**5. Discussion and conclusion**

The quantitative results show that the gifted students significantly outperformed the general students in number sense and had a high effect size. Previous studies have shown a positive relationship between number sense and mathematics achievement [15, 39]. Earlier studies also agreed that students who have good number sense should be able to develop and apply flexible and efficient strategies (including mental computation and estimation) to handle numerical problems [9, 17, 38, 39]. In addition,

#### *Number Sense Performance of Gifted and General Fourth Graders in Taiwan DOI: http://dx.doi.org/10.5772/intechopen.111752*

several studies reported that the gifted students have the ability to use various methods efficiently and flexibly when solving problems [13, 25, 27, 29]. Therefore, the result that the gifted students significantly outperformed the general students in number sense is reasonable. In addition, the data also show no significant difference between each number sense component for the gifted students. This is probably due to the facts that the gifted students can develop more flexible and efficient methods to solve problems. Therefore, they have more balanced development on each number sense component. However, a significant difference was found between each number sense component for the general students.

The general students' performance on F4 (recognizing the relative number size) was significantly higher than that on F2 (being able to decompose and compose numbers). This is probably because Taiwanese mathematics textbooks typically have several "recognizing the relative number size"-related problems, and Taiwanese students have limited exposure to problems in mathematics that require them to compose and decompose numbers. Therefore, these Taiwanese students performed well on "recognizing the relative number size"-related problems due to they have ample opportunities to solve these kinds of problems. This result is consistent with the findings of a previous study [38, 39]. In addition, decomposing and composing numbers to solve problems need more flexible thinking; therefore, it is reasonable to believe that general students not performed well on this number sense component. Moreover, the teachers of the gifted students also provided several challenging problems to deepen their mathematical learning and thinking. However, these problems are not necessarily related to decomposing and composing numbers.

The interview results showed that the gifted students outperformed the general students in using the number sense-based method. It is reasonable to believe that gifted students can flexibly apply number sense-based methods, including the use of benchmark, estimation, and so on to solve problems. This supports Sands' finding [40] that showed that the gifted students tend to develop multiple methods to solve problems which relate to flexibility in thinking. Therefore, the result that the gifted students outperformed the general students in using the number sense-based method is reasonable. Moreover, the general students obviously had more misconceptions regarding number sense than the gifted students did. This result is probably due to insufficient basic mathematics knowledge exist among the general students. In fact, there is still the lingering question of curricula, learning opportunities, etc. This will lead more studies in the future.

This study was conducted to examine whether the gifted students outperform general students on number sense. Additionally, variations in the use of number sense methods between the gifted and general students when solving number sense-related problems were examined. Although limited by a small sample size, this study provides three major contributions to mathematics education:


students are significantly higher in applying number sense-based method to solve problems than the general students.

3.The findings showed that the gifted students performed equally well on each number sense component. This is special and different from the earlier studies that students in Taiwan did not perform equally well on each number sense components [39]. Earlier studies showed that general students performed poor on judging the reasonableness of a computational result (Authors).

We do hope the findings in this study may contribute the future teaching and research relating to number sense and the gifted students.
