The Design of a Computer Algebra System to Effect a More Relevant Mathematics Curriculum

罗林斯学院这个为期三年的项目的重点是建立一个计算机环境--包括一个计算机代数系统--Maple，一个专门设计的与Maple的接口，一个超文本系统，以及其他软件-更适合于普通学生教和学微积分。这个计算机代数系统将演示专家的推理过程。其目的是让学生学习如何思考微积分，以及如何在计算机代数系统的帮助下解决问题。这种计算机环境适合于微积分预科、理工科课程设计。首席研究员道格拉斯·查尔德是美国第一个开发出一种简单方法来使用计算机代数系统的人，该系统既可以用来做微积分，也可以用来教授枫叶微积分。在斯隆基金会的资助下，蔡尔德和皮库尔茨开始为计算机代数系统开发课程和界面。微积分主题将重新排序。本课程早期将通过应用题来介绍差异化和整合性。课程将强调逻辑、语言的精确使用、数值方法、近似和数学建模。材料的试验性使用计划在大学和当地高中进行，这些学校有大约35名学生。全国传播将以文本的形式由Wadsworth/Brooks-Cole出版社出版。罗林斯学院通过实物服务贡献了该项目近四分之一的成本。

The focus of this three year project at Rollins College is the construction of a computer environment -- consisting of a computer algebra system - MAPLE, a specially designed interface to MAPLE, a hypertext system, and other software --- that is more suitable for teaching and learning calculus for the average student. This computer algebra system will demonstrate the reasoning processes of experts. The intent is that students will learn how to think about solving calculus as well as how to solve problems with the help of a computer algebra system. This computer environment is suitable for pre-calculus, science and engineering curriculum designs. The principal investigator Douglas Child is the first in the country to develop an easy way to use a computer algebra system both to do and to teach calculus with MAPLE. Child and co-PI Kurtz began developing curriculum and interfaces for computer algebra systems under grants from the Sloan Foundation. The calculus topics will be reordered. Differentiation and integration will be introduced early in the course via applied problems. There will be an emphasis on logic, precise use of language, numerical methods, approximations, and mathematical modelling. Experimental use of materials is planned at colleges and local high schools which have classes of approximately thirty-five students. National dissemination will be in the form of text to be published by Wadsworth/Brooks-Cole Publishers. Rollins College is contributing almost one-fourth of the project's cost with in-kind services.