針對線性變換及仿射變換設計動態幾何軟體之研究

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2010

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隨著科技快速的進步,數位學習逐漸嶄露頭角,針對學習課程所設計的電腦輔助教學軟體更是不勝枚舉,但以幾何教學為出發點的「動態幾何教學軟體」至今還尚未普遍應用在各種課程中,尤其是高等數學教育,若動態幾何軟體能妥善設計,將會對高等數學在證明與定義的思維有所幫助,本研究感興趣的主題,就是在於如何將動態幾何軟體應用在高等數學教學課程上,以大學課程中線性代數為例,針對線性變換與仿射變換的課程做動態幾何軟體的設計。除了利用軟體將變換結果具體呈現外,還設計讓學生能自由控制變換矩陣的平台,讓學生先經由不斷觀察圖形的變化例子對幾何內容做相關臆測後,再學習到線性變換矩陣是如何透過奇異值分解的幾何原理來得知變換的圖形,並製作相關動畫讓學生能夠動態的看到變換情況,進一步再去瞭解仿射變換的幾何意義,這樣對於課程內容才會比較有系統上的安排。軟體設計方面,利用OGRE圖形引擎為開發工具,在於希望藉由OGRE內獨特場景管理類別,達到奇異值分解幾何意義的成效。除此之外,本軟體也以RPG遊戲設計的思考方式去呈現,希望將遊戲與教學做結合,讓學生在遊戲當中也能學習到課程內容,引發學生的學習興趣與動機。
Educationists hope that dynamic geometry software tool can apply instruction on courses, above all advanced math. If the software designs well, it will be useful for proofing math theorems and solving questions. In order to these thoughts, we dicuss a research theme how to design a dynamic geometry software on linear and affine transformation.The software’s benefit is that we not only control translation matrix very simply, but also look its result instantly. By the method, students can conjecture the relation between linear translation and SVD and then realize their geometry principle. Finally, catching on affine transformation property. Moreover, we use game principle to design the software. We hope we may increase study interest and their motivation by combining teaching with video game.

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線性變換, 仿射變換, 遊戲式學習, OGRE

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