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  • 學位論文

如何利用電腦軟體和統計模擬來驗證或猜測問題之解之研究

Research on How to Use Computer Simulation to Verify or Guess the Problem

指導教授 : 吳裕振

摘要


使用電腦和程式,來解決數學問題,在現代教育是非常重要的。而本論文,就是找一些比較困難而且不容易思考的題目,我們起初都用電腦軟體或使用統計理論運用在程式上,先猜出答案,或者求得近似解,再想辦法去證明,才不會浪費很多時間在其他不對的思考模式。因此也讓我的視野更加寬廣,也靠著電腦的運用,使自己得到一些寶貴的經驗,以後在解決問題上多一個利器。 在高職教育環境中,對於數學教導總兢兢業業,也深知部份學生對於數學學習過程,遇到瓶頸,進而影響學習歷程。經過行動研究的分析後,發現高職生對於抽象的題型,很難立即做出解題反應,有時連問題是什麼都不知道,更何況要思考解題的方向及方法。正因如此,我在課堂間也常利用電腦來輔助教學,並借以軟體的應用,讓抽象算式變成可觀察的幾何圖型,使學生能具體知道問題和解題思維的關連性,在科技教具輔助下,增強學生對數學的學習興趣。 除了在算式和幾何中,用電腦做了學習的正向聯結。對於統計的問題上,數據的整理和歸納,研究的抽樣和方法,常常更耗時費力,在教學現場需立即給學生學習回饋,所以,借以科技的輔助下,濃縮了處理過程,讓學生可以看到成果呈現,了解統計及推論的學習意義。 本論文在於闡明軟體如何用於輔助數學學習,以期望在課程當中,能更彈性規劃教法及教材,收達學生最佳數學的功效。

關鍵字

電腦 模擬

並列摘要


Using computers and computer programs to solve math problem is very important in contemporary education. This thesis finds some difficult and unthinkable questions to solve. At first, we use computer software or apply statistical theory to the computer program to guess the answer first or find an approximate answer, and then we try to prove it correct. The purpose of the method is to help us not to waste much time thinking in the wrong direction. The process broadens my horizons , and application of the computer also helps me gain precious experience and has become an excellent instrument for me when solving problems. It takes a lot of effort and hard work to teach students math in vocational high school. If students encounter setback in the process of learning math, their motivation for learning may be decreased. After the analysis of action research, I found that it's difficult for vocational school students to respond to an abstract question and sometimes they don't figure out what the question is, not to mention the direction of solving problem. Therefore, I often use the computer a teaching aid. With the application of software, I turn the abstract question into a observable geometric pattern to let students see the question concretely and find out the connection between the question and the solution. With the help of technological teaching aid, students’ interest in learning math has been raised. Besides the questions of algebra and geometry in which the computer makes a positive contribution to learning, the computer is also helpful for the questions of statistics. For statistic questions, it usually takes a lot of time to do the arrangement and induction of the data and sampling of research; however, in the teaching situation, students need to get the feedback instantly. The aid of technology condenses the process of dealing with the information to let students see the presentation of solving problems sooner and understand the meaning of learning statistics and inference. This thesis is to clarify how software can be used to assist mathematics learning, in the hope that in the course, it can more flexibly plan teaching methods and teaching materials, and collect the best mathematics effect of students.

並列關鍵字

Computer Simulation

參考文獻


六、 參考文獻
[1 ] G.S.P 軟體
http://www.dynamicgeometry.com/
[2 ] 高中數學第五冊,三角函數,南一書局
[3 ] 高中數學第三冊,向量,南一書局

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