學生在臆測任務課堂表現的數學創造力評量

Assessment of Mathematical Creativity for Students Performing in Conjecturing Tasks

10.6173/CJSE.202012/SP_28.0002

林碧珍(Pi-Jen Lin)

國小學生 ； 評量架構 ； 數學創造力 ； 臆測任務 ； Primary School Students ； Assessment Framework ； Mathematical Creativity ； Conjecturing Tasks

科學教育學刊

28卷S期（2020 / 12 / 01）

429 - 455

繁體中文

本研究的目的是建立一個數學臆測任務融入於課堂實踐下，學生表現的數學創造力評量架構，此架構包含任務本身和學生數學創造力的兩個評分規準，透過檢驗兩個研究問題，來瞭解評分規準的可行性。本研究的數學創造力架構增加精緻性元素並修正自Leikin在2009年編製的評量架構。個案教師將分數乘法臆測任務融入於兩屆五年級班級課堂教學中，在10堂課中使用的兩個臆測任務和兩屆學生表現的個人猜想、小組猜想和全班猜想，是本研究蒐集的主要資料。本研究利用兩個評分規準，分析任務本身的教學目標和學生提出的數學猜想。研究發現臆測任務實踐脈絡下的數學創造力評量架構可以從數學創造力觀點評量不同臆測任務的特性，任務中具有概括性的教學目標，能驅動學生的精緻性思考。學生數學創造力的評分規準，是以猜想的數量、類別、新穎性及概括性作為評量學生在臆測任務表現的流暢性、變通性、原創性及精緻性思考的指標。

The purpose of the study was to construct and examine an assessment framework for measuring mathematical creativity in the use of conjecturing tasks. The assessment framework employed the element of elaboration adapted from Leikin's (2009) framework. Two research questions were investigated in this study. One teacher and the students in her two fifth-grader mathematics classes were the subjects of the study. The tasks and students' individual conjectures, group conjectures, and whole-class conjectures were the main sources of data collected for the study. Two scoring rubrics for the assessment framework were developed and used to evaluate students' cognitive learning outcomes and mathematical creativity. Results showed that researchers were successful in using this framework to evaluate students in various learning tasks from a mathematics creativity perspective. The generalization of an institutional objective is potential to ignite students' thinking of elaboration. The assessment framework revealed students' thinking in fluency, flexibility, originality, and elaboration while performing in conjecturing tasks, counting on the number, category, novelty, and generalization of the conjectures that students proposed in the classroom.

1. 林碧珍, P.-J.(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。
   連結：
2. 侯雅齡, Y.-L.(2009)。幼兒資優特質與科學創造力之關係：心流經驗之中介效果。特殊教育研究學刊，34(2)，101-118。
   連結：
3. Akgül, S.,Kahveci, N. G.(2017).Developing a model to explain the mathematical creativ-ity of gifted students.European Journal of Education Studies,3(8),125-147.
4. 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.
5. Cropley, A.(2006).Functional creativity: A socially-useful creativity concept.Baltic Journal of Psychology,7(1),26-38.
6. Ervynck, G.(1991).Mathematical creativity.Advanced mathematical thinking,Dordrecht, The Netherlands:
7. Finke, R. A.,Ward, T. B.,Smith, S. M.(1992).Creative cognition: Theory, research, and applications.Cambridge, MA:MIT Press.
8. 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.
9. Guilford, J. P.(1967).The nature of human intelligence.New York, NY:McGraw-Hill.
10. Haavold, P. Ø.(2018).An empirical investigation of a theoretical model for mathematical cre-ativity.The Journal of Creative Behavior,52(3),226-239.
11. Haylock, D.(1997).Recognising mathematical creativity in schoolchildren.ZDM-Mathematics Education,29(3),68-74.
12. Hong, E.,Milgram, R. M.(2010).Creative thinking ability: Domain generality and specific-ity.Creativity Research Journal,22(3),272-287.
13. 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.
14. Kaufman, J. C.,Beghetto, R. A.(2009).Beyond big and little: The Four C Model of creativ-ity.Review of General Psychology,13(1),1-12.
15. 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.
16. Krutetskii, V. A.(1976).The psychology of mathematical abilities in schoolchildren.Chicago, IL:University of Chicago Press.
17. Leikin, R.(2018).Openness and constraints associated with creativity-directed activities in mathematics for all students.Broadening the scope of research on mathematical problem solving,Cham, Switzerland:
18. Leikin, R.(2009).Exploring mathematical creativity using multiple solution tasks.Creativity in mathematics and the education of gifted students,Rotterdam, The Netherlands:
19. Leikin, R.(2013).Evaluating mathematical creativity: The interplay between multiplicity and insight.Psychological Test and Assessment Modeling,55(4),385-400.
20. 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
21. 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(Vol. 3),Seoul, South Korea:
22. 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.
23. Leikin, R.,Pitta-Pantazi, D.(2013).Creativity and mathematics education: The state of the art.ZDM-Mathematics Education,45(2),159-166.
24. 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.
25. Mason, J.,Burton, L.,Stacey, K.(2010).Thinking mathematically.London, UK:Pearson Education.
26. Milgram, R. M.,Hong, E.(2009).Talent loss in mathematics: Causes and solutions.Creativity in mathematics and the education of gifted students,Rotterdam, The Netherlands:
27. Polya, G.(1973).How to solve it.Princeton, NJ:Princeton University Press.
28. Runco, M. A.,Jaeger, G. J.(2012).The standard definition of creativity.Creativity Research Journal,24(1),92-96.
29. Shriki, A.(2010).Working like real mathematicians: Developing prospective teachers’ aware-ness of mathematical creativity through generating new concepts.Educational Studies in Mathematics,73(2),159-179.
30. Silver, E. A.(1997).Fostering creativity through instruction rich in mathematical problem solv-ing and problem posing.ZDM-Mathematics Education,29(3),75-80.
31. Silver, E. A.,Mesa, V.(2011).Coordinating characterizations of high quality mathemat-ics teaching: Probing the intersection.Expertise in mathematics instruction: An international perspective,Boston, MA:
32. Sriraman, B.(2005).Are giftedness and creativity synonyms in mathematics?.Journal of Secondary Gifted Education,17(1),20-36.
33. Sriraman, B.(2017).Mathematical creativity: Psychology, progress and caveats.ZDM-Mathematics Education,49(7),971-975.
34. Stein, M. K.,Smith, M. S.,Henningsen, M. A.,Silver, E. A.(2000).Implementing standards-based mathematics instruction: A casebook for professional development.New York, NY:Teach-ers College Press.
35. Sternberg, R. J.,Lubart, T. I.(1996).Investing in creativity.American Psychologist,51(7),677-688.
36. Sweller, J.,van Merrienboer, J. J. G.,Paas, F.(2019).Cognitive architecture and instruction-al design: 20 years later.Educational Psychology Review,31(2),261-292.
37. Torrance, E. P.(1974).Torrance tests of creative thinking.Princeton, NJ:Personal Press/Ginn and Company.
38. Vygotsky, L. S.(1978).Mind in society: The development of higher psychological processes.Cambridge, MA:Harvard University Press.
39. Weisberg, R. W.(2015).Toward an integrated theory of insight in problem solving.Thinking & Reasoning,21(1),5-39.
40. 吳雅晴, Y.-C.,李心儀, S.-Y.(2017)。探討國小師資培育生提升學生數學創造力之教學活動設計。教師專業研究期刊，13，1-36。
41. 吳衛東, W.-D.,林碧珍, P.-J.,章勤瓊, Q.-Q.(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，20，62-67。
42. 呂玉琴, Y.-C.,吳宣鋒, S.-F.(2015)。國小數學資優生解尋求規律數學問題的表現。國民教育，55(4)，67-72。
43. 林碧珍（編）, P.-J.(Ed.)(2019).數學臆測任務設計與實踐：整數、分數與小數篇.臺北市=Taipei, Taiwan:師大書苑=Shtabook.
44. 林碧珍, P.-J.(2020)。素養導向的數學臆測教學模式。小學教學，1，8-11。
45. 國家教育研究院(2014年11月28日)。十二年國民基本教育課程綱要：總綱。查詢日期：2020年4月21日，檢自https://www.naer.edu.tw/upload/1/16/doc/288/%E5%8D%81%E4%BA%8C%E5%B9%B4%E5%9C%8B%E6%95%99%E8%AA%B2%E7%A8%8B%E7%B6%B1%E8%A6%81%E7%B8%BD%E7%B6%B1.pdf。[National Academy for Educational Research. (2014, November 28). Curriculum guidelines of 12- year basic education: General guidelines. Retrieved April 21, 2020, from https://www.naer.edu.tw/upload/1/16/doc/288/%E5%8D%81%E4%BA%8C%E5%B9%B4%E5%9C%8B%E6%95%99%E8%AA%B2%E7%A8%8B%E7%B6%B1%E8%A6%81%E7%B8%BD%E7%B6%B1.pdf]
46. 教育部=Ministry of Education(2003).創造力教育白皮書.臺北市=Taipei, Taiwan:作者=Author.
47. 彭淑玲, P.-S.,陳學志, H.-C.,黃博聖, P.-S.(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。
48. 曾千芝, C.-C.,曾麗錚, L.-C.,黃博聖, P.-S.(2017)。本國籍子女與新移民子女在數學成就與數學創造力的相關研究—以桃園地區國小六年級生為例。創造學刊，8(2)，1-18。
49. 劉祥通, S.-T,洪筱柟, S.-J.(2020)。五年級資優生在非例行性數線問題解題表現的個案研究。臺灣數學教師期刊，41(1)，1-25。

1. (2024)。國中生數學符號運算素養的創造思考表現。臺灣數學教育期刊，11(1)，1-36。