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研究生: 許舜淵
Shun-Yuan, Xu
論文名稱: 動態幾何環境下大學生的幾何探索歷程分析
指導教授: 左台益
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2009
畢業學年度: 97
語文別: 中文
論文頁數: 79
中文關鍵詞: 拖曳行動思考實驗動態表徵
論文種類: 學術論文
相關次數: 點閱:146下載:14
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  • 本研究目的在從思考實驗、拖曳行動和動態表徵三個面向來探討與分析學生的幾何探索和推理論證過程。研究方法主要採取半結構的診斷活動方式,對二十四位數學系大學生在進行幾何作業時的觀察與訪談。以錄音及錄影方式收集原案資料,再採用質性分析,詮釋個案的探索歷程。
    研究結果顯示:1.學生在動態幾何環境下的幾何探索架構包含拖曳行動、動態表徵以及思考實驗三個主要元素,三者的交互作用會影響個體的幾何探索與推理。拖曳行動的認知行為影響個體對動態表徵的解讀,動態表徵的解讀會激發內在思考實驗,思考實驗會引導拖曳行動,三者之間的交互作用形成一個幾何探索的循環系統。
    2.學生在DGE下所發展出的思考實驗運作模式主要是以動態表徵外在的動態行為和內在的數學性質激發個體產生猜測,並透過模擬操作物件的動態行為來驗證猜測,進而產生宣告。學生通常模擬操作完後,會用GSP具體操作驗證自己的想法,或是當問題情境過於複雜或簡單時,會跳過模擬操作直接朝向具體操作圖形的方式來驗證猜測。
    3.學生在作思考實驗的過程中,有時會發生有如與第三者論證的自我對話現象。這個虛擬的第三者常常扮演提供解題或反思的角色,而電腦的作用則是激發第三者的產生。
    4.學生在DGE下所進行的幾何推理方式可分為幾何實驗、思考實驗和形式證明三大部分,其中思考實驗在推理過程中橋接幾何實驗(實驗歸納)與形式證明(演繹推理)。學生在幾何實驗中產生猜測或觀察動態表徵的變化,經由思考實驗來驗證猜測,並將推論的結果轉化為形式證明。

    目錄------------------------------------------------------i 附表目次-------------------------------------------------ii 附圖目次------------------------------------------------iii 附錄目次--------------------------------------------------v 第壹章 緒論----------------------------------------------1 第一節 研究背景與動機------------------------------------1 第二節 研究目的與問題------------------------------------5 第貳章 文獻探討------------------------------------------6 第一節 思考實驗------------------------------------------6 第二節 DGE下的幾何探索----------------------------------11 第三節 幾何推理方式與證明類型---------------------------15 第參章 研究方法-----------------------------------------20 第一節 研究設計-----------------------------------------20 第二節 研究過程與研究工具-------------------------------22 第肆章 研究結果與討論-----------------------------------25 第一節 思考實驗運作模式---------------------------------25 第二節 學生的思考實驗與拖曳行動及動態表徵的交互作用-----35 第三節 實驗歸納與演繹推理之間的互動關係-----------------48 第伍章 結論與建議---------------------------------------62 第一節 結論---------------------------------------------62 第二節 建議---------------------------------------------67 參考文獻-------------------------------------------------68 一、中文部分---------------------------------------------68 二、英文部分---------------------------------------------68 附錄-----------------------------------------------------72

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