| 摘要: | 近年來，透過高科技產品來教授數學課程，確實讓學生學習方法有很大的改進。然而，大部分的教師卻只利用計算機或電腦的繪圖功能、數值計算功能和符號運算功能，來教授較少抽象概念的數學基礎課程。甚少教師利用計算機或電腦來教授較為抽象的數學課程，如抽象代數課程。不可諱言的，大部分學生學習抽象代數概念感到十分困難。因此，作者企圖透過電腦教學活動的設計，將抽象代數概念具體化，來幫助學生從具體的層面再回到抽象的層面，藉以深入瞭解抽象代數概念。雖然本文只探討代數群的定義，但此構想應能延伸至其它的代數概念。故此，本文將描述如何把數學電腦語言ISETL融入抽象代數課程中。
Using technology as a tool to teach mathematics has caused significant changes in the way many students perceive mathematical concepts, processes, and problem solving. Although computers and calculators can help teachers to present topics form a better and more easily understood perspective, most of the teachers use them as a tool only in fundamental and less abstract courses, such as an introductory calculus course. Little has used them in more abstract courses like 'abstract algebra'. But, most college mathematics teachers would probably agree that students have insurmountable cognitive difficulties with the basic concepts of 'abstract algebra', such as that of groups. In an attempt to address these difficulties and make some of these rather complicated structures more accessible and more concrete, the author tries to introduce the definition of a group by modeling the concepts as concrete realities, computer activities, that would lead students from concrete to abstract. Moreover, the ideas can be generalized other concepts such as abelian group, subgroups, coset, and quotient group, etc. therefore, in this paper, the author will show how computers with mathematical programming language ISETL can be incorporated into the curriculum for 'abstract algebra'. |
