Based On The Classification Of Mathematical Cognitive Levels To Compare The Presentation Of Exercises In China And The United States Textbook

This paper compared the mathematical cognitive levels of "exponential function"exercises in Chinese and American textbooks.The purpose is to provide reference for the compilation of mathematics textbook in China.Firstly,compared the mathematics curriculum standards of China and the United States.Secondly,constructed the mathematical cognitive level framework on the basis of literature review:level-1:calculation operational memory level,level-2:concept conceptual memory level,level 3:comprehension illustrative understanding level,level 4:analysis exploratory understanding level.Finally,based on the framework of mathematical cognitive level,to classify and compare the exercises in two versions.The conclusions are as follows:(1)People's Education Press(Chinese version)mainly uses symbolic representation,while Core Plus Math1(California version)mainly uses literal representation and pays more attention to the use of multiple representations.(2)Core Plus Mathl focuses on creating problem situations that are closely related to students' life,so as to give students more mathematics experience.People's Education Press mainly focuses on the problems' abstractive and comprehensive.(3)The exercises of the two countries are compiled in a hierarchical way,and the difficulty of the exercises presents a gradient distribution.The characteristics of the same level' exercises are as follows:(1)the number of exercises in level-1 in Core Plus Mathl is far more than that in People's Education Press,but the latter is more difficult.(2)The quantity of level-2 exercises in Chinese and American textbooks is smaller,and the difficulty is lower.However,due to the different representation,solving the exercises in Core Plus Mathl is more complex,students need to transform the text representation into image representation.(3)For level-3 exercises,the problem situation of Core Plus Math is closer to students' life,while People's Education Press has more different types exercises,and the abstractness and comprehensiveness of the exercises are better.(4)In level-4,the proportion of situational exercises in the two versions is greater than the non-situational exercises,and the exercises in this level are mainly represented by words,but Core Plus Math1 has no symbolic representation.In general,the two versions of exercises are basically in line with the students'mathematical cognitive level and development law.Core Plus Math1 prefer to real problem situations,diversified representation and to create opportunities for students to "do mathematics",but pays less attention to the in-depth study of pure mathematics knowledge with abstraction and comprehensiveness than People's Education Press.People's Education Press attaches great importance to the mastery and in-depth study of pure mathematical knowledge,so that to cultivate students' high-level mathematical ability such as mathematical abstraction and logical reasoning.However,it needs to further enrich the situation of problems,strengthen the connection between knowledge and life practice,and strengthen students'consciousness and ability of "using mathematics".The enlightenments of this study on the compilation of textbook exercises in China are as follows:on the basis of increasing the total amount of textbook exercises,reasonably arrange the proportion of exercises at all levels of mathematical cognition;To increase the diversity of problem situations in textbooks,enrich the representation of mathematical problems,enhance the application of exponential function in textbooks,and cultivate students'high-level mathematical ability to solve problems from multiple perspectives.