本研究探討台灣中學生在多元解題任務上的解題表現，藉由解題之流暢性、靈活性及獨創性去評估學生之數學創造力，分析不同數學能力學生的解題表現，同時去觀察在台灣教師的數學教學中對於多元解題的看法。
　　透過調查研究法，進行「SAT-M」及「多元解題任務」之問卷施測。施測對象為新竹地區之國中二年級學生，總計3所學校之學生共計313人。施測結果以敘述性統計、相關係數、成對樣本 t 檢定、ANOVA單因子變異數分析等統計方法進行分析與討論。並透過半結構式訪談，訪談10位台灣中學數學教師對於多元解題看法。
　　研究結果顯示，在各題各項目平均分數上，問題三與問題五正確性分數低於其他題。流暢性、靈活性、獨創性及創造力分數平均皆為問題三最低，問題一最高。
　　個人解空間表現上，問題一大多數學生僅為2、3種；問題二、問題三及問題四絕大多數學生僅為1種；問題三亦有非常多的學生為0種；問題五大部分學生落在1、2種；問題6占最多數的則是0種。
　　在不同多元解題任務的兩兩比較上，幾何問題的兩題在正確性、流暢性以及靈活性皆達顯著差異，而獨創性及創造力則未達顯著差異。應用問題的兩題比較中，不管是正確性或者與創造力有關的各個成份上的表現都達顯著差異。而問題一的一般創造力問題分別與其他五題數學題目的比較上，所有項目全都達到顯著差異。
　　在數學能力表現與各題各項目的相關性上，可以發現皆沒有到達高度相關。其中相關性最高的落在數學能力表現與流暢性及靈活性。在問題五及問題六兩個成分的相關性最高有到.5，但也只是達到中度相關。
　　在不同數學能力組別學生對各題解題表現之差異上，各項目的平均分數大小順序幾乎與SAT-M四個組別的順序相同（僅問題二獨創性及創造力有些微不同）。而在單因子變異數分析上，結果皆達顯著差異，因此將所有項目進行事後比較。
　　訪談10位教師對於多元解題看法的結果可以發現，雖然大多中學數學教師會期望也會盡可能去指導學生使用多種解題方法，但在台灣的教學現場中對此並沒有到非常重視也不會以此要求學生，且多數教師也不太會向學生強調不同解法的價值。
　　最後，本研究將問題三之結果與以色列曾進行的研究進行對照。在流暢性、靈活性上，由以色列略高於台灣。而獨創性與創造力則由台灣高於以色列，但因為獨創性分數的標準不同，此處應進行更詳細的探討。

關鍵字：創造力、數學創造力、多元解題任務、國中

This research explores the problem-solving performance of Taiwanese middle school students on multiple solution tasks. Use the fluency, flexibility and originality of problem-solving to evaluate students' mathematical creativity. Analyze the problem-solving performance of students with different mathematics abilities, and at the same time observe the views on multiple problem-solving in the mathematics teaching of Taiwan teachers.
Through survey research, conducted "SAT-M" and " multiple solution tasks", surveying the questionnaire. The subjects of the test are second-year junior high school students in the Hsinchu area, with a total of 313 students from three schools. The test results are analyzed and discussed by statistical methods such as narrative statistics, correlation coefficients, paired sample t-tests, and ANOVA one-way variance analysis. Through semi-structured interviews, we interviewed ten Taiwanese middle school mathematics teachers about their views on multiple problem solving.
The results of the research show that in the average scores of each item of each question, the correctness scores of Question 3 and Question 5 are lower than those of other questions. The average scores for fluency, flexibility, originality, and creativity were the lowest in Question 3 and the highest in Question 1.
In terms of individual solution spaces performance, most students have only two or three types for Question 1; Question 2, 3 and 4 have only one type for the vast majority of students; Question 3 also has a very large number of students with zero types; in Question 5, most students have one or two types; and in Question 6, the most number is zero types.
In the comparison of different multiple solution tasks, the two geometric problems have significant differences in correctness, fluency, and flexibility, while the originality and creativity are not significantly different. In the comparison of the two questions of application problems, there are significant differences in the correctness or the various components related to creativity. Comparing the general creativity problem of Question 1 with the other five mathematical Questions, all items have reached significant differences.
In terms of the correlation between the performance of mathematical ability and each item of each question, it can be found that none of them have reached a high correlation. Among them, the most relevant are mathematics ability and fluency and flexibility. In Question 5 and Question 6, the correlation between the two components is as high as .5, but it is only moderately correlated.
　　In terms of the differences in the performance of students from different math ability groups in solving each problem, the order of the average scores for each item is almost the same as the order of the four groups of SAT-M (only Question 2 is slightly different in originality and creativity). In the ANOVA results, the results all reached significant differences, so all items are make a posteriori comparison.
The results of interviews with ten teachers on multiple problem-solving views. It is found that although most middle school mathematical teachers expect students to use multiple problem-solving methods, they will try to guide students to use multiple problem-solving methods as much as possible. However, in the teaching site in Taiwan, this is not very important and will not require students to use this, and most teachers are not likely to emphasize the value of different solutions to students.
Finally, this study compares the results of Question 3 with previous studies conducted in Israel. In terms of fluency and flexibility, Israel is slightly higher than Taiwan. The originality and creativity in Taiwan are higher than that in Israel, but because of the different standards for originality scores, a more detailed discussion should be conducted here.

Keywords: creativity, mathematical creativity, multiple solution tasks, junior high school

第一章 緒論 1
第一節 研究動機 1
第二節 研究目的與待答問題 3
第三節 研究限制 3
第四節 名詞解釋 4
第二章 文獻探討 5
第一節 現行政策及課程綱要 5
第二節 數學創造力之相關研究 6
第三節 數學創造力之評估 10
第三章 研究工具與實施 16
第一節 研究理念與架構 16
第二節 研究對象及背景 16
第三節 研究流程 17
第四節 研究工具 18
第五節 資料統計與分析 28
第四章 研究結果與分析 30
第一節 學生在多元解題任務之解題表現 30
第二節 不同數學能力學生之多元解題任務解題表現 49
第三節 教師在教學上對多元解題的看法 81
第五章 結論與建議 90
第一節 研究結論 90
第二節 研究建議 93
參考文獻 94
中文部分 94
英文部分 94
附錄 99
附錄一：多元解題任務問卷 99

中文部分：
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.

英文部分：
Askew, M. (2002). Policy, practices and principles in teaching numeracy: what makes a difference?. In Issues in mathematics teaching (pp. 121-136). Routledge.
Chamberlin, S. A., & Moon, S. (2005). Model-eliciting activities: An introduction to gifted education. Journal of Secondary Gifted Education, 17(1), 37-47.
Charles, R., & Lester, F. (1982). Teaching problem solving: What, why and how. Palo Alto, Calif.: Dale Seymour Publications.
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.
Cropley, A. (2006). In praise of convergent thinking. Creati vity Research Journal, 18 (3), 391–404.
Dhombres, J. (1993). Is one proof enough? Travels with a mathematician of the baroque period. Educational Studies in Mathematics, 24(4), 401-419.
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.
Goldenberg, E. P. (1996). “Habits of mind” as an organizer for the curriculum. Journal of Education, 178(1), 13-34.
Gómez-Chacón, I. M., & de la Fuente, C. (2018). Problem-solving and mathematical research projects: Creative processes, actions, and mediations. In Broadening the scope of research on mathematical problem solving (pp. 347-373). Springer, Cham.
Guilford, J. P. (1950). Creativity: American Psychologist. Citado en Dinámicas entre creación y procesos terapéuticos (2006)(coord. Coll). Murcia: Valle de Ricote. Universidad de Murcia.
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. (1987). A framework for assessing mathematical creativity in school chilren. Educational studies in mathematics, 18(1), 59-74.
Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, 65-97.
Hollands, R. (1972). Educational Technology: Aims and Objectives in Teaching Mathematics (Cont.). Mathematics in School, 1(6), 22-23.
Idris, N., & Nor, N. M. (2010). Mathematical creativity: usage of technology. Procedia-Social and Behavioral Sciences, 2(2), 1963-1967.
Jung, D. I. (2001). Transformational and transactional leadership and their effects on creativity in groups. Creativity Research Journal, 13(2), 185-195.
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. Zdm, 45(2), 167-181.
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. (2003). Problem-solving preferences of mathematics teachers: Focusing on symmetry. Journal of Mathematics Teacher Education, 6(4), 297-329.
Leikin, R. (2007, February). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In the proceedings of the Fifth Conference of the European Society for Research in Mathematics Education (pp. 2330-2339).
Leikin, R. (2009a). Bridging Research and Theory in Mathematics Education with Research and Theory in Creativity and Giftedness. Creativity in mathematics and the education of gifted students, 385.
Leikin, R. (2009b). 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., Berman, A., & Koichu, B. (2009). Creativity in mathematics and the education of gifted students. Brill.
Leikin, R., & Kloss, Y. (2011). Mathematical creativity of 8th and 10th grade students. In Proceedings of the 7th Conference of the European Society for Research in Mathemafics Educafion (pp. 1084-1093).
Leikin, R., & Lev, M. (2007, July). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In Proceedings of the 31st international conference for the psychology of mathematics education (Vol. 3, pp. 161-168).
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. (2009). Development of teachers’ conceptions through learning and teaching: The meaning and potential of multiple-solution tasks. Canadian Journal of Science, Mathematics and Technology Education, 9(4), 203-223.
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.
Leikin, R., & Sriraman, B. (2017). Creativity and giftedness. Bern, Swizerland: Springer.
Levav-Waynberg, A., & Leikin, R. (2009). Multiple solutions to a problem: A tool for assessment of mathematical thinking in geometry. The paper presented at the Sixth Conference of the European Society for Research in Mathematics Education–CERME-6.
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.
Levav-Waynberg, A., & Leikin, R. (2013). Using multiple solution tasks for the evaluation of students’ problem-solving performance in geometry. Canadian Journal of Science, Mathematics and Technology Education, 12(4), 311-333.
Levenson, E. (2011). Exploring collective mathematical creativity in elementary school. The Journal of Creative Behavior, 45(3), 215-234.
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., Livne, O. E., & Milgram, R. M. (1999). Assessing academic and creative abilities in mathematics at four levels of understanding. International Journal of Mathematical Education in Science and Technology, 30(2), 227-242.
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260.
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, Cham.
Molad, O., Levenson, E. S., & Levy, S. (2020). Individual and group mathematical creativity among post–high school students. Educational Studies in Mathematics, 104, 201-220.
Piirto, J. (1999). Identification of creativity. In J. Piirto (Ed.), Talented children and adults: Their development and education (pp. 136–184). Upper Saddle River, NJ: Prentice Hall.
Pitta-Pantazi, D., Sophocleous, P., & Christou, C. (2013). Prospective primary school teachers’ mathematical creativity and their cognitive styles. ZDM—The International Journal on Mathematics Education, 45(3).
Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
Romey, W. D. (1970). What is your creativity quotient?. School Science and Mathematics, 70(1), 3-8.
Runco, M. A., & Albert, R. S. (1985). The reliability and validity of ideational originality in the divergent thinking of academically gifted and nongifted children. Educational and Psychological Measurement, 45(3), 483-501.
Sarrazy, B., & Novotná, J. (2013). Didactical contract and responsiveness to didactical contract: A theoretical framework for enquiry into students’ creativity in mathematics. ZDM, 45(2), 281-293.
Schoenfeld, A. H. (1983). Problem Solving in the Mathematics Curriculum. A Report, Recommendations, and an Annotated Bibliography. MAA Notes, Number 1.
Sierpinska, A. (1994). Understanding in mathematics (Vol. 2). Psychology Press.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 29(3), 75-80.
Skemp, R. R. (1987). Th e Psychology of Learning Mathematics.
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.
Sriraman, B., Freiman, V., & LirettePitre, N. (Eds.). (2009). Interdisciplinarity, creativity, and learning: mathematics with literature, paradoxes, history, technology, and modeling. IAP.
Star, J. R., & Newton, K. J. (2009). The nature and development of experts’ strategy flexibility for solving equations. ZDM, 41(5), 557-567.
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., & Lubart, T. I. (1999). The concept of creativity: Prospects and paradigms. Handbook of creativity, 1, 3-15.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York, NY: The Free Press.
Tabach, M., & Friedlander, A. (2013). School mathematics and creativity at the elementary and middle-grade levels: how are they related?. ZDM, 45(2), 227-238.
Torbeyns, J., De Smedt, B., Ghesquière, P., & Verschaffel, L. (2009). Jump or compensate? Strategy flexibility in the number domain up to 100. ZDM, 41(5), 581-590.
Torrance, E. P. (1962). Guiding creative talent. Englewood Cliffs, NJ: Prentice-Hall.
Torrance, E. P. (1966). The Torrance Tests of Creative Thinking-Norms-Technical Manual Research Edition-Verbal Tests. Forms A and B-Figural Tests, Forms A and B.
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.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (pp.85-91). Cambridge, MA: Harvard University Press.
Watson, A. & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Lawrence Erlbaum.
Yakes, C., & Star, J. R. (2009). Using comparison to develop teachers' flexibility in algebra. Journal of Mathematics Teacher Education.
Zohar, A. (1990). Mathematical reasoning ability: Its structure, and some aspects of its genetic transmission. Hebrew University of Jerusalem..