研究生: |
黃哲男 |
---|---|
論文名稱: |
於動態幾何環境下國中生動態心像建構與幾何推理之研究 |
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: | 2002 |
畢業學年度: | 90 |
語文別: | 中文 |
論文頁數: | 222 |
中文關鍵詞: | 動態幾何軟體 、動態幾何環境 、心像 、心像操作 、動態心像 |
論文種類: | 學術論文 |
相關次數: | 點閱:448 下載:109 |
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摘 要
本研究主要為探索個體於幾何解題活動時之動態心像的類型與運作機制,以及動態幾何環境對建構動態心像的影響。據此目的,選擇台北市內湖區某公立國中二年級之兩個班級作為研究對象,並將其分實驗與控制兩組;全程參與之學生共計63名,並從實驗組分層隨機抽樣選取14名個案,以經審訂之問題進行個案訪談,依此探究個體原生型之動態心像的種類與運作機制,而後以動態的觀點整合GSP環境設計實驗教學活動。於活動中期及結束時各進行一次訪談,並於末了進行紙筆測驗,以瞭解學生的變化及評估實驗組相對於控制組的學習成效。
研究方法採質與量並重的方式進行,以質的詮釋性研究探究個體心像操作的機制,而以紙筆測驗之結果進行統計分析,由此獲得學習成效評估及各試題作答情形之關連性。依所得資料之類型,以紙筆測驗、個案動態心像類型、個案解題認知歷程分析與個案縱向分析等分別描述與討論本研究之發現。
針對研究目的,本研究之主要的研究結果如下:
1. 本研究發現14名個案皆會產生動態心像,且可將其引入解題活動中,然而不同的學生操作心像的頻率並不相同,與層次無關,唯高層次學生運用動態心像解題時較有系統。
2. 在以動態及靜態語意所佈置之問題情境中,台法兩地學生的表現恰好相反,其中台灣的學生較偏好動態語意情境,其原因為學生可因此引進動態心像,擬定自己所認為之較佳的解題策略。
3. 本研究所發現之動態心像類型有割補、變換、拓樸與動態模擬等四種主類型;除拓樸型之外,其餘三類可作為具威力之解題方法,而拓樸型雖不具此能力,然而仍對解題具有輔助的功能。
4. 個體於解題活動中所運用之動態心像類型通常與問題情境有關,不過某些學生易傾向某種類型之心像操作方式。
依據研究之結果,教師在進行教學時,應特別注意動態與靜態語意對學生理解方式與解題方法的影響,並且應以較為有系統的方式,配合動態幾何工具的使用,培養學生運用動態心像以增強學習的成效。未來則可以較多的樣本數、專家與生手的對比,以及幾何、分析與調和等類型的個體是否傾向使用某種特定類型之動態心像等方向進行相關的研究。
關鍵字:動態幾何軟體、動態幾何環境、心像、心像操作、動態心像
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