數學專題合作學習中創意的經營與評量

Developing Creativity through Web-Based Mathematics Project-Based Learning and Assessment

10.6384/CIQ.200407.0033

洪碧霞(Pi-Hsia Hung)；陳沅(Yun Chen)；林宜樺(I-Hua Lin)

數學專題 ； 創意教學 ； 歷程評量 ； Web-based ； Mathematics Project ； Process Assessment

課程與教學

7卷3期（2004 / 07 / 01）

33 - 54

繁體中文

數學專題學習提供更開放、真實的學習情境，尊重學生不同的專長背景與學習取向，其中合作式學習更是專題學習經營的主流。本研究的目的在探討數學專題合作學習中創意經營與評量的效益，研究中藉由歷程評量的監控與回饋，支持小組成員間開放而豐富的互動歷程，協助學生追求數學概念的多元激盪與共識進展。本文以參與數學專題合作學習兩到三年的實驗樣本為依據，擇取其中兩組學生為案例，說明如何在系列專題學習中以歷程評量的取向，提供學習的綱要規範與支持鷹架，持續而系統的記錄國小學生專題合作學習討論與書面報告中創意的進展狀態。本研究討論能力的評定包含尊重的態度和中肯的發言；書面報告包含數學概念與表徵創意。研究中操作性界定數學創意為討論時發言切題，並能以新鮮有趣的例子說明數學的概念；書面報告中概念清晰豐富，並能以多元的表徵進行解釋或是能提供獨特而富參考價值的結果資訊。經由五項專題學習的歷程紀錄顯示，參與數學專題合作學習學生討論語錄與書面報告中數學的創意確實呈現實質的進展。與家長、學生訪談紀錄也顯示，專題合作學習的活動深獲得支持與認同。隨著專題合作學習經驗的累積，學生數學發言多能漸趨中肯、有趣；書面概念表徵也逐漸更為適切、清晰、多元、並富參考價值。專題小組成員間多元的背景和想法，為學習注入新的活力；歷程評量回饋讓專題活動的觀摩激勵效能尤其顯著。國小學生數學創意的激發，不是一蹴可即；本研究顯示採專題合作的學習取向，佐之以適切的歷程評量，持續而誠懇的支持和回饋，創意可以植根萌芽。

The accelerating rate of change in the world is producing an environment that is more unpredictable than ever before with a wider range of options. The creative talents of citizens are crucial to their success. Our modern world requires people with increased flexibility and adaptability. The research literature strongly suggests that PBL is an effective curricular approach to developing scientific, mathematical, and technological talent and creativity. The alignment of learning activity and assessment during PBL is essential if this approach is to be effective. This paper described a three-years study undertaken in two Taiwan elementary schools which explored students' learning progresses in Web-based learning environment designed to support project-based learning (PBL). The results demonstrated the potential effect of creating a positive learning environment. By establishing a culture that stresses student self-management and self-direction; using models or exemplars of excellent work; and creating a virtual environment that will facilitate project work, the participants work hard happily and progress significantly. Creativity plays a major role in the learning process of PBL. Our creativity learning support involves environmental, activity, and feedback dimensions. The foundation for the development of creativity is established through a supportive, open-minded and innovative web-based PBL interaction environment. The learning activities encourage massive discussion between and within collaborative groups. And creativity is an element of all formative assessment designs. At their early experiences, students had difficulty with open-end situations and with ill-defined problems. It is unsatisfactory to have a teacher intervene and direct students in their inquiry, while it is equally unsatisfactory to allow students to flounder or to put in large blocks of time exploring unproductive ideas in their investigations. The results suggested that the effectiveness of PBL as an instruction method may depend on the scaffolding of formative assessment feedbacks. The study incorporated clear standards to guide beginning inquiry, with experienced peer or teacher on-line assessment feedback. On-line formative assessment feedback embedded guidance for or models of how to conduct an operation within project materials. The formative assessment also provides norms for individual accountability in the group and progress for each group. These results show that collective intelligence and creativity is an attainable dream even for the elementary school students.

1. Adler, M. J.(1986).Commentary: Why critical thinking programs won't work.Education Week,28
2. Basili, P. A.,Sanford, J. P.(1991).Conceptual change strategies and cooperative groups work in chemistry.Journal of Research in Science Teaching,28(4)
3. Boaler, J.(1998).Open and closed mathematics: student experiences and understandings.Journal for Research on Mathematics Education,29(1)
4. Project-based learning overview: four reasons to try
5. Cobb, P.,Wood, T.,Yackel, E.,Perlwitz, M.(1992).A follow-up assessment of a second-grade problem-centered mathematics project.Educational Studies in Mathematics,23
6. Erickson, D. K.(1999).A problem-based approach to mathematics instruction.Mathematics Teacher,92(6)
7. Gardner, H.(1993).Creating minds.
8. Hmelo, C. E.,Gotterer, G. S.,Bransford, J. D.(1997).A theory-driven approach to assessing cognitive effects of PBL.Instructional Science,25(6)
9. Krajcik, J. S.,Czemiak, C. M.,Berger, C.(1999).Teaching Children Science: A Project-based Approach.
10. Problem-based Learning in Mathematics
11. Lubienski, S. T.(1999).Problem-centered mathematics teaching.Mathematics Teaching in the Middle School,5(4)
12. Reynolds, F.(1997).Studying psychology at degree level. Would problem-based learning enhance students' experiences?.Studies in Higher Education,22(3)
13. Sharp, J. E.(1997).Using portfolio in classroom.Proceedings of 27th Frontiers in Education Conference,1
14. Smith, C. M.(1998).A Discourse on discourse: Wrestling with teaching rational equations.The Mathematics Teacher,91(9)
15. Stemberg, R. J.,Lubart, T. I.(1995).Defying the crowd: Cultivating creativity in a culture of conformity.
16. Swartz, R. J.(2003).Critical thinking and reasoning.
17. Wallach, M. A.,Kogan, N.(1965).Modes of thinking in young children: A study of the creativity-intelligence distinction.
18. 林宜樺(2003)。網路專題學習環境中國小學生專題探討能力發展特徵之研究。
19. 陳沅(2002)。國小數學專題學習活動發展與應用之研究。
20. 鄒慧英(2000)。發展小班教學宣導專書(5)-「新世紀優質學習的經營研討會論文集」。

1. 蔣世寶(2021)。基於問題導向課程活動之合作學習研究。中科大學報，8(2)，53-78。
2. 孫慧茹、洪碧霞(2013)。國民小學代數動態評量的發展與應用。數位學習科技期刊，5(2)，59-82。