數學寫作融入國三數學課室實踐歷程與影響之研究

Investigating the Processes and Influences of Mathematical Writing When Integrated into the Mathematics Classroom

10.6173/CJSE.2008.1604.03

楊德清(Der-Ching Yang)；姜淑珍(Shu-Zhen Jiang)

行動研究 ； 國中三年級 ； 數學寫作 ； 學習成效 ； Action Research ； Learning Attitude ； Mathematics Writing ； Ninth Grade

科學教育學刊

16卷4期（2008 / 08 / 01）

439 - 458

繁體中文

本研究的主要目的為探討一位國三數學教師如何運用行動研究，將數學寫作融入國三數學課室之教學所遭遇之困境與解決方法，以及對學生數學學習表現之影響。研究對象為南部地區某公立國中三年級學生。研究進行時間為一學期之每週國三數學複習課時間。資料收集之方式包含數學寫作學習單、學習日誌、研究者教學省思札記、以及研究觀察日誌等。研究結果顯示：數學寫作融入國三數學課室之初期所遭遇之困難為數學寫作會造成學生與老師的壓力、減少學生練習題目的時間，造成學生的質疑，稀釋了老師教學的時間，造成家長的質疑以及部分數學成績好的學生，在學習上亦會產生困擾。但是透過本研究所發展之「五步驟」解決方案之實施，對學生之數學學習表現具正面影響。這些正面影響包括：透過數學寫作學生能掌握數學寫作的要點、寫作可以幫助學生重新組織、統整及連結各種不同概念性知識與發展解題能力以及在數學學習成就上亦有正面之影響，例如參與數學寫作融入課室之學生在高中基測上之表現比未參與學生在統計上有顯著之差異，此亦對數學寫作融入課室有正面的鼓勵作用。

The purposes of this study were to investigate the processes and possible problems and effects on mathematics learning when a 9(superscript th)-grade mathematics teacher utilized action research to integrate mathematics writing into a 9(superscript th)-grade class. The mathematical writing worksheets, learning diaries, teacher's reflection diaries, and classroom observations were the sources of data. The results of this study indicated that the problems the teacher met included: increased pressure on students and teacher; increased students' questioning due to the decreased time devoted to doing math problems; increased questioning from parents due to the diluted instructional time; and increased confusion among high achieving students. However, there was a positive impact on students' mathematics learning due to the use of a five step strategy used in the study. The positive effects on mathematics learning included students mastering the key points in writing mathematics showing that mathematical writing can help students reorganize, integrate, and connect all kinds of conceptual knowledge and problem solving ability. There was also a positive relationship between mathematics achievement also and mathematical writing. For example, the results of ANCOVA showed a statistically significant difference, on the high school entrance examination, between students who participated in the mathematics writing as opposed to students who did not participate in mathematics writing. This indicates that integration of mathematics writing into mathematics instruction has positive effect on mathematics learning.

1. Anderson, M. A.,Little, D. M.(2004).On the write path; Improving communication in an elementary mathematics classroom.Teaching Children Mathematics,10(9),468-472.
2. Baxter, J. A.,Woodward, J.,Olson, D.,Robyns, J.(2002).Blueprint for writing in middle school mathematics.Mathematics Teaching in the Middle School,8,52-56.
3. Bell, F. S.,Bell, R. N.(1985).Writing and mathematics problem solving; arguments in favor of synthesis.School Science and Mathematics,85,210-221.
4. Borasi, R.,Rose, B. J.(1989).Journal writing and mathematics instruction.Educational Studies in Mathematics,20,347-365.
5. Brenner, M. F.,Herman, S.,Ho, H. Z.,Zim-mer, I. M.(1999).Cross-national comparison of representational competence.Journal for Research at Mathematics Education,30(5),541-547.
6. Bums, M.(1995).Writing in math class?.Absolutely. Instructor,104(7),40-47.
7. Cai, J.(2001).Improving mathematics learning lessons from cross national studies of Chinese and U.S. students.Phi Delta Kappan,83,400-404.
8. Connolly, P.,Vilarrii, T.(1989).Writing to learn mathematics and science.New York:Teachers College Press.
9. Countryman, J.(1992).Writing to learn mathematics.Portsmouth, N.H.:Heinemann.
10. Elliott, J.(1991).Action research for educational changes.Milton Keynes:Open University.
11. Etkina, E.(2000).Weekly reports; A two-way feedback tool.Science Education,84,594-605.
12. Flower, L.,F. P. Maimon,B. F. Nodine,F. W. O`Connor (Eds.)(1989).Thinking, reasoning, and writing.New York:Longman.
13. Forks, L. C.(1993).America,The University of Michigan, Michigan.
14. Goldsby, D. S.,Cozza, B.(2002).Writing samples to understand mathematical thinking.Mathematics Teach big in the Middle School,7(9),517-520.
15. Kemmis, S.,McTaggar, R. (Eds.)(1988).The action research planner.Gee-iong, Australia:Deakin University Press.
16. Liedtke, W. W.,Sales, J.(2001).Writing tasks.Mathematics Teaching in the Middle School,6(6),350-355.
17. McNiff, J.(1988).Action research: Principles and practices.London:Macmillan.
18. Miller, L. D.(1991).Writing to learn mathematics.Mathematics Teacher,84(7),516-521.
19. Miller, L. D.,England, D. A.(1989).Writing to learn algebra.School Science and Mathematics,89,299-312.
20. Mullis, I. V. S.,Martin, M. O.,Gonzalez, E. J.,Chrostowski, S. J.(2004).TIMSS 2003 international mathematics report: Findings from IEA`s Trends in International Mathematics and Science Study at the fourth and eighth grades.Chestnut Hill, MA:Boston College, TIMSS & PIRLS International Study Center.
21. Nahrgang, C. L.,Petersen, B. T.(1986).Using writing to learn mathematic.Mathematics Teacher,79,461-465.
22. National Council of Teachers of Mathematics(1989).Curriculum and evaluation standards for school mathematics.Reston, VA:NCLM.
23. National Council of Teachers of Mathematics(2000).The principles and standards fat school mathematics.Reston, VA:NCTM.
24. National Research Council(2001).Adding it up: Helping children learn mathematics.Washington, DC:National Academy Press.
25. Nixon, J.(1989).The teacher as researcher: Contractions and continuities.Peabody Journal of Education,64,116-127.
26. Ntenza S. P.(2006).Investigating forms of children.Educational Studies in Mathematics,61,321-345.
27. Pesek, D. D.,Kirshner, D.,J. Sowder,B. Schappelle (Eds.)(2002).Lessons learned from research.Reston, Va:NCTM.
28. Pugalee, D. K.(2001).Using communication to develop students’ mathematical literacy.Mathematics Teaching in the Middle School,6(5),296-299.
29. Rose, B.,P. Connolly,T. Vi-lard (Eds.)(1989).Writing to learning mathematics and science.New York:Teacher College.
30. Shield, M.,Galbraith, P.(1998).The Analysis of student expository writing in mathematics.Educational Studies in Mathematics,36(1),39-52.
31. Sullivan, P.,Clarke, D. J.(1991).Creating all abilities through `good question.`.Arithmetic Teacher,39(2),14-18.
32. Wade, E. G.(1994).A study of the effects of a constructivist-based mathematics problem solving instructional program on the attitudes, self-confidence, and achievement.Mexico:New Mexico State University, Mexico City.
33. Zuber-Skerrit, O.(1996).New directions in action research.London:Falmer Press.
34. 王文科(1995)。教育研究法（第四版）。台北:五南。
35. 陳惠邦(1998)。教育行動研究。台北:師大書院。
36. 陳億源(2007)。碩士論文(碩士論文)。花蓮市，慈濟大學教育研究所。
37. 黃政傑(1999)。課程改革。台北:漢文。
38. 蔡清田(2001)。教育行動研究。台北:五南圖書出版公司。

1. 張慈珊(2019).Students' Perceptions about Mathematics-Literature: A Pilot Study.淡江外語論叢,31,1-30.
2. 張慈珊,李雪甄(2019)。連結瞬間：見數學見文學見自己。通識學刊：理念與實務，7(1)，73-107。