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研究生: 薛麗卿
Li-Ching Hsueh
論文名稱: 數學寫作活動對國小學生解題能力及數學態度之影響
The Effects of Mathematical Writing Activities on Problem Solving Ability and Mathematics Attitude of Elementary School Students
指導教授: 張景媛
Chang, Ching-Yuan
學位類別: 碩士
Master
系所名稱: 教育心理與輔導學系
Department of Educational Psychology and Counseling
畢業學年度: 87
語文別: 中文
論文頁數: 173
中文關鍵詞: 數學寫作解題能力數學態度國小學生
英文關鍵詞: writing to learn mathematics, problem solving ablility, mathematics attitude, elementary school students
論文種類: 學術論文
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  • 本研究主要目的有四:(一)在探討數學寫作活動對於提升國小學生解題能力及改善數學態度的效果;(二)調查國小學生對數學寫作活動的支持程度;(三)分析數學寫作活動的內容了解學生實際寫作的情形;(四)探討數學寫作活動對學生解題歷程的影響。
    本研究中的數學寫作活動方案乃是將四種數學寫作活動:數學日記、自由寫作、過六關、我是小偵探融入日常數學課中,以台北市忠義國民小學六年級兩班共40名學生為對象,其中實驗組20人、控制組20人,實驗組由研究者擔任六上數學課怎樣解題(一)(二)(三)三個單元的教學並配合數學寫作活動,控制組則由原班老師擔任教學者,但無配合數學寫作活動。
    兩組別在經過一學期實驗處理後,以「五下數學科段考成績」及「怎樣解題成就測驗」得分為解題能力前後測成績,另以「數學態度量表」前後測得分作為數學態度改變的指標,兩者皆進行共變數分析來考驗假設,另外並進行實驗組學生對「數學寫作教學態度開放式問卷」、分析學生數學寫作的內容、及個別解題放聲思考測驗。
    本研究得到幾點結論:一、數學寫作活動在課內題部分對於實驗組前測成績低於90分的學生具有提升解題能力的作用,而在課外題部分實驗組與控制組則沒有顯著的差異。二、數學寫作活動對於實驗組與控制組數學態度的影響未達顯著。三、學生對於數學寫作活動普遍持正向支持的態度。四、數學寫作內容分析中發現包括基礎的記憶理解到高層的歸納評鑑等內容,且學生會嘗試使用文字、符號、圖形等不同表徵方式說明自己的想法,並進行自我對話及與老師溝通。五、在解題歷程分析中,實驗組的學生具有較習慣說出自己的想法、較常圖示題目,面對難題時較清楚問題的所在及較高的解題正確率的特徵。

    The purposes of this study were : (1) to explore the effect of mathematical writing activities on problem solving ability and mathematics attitude; (2) to investigate the attitude on mathematical writing activities of elementary school students; (3) to analyze the contents of mathematical writing for knowing what the students wrote; (4) to explore the effect of mathematical writing activities on the students' problem solving process.
    In this study, four mathematical activities: journals, freewriting, guided-response writing and expository writing were conducted to be used in daily mathematical curriculum. The subjects were 40 sixth grade students in two classes from Taipei Chung-Yi elementary school. There were twenty students in the experimental group and the others in control group. In experimental group, three chapters of mathematical courses (How to solve problems (1) (2) (3)) were taught by the researcher with mathematical writing activities, and without these activities taught by the original teacher in control group.
    When this program was finished, in order to measure students' problem solving ability, the researcher collected mathematical scores of each student in fifth grade as the pre-scores and the scores of "Problem solving ability test" as the post-scores. The scores of "Mathematics attitude scale" were collected for measuring students' mathematical attitude. The data obtained were analyzed by one-way ANCOVA. Besides, "Mathematical writing attitude Questionaire" was collected for investigating the attitude on mathematical writing activities of experimental group students. The researcher also analyzed the contents of students' mathematical writing and used "Thinking Aloud" to compare the differences of two group students' problem solving process. The major findings were as follows:1.In the curricular part of "Problem Solving ability test", mathematical writing activities enhanced problem solving abilities of experimental group students whose pre-scores were below 90; in the extracurricular part, the scores of two group didn't have significant differences.2.The influence of mathematical writing activities on students' mathematics attitude was insignificant.3.Most students supported the mathematical writing activities positively.4.The contents of analyzed mathematical writing involved basic declarative mathematical knowledge and advanced mathematical skill (ex: inductive evaluation). Furthermore, the students also attempted to use words, symbols, and diagrams to represent their thoughts, self-talk, and communication with teachers.5.In the analysis of students' problem solving process, the experimental group student expressed themselves smoothly, represented the problem mostly, faced problems clearly, and get higher proportion of correction.

    第一章 緒論 第一節 研究動機與目的…..…………………………… 1 第二節 待答問題…..…………………………………… 5 第三節 研究假設…..…………………………………… 5 第四節 名詞釋義…..…………………………………… ..7 第二章 文獻探討 第一節 數學寫作的理論基礎…….. …………………….10 第二節 數學寫作活動內容及實施原則……………….. .27 第三節 數學寫作的相關研究……..……………………. 37 第四節 數學寫作與目前數學教育改革的關係. ……….40 第三章 研究方法 第一節 研究對象…………………………………………44 第二節 研究設計………………………………………….45 第三節 研究工具………………………………………….47 第四節 實驗處理………………………………………… 52 第五節 實施程序………………………………………… 59 第六節 資料處理………………………………………… 62 第四章 研究結果 第一節 數學寫作教學對解題能力的效果分析………… 63 第二節 數學寫作教學對數學態度的影響……………… 66 第三節 學生對數學寫作的態度分析…………………… 68 第四節 數學寫作內容分析……………………………… 75 第五節 不同組別解題歷程分析…………………………105 第五章 討論 第一節 數學寫作教學對解題能力的影響………………111 第二節 數學寫作教學對數學態度的影響………………116 第三節 學生對數學寫作的態度…………………………118 第四節 數學寫作內容分析………………………………121 第五節 不同組別解題歷程分析…………………………124 第六章 結論與建議 第一節 結論………………………………………………126 第二節 建議………………………………………………128 參考文獻 中文部分………………………………………………….134 英文部分………………………………………………….136 附錄 附錄一 數學寫作教學課程活動設計…………………...142 附錄二 怎樣解題成就測驗………….…………………..148 附錄三 數學態度量表………….………………………..150 附錄四 數學寫作態度開放式問卷………….…………..153 附錄五 個別放聲思考測驗卷…….……………. ……….155 附錄六 數學日記指導語及活動單………………………156 附錄七 自由寫作指導語及活動單………………………158 附錄八 過六關活動單……………………………………160 附錄九 我是小偵探活動單………………………………161 附錄十 個別放聲思考測驗程逐字稿……………………162 表目錄 表3-1 本研究的樣本人數……………………………………. 44 表3-2 獨立樣本單因子設計…………………………………. 45 表3-3 「怎樣解題成就測驗」題目內容分配表…. …………48 表3-4 數學寫作教學課程摘要表……………………………. 56 表4-1 實驗組與控制組前後測得分之平均數與標準差……. 64 表4-2 「怎樣解題成就測驗」課外題後測分數之單因子共變數分析摘 要表…………………… 65 表4-3 兩組別「數學態度量表」前後測得分之平均數與標準差... 66 表4-4 「數學態度量表」前後測分數之單因子共變數分析摘要表..67 表4-5 實驗組與控制組個別施測答題正確率統計表……………..109 圖目錄 圖2-1 Hayes 和 Flowers 的寫作歷程模式………………….15 圖2-2 Wadlington 和 Hicks的寫作歷程圖………………….16 圖2-3 Glass 和 Holyoak 問題解決流程圖………………….19 圖4-1實驗組與控制組之組內回歸線相交點及差異顯著點….64 圖4-2實驗組學生對各類寫作喜愛度………………………...69 圖4-3 數學寫作教學對語文表達能力的幫助………………..70 圖4-4數學寫作教學對於數學態度的影響…………………...71 圖4-5數學寫作教學提高數學成績的程度………….. ………72 圖4-6數學寫作時的努力程度………………………………...73

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