Comparative Study On Composite Difficulties Of Examples Between Chinese And French High School Mathematics Textbooks

At present,a new round of curriculum reform of high school has been conducting both in China and Shanghai.Textbook,as the important media between intended and implemented curriculum,generally plays a role in transiting education policy and curriculum standard into practical teaching.In mathematics learning,the examples of textbook are important approaches for students to understand the concept of mathematical knowledge and comprehend mathematical thoughts and methods.We can grasp,to a certain extent,the difficulty of textbooks through studying the difficulty of textbook examples.In the comparative study of mathematics textbooks,the study on the difficulty of Chinese and French textbooks is relatively few.Based on this phenomenon,the version of People's Education Press(CN-PEP)in China and Sesamath Education(FR-ES)in French of high school mathematics textbooks have been chosen as the objects of this study.On the basis of composite difficulty model improved by Wang Jianpan and Bao Jiansheng(2014),literature research,text analysis and comparative research method are adopted to conduct the research which is both quantitative and qualitative in the following three parts:(1)The similarity and difference of content selection and arrangement between Chinese and French textbooks;(2)In general,the difference of examples' difficulty and difficulty factors between Chinese and French high school mathematics textbooks;(3)In the context of same mathematics contents in Chinese and French textbooks,the difference of examples between these two countries in composite difficulties.Finally,the research conclusions as follows:First of all,there are some similarities and differences of content setting between Chinese and French textbooks.On the content selection,in the field of algebra,the two sets of textbooks both regard the function as the core content;in French textbooks,the function content and the calculus content are merged together;in addition,the French textbooks don't involve the algorithm and the logical language content,while our textbooks do not cover the matrix content which is in the French elective textbook.In the field of geometry,French textbooks don't include conic section,the other contents in these two countries' textbooks are basically the same.In the field of probability statistics,contents are rich and certain deep concepts appear in French textbooks,not only covering all the contents in Chinese textbooks,but also include the continuous random variables,fluctuation range,confidence interval and other contents.Calculus contents appear in the textbooks of both countries which both pay attention to the meaning and calculation of derivative and integral,and its applications to the study of function,physical and geometry.However,in terms of breadth and depth,the contents in French textbooks is much higher than that in Chinese textbooks.For example,the definition of the "limit" appears in the French textbook,while term "limit" is used without definition in our textbooks.French elective textbooks also include some basic contents of number theory,which don't exist in Chinese textbooks.On the content arrangement,both of the two sets of textbooks are spiral in consideration of the stage of cognitive development of students.Secondly,in general,the composite difficulties of examples in Chinese textbooks are higher than French textbooks.On the five difficulty factors--problem context,the mathematical cognition,the computation complexity,the reasoning difficulty and the topic coverage,these two countries share almost the same degree of concern,and Chinese textbook examples are all more difficult than that of France.Finally,in the context of same mathematics contents in Chinese and French textbooks,the difficulty of function and geometry in the Chinese textbooks is much higher than that of France.But on probability and statistics,the difference of difficulty between these two countries are very close.France even surpasses China on the factor of reasoning difficulty.Based on the conclusions above,the author puts forward four suggestions as follows:(1)Focus on the connection between high school mathematics and university mathematics,and extend the content of textbooks appropriately;(2)Pay attention to the development of students' personality,and diversify the types of elective textbooks;(3)Follow the trend of the times,and increase the integration between textbooks and ICT;(4)Pay attention to mathematics practice and mathematical applications,the textbook contents should link with practice.