資訊科技融入數學教學模組實務的研究

Abstract

我們根據過去中學數學教學經驗，融合教育學習理念，參照Web-based的課程模式，選擇能彰顯網路學習之單元，設計以學生為中心的教學模組，撰寫教學方法，搭配適合呈現的軟體，以資訊科技之優勢，取代傳統的教學內容。同時也針對老師教學經常發生的困難，設計能改善學習成效的教學模組，以自然、直觀、易懂、易學的方式，把教學效果不彰的部分，改用網路學習的方式呈現出來。本研究已建構的教學模組包括(3) (4) (5) (6)四個單元以及(7-1) (7-2) (7-3)三項動態學習環境：(3)大衍求一術的再出發：是藉Excel來計算整數的輾轉相除與求一術的表格，用Maple計算多項式的HCF. (4)組合計數的實驗與探討：是藉由觀察VB程式呈現的不盡相異物的排列來建構容斥原理、笛摩根定律、與組合計數的概念。(5)三角公式證明的視覺化呈現：是設計19個靜態的圖解三角公式，並用PowerPoint以動態呈現二倍角公式與反三角函數。(6)以遞迴方法探索連續整數冪次和：是藉由PowerPoint呈現t 方和公式的遞迴關係，並由此求得t 方和公式的係數。(7-1)兩相關多邊形面積比：在藉由觀察Java程式，然後證明多邊形各邊固定的比率分點所圍成的內多邊形與原多邊形面積比是否為常數。(7-2)兩函數 與 的圖形交點個數的探索：是利用Excel與Gsp觀察兩函數圖形之交點，並找到交點個數變化的臨界點。(7-3)最小平方法的動態呈現：是利用GSP來建構迴歸直線的概念，再利用Excel觀察在原始分數座標系與標準分數座標系中的迴歸直線的圖形，使學生能由標準分數座標系中迴歸直線的簡單形式，來聯想原始分數座標系中的迴歸直線方程式。期望教學模組普及之後，教師能方便、快樂的教，學生能主動、興趣的學。

Based on our high school mathematics teaching experiences, we integrated our vision of education, referred to Wed-based curricular modes, and chose units that manifest internet-learning to design student-centered teaching modules and methods. With the help of suitable software, we replaced the disadvantages of old teaching style with the advantages of info-technology. Besides, in order to deal with the difficulties in teaching, we devised new teaching modules to improve learning efficiency. Grounds on the principles of learn naturally and directly, easy-to-understand and easy-to-learn, some parts that might fail in traditional teaching would be presented in internet-learning ways. The modules in this research include unit3, 4, 5, 6, and three active learning environments: 7-1, 7-2, and 7-3. Unit3: The revival of Euclidean Algorithm. Calculate Euclidean Algorithm of integers and its table with Excel, and calculate HCF of Polynomial with Maple. Unit4: Experiments and discussions on Combinatorial Counting. Build students’ concept of Principles of Inclusion-exclusion, DeMorgan’s Laws and Combinatorial Counting through observing permutation of objects that are not exactly alike presented by Visual Basic. Unit5: Visualize the process of proofing Formulas of Trigonometric Function. Design nineteen static graphic solutions to formula of trigonometric function, and present double angle formula and inverse trigonometric function dynamically with PowerPoint. Unit6: Find = , by means of recursion. Present the recursive relationship between and with PowerPoint, and look for the coefficient of Polynomial = , . 7-1: The ratio of two relative polygonal areas. By observing programs written with Java, we proof if the rate of a polygon’s area and the area of another polygon which is formed by connecting dots that divide the former polygon’s each side with fixed ratio is a constant. 7-2: Discuss the number of intersections of two functions and . Observe the intersections of two functions presented by Excel and GSP, and find the critical point of changing intersection numbers. 7-3: Dynamical present of Least Squares Method. Use GSP to construct the concept of Regression Line, and then use Excel to observe graphs of Regression Line in original coordinate system and standard coordinate system. Make the students able to associate regression line equation in original coordinate with the form of Regression Line in standard coordinate system which is easier. With the popularity of modules, we really hope that students could be simulated and active in learning, and teachers could enjoy their teaching as well.