A Comparative Study On Power, Exponential And Logarithmic Function In Textbooks From China, German And American

This study has made a comparative analysis of Shanghai, German and American high school mathematical textbooks on both macroscopical and microscopic sides depended on power function, exponential function and logarithmic function. Using research tools of content analysis, comparison, interview, conception map and so on; according to quantitative and qualitative analysis, we hope to find out the similarity and divergence of these textbooks on aspects of overall features, the choose of the main content, the order of the layout, the structure of knowledge, the presentation of the content,requirements for students and so on.The macro aspect:1. On the aspect of overall characteristic and appearance, the textbooks of Germany and America are considerably exquisite and colorful with substantial high price. However, Chinese shanghai version tends to be more unpretentious, chiefly in white and black with less pages and lower price. As for the aspect of composition, Chinese shanghai version and American textbooks have bigger letter print, more blank space, more hints and labels, which are convenient for students to read and summary. German and American textbooks have numerous column settings. In contrast, Chinese shanghai version is very succinct.2. American textbooks have the most substance, followed by German textbooks. Furthermore, the German textbooks have deeper continuation and prolongation based on the explanation of the fundamental knowledge. The American textbooks take a prefered concentration on the practicality of mathematics. The three versions of textbooks show the biggest difference especially on choosing of the main content of exponential function.3. About the ways of introduction into exponential function, logarithm and logarithm function, the three versions are quite different. Chinese shanghai version and German textbooks basically have no repeated appearance of the same knowledge of power function, exponential function and logarithmic function. On the other hand, American textbooks are not.The micro aspects:1. The German textbooks embrace a variety of knowledge with wider scope and deeper profundity. Also the connection levels between knowledge are much higher than the other two versions. In the meantime, although the American textbooks embrace a variety of knowledge with the widest scope, the deepest profundity and the most complicated conception maps, the connection levels between knowledge are awfully low.2. On the aspect of conception presentation, the three versions are distinctly characteristic and different on explanation, exemplification, chart and summary.3. As the aspect of the requirements of students, American textbooks have the most abundant types of exercises and more complete arrangements. Three versions of textbooks are strongly exercise-oriented based on pure math.Demand of writing out the solving process of the exercises has the biggest proportion.Finally, based on the research conclusion above,the author summarized some features in the three versions,and interviewed three high school mathematics teachers,and proposed several suggestions at the end of the paper.