A Comparative Study Of Chinese And American High School Mathematics Textbooks From The Perspective Of HPM

Theory and thought of function runs through the whole process of mathematics learning,and the history of mathematics is of great significance to mathematics education.Under the guidance of the principle of historical occurrence,the principle of "re-creation" and the principle of historical similarity,this paper takes the function as the carrier and compares the high school mathematics teaching materials between China and the United States from the perspective of HPM,which is divided into the following parts:First of all,from the two aspects of textbook layout and knowledge points,through the content analysis method,the arrangement of Chinese and American textbook function content is compared.The textbook catalogues of both countries are mainly based on the main line of “chapter entry-summary-test questions”.The column structure is based on the main line of “before text—the text—after the text”,but the “before the text” is the beginning of the chapter,the Chinese version A textbook is mainly based on "cultural background knowledge",and the M edition of the textbook in the United States puts forward the "learning goal";in the aspect of knowledge compilation,Chinese version A is mainly "linear" and pays attention to the formation of systematic knowledge,the M edition of the United States is mainly“spiral”,focusing on the practical application of knowledge.Secondly,through the discussion of the comparative dimension,the software Excel and the statistical analysis software SPSS20.0 are used to input and analyze the data,and the application of the mathematical history of the teaching material function in the two countries is studied.By using Pearson chi-square test and Fisher accurate test,the similarities and differences of knowledge module distribution,column distribution,application mode and presentation mode of mathematics history are analyzed.Generally speaking,there is no significant difference in the distribution of knowledge modules and columns in the history of mathematics between the two countries,but there are significant differences in the way of application andpresentation.The significant difference is reflected in the fact that there is no history of "restructured" mathematics in the Chinese version A textbook,and the frequency of each application mode is quite different.The five ways of using the M edition textbook in the United States are involved,and the frequency difference of each application mode is not significant;in the way of presentation,the proportion of dominant mathematics history in Chinese version A textbook is slightly higher than that in China.Compared with China,there is no significant difference between the frequency of dominant mathematics history and implicit mathematics history in the content of American textbook function.Then,use the literature analysis method and the content analysis method,combined with the historical expansion of the "function concept","exponential function","trigonometric function",draw the history and textbook structure map,scatter plot,according to the graph structure and changes trends,analyze the similarities and differences and similarity degree between the order of writing Chinese and American textbooks and the order of history.The US M version of the textbook "function concept","exponential function" is written in a sequence closer to the historical expansion order.The Chinese A version of the textbook "trigonometric function" is written in a more recent order of historical expansion.Finally,based on the above research results,this paper puts forward some constructive suggestions on the compilation of senior high school mathematics teaching materials.Adjust the distribution of mathematics history columns and re-examine the application of mathematics history in teaching materials.Based on the historical similarity,the order of knowledge content should be adjusted appropriately.