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研究生:吳佳榮
研究生(外文):Chia-Jung Wu
論文名稱:國小五年級學童數學建模歷程的特徵及其數學態度改變影響之研究
論文名稱(外文):A Study on the Characteristic of the Fifth Graders’ Processes in Mathematical Modeling and Changes in Mathematical Attitudes
指導教授:李源順李源順引用關係
指導教授(外文):Yuan-Shun Lee
學位類別:碩士
校院名稱:臺北市立教育大學
系所名稱:數學資訊教育學系數學資訊教育教學碩士學位班
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:2011
畢業學年度:99
語文別:中文
論文頁數:123
中文關鍵詞:數學建模數學態度
外文關鍵詞:mathematical modelingmathematical attitudes
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本研究主要目的是以自編的數學建模問題做為研究工具,探討國小五年級學童數學建模歷程的特徵與數學態度之影響。研究設計採詮釋性研究法,研究對象為研究者任教班級二十六位學生,五或六人一組,共分成五組。
在建模活動前後進行數學態度量表的施測,用以分析學生數學態度的差異。數學建模活動中,以小組討論的方式進行活動,若學童無法順利進行數學建模時,研究者則適時介入引導學童進行建模教學活動。根據課堂錄影、小組記錄單、晤談結果、教學札記等資料,探討學童數學建模歷程的特徵。
主要研究結果如下:
一、學童數學建模歷程的特徵
(一)簡化與結構化:
1. 實際問題愈貼近學童的生活經驗,學童愈容易考量生活中具體因素。
2. 若有類似的解題經驗有助於學童形成理想化的真實模型。
(二)數學化:
1. 若無類似的解題經驗,學童起初容易以猜測方式,建立簡單的模型。
2. 若有舊的類似解題經驗,學童容易引用解題模型。
3. 建立模型方式有猜測、舉例說明、圖示說明、引用舊經驗等情況出現。
(三)數學運算:
1. 國小學童皆能順利運算出數學結果。
2. 學童能利用計算機工具幫助求解。
(四)解釋評估:
1. 學童皆能將數學結果套回真實模型問題,解釋數學結果的意義。
2. 學童通常認為將數學結果轉譯回真實模型後,便認為解決了原始情境的問題。
3. 學童很少主動出現模型的驗證評估階段。
二、數學建模對學童數學態度之改變
學童在數學建模活動之後,雖然學童在學習數學的信心、數學動機並無明顯提升,但在認識數學有用性及降低數學焦慮有幫助,因而數學建模對學童數學態度是有所助益。
研究者根據研究結果,提出一些未來數學建模教學及研究方面之建議。

This study is an interpretation research and aims to investigate the characteristic of the fifth graders’ processes in mathematical modeling and changes in mathematical attitudes.
Twenty-six students participated in this study. The students were grouped into five teams, five or six students on a team. Self-editing mathematical modeling questions were conducted as the study technique. The mathematical modeling activities were manipulated in the form of team discussion. If the students were unable to discuss smoothly, a guiding discussion was intervened during the mathematical modeling activities. Class video taping, student worksheets, team interview, and teaching journals were collected to analyze the characteristic of students’ processes in mathematical modeling. An questionnaire as a pre –and post –test was also implemented to analyze students’ changes in mathematical attitudes.
The main findings of the study were as follows:
I. The characteristic of students’ processes in mathematical modeling
1. Simplify or Structure:
A. The more authentic the question is; the more real factors are taken into consideration.
B. Similar experience in problem solving among students benefits the construction of an ideal real model.
2. Mathematise:
A. Students without similar experience in problem solving are prone to take a guess as a start to build up a simple mathematical model.
B. Students with similar experience in problem solving tend to apply the problem solving models to the questions.
C. Guess taking, examples, diagram using, former experience application are observed in constructing mathematical models.
3. Mathematical Operations
A. Elementary students are all able to obtain correct outcomes of mathematical questions.
B. Calculators are used to find out the results.
4. Re-interpreting or Applying
A. Students are all able to retranslating the results to the real model questions to define the meaning of the results.
B. After retranslating the mathematical model to the real model, the problems in original situation are usually considered solved with the mathematical model applied.
C. This stage is seldom observed in this research.
II. The changes in students’ mathematical attitudes
After the mathematical modeling activities, there are no significant differences in confidence and motivation in learning mathematics. However, it not only enhances students’ cognition in usefulness of mathematics but also reduces students’ mathematics anxiety. Thus, mathematical model have positive impact on the changes in students’ mathematical attitudes.
Based on the research findings, some suggestions regarding further mathematical modeling teaching and studies are proposed.

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...........................3
第三節 名詞釋義....................................4
第四節 研究限制....................................5
第二章 文獻探討.............................................7
第一節 數學建模的理論...............................7
第二節 數學建模之學習理論...........................20
第三節 數學建模之相關研究 ...........................26
第四節 數學態度....................................29
第五節 數學態度之相關研究 ...........................32
第三章 研究方法............................................35
第一節 研究設計....................................35
第二節 研究流程....................................36
第三節 研究對象....................................39
第四節 研究工具....................................39
第五節 資料蒐集與分析...............................45
第四章 研究結果與討論.......................................47
第一節 學童數學建模歷程的特徵........................47
第二節 數學建模對學童數學態度的影響...................89
第五章 結論與建議...........................................95
第一節 結論........................................95
第二節 建議........................................97
參考文獻..................................................101
中文文獻............................................101
英文文獻............................................102
附錄.....................................................107
附錄一 春夏宴記錄單.................................107
附錄二 美麗華摩天輪記錄單............................108
附錄三 花博饗宴記錄單................................109
附錄四 數學態度量表..................................110


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