Understanding Of Rational Number On Shanghai 6～(th)～9～(th) Students

This paper does a research on the recognition of rational numbers for school student by questionnaire investigation survey of students from grade 6 to grade 9 in Shanghai. The focus on the paper is the recognition of the five subconstructs of rational numbers and density of the rational numbers for students.First ,the research finds out that the students for grade 6 to 9 have some different and unique recognitions for the subconstructs (part-whole, quotient, measure, ratio, operator) as following:a. Comparing with other subconstructs, students lack a good recognition of measure and ratio subconstructs.b. Students have a difference in recognizing unit 1 between different figures. Comparing with continuous figures, students have a better understanding of unit 1 with discrete figures.c. Students in different grade have a significant various recognitions of the five subconstructs.d. Students of the different gender have an obvious various recognitions of measure subconstruct.Second , allocating various answers by SOLO, it is found that:a. the answers converge to M and L levels and the proportion of E level is less.b. Based on SOLO, it is detected that grade 9 have the best performance, and grade 8 second, and grade 7 the worst.At last we find out that students with lower grade have a significant influence of discrete integer number students with higher grade have great influence of irrational numbers when recognizing the rational numbers.