To examine the relative performance in number sense among low-SES students, new immigrant students, and typical learners in grades 4 through 6, data were collected through a number sense web-based, two-tier test. A total of 628 fourth graders, 535 fifth graders, and 524 sixth graders in Taiwan participated in this study. Results showed that there were statistically significant differences in number sense performance among new immigrant children, low-SES students, and typical learners in the fourth, fifth, and sixth grades. The subsequent post hoc comparisons indicated that there was a statistically significant difference between typical learners and new immigrant children in fourth and fifth grades. Moreover, there were statistically significant differences between typical learners and low-SES students in fifth and sixth grades. The Chi-squared test results also showed that there were significant differences in the uses of solution methods between the fourth, fifth, and sixth graders. Implications of this study and suggestions for the future studies are discussed.

In this paper, our study aimed to use Grey entropy to help decide which attributes, so called items in educational assessment, should be eliminated to prevent the Bayesian network modeling process from over-fitting and to obtain better accuracy. Although Bayesian network is proving to be the best technology available for diagnosing students' learning status in educational assessment, in the process of constructing a Bayesian network, the criteria of selecting testing attributes such as items or tasks will influence the diagnosing accuracy. Experiment results indicats that the Bayesian network with Grey entropy data pre-processing obtains the better more than 10% in accuracy than the man-made Bayesian network.

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