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題名 | 動態微積分基本概念之電腦教學設計=Dynamic Visual Computer Designs for Instruction of Basic Calculus Concepts |
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作者 | 謝哲仁; Hsieh, Che-jen; |
期刊 | 美和技術學院學報 |
出版日期 | 20030400 |
卷期 | 22:1 2003.04[民92.04] |
頁次 | 頁233-254 |
分類號 | 521.593141 |
語文 | chi |
關鍵詞 | 微積分學習; 電腦輔助學習; Calculus learning; Computer-assisted learning; |
中文摘要 | 現有的微積分教科書較注重數學知識的呈現,較少融入認知科學的理論,如強調學習者可從直接操作圖形的直觀學習。圖形在現行微積分的學習只是用來說明某種概念知識而已,這種不強調行動操作的靜態課程,使得我們的學生只在課堂上,進行教師認為有意義但學生卻認為沒有意義的學習和速度的練習。因此,大部分的學生就認為,微積分只是一堆符號的演繹證明及一堆計算的公式。 科技可以被有效的使用幫助學生蒐集資料、測試修改推測、尋找不變性、視覺變化、連續的驗證。傳統式的微積分課程是靜態的計算過程,演繹的證明往往是單向式的陳述。靜態的文字陳述實不易導引探索的情境出來,因此不容易引導學生主動式的學習。此外,現有的電腦微積分設計大部份從代數表徵開始,有違必須先從較具體的數值或圖形設計起,因此本文利用電子試算表及電子幾何板兩種較普遍性的軟體,設計出具體的例子,試圖解決現有微積分教科書的缺點。本文的設計將以動態、可操作的物件情境為主。所謂的動態是經由適當的輸入(如滑鼠、數字鍵盤)直接操控物件(數值、圖形),銀幕上的物件會隨著行動的改變而有立即的反應。而所涉及的設計包含極限、微分、反導及積分等基本概念的學習。 |
英文摘要 | In Mathematics curriculum, materials for the concepts of calculus have always intimidated student learning. Many students do not understand its dynamic meaning in nature but mimic of textbook or teachers' calculation method. Constructivists treat students as subjects for cognition and emphasize the activeness and constructiveness in cognition. Therefore, the final goals for all instructional strategies are to guide students in constructing an individualized body of knowledge by themselves. Technology has constantly advanced itself. The introduction of Windows interface enables us to use a mouse for manipulating icons. The phenomena of putting students in constant control of abstracting the invariance from variances may well comply with the active spirit of constructivism. Traditional computer-assisted instructional (CAI) design focuses mainly on drills and question displays and stresses upon computer-managed tutorials or programmed learning and is in fact not compatible with the new curricula. Consequently, in view of CAI as instructional and learning tools, where the computer serves an instrument, teachers may see the urgent needs of designing instructional instruments or student helpers in accordance with the features of curriculum and materials. Thus, this study takes the basic calculus as contents of instruction to construct some dynamic-linking examples of multiple representational learning situations in the hope of helping students to develop their calculus concepts. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。