本研究旨在探究數學臆測任務下的數學教學課堂中，高年級學生所展現的數學創思力樣貌，以林碧珍教授（2020）的數學臆測任務的數學創思力評量架構為基礎，修正自Leikin（2013）的多元解答任務評量架構，探究臆測教學中任務的創思力潛能與學生的數學創思力表現。
本研究為方法為行動研究法，以研究者任教的高年級為研究場域，研究單元挑選幾何為主題，分別在五個單元中執行創思力導向的數學臆測教學，並針對立體形體以及垂直平行關係兩個單元進行分析。研究期間透過教學現場錄影、學生的猜想單、和諍友的對話等資料搜集與分析，進行教學反思和改進。
本研究在培養數學創思力的四個元素，分別是流暢性、變通性、原創性、精緻性。培養流暢性要造出多種正確例子、提出正確且有憑有據的猜想、小組和全班正確檢驗；培養變通性要組間例子類型不重複、辨別猜想類型並進行歸類；培養原創性需要從不同角度觀察的思維、判斷自己所寫的猜想是否為少數並歸類；培養精緻性要使用精緻性數學語言加入前提、梳理猜想間的邏輯包含關係。
研究結果發現：數學創思力與創思力導向數學臆測教學實施密不可分，透過創思力導向數學臆測教學，教師能找出相對應的有效策略，藉由創思力導向數學臆測教學規範解決教學中的困難，以培養學生數學創思力。
最後，本研究對使用創思力導向數學臆測教學之教學者給予建議並提出在數學臆測教學中不同類型單元未來可研究的方向。

This study aimed to explore the manifestations of mathematical creativity of upper grade primary students during mathematical conjecturing tasks in the classroom. Building upon Professor Pi-Jen Lin 's framework for assessing mathematical creativity in conjecturing tasks, and modifing Leikin's framework for assessing multiple solution tasks, this research investigates the potential of creativity in conjecturing tasks and students' performance in mathematical creativity within a conjecturing teaching.
This study adopts an action research methodology and focuses on upper grade classrooms . Geometry was chosen as the thematic unit, and five units are implemented with creativity-directed mathematical conjecturing teaching. Analysis was conducted specifically on the units related to solid figures and vertical parallel relationships. During the research period, data collection and analysis are carried out through classroom video recordings, students' conjecture sheets, and discussions with colleagues, facilitating teaching reflection and improvement.
The study emphasized four elements in fostering mathematical creativity: fluency, flexibility, originality, and elaboration. Fostering fluency involved generating multiple correct examples, proposing correct and well-founded conjectures, and conducting accurate checks within groups and the whole class. Fostering flexibility required differentiating the types of examples used among groups and categorizing conjecture types accordingly. Fostering originality involved thinking from different perspectives and determining whether one's conjecture belongs to a minority category. Fostering elaboration involved using precise mathematical language to incorporate premises and clarify the logical relationships among conjectures.
The research findings indicated an inseparable connection between mathematical creativity and creativity-directed mathematical conjecturing teaching. Through this teaching approach, teachers can identify effective strategies to address difficulties and cultivate students' mathematical creativity.
Finally, this study provided recommendations for educators using creativity-directed mathematical conjecturing teaching and suggests future research directions for different types of units in mathematical conjecturing teaching.

Keywords: mathematical creativity, creativity- directed mathematical conjecturing teaching.

余姿縈(2018)。初任教師建立數學臆測規範之行動研究:以高年級為例。未出版碩士論文。國立清華大學數理教育研究所。
吳長恩(2018)。數學臆測教學下教師提問類型之個案研究。未出版碩士論文。國立清華
大學數理教育研究所。
呂沅潤(2015)。數學臆測教學課室中國小四年級學生論證結構之比較。未出版碩士論
文。國立新竹教育大學碩士論文。
林碧珍(2021)。素養導向數學臆測教學模式之理論與實務。師大書苑。
林碧珍、陳姿靜(2021)。數學臆測教學模式教戰守則。師大書苑。
林碧珍(2020)。學生在臆測任務課堂表現的數學創思力評量。科學教育學刊
28(S),429-455。
林碧珍(2020)。素養導向的數學臆測教學模式。小學教學(數學版)，(1)5，8-11。
林碧珍(2019)。數學臆測任務設計與實踐－幾何量與統計篇。師大書苑。
林碧珍、鄭俊彥、蔡寶桂(2018)。國小六年級學生「數學論證評量工具」之建構。測驗
學刊，65(3)，257-289。
林碧珍、鄭章華、陳姿靜(2016)。數學素養導向的任務設計與教學實踐─以發展學童的
數學論證為例。教科書研究，9(1)，109-134。
林慧茵(2011)。探討以臆測為中心的探究教學對高職實用技能學程學生數學學習動機 之影響。未出版碩士論文。國立彰化師範大學科學教育研究所。
林緯倫、連韻文(2001)。如何能發現隱藏的規則?從科學資優生表現的特色，探索提升規則發現能力的方法。科學教育學刊，9(3)，1-24。
周欣怡(2015)。數學臆測教學課室中國小三年級學生論證結構發展之研究。未出版碩士論文。國立清華大學數理教育研究所。
洪神佑(2016)。在數學臆測教學下一組國小六年級學生論證結構發展之研究。未出版碩士論文。國立清華大學數理教育研究所。
陳正曄(2020)。在數學臆測教學下學生創思力的展現。未出版碩士論文。國立清華大學數理教育研究所。
陳佳明(2018)。一位國小五年級教師建立從造例到提出猜想臆測教學規範之行動研究。 未出版碩士論文。國立清華大學數理教育研究所。
陳惠邦(1998)。教育行動研究。台北：師大書苑。
張廖珮鈺(2018)。數學臆測教學的教師角色之研究。未出版碩士論文。國立清華大學數理教育研究所。
張桂惠(2016)。一位國小五年級教師將數學臆測融入教學實踐之行動研究。未出版碩士論文。國立清華大學數理教育研究所。
游淑美(2018)。一位體制外教師三年級數學臆測任務設計及實踐之行動研究。國立清華大學碩士論文。
教育部(2003)。創造力教育白皮書。臺北市：作者。
教育部(2014)。十二年國民基本教育課程綱要。臺北市：作者。
蕭淑惠(2016)。實施以臆測為中心的教學探討四年級學生臆測思維歷程與主動思考 能力展現之行動研究。未出版碩士論文。國立彰化師範大學科學教育研究所。
藍敏菁(2016)。一位國小三年級教師設計臆測任務融入數學教學之行動研究。未出版碩
士論文。國立新竹教育大學數理教育研究所。
 
英文文獻
Aiken Jr, L. R.(1973). Ability and creativity in mathematics. Review of Educational Research, 43(4), 405-432.
Cañadas, M. C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, O. (2007). The conjec- turing. process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55-72. doi:10.22329/jtl.v5i1.82
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.
Guberman, R. & Leikin, R. (2013). Interesting and difficult mathematical problems: Chang- ing. teachers’ views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56. doi:10.1007/s10857-012-9210-7
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 children. Educational Studies in Mathematics, 18(1): 59–74.
Jeon, K.-N., Moon, S. M., & French, B. (2011). Differential effects of divergent thinking, do- main knowledge, and interest on creative performance in art and math. Creativity Research Journal, 23(1), 60-71. doi:10.1080/10400419.2011.545750
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting. mathematical creativity to mathematical ability. ZDM, 45(2), 167-181.
Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four c model of. creativity. Review of general psychology, 13(1), 1-12.
Krainer, K. (2006). Editorial: Action research and mathematics teacher education. Journal of Mathematics Teacher Education, 9, 213–219.
Kim, B., & Peppas, N. A. (2003). In vitro release behavior and stability of insulin in. complexation hydrogels as oral drug delivery carriers. International journal of pharmaceutics, 266(1-2), 29-37.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn. mathematics(Vol. 2101). National research council (Ed.). Washington, DC: National Academy Press.
Krutetskii, V. A. (1976). In J. Kilpatrick & I. Wirszup. The psychology of mathematical. abilities in schoolchildren.
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 mathemat- ics teachers. International Journal of Educational Research, 102. Retrieved April 18, 2020, from https://doi.org/10.1016/j.ijer.2019.04.002
Leikin, R. (2018). Openness and constraints associated with creativity-directed activities in. mathematics for all students. In N. Amado, S. Carreira, & K. Jones (Eds.), Broadening the scope of research on mathematical problem solving (pp. 387-397). Cham, Switzerland: Spring- er. doi:10.1007/978-3-319-99861-9_17
Leikin, R. (2016). Interplay between creativity and expertise in teaching and learning of. mathematics. In Proceedings of the 40th Conference of the International Group for the psychology of mathematics education (Vol. 1, pp. 19-34).
Leikin, R., Waisman, I. & Leikin, M. (2016). Does solving insight-based Problems differ from solving learning-based problems?
Leikin, R. and Elgrably, H. (2015). Creativity and expertise – The chicken or the egg? Discovering properties of geometry figures in DGE.
Leikin, R (2014). Challenging mathematics with multiple solution tasks and mathematical investigations in geometry.
Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically. excelling adolescents: What makes the difference? ZDM―Mathematics Education, 45(2), 183- 197. doi:10.1007/s11858-012-0460-8
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM―Mathematics Education, 45(2), 159-166. doi:10.1007/s11858-012-0459-1
Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight. Psychological Test and Assessment Modeling
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM―Mathematics Education, 45(2), 159-166. doi:10.1007/s11858-012-0459-1
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In Creativity in mathematics and the education of gifted students (pp. 129-145). Brill Sense.
Lin, P. J. (2018)：The development of students’ mathematical argumentation in a. primaryclassroom. Educação & Realidade, 43(3), 1171-1192.
Lin, P. J. (2017)：Fostering novice teachers’ knowledge of students’ errors on fractions division by using researched-based cases
Levenson, E.(2013).Tasks that may occasion mathematical creativity: teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269-291.
Miri Lev and Roza Leikin (2013).THE CONNECTION BETWEEN MATHEMATICAL CREATIVITY AND HIGH ABILITY IN MATHEMATICS.
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the. Gifted, 30(2), 236-260.
Reston, V. NCTM, 2000. Dorothy Y. White For the Editorial Panel.
Sheffield, L. J. (2009). Developing mathematical creativity–Questions may be the answer. In. Creativity in mathematics and the education of gifted students (pp. 87-100). Brill Sense.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? Journal of Secondary Gifted Education, 17(1), 20-36. doi:10.4219/jsge-2005-389
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem. solving and problem posing. Zdm, 29(3), 75-80.
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.
Torrance, E. P. (1974) Torrance Tests of Creative Thinking: norms and technical manual. Bensenville, IL: Scholastic Testing Services.
Whitenack, J., & Yackel, E. (2002). Making mathematical arguments in the primary grades: the importance of explaining and justifying ideas.(Principles and Standards). Teaching Children Mathematics, 8(9), 524-528.