| Summary: | 碩士 === 國立交通大學 === 網路學習學程碩士班 === 91 === 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.
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