A Comparison Of Understanding Of Shanghai Local Freshmen And Non Local Freshmen In Concept Of Derivatives In University

Mathematics curriculum standard of primary and secondary schools in Shanghai and the national high school mathematics curriculum standard in the high school stage on the derivative are very different:There is no derivatives in Shanghai’s curriculum standards, but the national curriculum standards add derivatives into the series of elective 2.Therefore, the differences of Shanghai students and non Shanghai students in learning derivatives are worth researching.So the main content of this research is to compare with understanding of Shanghai local students and non local students when they learn derivatives,to gain meaningful conclusions, and to leave some data in practice. Using the method of qualitative analysis and quantitative analysis, this paper is based on the APOS theory,to compare with these two kinds of students.The major questions to research are as following:(1)What are these students’ levels of cognitive.after these students learn derivatives in university? (2)Is students’ understanding of derivatives different,after these students learn derivatives in university?The second question is based on the first question.According to students’ actual situation,the author design a test on derivatives based on APOS theory.After per study,the author modifies the test and selects students in ECNU where they study finance in 2013 to test.After testing,the author uses SPSS 19 to write descriptive and inferential statistics,and selects 3 students to interview.The author acquires two conclusions:1、 After these students learn derivatives in university,two kinds of students have been reaching in "action" or "process" level.2、After these students learn derivatives in university,there is no significant difference in two kinds of students in concept of derivatives.Finally,according to the result of qualitative analysis and quantitative analysis,the author thinks that students in high schools are not necessary to learn derivatives.At the same time,the author interpret that reason,hoping to provide some useful suggestions to reform of education.