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| 題 名 | 數學教學的自動化--以一元二次方程式配方法求解為說明=Automation of Mathematics Teaching--Demonstration by a Method of Completing the Square in Solving a Quadratic Equation |
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| 作 者 | 郭青松; | 書刊名 | 樹德科技大學學報 |
| 卷 期 | 15:2 2013.07[民102.07] |
| 頁 次 | 頁43-57 |
| 分類號 | 521.5931 |
| 關鍵詞 | 符號代數系統; 配方法; 一元二次方程式; 講解示範自動化; Symbolic algebraic system; Method of completing the square; Quadratic equation; Automatic demonstration; |
| 語 文 | 中文(Chinese) |
| 中文摘要 | 傳統數學單元的授課方式,大致上由授課老師在黑板上書寫各單元的概念起源(部份單元也許沒有強調觀念的源由)、理論說明(定理或性質及其證明)、接著再以實例說明或演練,最後再指定習題供學生做為課後練習的作業。由於現今電腦和網路科技的進步,促使學生的學習可以多樣化外,數學自由軟體wxMaxima不僅能做為學習輔助,如描繪函數或方程式圖形、計算並驗證結果,也能輔助平常教學的不足,例如請假缺課的同學,可藉由教學檔案(語音和影像),自行補足所遺漏的課程內容。本文以功能強大的免費數學軟體wxMaxima(人工智慧語言LISP 程式),搭配因應各單元特性所撰寫的程式,做為課堂上整個學習過程的完全自動化示範。由理論源由的介紹(聲音和影像顯現方式,比單調的文字敘述較吸引學習者的注意,此階段一般會注重引介入多媒體介面)、再加強理論的講解或說明(此階段描述單元性質的普遍性)、再來就是實例和代表性範例的說明和示範講解、以及課後學生演算習題的互動(此階段學生可自行輸入同類型的習題,得到一連串的解題步驟和結果,並對照自己的做法是否正確)。 |
| 英文摘要 | There were generally some steps used in traditional mathematics teaching, including writing down the origin of each topic or idea on the blackboard (maybe some topics lack of introducing the origins for simplicity), explanation of the theorems or properties, and proof, demonstration or practicing of some examples in solving steps, and corresponding homework assigned to students. Owing to the more progress in computer and network techniques than before, students learn by using these skills in many ways now, and get more help or assistance from the aided learning ways, for example, mathematics software wxMaxima helps to draw the graphs of functions and validate the computed results, and sometimes these modern technologies or facilities help students make up the absent classes by teaching files (audio-and-video or image files).This study plans to get a thorough and automatic way in learning mathematics by using the free and powerful software wxMaxima (an artificial intelligence language, LISP) as a basis. The authors try to program the series of demonstration steps into codes in wxMaxima, and then integrate these steps into a final mathematical class for specific topic teaching use. First by use of a multimedia interface to introduce the source or origin of the topic to the beginner (maybe more interesting and attracting than the dull and pure texts statements), and then the full explanation of the theorems and inference of their properties (stress on the generality or universality on the theorems), examples and practicing and special instances occurring in this topic. Finally, assigning the homework for students to really interact with the software to solve their problems encountered in this learning stage, students can key in the same kind of problems to get the solving processes in a series of demonstration in wxMaxima and to contrast with the results of their self-practice. |
本系統中英文摘要資訊取自各篇刊載內容。