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研究生: 王昭傑
Wang Jhao- Jie
論文名稱: 靜像式情境數學模組(SIMSP)在國小資優班施行成效研究-以奧林匹亞數學三國誌為例
The Effect of Situated Instruction in Mathematics Using Still Pictures for Elementary Gifted Students –Based on the Example of Mathematics Olympiad “the Three Kingdoms”
指導教授: 陳美芳
Chen, Mei-Fang
學位類別: 碩士
Master
系所名稱: 特殊教育學系
Department of Special Education
論文出版年: 2011
畢業學年度: 99
語文別: 中文
論文頁數: 223
中文關鍵詞: 奧林匹亞數學靜像式情境數學模組基模知識學習保留資優生
英文關鍵詞: Mathematics Olympiad, situated instruction in mathematics using still pictures (SIMSP), schema knowledge, learning retention, gifted student
論文種類: 學術論文
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  • 本研究採準實驗研究設計,探究「靜像式情境數學模組」(Situated Instruction in Mathematics using Still Pictures,以下簡稱SIMSP)對國小資優班學生「立即學習成就」、「學習保留能力」、「基模知識量」及「學習意向」之影響。實驗教學包含「速率」、「牛吃草」及「排列組合」三大單元。研究對象為台北市11所國小高年級資優生共60名,包含實驗組與對照組各30名,實驗組接受SIMSP教材進行教學、對照組則接受傳統式奧林匹亞數學教材教學,兩組課程均為18堂課。本研究採自編工具由學習成就(包含立即學習成就及學習保留能力)、基模知識(包含陳述性及程序性基模知識)與學習意向等三方面檢驗實驗效果;另進行問卷與訪談蒐集學生之回饋資料。本研究採單因子共變數分析(ANCOVA)進行實驗效果之統計分析,主要研究發現如下:

    一、學習成就表現上的影響
    SIMSP明顯有助於提升實驗組學生在「牛吃草」及「排列組合」單元之立即學習成就表現,而在學習保留能力的展現上亦有相同的效果。

    二、基模知識表現上的影響
    在「陳述性基模知識」部分,SIMSP明顯有助於提升實驗組學生在「牛吃草」單元的基模知識量。而在「程序性基模知識」部分,則在「牛吃草」及「排列組合」單元明顯有助於提升實驗組學生的基模知識量,另外在「速率」單元則呈現部份效果。
    三、學習意向上的影響
    SIMSP對國小資優班學生在奧林匹亞數學的喜好程度有明顯提升效果,而兩組學生大部分認為奧林匹亞數學對其數學能力有正向幫助。另外,實驗組學生並認為SIMSP明顯有助其自覺性的知識脈絡提取。

    綜合而言,本研究發現:使用SIMSP的情境脈絡布題方式,除能有效提升資優生學習動機外,並能有效建立學生相關脈絡知識的完整性及提升其在解題程序知識的習得與保留。最後研究者並根據本研究發現,針對奧林匹亞數學相關後續研究提出相關建議。

    The aim of this quasi- experimental designed research was to explore the effect of “Situated Instruction in Mathematics using Still Pictures” (SIMSP) for elementary gifted students. The subjects were 60 gifted students from 11 elementary schools in Taipei; they were evenly divided into experimental group and compare group. The effect of the experimental instruction was examined by “the immediate learning achievement”, “the learning retention ability”, “the quantity of schema knowledge” and “the learning intention”. The mathematic units in the experiments included: “Velocity”, “Cow and Grass” and “Permutation and Combination”. The experimental group attended 18 SIMSP classes, while the control group attended 18 classes using traditional Mathematics Olympiad. Self made test instruments, questionnaires and interviews were undertaken to examine the experimental effects and to collect feedbacks from the students. The data were analyzed by ANCOVA. The major findings were as follows:
    1. SIMSP helped the students in the experimental group enhancing their immediate learning achievements as well as learning retention in the units of “Cow and Grass” and “Permutation and Combination”.
    2. SIMSP helped the students in the experimental group enlarging their schema knowledge in the unit of “Cow and Grass” and their procedural schema knowledge in the units of “Cow and Grass” and “Permutation and Combination”. However, the effect in the unit of “Velocity” is partial.
    3. SIMSP attracted gifted students’ positive intentions towards Mathematics Olympiad. Most students in both groups agreed that Mathematics Olympiad enhanced their mathematic abilities. Furthermore, the students in the experimental group agreed that SIMSP helped them extract the contextual knowledge at the beginning of mathematic problem-solving.
    To sum up, this study indicated that, SIMSP, with the questions designed in situations and contexts effectively help the gifted students raising learning motivation, establishing more comprehensive contextual knowledge, and enhancing the learning and maintaining the knowledge /skills of mathematic problem-solving. Suggestions are proposed at the final for future research and instruction of Mathematics Olympiad.

    目 錄 中文摘要…………………………………………………………………I 英文摘要………………………………………………………………..III 目錄...……………………………………………………………………V 圖目錄…………………………………………………………….....….IX 表目錄…………………………………………………...………………X 第一章 緒論 第一節 研究動機與目的……………………………………………1 第二節 待答問題與研究假設………………………………………7 第三節 名詞解釋..…………………………………………………10 第二章 理論基礎與文獻探討..………………………………………..13 第一節 數學解題歷程及其相關因素探究..………………………13 一、數學解題歷程的論述與分析.….……….………………13 二、基模知識的相關論述及其在數學解題上的定位……..20 第二節 情境學習理論在數學教學上的應用.…….………………30 一、情境式學習的理論基礎及相關論述.….………………30 二、故事情境數學研究的相關探討.……….………………38 第三節 資優生特質與數學學習的關係.………….………………42 一、資優生的一般特質與過度激動特質.…………………42 二、資優生特質與情境數學學習的關係探討..……………45 第四節 資優課程理論與數學教育的關係探究.…….………….50 一、資優課程理論及其相關論述.…………….…………50 二、區分性課程與奧林匹亞數學的互動關係..…………55 第三章 研究方法.…………………………………………...…………65 第一節 研究架構與設計.…………………………….……………66 第二節 研究對象.…………………………………….……………77 第三節 研究工具.…………………………………….……………78 第四節 資料處理與分析.…………………………….……………86 第四章 研究結果與討論.…………………………………….………..89 第一節 立即學習成就的分析討論.…………………….…………89 第二節 學習保留能力的分析討論.…………………….…………93 第三節 基模知識量的分析討論.……………………….…………99 第四節 學習意向分析討論………………………………………109 第五節 綜合討論…………………………………………………118 第五章 結論與建議..…………………………………………………125 第一節 結論…..…………………………………………………..125 第二節 建議…...………………………………………………….127 參考文獻 中文部分.………………………………………………………...133 西文部份.………………………………………………………...136 附錄 附錄一 SIMSP教材…………………………………………..…147 附錄二 傳統式奧林匹亞數學教材..……………………………165 附錄三 奧林匹亞數學成長營練習教材-快樂分享餐…………180 附錄四 奧林匹亞數學學習成就甲式測驗…………..…………188 附錄五 奧林匹亞數學學習成就乙式測驗………..……………191 附錄六 奧林匹亞數學學習成就丙式測驗.…………...………..194 附錄七 國小學童奧林匹亞數學基模知識檢核表………..……197 附錄八 教師用-基模知識檢核表示例…………………………198 附錄九 基模知識檢核題……………………………………….199 附錄十 「寒假奧林匹亞數學實驗成長營」實施計畫……….205 附錄十一 螢橋寒假數學實驗成長營數學意向調查(全)……..207 附錄十二 「奧林匹亞數學成長營」課後調查(上午班)……..208 附錄十三 「奧林匹亞數學成長營」課後調查(下午班)……..209 附錄十四 「奧林匹亞數學三國誌」-SIMSP示意…….……..210 圖 目 錄 圖2-1-1 數學解題動態歷程…………………………….……………17 圖2-1-2 解題歷程與知識的關係……………….…...….……………26 圖2-1-3 數學解題內在基模知識比對歷程…….……….…………...28 圖2-2-1 Collins認知學徒制學習脈絡………….……….…...………34 圖2-3-1 情境脈絡數學概念產出轉化模式…….……………………47 圖2-4-1 區分性課程的整合課程模式……………….………………55 圖3-1-1 研究架構…………………………………….………………66 圖3-1-2 研究方法示意圖…………………………….………………67 圖3-1-3 研究程序…………………………………….………………73 圖4-2-1 學習成就分數改變曲線圖…..…………………..……...…..95 圖4-3-1 基模知識分數改變曲線圖……..…………………….……100 圖4-3-2 速率單元之程序性基模知識量的組內迴歸線示意圖…...104 表 目 錄 表2-1-1 各學者對於數學解題歷程的看法..…..………………….…15 表2-2-1 Collins認知學徒制與Caine大腦學習程序比較……….…36 表2-4-1 區分性課程實施要點檢核表..…………………………...…58 表2-4-2 蛋糕切割解題思考脈絡…….………………………………61 表2-4-3 奧數本質與整合課程模式比對表………….………………62 表3-1-1 立即學習成就及學習保留能力實驗設計………………….68 表3-1-2 基模知識量檢測實驗設計………………………………….69 表3-1-3 實驗課程之內容編配表……..…………………...…………72 表3-1-4 SIMSP及傳統式奧林匹亞數學教材實驗形式內容差異….75 表3-1-5 SIMSP及傳統式奧林匹亞數學教材內容構念差異表.……76 表3-2-1 研究樣本人數分配情形表………………………………….77 表3-3-1 甲式及乙式題目相關概念分析表..……………………...…79 表3-3-2 奧林匹亞數學學習成就丙式追蹤測驗內容概念分析表….79表3-3-3 信度建置之抽樣人數區域配置表……..…………….……..80 表3-3-4 測驗工具信效度檢核表…….………………………………81 表3-3-5 實驗單元基模知識評判對照表…………………………….82表3-3-6 基模知識量評量紀錄表(例)…………………………….….83 表3-3-7 基礎速率問題的基模知識檢核題與評判指標對應表….…84 表4-1-1 兩組學生在實驗三單元的測驗得分情形……………….....90 表4-1-2 實驗三單元迴歸係數同質性考驗摘要表……………….…90 表4-1-3 實驗三單元單因子共變數分析摘要表………….…………91 表4-2-1 參與及未參與追蹤測驗學生同質性考驗摘要表……….…93 表4-2-2 參與追蹤測驗學生在實驗三單元的學習保留得分情形….94 表4-2-3 實驗三單元迴歸係數學習保留同質性考驗摘要表……….95 表4-2-4 實驗三單元單因子共變數分析摘要表…………………….96 表4-3-1 兩組學生在實驗三單元基模知識量的測驗得分情形…….99 表4-3-2 實驗三單元基模知識量迴歸係數同質性考驗摘要表.…..101 表4-3-3 實驗三單元基模知識量之單因子共變數分析摘要表…...102 表4-3-4 速率單元的「程序性基模知識」詹森-內曼法校正結果..104 表4-3-5 速率單元之程序性基模知識量的組內迴歸線相交點與 差異顯著點………………………………………………..105 表4-3-6 實驗組與對照組基模知識量的結果比較………………..106 表4-4-1 寒假數學成長營參加意願調查…………………………..109 表4-4-2 參與學生對於奧林匹亞數學意向調查…………………..110 表4-4-3 奧林匹亞數學學習成效幫助自評調查…………………..113 表4-4-4 知識脈絡回憶幫助程度調查……………………………..114 表4-5-1 實驗成效綜合分析表…………………………….……….118

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