本研究探討台灣中學數學資優學生之數學創造力，透過學生對開放性數學問題的多元解題表現評估其完備性、流暢性、變通性、獨創性與創造性，並進行不同年級與不同題型、領域的比較了解學生數學創造力表現，最後透過訪談了解學生對於多元解題的需求與看法。
本研究透過調查研究法，進行數學創造力測驗之問卷施測，施測題目共7題多元解題任務，分別為1題一般創造力與6題數學創造力問題，其中共有3題方法開放、2題結論開放及1題條件開放之數學問題。施測對象為國中七、八、九年級之數學資優生，總計5所學校之學生共292人，其中七年級89人、八年級121人、九年級82人。施測結果以描述性統計、相關係數、成對樣本t檢定、ANOVA單因子變異數分析等方法進行研究結果分析與討論。並於施測後對11位學生進行半結構式訪談，了解學生對於數學能力與數學創造力的看法。
研究結果顯示，部分題目完備性、流暢性與變通性隨著年級增加而提高，但獨創性與創造性分數卻隨著年級增加而降低。而部分題目的完備性、流暢性、變通性、獨創性與創造性分數皆隨著年級而增高。一般創造力的各項指標分數則是隨著年級增加反而減少。而從學生提出的解法可以發現，常見的題目中，常規性解法出現的比例隨著年級增加而提高，部分特殊解法隨著年級增加而減少，甚至消失。
訪談11位學生對於多元解題的看法可以發現，多數學生並未主動將多元解題納入數學課希望學到的內容中，當問及是否希望在數學課中聽到老師講解多種解法時才紛紛表示同意。對於多元解題的能力，多數學生表示若提出的多種方法只是依靠記憶而無創新或獨特的話，並不認同其數學能力較佳，能提出容易讓人理解又有效率的方式才是學生認為好的解法。且多數學生在面對稍有挑戰、或是原本的解法不夠滿意的題目時，才會有多元解題的動作，比起找到多種解法，學生更樂於找最佳的解法。

This research explores the mathematical creativity of mathematically gifted students in Taiwan middle school. It evaluates their completeness, fluency, flexibility, originality and creativity through students' multiple problem-solving performance on open-ended mathematical problems. Then compare different grades, different question types and fields to understand students' mathematical creativity performance. At last through interviews to understand students' needs and views on multiple problem solving.
This study was conducted through the survey research method by using the questionnaire of the Mathematical Creativity Test. There were 7 multiple-solution tasks in the test, including 1 problem on general creativity and 6 problems on mathematics creativity, of which 3 problems were open-method, 2 problems were open-completion and 1 problem was open-prerequisite. The subjects of this test were mathematics gifted students in the seventh, eighth and ninth grades of middle school. There were a total of 292 students from 5 schools, including 89 in seventh grade, 121 in eighth grade, and 82 in ninth grade. The test results were analyzed and discussed by means of descriptive statistics, correlation coefficient, paired sample t test, ANOVA single factor analysis of variance. And after the test, semi-structured interviews were conducted with 11 students to understand the students' views on mathematical ability and mathematical creativity.
The results of the study showed that the completeness, fluency and flexibility of some problems increased with increasing grades, but originality and creativity decreased with increasing grades. For others, completeness, fluency, flexibility, originality, and creativity all increased with grades. In the general creativity problem, the scores of all indicators of creativity decrease with the increase of grade. From the solutions proposed by students, it can be found that among common problems, the proportion of common solutions increases with the increase of grades, and some special solutions decrease or even disappear with the increase of grades.
By interviewing 11 students about their views on multiple solutions, it can be found that most students did not take the initiative to incorporate multiple solutions into the content they hope to learn in mathematics class. But when asked if they would like to learn multiple solutions in math class, they all agreed. Regarding the ability to solve problems with multiple solutions , most students said that if the various methods proposed only rely on memory and are not innovative or unique, they do not agree that their mathematical ability is better, and they think it is good to be able to propose methods that are easy to understand and efficient solution.

第一章 緒論
第一節 研究動機 1
第二節 研究目的與待答問題 2
第三節 研究限制 2
第四節 名詞解釋 3
第二章 文獻探討
第一節 資賦優異理論與實徵研究 4
第二節 課程綱要中的創造力 5
第三節 創造力與數學創造力的內涵 9
第四節 開放性數學問題 16
第三章 研究工具與實施
第一節 研究理念與架構 23
第二節 研究對象與背景 23
第三節 研究流程 26
第四節 研究工具 26
第五節 資料統計與分析 35
第四章 研究結果與分析
第一節 學生在數學創造力測驗的表現 38
第二節 不同年級學生在數學創造力測驗的表現 76
第三節 學生對多元解題的看法 101
第五章 研究結果與建議
第一節 研究結論 110
第二節 研究建議 112
參考文獻
中文部分 114
英文部分 115
附錄
附錄一：問卷(數學創造力測驗A) 118
附錄二：問卷(數學創造力測驗B) 121

中文部分：
孙思雨, & 郑鸿琴. (2017). 数学开放题: 测量学生创造力的有效途径. 教育测量与评价(10), 56-62.
成露茜, & 羊憶蓉. (1997). 從澳洲「關鍵能力」探討臺灣的「能力本位教育」。. 社教雙月刊, 78, 17-21.
何偉雲. (2004). 發散性思考測驗的同質性分析-以國小物理問題測驗爲例. 科學教育學刊, 12(2), 219-239.
吳武典. (1986). 資優教育的 [正思] 與 [迷思]. 資優教育季刊, 19, 23-25.
吳武典. (2013). 臺灣資優教育四十年 (一): 回首前塵. 資優教育季刊(126), 1-11.
吳璧純, & 詹志禹. (2018). 從能力本位到素養導向教育的演進, 發展及反思. Journal of Educational Research, 14(2), 35-64.
呂玉琴, & 溫世展. (2015). 國小五年級數學資優生解等差級數的表現 [The Performance of Elementary School Mathematically-Gifted Fifth Graders in Solving Arithmetical Sequence Questions]. 國民教育, 55(4), 63-66.
柯怡君, & 張靜嚳. (1995). 以問題為中心的數學教學策略在資優班與普通班實施之比較 [A Comparison of Using Problem-Centered Mathematical Teaching Strategies in Gifted and Normal Classes]. 科學教育(6), 181-207. https://doi.org/10.6767/jse.199502.0181
徐偉民, 陳佳萍, & 蔡桂芳. (2016). 國小資優資源班數學課程實施之個案研究 [A Case Study on Mathematics Curriculum Implemented in a Gifted Class of an Elementary School]. 課程與教學, 19(2), 129-159. https://doi.org/10.6384/ciq.201604_19(2).0006
國家教育研究院. (2014). 十二年國民基本教育課程發展指引.
國家教育研究院課程及教學研究中心核心素養工作圈. (2015). 十二年國民基本教育領域課程綱要核心素養發展手冊.
張芸夢. (2021). 台灣中學生數學創造力之研究 國立清華大學].
身心障礙及資賦優異學生鑑定辦法, (2013).
教育部. (2014). 十二年國民基本教育課程綱要總綱.
教育部. (2018). 十二年國民基本教育課程綱要國民中小學暨普通型高級中等學校-數學領域.
教育部. (2020). 一○九年度特殊教育統計年報.
教育部國民及學前教育署. (2019). 十二年國民基本教育資賦優異相關之特殊需求領域課程綱要.
郭奕龍. (2004). 創造力理論在創造能力資優生鑑定上之應用.
郭靜姿. (2001). 出席第十四屆世界資優會議紀實. 資優教育季刊, 80, 1-3.
陳玉樹, & 周志偉. (2009). 目標導向對創造力訓練效果之影響: HLM 成長模式分析. 課程與教學, 12(2), 19-45.
彭淑玲, 陳學志, & 黃博聖. (2015). 當數學遇上創造力：數學創造力測量工具的發展 [When Mathematics Encounters Creativity: The Development of a Measuring Tool for Mathematical Creativity]. 創造學刊, 6(1), 83-107.
劉世南, & 郭誌光. (2001). 創造力的概念與定義. 資優教育季, 102, 1-7.
劉宣谷. (2015). 數學創造力的文獻回顧與探究 [Survey and Discussion of Mathematical Creativity]. 臺灣數學教育期刊, 2(1), 23-40.
蕭佳純. (2019). 國內運用創造力教學模式對學生創造力影響之後設分析. 特殊教育研究學刊, 44(3), 93-120.

英文部分：
Balka, D. S. (1974). Using research in teaching: Creative ability in mathematics. The Arithmetic Teacher, 21(7), 633-636.
Baran, G., Erdogan, S., & Çakmak, A. (2011). A study on the relationship between sixyear-old children's creativity and mathematical ability. International Education Studies, 4(1), 135-148.
Diakidoy, I.-A. N., & Constantinou, C. P. (2001). Creativity in Physics: Response Fluency and Task Specificity. Creativity research journal, 13(3-4), 401-410. https://doi.org/10.1207/S15326934CRJ1334_17
Guilford, J. P. (1950). Creativity. American Psychologist, 5(9), 444-454. https://doi.org/10.1037/h0063487
Guilford, J. P. (1977). Way beyond the IQ. Creative Education Foundation.
Hadamard, J. (1954). An essay on the psychology of invention in the mathematical field. Dover.
Hanson, M. H. (2014). Converging paths: creativity research and educational practice. Knowledge quest, 42(5), 8.
Haylock, D. (1997). Recognising mathematical creativity in schoolchildren. Zdm, 29(3), 68-74.
Haylock, D. W. (1984). Aspects of mathematical creativity in children aged 11-12 University of London].
Haylock, D. W. (1987). A framework for assessing mathematical creativity in school chilren. Educational studies in mathematics, 18(1), 59-74.
Hollands, R. (1972). Educational Technology: Aims and Objectives in Teaching Mathematics (Cont.). Mathematics in School, 1(6), 22-23.
Jackson, P. W., & Messick, S. (1965). The person, the product, and the response: conceptual problems in the assessment of creativity. Journal of personality.
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. Zdm, 45(2), 167-181.
Kim, H., Cho, S., & Ahn, D. (2004). Development of mathematical creative problem solving ability test for identification of the gifted in math. Gifted Education International, 18(2), 164-174.
Kleinmintz, O. M., Goldstein, P., Mayseless, N., Abecasis, D., & Shamay-Tsoory, S. G. (2014). Expertise in musical improvisation and creativity: The mediation of idea evaluation. PloS one, 9(7), e101568.
Krutetskii, V. (1969). Mathematical aptitudes. Soviet studies in the psychology of learning and teaching mathematics, 2(1), 113-128.
Krutetskii, V. A., WIRSZUP, I., & Kilpatrick, J. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
Leikin, R. (2006). About four types of mathematical connections and solving problems in different ways. Aleh-The (Israeli) Senior School Mathematics Journal, 36, 8-14.
Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. the proceedings of the Fifth Conference of the European Society for Research in Mathematics Education,
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. Creativity in mathematics and the education of gifted students, 9, 129-145.
Leikin, R. (2018). Giftedness and High Ability in Mathematics. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 1-11). Springer International Publishing. https://doi.org/10.1007/978-3-319-77487-9_65-4
Leikin, R. (2021). When practice needs more research: the nature and nurture of mathematical giftedness. Zdm, 1-11. https://doi.org/10.1007/s11858-021-01276-9
Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. Proceedings of the 31st international conference for the psychology of mathematics education,
Leikin, R., & Lev, M. (2012). Mathematical creativity in generally gifted and mathematically excelling adolescents: what makes the difference? Zdm, 45(2), 183-197. https://doi.org/10.1007/s11858-012-0460-8
Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers’ knowledge. Canadian Journal of Science, Mathematics and Technology Education, 8(3), 233-251.
Levav-Waynberg, A., & Leikin, R. (2006). SOLVING PROBLEMS IN DIFFERENT WAYS: TEACHERS'KNOWLEDGE SITUATED IN PRACTICE.
Liberman, N., Polack, O., Hameiri, B., & Blumenfeld, M. (2012). Priming of spatial distance enhances children’s creative performance. Journal of experimental child psychology, 111(4), 663-670. https://doi.org/10.1016/j.jecp.2011.09.007
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the learning of mathematics, 26(1), 17-19.
MacKinnon, D. W. (1962). The personality correlates of creativity: A study of American architects.
Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. University of Connecticut.
Mednick, S. (1962). The associative basis of the creative process. Psychological review, 69(3), 220.
Osborn, A. F. (1953). Applied imagination.
Parnes, S. J. (1967). Creative behavior guidebook. Scribner.
Parr, P. G. (1974). The Phenomenon of Mathematical Invention. Mathematics Teaching, 66, 56-58.
Poincaré, H. (1952). Mathematical creation in Ghiselin B. The creative process, 22-31.
Polya, G. (1973). How to solve it; : a new aspect of mathematical method (2nd ed. ed.). Princeton University Press.
Renzulli, J., & Reis, S. (1986). M.(1986). The three-ring conception of giftedness: A developmental model for creative productivity. Conceptions of giftedness, 53-92.
Renzulli, J. S., Smith, L. H., White, A. J., Callahan, C. M., Hartman, R. K., & Westberg, K. L. (2002). Scales for rating the behavioral characteristics of superior students. Technical and administration manual. ERIC.
Richard, V., Ben Zaken, S., Siekańska, M., & Tenenbaum, G. (2021). Effects of Movement Improvisation and Aerobic Dancing on Motor Creativity and Divergent Thinking. The Journal of creative behavior, 55(1), 255-267.
Sadler-Smith, E. (2015). Wallas’ four-stage model of the creative process: More than meets the eye? Creativity research journal, 27(4), 342-352.
Shriki, A. (2010). Working like real mathematicians: Developing prospective teachers’ awareness of mathematical creativity through generating new concepts. Educational studies in mathematics, 73(2), 159-179.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
Siyu, S. (2017). MEASURING THE MATHEMATICAL CREATIVITY OF MIDDLE SCHOOL STUDENTS IN SHANGHAI BY OPEN-ENDED PROBLEMS. ICMI-EARCOME8, 363.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? Journal of Secondary Gifted Education, 17(1), 20-36.
Starko, A. J. (2017). Creativity in the classroom: Schools of curious delight. Routledge.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development.
Sternberg, R. J. (1999). Handbook of creativity. Cambridge University Press.
Sternberg, R. J. (2006). The nature of creativity. Creativity research journal, 18(1), 87.
Sternberg, R. J. (2017). ACCEL: A new model for identifying the gifted. Roeper review, 39(3), 152-169.
Torrance, E. P., & Goff, K. (1989). A Quiet Revolution. The Journal of creative behavior, 23(2), 136-145. https://doi.org/10.1002/j.2162-6057.1989.tb00683.x
Treffinger, D. J. (1995). Creativity, creative thinking, and critical thinking: In search of definitions. Center for Creative Learning.
Treffinger, D. J., Young, G. C., Selby, E. C., & Shepardson, C. (2002). Assessing Creativity: A Guide for Educators. National Research Center on the Gifted and Talented.
Wallas, G. (1926). The art of thought.
Wang, H.-c., & Cheng, Y.-s. (2016). Dissecting language creativity: English proficiency, creativity, and creativity motivation as predictors in EFL learners’ metaphoric creativity. Psychology of aesthetics, creativity, and the arts, 10(2), 205.
Weisberg, R. W. (1999). Creativity and knowledge: a challenge to theories.