.Followed by the two version of the mathematics teaching material's overall comparison.By integrated content analysis method and comparative research method to compared and analyzed the two versions teaching material in three respects,which is “the overall structure”,“the content arrangement” and “the content Settings of selected section”.Aiming at clear the similarities and differences between two versions body content,and made matting for the comparative study of exercises.Nextly,used the two version of junior middle school mathematics teaching material to compare geometric exercises.Comparing surface dimensions such as the layout of exercises,quantity,contextual features,illustrations,and problem-solving strategies,etc.Combing with statistical knowledge,based on the Van Hiele's theory of geometric thinking,compared two versions in two deep dimensions including the background of the exercises and the geometrical thinking level.Common ground: both versions are layered set exercises,pay attention to the problem solving independently,the geometry thinking level of exercises is higher,but they ignored the information technology,lacking of cooperation consciousness,being short of interaction with other disciplines.Differences: CM lay emphasis on exploration process,PEP focus on problem solving ability;CM version highlighted associated knowledge content;CM version focus more on multi-purpose of one problem,and pay attention to restore the original situation of real life;CM version has abundant illustrations types,PEP are relatively lack of “real object” consciousness;PEP has higher levels of geometric thinking.Finally comprehensived the conclusion of the comparative analysis above,then provided the following enlightenment for geometry exercises' compilation of our junior middle school mathematical teaching materials:(1)Emphasis on information technology,enrich the type of illustrations,enhance the intuitive perception;(2)strengthen the cooperation study,pay attention to investigation and experiment,cultivate the literacy of data analysis;(3)rich the type of background,pay attention to the discipline-crossing,improve mathematical abstraction literacy;(4)pay attention to the knowledge sources,Set a variety of mathematical situations,Cultivate mathematical modeling;(5)Focus on activity processes,review the details of inquiries,improve thinking ability;(6)Balance the geometry thinking level,increase the difficulty of exercises slowly,implement rising steadily.At the same time,explained some enlightenments supplemented by cases,and made the research prospects.