Since the data is hierarchical structure, correlation analysis of the hierarchical variable is conducted, based on
the method of nonparametric test, with the Spearman and Kendall’s tau_b rank correlation coefficient to measure
the linear correlation between variables. The correlation analysis of rank variable is mainly used to deal with the
ordinal variable, and the size of value of ordinal variable can represent a certain order of relations (grade, orientation
or size, etc.) of the observed objects, also based on the “quality” factor of the variables. The evaluation values
of the two kinds of scientific understanding are: 0-unclear, 1-naive, 2-traditional, 3-informed, and the value from
small to large represent the cognitive level. Tested by SPSS19.0 (Table 3), the Spearman and Kendall s tau_b rank
hierarchical coefficient are significantly correlated at the level of 0.01 between science teachers from Shanghai
and Chicago, which means science teachers in both of the countries have a correlation in the understandings of
NOS and SI.