本研究的目的是在探究數學臆測任務中，五年級學生所展現的數學創造力。本研究的個案班級導師是進行臆測活動長達六年時間的國小教師，此班級學生多為第一年接觸數學臆測教學。研究中的資料蒐集，主要來自研究者擔任研究助理期間拍攝的科技部計畫資料，以及臆測教學專書中的案例。學生數學創造力的評分架構是參照Leikin(2013)的評分方式，該架構以數學思維方式的流暢性、變通性及原創性來評估學生的數學創造力表現。
　　初步研究結果發現：(1) 兩臆測任務中，學生提猜想的原創性表現較弱，顯示學生提猜想時，比較容易注意到數據表面的共通現象，但多數學生有能力提出不同類型的猜想；(2) 高分組創造力學生能看見更多資料中的規律、差異和相似性並提出數學猜想。而低分組創造力學生提出的猜想以低原創性為主，但有能力解讀數據間的關係；(3) 臆測任務中學生猜想的原創性分數與創造力分數之間具高相關，顯示臆測任務是評量數學創造力的有效工具，因為它與創造「有用的新產品」此數學創造力定義相匹配；(4) 造例數據類型多寡及學生數學先備知識可能會影響猜想的變通性表現。但同構的造例數據，不會因組織分類方式影響學生形成個人猜想的創造力表現；(5) 兩臆測任務中，學生猜想的流暢性、變通性、原創性沒有顯著差異，但分數乘法任務中學生猜想創造力的品質較梯形面積任務佳。

　　The objective of this study was to investigate the mathematical creativity 5th graders showed in mathematics conjecturing tasks. The participants of this research include an elementary school homeroom teacher who has been conducting conjecturing instructions for six years and the students mostly involved in mathematical conjecturing instructions for the first time. The data of this research was mainly collected by the researcher who photographed the information when he worked as the research assistant in Ministry of Science and Technology and partly from the cases in the books of conjecturing instructions. The criteria of students’ mathematical creativity refers to Roza Leikin (2013) scoring methods, with the framework of assessing students’ performance of mathematical creativity based on the fluency, flexibility and originality of their mathematical way of thinking.
　　The preliminary research findings are as follows: (1) In two mathematical conjecturing tasks, the majority of the students is those who with low flexibility and low originality. It shows that most students focus on common phenomenon of surface data when they formulate the conjecturing. Nonetheless, most students have the ability to formulate different types conjecturing. (2) Students with high creativity can see more regularity, difference and similarity in the data, and therefore formulate mathematical conjecturing, while those who with low creativity formulate conjecturing with low originality yet are able to interpret the relationship between data. (3) In the task, the originality score of conjecturing has high correlation with creativity score, which shows conjecturing tasks are an effective tool in evaluating mathematical creativity for it matches the definition of “creating useful new products”. (4) The number of example data types and students’ prior knowledge might affect the flexibility of conjecturing performance. However, the example data of the same type do not affect students’ personal performance of conjecturing creativity even with different grouping methods. (5) In these two conjecturing tasks, there is no significant difference in students’ creativity performance of conjecturing formulation. Still, in the task of fractional multiplication, the quality of students’ conjecturing creativity outdid that in the task of trapezoidal area.

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 4
第三節 名詞解釋 5
壹、數學創造力 5
貳、數學臆測教學 5
第四節 研究限制 6
第二章 文獻探討 7
第一節 數學創造力 7
壹、創造力的重要性 7
貳、數學創造力的意義 8
參、學校中的數學創造力 9
第二節 數學創造力的培養 11
壹、培養數學創造力的重要性 11
貳、培養數學創造力的阻力 12
參、培養數學創造力的助力 13
肆、數學臆測教學模式 18
第三節 數學創造力的評量 33
壹、評量數學創造力的重要性 33
貳、影響創造力表現的因素 34
參、數學創造力評量的實徵研究 36
第三章 研究設計與實施 43
第一節 研究架構 44
第二節 研究情境與對象 45
壹、研究情境 45
貳、研究對象 45
第三節 研究資料 46
壹、研究資料來源 46
貳、臆測教學任務 46
第四節 研究流程 50
第五節 資料蒐集與分析 51
壹、資料蒐集方法 51
貳、資料分析方法 52
參、資料分析舉隅 66
肆、資料的三角校正 69
第四章 研究結果與分析 70
第一節 學生在臆測任務提出猜想的數學創造力表現 70
壹、兩臆測任務中學生提出猜想的原創性表現較弱 71
貳、學生在兩臆測任務的變通性表現 75
參、高分組創造力學生在流暢性、變通性上的表現皆比低分組好 76
肆、高分組與低分組創造力學生提出猜想的原創性表現 76
伍、兩任務中學生提出猜想的流暢性、變通性、原創性之間的相關性 79
第二節 影響學生提出猜想的數學創造力表現的因素 82
壹、數學先備知識影響學生的創造力表現 82
貳、兩任務中造例數據的類型數量多寡會影響學生猜想的流暢性和變通性 83
參、造例數據的類型及組織分類方式對學生猜想原創性分數影響的分析 86
第三節 學生在兩個臆測任務表現的差異比較 88
壹、學生提出猜想的流暢性、變通性、原創性不因臆測任務不同而有差異 88
貳、分數乘法任務中提出重複猜想的人數比梯形面積任務少 89
參、分數乘法任務中學生低原創性的猜想比梯形面積少且中原創性猜想變多 92
肆、分數乘法任務中學生猜想創造力的品質較梯形面積任務佳 93
伍、部分學生在兩任務中的創造力分數差異極大 93
第五章 結論與建議 95
第一節 結論 95
壹、學生在臆測任務提出猜想的數學創造力表現 95
貳、臆測任務中影響學生創造力表現的因素 97
參、學生在兩臆測任務表現的差異比較 98
第二節 建議 99
壹、對使用臆測任務的教師在教學上的建議 99
貳、數學臆測教學下各階段所可能產生的創造力研究 99
參、對數學臆測任務下學生數學創造力表現後續研究工具的建議 99
參考文獻 100
中文文獻 100
英文文獻 102
附錄 112

中文文獻
毛連塭、郭有遹、陳龍安、林幸台(2000)。創造力研究。台北：心理。
王睿千、林靜萍(2009)。創造思考教學模組對體育師資生創造力的影響。大專體育學刊，11(3)，39-51。
江秀娟(2017)。翻轉學習對國小學生創造力效應之行動研究。國立臺北教育大學教育經營與管理學系學位論文，1-183。
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。國立清華大學碩士論文。
吳衛東、林碧珍、章勤瓊(2018)。變學科邏輯為教學邏輯：臺灣 “素養導向臆測教學模式”的教育學審視。教育發展研究，38(20)，62-67。
林幸台、王木榮(1994)。威廉斯創造力測驗指導手冊。臺北市: 心理。
林碧珍(2015)。以課堂教學導向促進學生數學學習的教師專業發展：學生+教師+培育者(總計畫含子計畫一)。發展學生論證的在職教師專業發展：以臆測教學為進路(1/3)。(計畫編號： MOST 104-2511-S-134 -003 -MY3)，未出版。
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。
林碧珍(2016)。數學臆測任務設計與實踐。臺北:師大書苑。
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、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。
林碧珍、鍾雅芳(2013)。六年級學生解決數字規律性問題的數學臆測思維歷程。2013 年第五屆科技與數學教育國際學術研討會暨數學教學工作坊論文集(pp.100-110)(Proceeding of 2013 The Fifth International Conference on Technology and Mathematics Education and Workshop of Mathematics Teaching)，6 月 8-9 日。國立台中教育大學數學教育學系。
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。
秦爾聰、劉致演、張克旭、段曉林(2015)。數學臆測探究教學對商職學生數學學習成就與動機之影響。臺灣數學教育期刊。
張世彗(2011)。創造力教學、學習與評量之探究。教育資料與研究雙月刊，(100)，1-21。
張春興(2004)。心理學概要。台北：東華書局。
張廖珮鈺、林碧珍(2019)。教師在數學臆測教學扮演協調者角色的教學行為。2019 第十一屆科技與數學教育國際學術研討會暨數學教學工作坊手冊(Proceeding of 2019 The Eleventh International Conference on Technology and Mathematics Education and Workshop of Mathematics Teaching)。5 月 25-26 日。國立台中教育大學數學教育系。
教育部(2014 年 11 月 28 日)。十二年國民基本教育課程綱要。取自http://www.naer.edu.tw/ezfiles/0/1000/attach/87/pta_5320_2729842_56626.pdf
連韻文(2007)。鷹架理論在數位學習環境的應用與調整: 探討中小學生歸納推理與幾何的學習-子計畫三: 在數位與非數位學習環境中學童歸納推理能力的探討。(2/2)。
陳李綢(2006)。國小數學創造力診斷與認知歷程工具研發。教育心理學報。
陳佳明、林碧珍(2019)。檢驗猜想規範的形成之教學策略。2019 第十一屆科技與數學教育國際學 術研討會暨數學教學工作坊手冊(Proceeding of 2019 the Eleventh International Conference on Technology and Mathematics Education and Workshop of Mathematics Teaching)。5 月 25-26 日。 國立台中教育大學數學教育系。
陳英娥、林福來(1998)。數學臆測的思維模式。科學教育學刊，191-218。
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。創造學刊，6(1)，83-107。
詹志禹(2002)。創造力教育政策白皮書—小學階段。臺北: 教育部。
趙偉順(2012)。國中生認知風格與科技創作表現關係之研究。國立臺灣師範大學碩士論文。
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。
劉珈妤、林緯倫、蔡秉勳(2016)。對的風格遇上對的人，謂之創意-人格特質，認知風格與兩類創造力之關係探討。教育心理學報。
薛千薇(2015)。國小四、六年級學生數學創造力之探究。國立臺北教育大學數學暨資訊教育學系學位論文，1-168。


 
英文文獻
Aiken Jr, L. R.(1973). Ability and creativity in mathematics. Review of Educational Research, 43(4), 405-432.
Akgül, S., & Kahveci, N. G. (2017). Developing a model to explain the mathematical creativity of gifted students. European Journal of Education Studies, 3(8), 125-147.
Anderson, V. P., Cornwall, J., Jack, S., & Gibson, R. S. (2008). Intakes from non‐breastmilk foods for stunted toddlers living in poor urban villages of Phnom Penh, Cambodia, are inadequate. Maternal & Child Nutrition, 4(2), 146-159.
Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: a catalyst for change? Journal of Mathematics Teacher Education, 8(6), 499-536.
Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. Mathematics, teachers and children, 216, 235.
Barnes, M. (2000). Magical moments in mathematics: Insights into the process of coming to know. For the Learning of Mathematics, 20(1), 33–43.
Beghetto, R. A. (2017). Lesson unplanning: toward transforming routine tasks into non-routine problems. ZDM, 49(7), 987-993.
Beghetto, R. A., & Schreiber, J. B. (2017). Creativity in doubt: Toward understanding what drives creativity in learning. In Creativity and Giftedness (pp. 147-162). Springer, Cham.
Benbow, C. P., & Arjmand, O. (1990). Predictors of high academic achievement in mathematics and science by mathematically talented students: A longitudinal study. Journal of Educational Psychology, 82(3), 430.
Blazhenkova, O., & Kozhevnikov, M. (2010). Visual-object ability: A new dimension of non-verbal intelligence. Cognition, 117(3), 276-301.
Boden, M. A. (2004). The creative mind: Myths and mechanisms. Psychology Press.
Brinkmann, A. (2004). The experience of mathematical beauty. In P. C. Clarkson & M. Hannula (Organizers), Students’ motivation and attitudes toward mathematics and its study: Proceedings of the 10th International Congress of Mathematics Education (Topics Study Group 24 [CD-ROM]). Copenhagen, Denmark.
Bruner, J. S. (1961). The act of discovery. Harvard educational review.
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.
Cheetham, J. M., Rahm, B., Kaller, C. P., & Unterrainer, J. M. (2012). Visuospatial over verbal demands in predicting Tower of London planning tasks. British Journal of Psychology, 103(1), 98-116.
Chen, Y. C., Hand, B., & Norton-Meier, L. (2017). Teacher roles of questioning in early elementary science classrooms: A framework promoting student cognitive complexities in argumentation. Research in Science Education, 47(2), 373-405.
Ching, J. (1997). Mysticism and Kingship in China the Heart of Chinese Wisdom.
Chiou, W. B., Wan, C. S., & Lee, H. Y. (2008). Virtual experience vs. brochures in the advertisement of scenic spots: How cognitive preferences and order effects influence advertising effects on consumers. Tourism Management, 29(1), 146-150.
Chrysostomou, M., Tsingi, C., Cleanthous, E., & Pitta-Pantazi, D. (2011). Cognitive styles and their relation to number sense and algebraic reasoning. Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education(pp. 387-396).
Cropley, A. (2006). Functional creativity: A socially-useful creativity concept. Baltic Journal of Psychology, 7(1), 26-35.
Csikszentmihalyi, M. (1988). Motivation and creativity: Toward a synthesis of structural and energistic approaches to cognition. New Ideas in psychology, 6(2), 159-176.
Csikszentmihalyi, M. (2015). The systems model of creativity: The collected works of Mihaly Csikszentmihalyi. Springer.
Davis, F. (1992). Fashion, Culture. Identity.
Denzin, N. K., & Lincoln, Y. S. (2005). Paradigms and perspectives in contention. The Sage handbook of qualitative research, 183-190.
Dietrich, A., & Kanso, R. (2010). A review of EEG, ERP, and neuroimaging studies of creativity and insight. Psychological bulletin, 136(5), 822.
Dominowski, R. L. (1995). Content effects in Wason’s selection task. Perspectives on thinking and reasoning: Essays in honour of Peter Wason, 41-65.
Dreyfus, T., & Eisenberg, T. (1986). On the aesthetics of mathematical thought. For the learning of mathematics, 6(1), 2-10.
Dreyfus, T., & Eisenberg, T. (1996). Mathematical Thinking. The nature of mathematical thinking, 253-284.
Dunbar, K. R., & Heintz, R. A. (1997). Chemistry of transition metal cyanide compounds: Modern perspectives. Progress in Inorganic Chemistry, 45, 283-392.
Edwards, T. (2003). Liquid fuels and propellants for aerospace propulsion: 1903-2003. Journal of propulsion and power, 19(6), 1089-1107.
Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht, Netherlands: Kluwer.
Eysenck, H. J. (1993). Creativity and personality: Suggestions for a theory. Psychological inquiry, 4(3), 147-178.
Feist, G. J. (1998). A meta-analysis of personality in scientific and artistic creativity. Personality and social psychology review, 2(4), 290-309.
Feldhusen, J. F. (1995). Creativity: A knowledge base, metacognitive skills, and personality factors. The Journal of creative behavior, 29(4), 255-268.
Gardner, H. E. (2000). Intelligence reframed: Multiple intelligences for the 21st century. Hachette UK.
Garofalo, J. (1989). Beliefs and their influence on mathematical performance. The Mathematics Teacher, 82(7), 502-505.
Ginsburg, H. P. (1996). Toby’s math. In R. J. Sternberg & T. BenZeev (Eds.),The nature of mathematical thinking(pp. 175–282). Mahwah, NJ: Lawrence Erlbaum.
Ginsburg, J., & Prelevic, G. M. (1996). Cause of vaginal bleeding in postmenopausal women taking tibolone. Maturitas, 24(1-2), 107-110.
Goldin, G. A. (2017).Mathematical creativity and giftedness: perspectives in response. ZDM, 49(1), 147-157.
Gruber, H. E., & Wallace, D. B. (1999). The case study method and evolving systems approach for understanding unique creative people at work. Handbook of creativity, 93, 115.
Guberman, R., & Leikin, R. (2013). Interesting and difficult mathematical problems: changing teachers’ views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56.
Guilford, J. P. (1950). Creativity research: Past, present and future. American psychologist, 5(1), 444-454.
Guilford, J. P. (1959). Three faces of intellect. American psychologist, 14(8), 469.
Guilford, J. P. (1967). Creativity: Yesterday, today and tomorrow. The Journal of Creative Behavior, 1(1), 3-14.
Haavold, P. Ø. (2018). An empirical investigation of a theoretical model for mathematical creativity. The Journal of Creative Behavior, 52(3), 226-239.
Haavold, P., Sriraman, B., & Lee, K. H. (2020). Creativity in Mathematics Education. Encyclopedia of Mathematics Education, 145-154.
Hadamard, J. (1945). The psychology of invention in the mathematical field Princeton University Press. Hadamard The Psychology of Invention in the Mathematical Field1945.
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.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for research in mathematics education, 524-549.
Hershkowitz, R., Tabach, M., & Dreyfus, T. (2017). Creative reasoning and shifts of knowledge in the mathematics classroom. ZDM, 49(1), 25-36.
Hong, E., & Aqui, Y. (2004). Cognitive and motivational characteristics of adolescents gifted in mathematics: Comparisons among students with different types of giftedness. Gifted Child Quarterly, 48(3), 191-201.
Hong, E., & Milgram, R. M. (2010). Creative thinking ability: Domain generality and specificity. Creativity Research Journal, 22(3), 272-287.
Iaea, U., & Iea, P. E. (2005). Energy indicators for sustainable development: Guidelines and methodologies. Science, 195, 968.
Jackson, P. W., & Messick, S. (1965). The person, the product, and the response: Conceptual problems in the assessment of creativity, Journal of Personality, 33(3), 309-329.
Jonassen, D. H., & Grabowski, B. (1993). Individual differences and instruction. New York: Allen & Bacon.
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.
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.
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.
Kozhevnikov, M., Blazhenkova, O., & Becker, M. (2010). Trade-off in object versus spatial visualization abilities: Restriction in the development of visual-processing resources. Psychonomic bulletin & review, 17(1), 29-35.
Kozhevnikov, M., Hegarty, M., & Mayer, R. E. (2002). Revising the visualizer-verbalizer dimension: Evidence for two types of visualizers. Cognition and instruction, 20(1), 47-77.
Kozhevnikov, M., Kosslyn, S., & Shephard, J. (2005). Spatial versus object visualizers: A new characterization of visual cognitive style. Memory & cognition, 33(4), 710-726.
Krummheuer, G. (1995). The ethnography of argumentation. Lawrence Erlbaum Associates, Inc.
Krutetskii, V. A. (1976). In J. Kilpatrick & I. Wirszup. The psychology of mathematical abilities in schoolchildren.
Kurtzberg, T. R., & Amabile, T. M. (2001). From Guilford to creative synergy: Opening the black box of team-level creativity. Creativity Research Journal, 13(3-4), 285-294.
Lampert, C. M. (2003). Large-area smart glass and integrated photovoltaics.Solar Energy Materials and Solar Cells, 76(4), 489-499.
Lan, Y., Gao, H., Ball, M. O., & Karaesmen, I. (2008). Revenue management with limited demand information. Management Science, 54(9), 1594-1609.
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).
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.
Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight1. Psychological Test and Assessment Modeling, 55(4), 385.
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. (2018). Openness and constraints associated with creativity-directed activities in mathematics for all students. In Broadening the Scope of Research on Mathematical Problem Solving (pp. 387-397). Springer, Cham.
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). 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). Seoul, Korea: The Korea Society of Educational Studies in Mathematics.
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.
Lev, M., & Leikin, R. (2013, January). 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).
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.(2013).Tasks that may occasion mathematical creativity: teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269-291.
Lichtman, M. (2010). Understanding and evaluating qualitative educational research. Sage Publications.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the learning of mathematics, 26(1), 17-19.
Lin, F. L., Yang, K. L., Lee, K. H., Tabach, M. & Stylianides, G. (2012). Principles of task design for conjecturing and proving. In Proof and proving in mathematics education. Dordrecht: Springer Netherlands.
Lin, P. J. & Horng, S. Y.(2017). The Conjecturing contributing to the group argumentation in primary Classrooms. Paper presented at the 9th Classroom Teaching Research for All Students Conference. July 12 – 15, Dalian University, China.
Lin, P. J. & Miao, J. Y. (2018). Teachers' supports for students engaging in mathematical argumentation. Proceedings of the Clute International Conference (pp.327-1~327-8). August 5-9. Clute Institute. San Francisco, California, USA. (ISSN2157-9660 on line)
Lin, P. J. (2016). The quality of students’ argumentation used in a fourth-grade classroom. Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, (vol.3, 211-218). Aug. 3 -7, University of Szeged, Hungary.
Lin, P. J. (2017). Enhancing students’ mathematical argumentation in primary classroom. Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education, (vol. 1, 237). July, 18-22, National Institute of Education, Singapore.
Lin, P. J. , & Tsai, W. H. (2015). Provoking Students’ Argumentation Through Conjecturing in Fourth-Grade Classroom. In Catherine Vistro Yu (Ed.), In pursuit of quality mathematics education for all: Proceedings of the 7th ICMI-East Asia Regional Conference on Mathematics Education (EARCOME7)(pp.493-500)., Cebu City, May 11-15. Quezon City: Philippine Council of Mathematics.
Lin, P. J.(2018). The Development of Students’ Mathematical Argumentation in a Primary Classroom. Educação & Realidade, 43(3), 1171-1192.
Lin, P. J., & Tsai, W. H. (2016). Enhancing Students’ Mathematical Conjecturing and Justification in Third-Grade Classrooms: the sum of even/odd numbers. Journal of Mathematics Education, 9(1), 1-15.
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255-276.
Littlewood, J. E. (1986). Littlewood's miscellany. Cambridge University Press.
Lubart, T. I., & Sternberg, R. J. (1995). An investment approach to creativity: Theory and data. The creative cognition approach, 269-302.
Maher, C. A., & Martino, A. M. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 194-214.
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260.
Martindale, C. (1995). Creativity and connectionism. The creative cognition approach, 249, 268.
Middleton, J. A., & Spanias, P. A. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for research in Mathematics Education, 65-88.
Milgram, R. M., & Hong, E. (2009). Talent loss in mathematics: Causes and solutions. In Creativity in mathematics and the education of gifted students (pp. 147-163). Brill Sense.
Nickerson, R. S. (1999). Enhancing Creativity. Handbook of creativity, 392.
Niss, M. (2003, January). Mathematical competencies and the learning of mathematics: The Danish KOM project. In 3rd Mediterranean conference on mathematical education (pp. 115-124).
Paivio, A. (1971). Imagery and language. Imagery(pp. 7-32). Academic Press.
Paulus, P. B., & Yang, H. C. (2000). Idea generation in groups: A basis for creativity in organizations. Organizational behavior and human decision processes, 82(1), 76-87.
Pehkonen, E., & Vaulamo, J. (1999). Pupils in lower secondary school solving open-ended problems in mathematics. In Proceedings of the Conference of the International Group for (Vol. 100, p. 1198).
Peirce, C. S. (1908/1960). A neglected argument for the reality of God. In C. Hartshorne & P. Weiss(Eds.), Collected papers of Charles Sanders Peirce (Vol. 6: Scientific metaphysics). Cambridge, MA: Harvard University Press.
Pelczer, I., & Rodríguez, F. G. (2011). Creativity assessment in school settings through problem posing tasks. The Mathematics Enthusiast, 8(1), 383-398.
Pellegrino, J. W., & Hilton, M. L. (2012). Committee on defining deeper learning and 21st century skills. Center for Education.
Peressini, D., & Knuth, E. (2000). The role of tasks in developing: Communites of mathematical inquiry. Teaching Children Mathematics, 6(6), 391.
Piirto, J. (1999). Implications of postmodern curriculum theory for the education of the talented. Journal for the Education of the Gifted, 22(4), 324-353.
Platt, J. R.(1964). Strong inference. science, 146(3642), 347-353.
Plucker, J. A., & Beghetto, R. A. (2004). Why creativity is domain general, why it looks domain specific, and why the distinction does not matter.
Poincaré, H. (1908). L'invention mathématique.
Posamentier, A. S., Smith, B. S., & Stepelman, J. (2010). Teaching secondary mathematics: Techniques and enrichment units. Allyn & Bacon.
Reid, D. A., & Knipping, C. (2010). Proof in mathematics education. Research, learning and teaching.
Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180.
Reston, V. NCTM, 2000. Dorothy Y. White For the Editorial Panel.
Richardson, A. (1977). Verbalizer-visualizer: a cognitive style dimension. Journal of mental imagery.
Riding, R., & Cheema, I. (1991). Cognitive styles-an overview and integration. Educational psychology, 11(3-4), 193-215.
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.
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.
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.
Shulman, L. S.(1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 29(3), 75-80.
Silver, E. A., & Mesa, V.(2011). Coordinating characterizations of high quality mathematics teaching: Probing the intersection. Expertise in mathematics instruction(pp. 63-84). Springer, Boston, MA.
Silvia, P. J., Kaufman, J. C., & Pretz, J. E. (2009). Is creativity domain-specific? Latent class models of creative accomplishments and creative self-descriptions. Psychology of Aesthetics, Creativity, and the Arts, 3(3), 139.
Simonton, D. K.(1989). Chance-configuration theory of scientific creativity. Cambridge University Press.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics?. Journal of Secondary Gifted Education, 17(1), 20-36.
Sriraman, B. (2017). Mathematical creativity: psychology, progress and caveats. ZDM, 49(7), 971-975.
Sriraman, B., Haavold, P., & Lee, K. (2013). Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward. ZDM, 45(2), 215-225.
Sriraman, B., Yaftian, N., & Lee, K. H.(2011). Mathematical creativity and mathematics education: A derivative of existing research. The elements of creativity and giftedness in mathematics(pp. 119-130). Brill Sense.
Stanley Budner, N. Y. (1962). Intolerance of ambiguity as a personality. Journal of personality, 30(1), 29-50.
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American educational research journal, 33(2), 455-488.
Sternberg, R. J. (2017). ACCEL: A new model for identifying the gifted. Roeper Review, 39(3), 152-169.
Sternberg, R. J.(2005).Creativity or creativities?. International Journal of Human-Computer Studies, 63(4-5), 370-382.
Sternberg, R. J., & Davidson, J. E. (Eds.). (2005). Conceptions of giftedness. Cambridge University Press.
Sternberg, R. J., & Lubart, T. I. (1996). Investing in creativity. American psychologist, 51(7), 677.
Sternberg, R. J., & Lubart, T. I. (1999). The concept of creativity: Prospects and paradigms. Handbook of creativity, 1, 3-15.
Stylianides, A., & Styliandes, G.(2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in ‘real-life’ contexts. Teaching and Teacher Education, 24(4), 859–875.
Tammadge, A. (1979). Creativity: Presidential address to the mathematical association at the annual conference, April 1979. The Mathematical Gazette, 63(425), 145-163.
Tan, A. G., & Sriraman, B. (2017). Convergence in creativity development for mathematical capacity. In Creativity and Giftedness (pp. 117-133). Springer, Cham.
Torrance, E. P. (1966). Torrance tests of creative thinking: Norms-technical manual: Verbal tests, forms a and b: Figural tests, forms a and b. Personal Press, Incorporated.
Torrance, E. P. (1974) Torrance Tests of Creative Thinking: norms and technical manual. Bensenville, IL: Scholastic Testing Services.
Toulmin, S. E. (1958). The philosophy of science(Vol. 14). Genesis Publishing Pvt Ltd.
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.
Usiskin, Z. (2000). The development into the mathematically talented. Journal of Secondary Gifted Education, 11(3), 152-162.
Vartanian, O., Martindale, C., & Kwiatkowski, J.(2003). Creativity and Inductive Reasoning: The Relationship between Divergent Thinking and Performance on Wason's 2-4-6 Task. The Quarterly Journal of Experimental Psychology Section A, 56(4), 1-15.
Von Neumann, J., & Morgenstern, O. (2007). Theory of games and economic behavior (commemorative edition). Princeton university press.
Vygotsky, L. S. (1984). Imagination and creativity in adolescent. In R. W. Rieber (Ed.), The collected works of L. S. Vygotsky: Vol. 5, child psychology. (pp. 151-166). New York, NY: Springer.
Walker, R. W., & Ellwood, J. (2009). The management of difficult intubation in children. Pediatric Anesthesia, 19, 77-87.
Wallas, G. (1926). The art of thought. New York, NY: Harcourt Brace.
Watson, A., & Mason, J.(2007). Taken-as-shared: A review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education, 10(4-6), 205-215.
Weisberg, R. (1993). Creativity: Beyond the myth of genius. WH Freeman.
Weisberg, R. W. (2015). Toward an integrated theory of insight in problem solving. Thinking & Reasoning, 21(1), 5-39.
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.
Winicky-Landman, G., & Leikin, R. (2000). On equivalent and nonequivalent definitions I. For the Learning of Mathematics, 20(1), 17–21.
Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. The Journal of Mathematical Behavior, 21(4), 423-440.