國中八年級學生在數學創造力問題表現之分析

Taiwanese 8th Grade Students Performance on Mathematical Creativity Problems

本研究主要目的是以調查研究法瞭解臺灣學生數學創造力的表現。研究以Leikin所發展的測驗工具瞭解臺灣學生創造力的表現，並以數學成就測驗SAT-M將學生區分為高、中、低三群，探究數學成就是否影響數學創造力表現，最後，探究數學創造力與一般創造力是否存在關聯性。研究樣本為新竹地區三所國中共313位八年級學生。研究結果包括：（1）八年級學生在四題數學創造力問題流暢性、靈活性、獨創性、和創造力面向的表現均呈現顯著差異。其中，距離問題在流暢性、靈活性、獨創性和創造力表現最佳。而果醬問題則在流暢性、靈活性、獨創性和創造力表現最差。進一步將四題數學創造力問題區分為幾何和代數，分析顯示學生在流暢性、靈活性、獨創性、創造力，幾何均顯著高於代數。（2）不同數學成就的學生在流暢性、靈活性、獨創性、創造力等部分皆達顯著性差異，此現象顯示學生的數學成就影響其數學創造力表現。（3）八年級學生的數學創造力與一般創造力表現呈現顯著低相關。若以數學成就作為調節變項，排除此變項的影響，再進行皮爾森偏相關性分析，結果顯示：學生的數學創造力與一般創造力表現則未達顯著性相關。此研究結果顯示數學創造力的發展獨立於一般創造力之外。文章最後，本文提出未來數學創造力研究和教學實務的討論與建議。

In this study, we aimed to examine the mathematical creativity of Taiwanese 8th-grade students using a survey instrument developed by Leikin. The students were categorized into high-, middle-, and low-achievement groups based on the SAT-M test to assess whether mathematical achievement influences performance on mathematical creativity problems. We also explored the relationship between mathematical creativity and general creativity. With a sample of 313 8th-grade students from three middle schools, the analysis revealed the following findings: First, students' performance on the four mathematical creativity problems—assessed in terms of fluency, flexibility, originality, and overall creativity—showed significant differences. Students performed best on the Distance problem and worst on the Jam problem across all creativity dimensions. When the creativity problems were further grouped into geometry and algebra, students performed significantly better on geometry problems than on algebra problems in terms of fluency, flexibility, originality, and creativity. Second, significant differences in fluency, flexibility, originality, and creativity were found among students in the high-, middle-, and low-achievement groups, indicating a consistent relationship between mathematical achievement and mathematical creativity. Third, there was a significant but low correlation between mathematical creativity and general creativity. However, partial correlation analysis, using mathematical achievement as a moderator variable, showed no significant correlation, suggesting that the two variables are independent of each other. The study concludes with discussions and implications for future research and instructional practices.