本研究探討國中學生之數學創造力，透過開放性數學問題的多元解答任務之解題表現評量其數學創造力。並進行不同數學能力、不同年級、不同性別，檢測其數學創造力是否有差異。最後將不同數學主題之創造力進行比較，探討彼此間是否相關。
透過調查研究法，進行數學創造力評量之問卷施測，施測題目共計3題多元解答任務，對象為國中七、八、九年級共530名學生。數學創造力之評分架構係參照Leikin（2013）的模式，該架構以數學思維方式之流暢性、變通性、原創性評量學生之數學創造力表現。
研究結果顯示，數學能力較高的學生也具有較高的數學創造力。數學創造力之各項指標，大致上皆為高年級優於低年級，僅在數列問題中，七年級之流暢性分數高於八年級達顯著差異。分析不同年級之解答空間可發現，常規性解法出現比例隨著年級增加而提高。不同性別在數學創造力表現則並無顯著差異。最後，不同主題之數學創造力之間皆呈正相關，並且全數達顯著相關，而唯一未達顯著相關的例外為數列問題和九點問題的流暢性。

This study explored the mathematical creativity of junior high school students and evaluated their mathematical creativity through their performance in answering multiple solutions tasks of open-ended mathematical questions. Comparisons were made among different mathematical ability, grade level, and gender to see if there were differences among their mathematical creativity. Lastly, comparisons were made among creativity of different mathematical topics to explore if relevance existed.
The survey research method was adopted for this study and questionnaires were circulated to assess mathematical creativity. The questionnaire consisted of three multiple solutions tasks and the participants were 530 students from the seventh, eighth and ninth grades in junior high school. The scoring framework for evaluating mathematical creativity was based on the model proposed by Leikin (2013), which evaluates the performance of students’ mathematical creativity by taking into account the fluency, flexibility, and originality of their mathematical thinking.
The results showed that students with higher mathematical ability also have higher mathematical creativity. Higher graders generally scored higher than lower graders in the various indicators of mathematical creativity, with the exception of the Sequence Problem where the fluency scores of seventh graders were higher than those of eighth graders and significant differences were found. An analysis on the solution spaces of different grade levels found that the percentage of conventional solutions increased as students’ grade level got higher. In terms of gender, no significant differences were found in their mathematical creativity performance. Finally, there were positive correlations among mathematical creativity of different topics, and all of them are significantly correlated. The only exception is the fluency of the Sequence Problem and the Nine-dot Problem, which did not reach a significant correlation.

第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與待答問題 3
第三節 名詞解釋 4
第四節 研究限制 5
第二章 文獻探討 6
第一節 創造力 6
第二節 數學創造力 9
第三節 數學創造力之評量 14
第三章 研究方法 20
第一節 研究架構 20
第二節 研究對象 21
第三節 研究流程 22
第四節 研究工具 23
第五節 資料統計與分析 36
第四章 研究結果與分析 37
第一節 學生在數學多元解答任務之表現 37
第二節 不同變項在數學多元解答任務之表現 56
第三節 數學多元解答任務中各項數學創造力間之關係 77
第五章 研究結論與建議 79
第一節 研究結論 79
第二節 研究建議 81
參考文獻 82
中文部分 82
英文部分 83

中文部分：
江雅惠（2020）。從擬題活動觀察國小五年級學童在數學創造力表現─以小數概念為例。國立臺北教育大學，臺北市。https://hdl.handle.net/11296/tv7c9b
林碧珍（2020）。學生在臆測任務課堂表現的數學創造力評量。科學教育學刊， 28(S)，429-455。
邱品瑜（2021）。國小資優生數學創造力檢測系統開發。國立臺中教育大學，臺中市。https://hdl.handle.net/11296/s7x6jq
柯中竣（2021）。探討高中生在極座標與圖形設計課程中的數學創造力。國立臺灣師範大學，臺北市。https://hdl.handle.net/11296/yph3nj
張芸夢（2021）。台灣中學生數學創造力之研究。國立清華大學，新竹市。 https://hdl.handle.net/11296/ku46fg
陳正曄（2020）。在數學臆測教學下學生數學創造力的展現。國立清華大學，新竹市。https://hdl.handle.net/11296/4twuh7
曾麗錚（2016）。國小六年級一般生學童與新移民學童在數學成就與數學創造力的相關性研究-以桃園地區為例。玄奘大學，新竹市。 https://hdl.handle.net/11296/eb4ad9
楊津佩（2019）。國小高年級資優生數學創造力之探究。國立臺北教育大學，臺北市。https://hdl.handle.net/11296/53rtjz
葉憲明（2022）。台灣中學數學資優生數學創造力之研究。國立清華大學，新竹市。https://hdl.handle.net/11296/93uht2
劉宣谷（2015）。數學創造力的文獻回顧與探究。臺灣數學教育期刊，2(1)，23-40。
薛千薇（2015）。國小四、六年級學生數學創造力之探究。國立臺北教育大學，臺北市。https://hdl.handle.net/11296/bd83cv
謝定澄（2022）。六年級學生在臆測教學下數學創造力的表現。國立清華大學，新竹市。https://hdl.handle.net/11296/7mnnub

英文部分：
Bahar, A. K., & Maker, C. J. (2011). Exploring the relationship between mathematical creativity and mathematical achievement. Asia-Pacific Journal of Gifted and Talented Education, 3(1), 33-48.
Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Secondary Gifted Education, 17(1), 37-47.
Charles, R. E., & Runco, M. A. (2001). Developmental trends in the evaluative and divergent thinking of children. Creativity Research Journal, 13(3-4), 417-437.
Chiu, M.-S. (2009). Approaches to the teaching of creative and non-creative mathematical problems. International Journal of Science and Mathematics Education, 7(1), 55-79.
Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. Zdm, 41(5), 605-618.
Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht: Kluwer.
Evans, E. W. (1964). Measuring the ability of students to respond in creative mathematical situations at the late elementary and early junior high school level. University of Michigan.
Ganihar, N. N., & Wajiha, A. H. (2009). Factor affecting academic achievement of IX standard students in mathematics. Edutracks, 8(7), 25–33.
Ginsburg, H. P. (1996). Toby’s math. The nature of mathematical thinking, 175-282.
Guilford, J. P. (1950). Creativity. American psychologist, 5(9).
Guilford, J. P. (1967). The nature of human intelligence.
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.
Hong, E., & Milgram, R. M. (2010). Creative thinking ability: Domain generality and specificity. Creativity Research Journal, 22(3), 272-287.
Jensen, L. R. (1973). The relationships among mathematical creativity, numerical aptitude and mathematical achievement. The University of Texas at Austin.
Jeon, K.-N., Moon, S. M., & French, B. (2011). Differential effects of divergent thinking, domain knowledge, and interest on creative performance in art and math. Creativity Research Journal, 23(1), 60-71.
Jung, D. I. (2001). Transformational and transactional leadership and their effects on creativity in groups. Creativity Research Journal, 13(2), 185-195.
Kattou, M., Christou, C., & Pitta-Pantazi, D. (2015). Mathematical creativity or general creativity? CERME 9-Ninth Congress of the European Society for Research in Mathematics Education,
Kattou, M., Christou, C., & Pitta-Pantazi, D. (2016). Characteristics of the creative person in mathematics. In. Nova Science Publishers.
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. Zdm, 45(2), 167-181.
Kaufman, J. C., Cole, J. C., & Baer, J. (2009). The construct of creativity: Structural model for self‐reported creativity ratings. The Journal of Creative Behavior, 43(2), 119-134.
Kim, K. H. (2011). The creativity crisis: The decrease in creative thinking scores on the Torrance Tests of Creative Thinking. Creativity Research Journal, 23(4), 285-295.
Kim, K. H., & Pierce, R. A. (2013). Torrance’s innovator meter and the decline of creativity in America. In The Routledge international handbook of innovation education (pp. 183-197). Routledge.
Kim, M. K., Roh, I. S., & Cho, M. K. (2016). Creativity of gifted students in an integrated math-science instruction. Thinking Skills and Creativity, 19, 38-48.
Kwon, O. N., Park, J. H., & Park, J. S. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7(1), 51-61.
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). 23. Bridging research and theory in mathematics education with research and theory in creativityand giftedness. Creativity in mathematics and the education of gifted students, 385.
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. Creativity in mathematics and the education of gifted students, 9, 129-145.
Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight1. Psychological Test and Assessment Modeling, 55(4), 385.
Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424.
Leikin, R., & Kloss, Y. (2011). Mathematical creativity of 8th and 10th grade students. Proceedings of the 7th Conference of the European Society for Research in Mathematics Education (pp. 1084-1093). Rzeszñw, Poland: European Society for Research in Mathematics Education.
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. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? Zdm, 45(2), 183-197.
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.
Leikin, R., Levav-Waynberg, A., Gurevich, I., & Mednikov, L. (2006). Implementation of Multiple Solution Connecting Tasks: Do Students' Attitudes Support Teachers' Reluctance? Focus on learning problems in mathematics, 28(1), 1.
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. Zdm, 45(2), 159-166.
Lev, M., & Leikin, R. (2013). The connection between mathematical creativity and high ability in mathematics. In Proceedings of the Eight Congress of the European Society for Research in Mathematics Education (CERME8) (pp. 1204-1213). Ankara, Turkey: ERME.
Levav-Waynber, A., & Leikin, R. (2010). Multiple solutions for a problem: A tool for evaluation of mathematical thinking in geometry. In Proceedings of CERME (Vol. 6, No. 2010, pp. 776-785).
Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31(1), 73-90.
Levenson, E., Swisa, R., & Tabach, M. (2018). Evaluating the potential of tasks to occasion mathematical creativity: Definitions and measurements. Research in Mathematics Education, 20(3), 273-294.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the learning of mathematics, 26(1), 17-19.
Livne, N. L., & Milgram, R. M. (2006). Academic versus creative abilities in mathematics: Two components of the same construct? Creativity Research Journal, 18(2), 199-212.
Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. University of Connecticut.
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260.
Mann, E. L. (2009). The search for mathematical creativity: Identifying creative potential in middle school students. Creativity Research Journal, 21(4), 338-348.
Mann, E. L., Chamberlin, S. A., & Graefe, A. K. (2017). The prominence of affect in creativity: Expanding the conception of creativity in mathematical problem solving. In Creativity and Giftedness (pp. 57-73). Springer.
Molad, O., Levenson, E. S., & Levy, S. (2020). Individual and group mathematical creativity among post–high school students. Educational Studies in Mathematics, 104(2), 201-220.
Pelczer, I., & Rodríguez, F. G. (2011). Creativity assessment in school settings through problem posing tasks. The Mathematics Enthusiast, 8(1), 383-398.
Pitta-Pantazi, D., Kattou, M., & Christou, C. (2018). Mathematical creativity: Product, person, process and press. In Mathematical creativity and mathematical giftedness (pp. 27-53). Springer.
Plucker, J., & Zabelina, D. (2009). Creativity and interdisciplinarity: One creativity or many creativities? Zdm, 41(1), 5-11.
Polya, G. (1973). How to solve it; a new aspect of mathematical method.
Rhodes, M. (1961). An analysis of creativity. The Phi delta kappan, 42(7), 305-310.
Romey, W. D. (1970). What is your creativity quotient? School Science and Mathematics, 70(1), 3-8.
Runco, M. A., & Jaeger, G. J. (2012). The standard definition of creativity. Creativity Research Journal, 24(1), 92-96.
Sak, U., & Maker, C. J. (2006). Developmental variation in children's creative mathematical thinking as a function of schooling, age, and knowledge. Creativity Research Journal, 18(3), 279-291.
Sheffield, L. J. (2009). Developing mathematical creativity—Questions may be the answer. Creativity in mathematics and the education of gifted students, 87-100.
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.
Smith, G., & Carlsson, I. (1985). Creativity in middle and late school years. International Journal of Behavioral Development, 8(3), 329-343.
Smith, G. J., & Carlsson, I. (1983). Creativity in early and middle school years. International Journal of Behavioral Development, 6(2), 167-195.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? Journal of Secondary Gifted Education, 17(1), 20-36.
Sriraman, B. (2009). The characteristics of mathematical creativity. Zdm, 41(1), 13-27.
Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and instruction, 18(6), 565-579.
Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408-426.
Sternberg, R. J. (2009). The nature of creativity. The Essential Sternberg: Essays on intelligence, psychology and education, 103-118.
Sternberg, R. J. (2017). ACCEL: A new model for identifying the gifted. Roeper Review, 39(3), 152-169.
Stigler, J. W., & Hiebert, J. (2009). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. Simon and Schuster.
Torrance, E. P. (1962). Guiding Creative Talent. Englewood Cliffs, New Jersey Prentlce-Hall. In: Inc.
Torrance, E. P. (1966). Nurture of creative talents. Theory Into Practice, 5(4), 167-173.
Torrance, E. P. (1968). A longitudinal examination of the fourth grade slump in creativity. Gifted Child Quarterly, 12(4), 195-199.
Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL: Scholastic Testing Service.
Treffinger, D. J. (1995). Creative problem solving: Overview and educational implications. Educational Psychology Review, 7(3), 301-312.
Walia, P. (2012). Achievement in relation to mathematical creativity of eighth grade students. Indian Streams Research Journal, 2(2), 1-4.
Weisberg, R. W. (1999). 12 Creativity and Knowledge: AC hallenge. Handbook of creativity, 226.
Weisberg, R. W. (2006). Creativity: Understanding innovation in problem solving, science, invention, and the arts. John Wiley & Sons.