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研究生:林志峰
研究生(外文):Lin Chih-Feng
論文名稱:國小四年級學生數學解題歷程的行為之研究
論文名稱(外文):Perspective of Mathematics Behavior on Mathematics Problem-Solving Processes for Grade Four Elementary Students
指導教授:周進洋周進洋引用關係
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:科學教育研究所
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:98
中文關鍵詞:數學行為數學解題歷程問題解決
外文關鍵詞:Mathematics BehaviorMathematics Problem-Solving ProcessesMathematics Problem Solving
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本研究採用數學行為的觀點來探討國小四年級學生數學解題歷程中所產生的現象,藉由數學解題歷程和數學行為等兩個層面的分析,來探討國小四年級學生的數學解題。總共有三個研究問題:一、國小四年級學生的數學解題歷程為何?二、國小四年級學生數學解題歷程中的數學解題行為為何?三、成功解題者的數學解題行為有何特徵?

作者透過使用對於學童較為陌生的澳洲數學能力檢定(Australian Mathematics Competition)中適合國小一年級到國中一年級的初級數學題目,讓六位國小四年級的個案學生以放聲思考的作答方式加上刺激晤談,來了解與分析六位個案學生在六個數學題目中的解題過程與結果。主要的研究結果有:一、除了一般的數學解題歷程之外,數學行為具有整個數學解題歷程的控制功能,加入數學行為的觀點才是較為完整的數學解題歷程。二、相同的數學題目,對於不同的學生而言,適合他的捷思法或解題方法可能會因人而異,但是都能夠正確解題。三、對於數學題目國小學童缺乏正確的驗算認知與習慣。
In this study, the perspective of mathematics behavior was employed to explore what happened during grade four elementary students’ phases of the mathematics problem-solving processes. By means of analyzing two aspects of phases of the mathematics problem-solving processes and mathematics behavior, this study explored the mathematics problem-solving processes of grade four elementary students. There were three aspects focused in this research: 1. grade four elementary students’ phases of the mathematics problem-solving processes, 2. grade four elementary students’ mathematics behavior in the mathematics problem-solving processes, 3. the characteristics of mathematics behavior of those who solve mathematics problems in success.

This research used the problems of the level for grade one to grade seven students in Australian Mathematics Competition, let six grade four elementary students answer by thinking aloud and then had students interviewed. Then this study analyzed the results and processes of problem-solving of the six students in six problems. The findings were as follows:
1. In addition to the regular problem-solving processes, the mathematics behavior with the control function on the entire mathematics problem-solving processes, the processes with the mathematics behavior would be the completed processes.
2. For different students in the same mathematics problem, there would be different kinds of heuristics or ways to solve the problem in success.
3. In mathematics problems, elementary students had a lack of the right conception and habits of verifying the correctness of the answers.
摘要………………………………………………………………… I
英文摘要…………………………………………………………… II
目錄………………………………………………………………… IV
表次………………………………………………………………… VI
圖次………………………………………………………………… VIII
第壹章 緒論……………………………………………………… 1
第一節 研究背景與動機…………………………………… 2
第二節 研究目的…………………………………………… 5
第三節 研究問題…………………………………………… 6
第四節 名詞解釋…………………………………………… 7
第貳章 文獻探討………………………………………………… 9
第一節 數學問題…………………………………………… 10
第二節 數學解題歷程……………………………………… 18
第三節 數學行為…………………………………………… 28
第叁章 研究方法………………………………………………… 31
第一節 研究架構…………………………………………… 32
第二節 研究流程…………………………………………… 33
第三節 研究對象…………………………………………… 35
第四節 研究工具…………………………………………… 36
第五節 資料收集…………………………………………… 39
第六節 資料分析…………………………………………… 40
第肆章 研究結果………………………………………………… 47
第一節 數學解題歷程……………………………………… 48
第二節 研究發現…………………………………………… 73
第三節 研究主張…………………………………………… 82
第四節 成功解題者的數學行為之特徵…………………… 88
第伍章 結論……………………………………………………… 91
第一節 研究結論…………………………………………… 92
第二節 研究建議…………………………………………… 94
參考文獻…………………………………………………………… 96
一、中文參考文獻

1. 胡炳生(1999):數學解題思維方法。台北市:九章。

2. 涂金堂(1995):國小學生後設認知、數學焦慮與數學解題表現之相關研究。國立高雄師範大學教育研究所碩士論文,未出版,高雄市。

3. 孫達剛(1992):雄中、雄女學生數學解題之研究—Polya 解題四階段論取向。國立高雄師範大學數學教育研究所碩士論文,未出版,高雄市。

4. 教育部(1999):國民中小學九年一貫課程暫行綱要。台北市:教育部。

5. 教育部(2000):基本能力實踐策略專題研究報告。台北市:教育部。

6. 劉貞宜(2000):數學資優生的解題歷程分析。國立台灣師範大學特殊教育研究所碩士論文,未出版,台北市。



二、英文參考文獻

1. Benacerraf, P. and Putnam, H. (Ed.) (1983). Philosophy of Mathematics, 2nd edition. New York : Cambridge University Press.

2. Carlson, M.P. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success, Educational Studies in Mathematics, 40, 237–258.

3. DeFranco, T.C. (1996). A perspective on mathematical problem-solving expertise based on the performances of male Ph.D. mathematicians, Research in Collegiate Mathematics, II, Vol. 6, American Mathematical Association, Providence, RI, 195–213.

4. Geiger, V. and Galbraith, P. (1998). Developing a diagnostic framework for evaluating student approaches to applied mathematics problems, International Journal of Mathematics, Education, Science and Technology, 29, 533–559.

5. Kilpatrick, J. (1985). A retrospective account of the past 25 years of research on teaching mathematical problem solving. In Silver, E. A. (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives, 1-15. Hilsdale, N.J. : Erlbaum Associates.

6. Lester, F. K. (1980). Problem solving: Is it a problem? In M. M. Lindquist (Ed.), Selected issues in mathematics education, 29-45. Berkeley Calif. : McCutchan.

7. Lester, F.K. (1994). Musings about mathematical problem solving research: 1970–1994, Journal for Research in Mathematics Education, 25, 660–675.

8. Mayer, R. E. (1992). Thinking, problem solving, cognition. New York : W. H. Freeman and Company Press.

9. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Palo Alto, Calif. : Dale Seymour Publications Press.

10. Polya, G. (1957). How To Solve It; A New Aspect of Mathematical Method. Princeton, N.J. : Princeton University Press.

11. Polya, G.(1962). Mathematical discovery: On understanding , learning and teaching problem solving (Vol I). New York : Wiley Press.

12. Schoenfeld, A.H. (1983). The wild, wild, wild, wild, wild world of problem solving: A review of sorts, For the Learning of Mathematics, 3, 40–47.

13. Schoenfeld, A. H. (1985). Mathematical problem solving. New York : Academic Press.

14. Schoenfeld, A.H. (1989). Explorations of students’ mathematical beliefs and behavior, Journal for Research in Mathematics Education, 20, 338–355.

15. Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics, in D.A. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning, 334–370. New York : Macmillan Publishing Company.

16. Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning, Educational Studies in Mathematics, 34, 97–129.
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