Comparative Study On Mathematics Application Levels In Chinese And American Textbooks

During the last30years, mathematics applications and mathematical modeling is one of the essential topics in mathematics education. As the wide applicability of mathematics, mathematics applications play increasingly important roles in mathematics curriculum. Researchers focused on how to cultivate the students’ability of solving problems in real-world. However, the features of mathematics applied inside mathematics were neglected. Yoneyama Kunikura, a famous Japanese mathematics educator, argued that they are crucial in the development of mathematics: from several axioms to self-contained system. This study described different applications characters of high school mathematics textbooks which are used in different countries from both inside and outside mathematics perspectives.In this paper, there is a comparative study on mathematics in high school textbooks used in Chinese Mainland and US.Firstly, based on mass of literature review, one theoretical framework for the analysis of mathematics application is informed.Secondly, via the analysis framework, we analyzed different mathematics application levels in textbooks used in China and US. And the following conclusions are drawn:1) PEP occupies the highest level of external mathematics application, while SEP has the lowest one. Although PH used in American has a lower EMA level than PEP, it has the largest number of application problems. And the problems have abundant real-world contexts.2) Both of the Chinese textbooks have higher IMA levels than the one of America. Chinese textbooks have larger percentages of mathematics problems which have more than one type of knowledge, and many of the problems have higher transfer distances and abundant mathematical contexts. Between the two Chinese textbooks, SEP has higher IMA transfer level. 3) Both of the Chinese textbooks have higher cognitive levels than the one of America. Chinese textbooks have larger percentages of mathematics problems which belong to level2and level3, while PH contains more level1problems. Between the two Chinese textbooks, PEP has higher a cognitive level.