| Summary: | 碩士 === 國立臺南大學 === 應用數學系碩士班 === 106 === The purpose of this study was to investigate the problem-solving performance of the different representations of the ninth grade students and the relationship between different genders and different mathematical abilities. In this study, data was collected through examinations. Participants were ninth grade students from one suburb school in Kaohsiung City. Problem-solving performance of those ninth grade students was measured using the linear function examination designed by the researcher. Statistical methods of Descriptive statistics, Independent-Sample t test, One-way ANOVA, Two-factor ANOVA and Pearson-product moment Correlation, etc. were then employed to analyze the problem-solving performance of the different representations of the ninth grade students, the relationship between different genders and different mathematical abilities, whether there were interactions between different genders or different mathematical abilities and whether the ability to represent conceptual reciprocal problems has a significant correlation.
The research results were as follows:
1. There was no significant difference in the problem-solving performance of the ninth grade students by the different representations of the linear function.
2. There was no significant difference between genders among the ninth grade students in the performance of linear function examination.
3. There were significant differences among the ninth-grade students with different mathematical ability in the performance of linear function examination.
4. There were no remarkable interaction effects between different representations of the linear function and different genders.
5. There were remarkable interaction effects between different representations of the linear function and different mathematical abilities.
6. There was significant positive correlation between the performance of the ninth-grade students in the representation of the transforming ability of the concept reciprocal question.
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