**1. Introduction**

Number sense plays an important role in the elementary and middle-grade mathematics curricula [1–5]. Many of number sense-related studies have been conducted worldwide [6–11]. In addition, there are many studies which focus on examining the gifted students' performance on mathematics [12–14]. However, few researchers have investigated the gifted students' number sense performance. Moreover, there are not studies dedicated exclusively to the variations on the topic of number sense between the gifted and general students. Whether the number sense of the gifted students is superior to that of general students should be determined. Results show that number sense is a good predictor for further mathematics achievement [15]. In addition, data also show that the gifted children can apply multiple methods to solve problems flexibly [13, 14]. Children who have good number sense should develop and apply flexible and efficient methods to solve problems [4, 16]. Therefore, the number sense performance and methods used to solve number sense related questions for the gifted students should be examined. The more understanding the thinking and performance of number sense methods used by the gifted students, the more we can design a better approach to help them develop number sense. The kinds of differences should be examined to pursue better mathematics education for the gifted students in the future. Thus, the two research questions are as follows:

