A Comparative Study Of Exponential And Logarithmic Function From Mathematics Textbooks In Senior High School Between China And Australia

In the transitional period of “new curriculum standards and new textbooks”,the study of textbook comparison is a hot topic.With the development of the new curriculum reform,In high school mathematics textbooks,the function contents has changed a lot.As everyone knows,The function concept is one of the central topics in high school mathematics and it appears like a thread throughout high school mathematics,exponential function,logarithmic function are two most important types of basic elementary function.This purpose of this paper is to discuss the contents of “exponential function and logarithmic function” in Chinese PEP(A)edition which is used by Chinese high school,and?Mathematics HL(core)?which is published by Haese &Harris Mathematics Publishing House of Australia for IBDP.The article mainly uses several kinds of methods synthetically such as the literature survey,the comparative research,the statistics analysis.This paper mainly makes a comparative analysis from three aspects: the macroscopic structure of the textbook,the microscopic content of "exponential function and logarithmic function",and the comprehensive difficulty of the course,and summed up their respective features of two textbooks.Draw the following conclusions:(1)In terms of content structure,The two textbooks differ greatly in their treatment of knowledge,MHL textbooks focus on the comprehensive analysis of the function image,PEP(A)textbooks focus on the properties of the function,the penetration of mathematics thinking methods and the summary of knowledge points.(2)In general content,MHL textbooks have more knowledge points than PEP(A)textbooks,and the two textbooks have their own characteristics for the arrangement of knowledge points.(3)On the structural system,PEP(A)textbooks present a structure of spiral ascending layer by layer,it focus on the process of students' self-exploration of new knowledge,andnatural in the transition of knowledge.MHL textbooks present a structure of straight line,it has clearer sequence of thought and frame to knowledge,and focus on the learning process from the special to the general.(4)In terms of presentation,PEP(A)'s columns are more diverse,and pay attention to the further expansion and extension of knowledge.(5)In the application of information technology,MHL textbooks place greater emphasis on the use of information technology,the use of information technology tools in the MHL textbook is advanced,and the frequency of integration is higher.(6)On the number of examples,MHL textbooks have more than PEP(A)textbooks,but MHL textbooks' exercises are simple,PEP(A)textbooks' exercise are rich and diverse.In terms of the difficulty of examples and exercises,PEP(A)textbooks have more difficult than MHL textbooks.(7)In terms of the difficulty of the course,MHL textbooks reflect the “broad and shallow” writing pattern,PEP(A)textbooks reflect the “narrow and deep” writing pattern.According to Professor Shi Ningzhong's difficulty model formula,the difficulty coefficient of the two textbooks is calculated,PEP(A)textbook is higher than MHL textbook through comparison.Finally,combine the above conclusions,there several suggestions for the preparation of teaching materials:(1)Appropriately add the study of “exponential function and logarithmic function” images,and highlight the importance of the function graph.(2)Enrich the relevant knowledge points in the textbook,add and adjust the appropriate content.(3)Increase the number of examples and exercises,pay attention to the integration of life situation in the exercises and strengthen the connection with real life.(4)Pay attention to the use of information technology,strengthen the combination of teaching materials and information technology,add illustrations of information technology operations.And this paper displays some advice for high math teacher:(1)Improve the level of information technology application of teachers,effective application of information technology,promote the teaching and learning of mathematicsclassroom.(2)Give full play to the leading role of the introduction part,and naturally infiltrate the mathematics culture into the classroom.(3)Attach importance to the expansion columns in the textbooks,and give full play to the advantages of expanding columns.(4)Increase the breadth as well as the time of the course.