dc.description.abstract | This study examined the representation of the positive and negative numbers in students during different stages of development in Taiwan. The sample included second graders, fourth graders, sixth graders, eighth graders and the learning disability students.
In the first experiment, all children were evaluated with number-line estimation task, which incorporated four kinds of ranges, expanding from 0-through-100000. The last three groups in the sample were also evaluated by the same task for the -10 through 10 and -100 through 100 ranges. In addition, students’ learning backgrounds were also collected by using questionnaires and their average mathematics achievement in the semaster. In the second experiment, sixth and eighth graders were chosen from the first experiment to access with the additional numerical comparison task.
The results indicate that in the number-line task, the main improvement occur in the fourth grade from the number 0 through 100000. The performance score is similar to how the adult college students performed in other countries. Second, sixth grade also show significant improvement in the negative range number-line task, which indicates that was some strategies maybe used by the students when solving the estimation task with negative numbers despite the fact that students have not learned the negative numbers yet. Third, eighth grade learning disabilities student also showed significant improvement in the small range numbers in between -100 and 100, however, had some difficulties in range above 100000. This could be a potential explanation of what causes the students failed the mathematic achievement. Forth, the results of numerical comparison task indicate that sixth graders may had presented with components representation in mind and that the eighth graders can presented both the component and/or the holistic representations when needed for the task.
We also test the correlation between the two tasks and the math grades; the result shows that the correlation was significant under the sixth grade but not in the eighth grade and learning disabilities students. Overall, the results suggest that children should learn more to solve the more difficult mathematical problems when get into the junior high school, even they have improved in the numerical representation.
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