本研究旨在探討一位五年級教師如何設計與實踐數學創思力導向臆測教學於課堂中。數學創思力導向臆測教學是發展學童的創造性思考技能(簡稱為數學創思力)為教學目標來設計與實踐於教學中。
　　本研究將數學創思力導向臆測教學融入於五年級數學課程中的「小數乘法關係」與「比率與百分率」單元，透過臆測教學模式的四個階段：造例、提猜想、效化、一般化階段，來發展學童的數學創思力。
　　資料蒐集包含：全班27位學童的個人造例單、小組工作單、個人猜想單、小組猜想單、全班猜想單、8節課教學錄影逐字稿以及與諍友晤談逐字稿。數學創思力的資料分析採用林碧珍(2020)數學創思力評量架構來分析個人、小組和全班學童在二單元的數學創思力表現，包含：流暢性、變通性、原創性與精緻性四個元素。
　　研究結果：(一)流暢性建立五項目標，協助學童造例與造例統整，進而觀察資料規律提出多個有憑有據的猜想，提高流暢性得分；(二)變通性建立三項目標，協助學童將造例單分類，教導分類與歸類原則並針對猜想單分類與歸類，提高變通性得分；(三)原創性建立三項目標，鼓勵、具體化與引導學童大膽提出獨特猜想，協助學童連結舊經驗與不侷限於課本框架，提高原創性得分；(四)精緻性建立四項目標，協助學童將猜想修正為數學語言、化繁為簡，並加入前提與全稱量詞，提高精緻性得分。(五)原創性是數學創思力得分關鍵。(六)林碧珍(2020)數學創思力評量架構具備有效性且便於診斷；(七)掌握學童與各組數學創思力程度，作為分組參考

關鍵字 ：數學創思力、數學創思力評量架構、數學臆測教學模式

The main purpose of this research is to study a fifth-grade teacher designs and practice of mathematical creativity-based conjecturing teaching in mathematics. Mathematical creativity-based conjecturing teaching is designed and practice in teaching aims to promote students' creative thinking skills (referred to as mathematical creativity).
The study integrates mathematical creativity-based conjecturing teaching into the "Decimal Multiplication Relationships" and "Ratio and Percentage" units of the fifth-grade mathematics curriculum. It promotes students' mathematical creativity through four stages of conjecturing teaching : construction stage, formulation stage, validating the conjecture, and Generalizing the conjecture
Researcher collects the date includes 27 individual worksheets, group worksheets, individuals, groups, as well as whole class conjecturing, transcripts of eight lessons recorded on video, and transcripts of discussions with academic peers. The data analysis of mathematical creativity is based on Professor Pi-Jen Lin’s assessment framework of mathematical creativity, which assessing students’ performance of individual, group, and whole-class students in the two units of mathematical creativity, including fluency, flexibility, originality, and elaboration.
Research findings: (1) Fluency establishes five objectives, assisting students in individual worksheets and integrating worksheets, observing data patterns to formulation multiple well-founded conjecturing, and increasing fluency scores. (2) Flexibility establishes three objectives, assisting students in classifying worksheets, teach classification and categorization principles, and classify and categorize conjecture to increase flexibility scores. (3) Originality establishes three objectives, encourage, concretize, and guide students to boldly formulate unique conjecture, assisting students connect prior knowledge and go beyond textbook frameworks, and increase originality scores.(4) Elaboration establishes four objectives, assisting students revise conjecture into mathematical language, simplify complexity, and add premises and quantifiers, increasing elaboration scores.(6) Originality is the key factor in scoring mathematical creativity. (7) Lin (2020) assessment framework of mathematical creativity is effective and easy to diagnose. (8) Assessing students' and groups' levels of mathematical creativity serves as a benchmark for grouping.

Keywords： Mathematical Creativity, Assessment Framework of Mathematical Creativity, Teaching Conjecturing in mathematics

一、中文文獻
1. 王金國(2018)。以專題式學習法培養國民核心素養。臺灣教育評論月刊，7(2)，107-111。
2. 王珮均(2023)。一位六年級教師實施批判力導向的數學臆測教學之行動研究。國立清華大學。
3. 江新合(1997)。邁向二一世紀的科學教育。物理教育，1(2)，110-120.
4. 吳明隆(2001)。敎育行動硏究導論: 理論與實務。五南圖書出版股份有限公司。
5. 吳清山(2011)。發展學生核心素養，提升學生未來適應力。研習資訊，28(4)，1-3。
6. 吳清山(2019)。教師執行新課綱之新挑戰、新思維與新作為。師友，613，7-12。
7. 周姝聿(2018)。一位體制外教師實施臆測教學在造例階段的任務設計之行動研究。國立清華大學。
8. 林劭帆(2020)。融入泰雅文化學校本位課程之臆測任務設計與實踐之行動研究。國立清華大學。
9. 林勇吉(2017)。真的只有教師知識和信念嗎？數學教師覺察力：從另一個觀點來看待教師的專業能力。科學教育月刊，402，2-15。
10.林碧珍(2015)國小三年級課室以數學臆測活動引發學生論證初探。科學教育學刊, 23(1), 83-110.
11.林碧珍(2018)。數學臆測引發數學論證的課堂實踐(上)。小學教學(數學版)，4，4-7。
12.林碧珍(2020)。素養導向的數學臆測教學模式。小學教學，1，8-11。
13.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。
14.林碧珍(2021)。素養導向的數學臆測教學模式之理論與實務。臺北市 ： 師大書苑。
15.林碧珍、陳姿靜(2021)。數學臆測教學模式教戰守則。台北市：師大書苑。ISBN：978-957-496-847-3。
16.林碧珍、蔡文煥(2005)。TIMSS 2003 國小四年級數學新試題的開發及建構反應試題診斷性編碼系統的製定。科學教育，280，51-62。
17.康軒文教事業有限公司(2022)。國民小學數學課本 (主編：楊瑞智，修訂版，第十冊，五下)。臺北：康軒。
18.張世慧(2013)。創造力：理論，技法與教學。台灣五南圖書出版股份有限公司。
19.張芬芬、陳麗華、楊國楊(2010)。臺灣九年一貫課程轉知議題與因應。教科書研究，3(1)，1-38。
20.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。國立新竹教育大學。
21.張廖佩鈺、林碧珍(2020) 數學臆測教學中教師擔任協調者角色之教學行為。台灣數學教育期刊，7(2)，1-23。doi: 10.6278/tjme.202010_7(2).0001。
22.教育部(2003)。創造力教育白皮書。台北市：教育部。
23.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。
24.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。國立清華大學。
25.陳英娥、林福來(1998)。數學臆測的思維模式。科學教育學刊，第六卷第二期191-218。
26.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。
27.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。
28.蔡清田(2007)。課程行動研究的實踐之道。課程與教學，10(3)，75-89。
29.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。
30.謝雅芸(2018)。從電視劇《你的孩子不是你的孩子》談升學主義下的家庭角色。臺灣教育評論月刊，7(10)，246-249。
31.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。國立新竹教育大學。
32.顏銘霆、林碧珍(2023年10月14日)。創思力導向臆測任務設計與實踐：一位初任教師五年級的數學課堂。2023年E時代的教育前瞻國際學術研討會(2023 International Conference on Educational Perspective in the E Era)－永續發展教育在全球化時代的挑戰與展望論文集(Challenge and Perspective of Education for Sustainable Development in the Globalization Era) (pp.244-271)。國立臺中教育大學教育學系。
33.顏銘霆、林碧珍(2024年5月4日-5月5日)。學生在數學創思力導向臆測任務下的創思力表現。2024台灣數學教育學會年會暨第十六屆科技與數學教育國際學術研討會(Proceeding of 2024 The Sixteenth International Conference on Technology and Mathematics Education and Workshop of Mathematics Teaching)) (p.61)。國立臺中教育大學數學教育學系。

二、英文文獻
1. Anderson, L. W. (2001). In Anderson LW, Krathwohl DR. A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives.
2. Beghetto, R. (2013). Nurturing creativity in the micro-moments of the classroom. In K. H. Kim, J. Kaufman, J. Baer, & B. Sriraman (Eds.), Creatively gifted students are not like other gifted students: Research, theory, and practice (pp. 3-15). Rotterdam, The Netherlands: Sense.
3. Bloom, J. W. (2014). Complexity, patterns, and creativity. In D. Ambrose, B. Sriraman, & K. M. Pierce (Eds.), A critique of creativity and complexity: Deconstructing clichés (pp. 199-214). Rotterdam: Sense.
4. Bonotto, C. (2013). Artifacts as sources for problem-posing activities.
5. Cañadas, M. C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, O. (2007). The conjecturing process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55-72. doi:10.22329/jtl.v5i1.82
6. 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.
7. Ching, J. (1997). Mysticism and Kingship in China the Heart of Chinese Wisdom.
8. Cropley, A. (2006). Functional creativity: A socially-useful creativity concept. Baltic Journal of Psychology, 7(1), 26-38.
9. Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. New York, NY.
10.Dagsdóttir, Ó. (2022). Creative Mathematics-Professional Development in an Icelandic Compulsory School.
11.Daniels, E. A. (2013). Fighting, loving, teaching: An exploration of hope, armed love and critical urban pedagogies (Vol. 4). Springer Science & Business Media.
12.Educational Studies in Mathematics, 83(1), 37–55.
13.Edwards, T. G. & Hensien, S. M. (1999). Changing instructional practice through action research.Journal of Mathematics Teacher Education, 2, 187–206.
14.Ervynck, G. (1991). Mathematical creativity. In Advanced mathematical thinking (pp. 42-53). Dordrecht: Springer Netherlands.
15.Fullan, M., Quinn, J., & McEachen, J. (2017). Deep learning: Engage the world change the world. Thousand Oaks, CA: Corwin Press.
16.Grohman M. G., Szmidt K. J. (2013) Teaching for creativity: How to shape creative attitudes and skills in students and teachers in: Teaching creatively and teaching for creativity, M. B. Gregorson, H. T. Snyder, J. C. Kaufman (eds.), New York, NY: Springer Publishing Company: 16–36.
17.Guilford, J. P. (1950). Creativity. American Psychologists, 5, 444-454.
18.Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw-Hill.
19.Guilford, J. P. (1986).Creative talents: Their nature, uses and development. Bearly limited.
20.Haylock, D. (1997). Recognising mathematical creativity in schoolchildren. ZDM― Mathematics Education, 29(3), 68-74. doi:10.1007/s11858-997-0002-y
21.Haylock, D. W. (1987). A framework for assessing mathematical creativity in school chilren. Educational studies in mathematics,18(1), 59-74.
22.Jeffrey, B., & Craft, A. (2004). Teaching creatively and teaching for creativity: distinctions and relationships. Educational Studies in Mathematics, 30(1), 77–87.
23.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. doi:10.1080/10400419.2011.545750
24.Junaedi, I., Suyitno, A., Sugiarto, E. and Eng, C.K., 2015. Disclosure Causes of Students Error in Resolving Discrete Mathematics Problems Based on NEA as A Means of Enhancing Creativity. International Journal of Education, 7(4), pp.31-42.
25.Kettler, T., Lamb, K. N., & Mullet, D. R. (2018). Developing creativity in the classroom: Learning and innovation for 21st-century schools. Waco, TX: Prufrock Press.
26.Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel?. Educational Studies in Mathematics, 105(3), 349-365.
27.Kosko, K. W., & Wilkins, J. L. (2011). Communicating quantitative literacy: An examination of open-ended assessment items in TIMSS, NALS, IALS, and PISA. Numeracy, 4(2), Article 3. DOI: 10.5038/1936-4660.4.2.3
28.Küchemann, D., & Hoyles, C. (2006). Influences on students’mathematical reasoning and patterns in its development: Insights from a longitudinal study with particular reference to geometry. International Journal of Science and Mathematics Education, 4(4), 581-608.
29.Lakatos, I. (1976).Falsification and the methodology of scientific research programmes (pp. 205-259). Springer Netherlands.
30.Lee, K. H. (2017). Convergent and divergent thinking in task modification: A case of Korean prospective mathematics teachers’ exploration. ZDM Mathematics Education, 49(7), 995–1008.
31.Leikin, R. (2007). 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).
32.Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin,A. Berman, & B. Koichu (Eds.),Creativity in mathematics and the education of gifted students(pp. 129-145). Rotterdam, The Netherlands: Sense Publishers. doi:10.1163/9789087909352_010
33.Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight. Psychological Test and Assessment Modeling, 55(4), 385-400.
34.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.
35.Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education (Vol. 3, pp.161-168). Seoul, South Korea: Korean Society of Educational Studies in Mathematics.
36.Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM, 45(2), 159-166. doi:10.1007/s11858-012-0459-1
37.Leikin, R., & Sriraman, B. (2022). Empirical research on creativity in mathematics (education): From the wastelands of psychology to the current state of the art. ZDM–Mathematics Education,54(1), 1-17.
38.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.
39.Mason, J., Burton, L., & Stacey, K. (1982). Thinking Mathematically ally.
40.Mills, G. E. (2007). Action research: A guide for the teacher researcher. Upper Saddle
41.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.
42.Mrayyan, S. (2016). Investigating mathematics teacher’s role to improve students’ creative thinking. American Journal of Educational Research, 4(1), 82-90.
43.National Research Council. (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. National Academies Press.
44.Ngiamsunthorn, P. S. (2020). Promoting creative thinking for gifted students in undergraduate mathematics. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(1), 13-25.
45.Novotna, J., & Sarrazy, B. (2014). Learning. In D. Ambrose, B. Sriraman, & K. M. Pierce (Eds.), A critique of creativity and complexity: Deconstructing clichés (pp. 19-33). Rotterdam: Sense.
46.Nugroho, A. A., Nizaruddin, N., Dwijayanti, I., & Tristianti, A. (2020). Exploring Students' Creative Thinking in the Use of Representations in Solving Mathematical Problems Based on Cognitive Style. Journal of Research and Advances in Mathematics Education, 5(2), 202-217.
47.OECD (2018). PISA 2021 Mathematics Framework (Draft).
48.Organisation for Economic Co-operation and Development (2003). The definition and selection of key competencies: Executive summary. Retrieved from https://www.oecd.org/pisa/35070367.pdf
49.P21, The Partnership for 21st Century Learning (2003). Framework for 21st Century Learning. Retrieved from http://www.p21.org/storage/documents/docs/P21_framework_0116.pdf
50.Polya, G. (2020). Mathematics and plausible reasoning, Volume 1: Induction and analogy in mathematics. Princeton University Press.
51.Popper, K. (1963). What is dialectic? Conjectures and refutations, 334.
52.Ranjan, A., & Gabora, L. (2013). Creative ideas for actualizing student potential. In M. Gregerson, J. Kaufman, & H. Snyder (Eds.), Teaching creatively and teaching creativity (pp. 119-131). New York, NY: Springer.
53.Romey, W. D. (1970). What is your creativity quotient? School Science and Mathematics, 70(1), 3-8.
54.Runco, M. A., & Jaeger, G. J. (2012). The standard definition of creativity. Creativity Research Journal, 24(1), 92-96. doi:10.1080/10400419.2012.650092
55.Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM―Mathematics Education, 29(3), 75-80. doi:10.1007/s11858-997-0003-x
56.Silver, E. A., & Mesa, V. (2011). Coordinating characterizations of high quality mathematics teaching: Probing the intersection. Expertise in mathematics instruction: An international perspective, 63-84.
57.Snyder, H., Gregerson, M., & Kaufman, J. (2013). Preface. In M. Gregerson, J. Kaufman, & H. Snyder (Eds.), Teaching creatively and teaching creativity (pp. xi-xiv). New York, NY: Springer.
58.Sprague, M. E., & Parsons, J. (2012). The promise of creativity. LEARNing Landscapes, 6(1), 389-407.
59.Sriraman, B. (2017). Mathematical creativity: Psychology, progress and caveats. ZDM, 49(7), 971-975. doi:10.1007/s11858-017-0886-0
60.Sriraman, B., Haavold, P., & Lee, K.-H. (2013). Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward. ZDM, 45(2), 215-225. doi:10.1007/s11858-013-0494-6
61.Starko, A. J. (2018). Creativity in the classroom (6th ed.). New York, NY: Routledge.
62.Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standard based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press.
63.Sternberg, R. J. (2017). School mathematics as a creative enterprise. ZDM, 49(7), 972-986. doi:10.1007/s11858-017-0884-2
64.Tabach, M., & Friedlander, A. (2013). School mathematics and creativity at the elementary and middle-grade levels: How are they related? ZDM the International Journal on Mathematics Education, 45(2), 227-238.
65.Torrance, E. P. (1974). Torrance tests of creative thinking. Princeton, NJ: Personal Press/Ginn and Company.
66.Vygotsky, L. S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. Harvard university press.
67.Wallas, G. (1926). The art of thought. New York, NY: Harcourt Brace.
68.World Economic Forum. (2020). The future of jobs report 2020. World Economic Forum, Geneva, Switzerland.