Using Computers to Expand Reform Beyond Calculus

该项目正在将微积分“改革”的教学改革和技术的适当使用扩展到线性和抽象代数、几何和计算机科学课程。主要的重点是证明为导向的课程，在介绍线性代数，抽象代数和高级线性代数，其目标是利用技术来发展学生的能力。 直觉和概念的理解，同时支持，而不是取代，一个公理化的治疗的主题。这样的待遇是重要的所有数学专业，包括未来的中学教师，其认证要求包括抽象代数和公理系统的熟悉。教材使用各种软件来促进可视化，并说明相关定理的广泛适用性。课堂活动和学生项目利用专业程序，如易于使用但范围有限的Group Analyzer，以及更全面的软件包，如GAP和Maple，这些软件包专为专业用途而设计，但可以适用于仍在学习数学概念的学生。一些现有的线性代数材料被称为ATLAST正在适应Maple。该项目还在为未来的小学和中学教师编写非正式几何教学材料。这些材料使用现有的软件包，以发展的抽象概念的基础上，他们的学生将在学前班课堂上进行的具体活动的理解。该项目所涉及的计算机科学课程主要为科学，工程和教育专业的学生提供服务。新的教学策略正在被纳入，新的材料正在为学生提供与其主要学科相关的大型编程项目的经验。

This project is extending the pedagogical changes and appropriate use of technology that characterize calculus "reform" to courses in linear and abstract algebra, geometry, and computer science. The major focus is on proof-oriented courses in introductory linear algebra, abstract algebra, and advanced linear algebra, where the objective is to use technology to develop students' intuition and conceptual understanding while supporting, rather than supplanting, an axiomatic treatment of the subject. Such a treatment is important for all mathematics majors, including future secondary school teachers, whose requirements for certification include a familiarity with abstract algebra and axiomatic systems. Instructional materials use a variety of software to foster visualization and illustrate the broad applicability of relevant theorems. In-class activities and student projects utilize specialty programs like Group Analyzer that are easy to use but of limited range, as well as more comprehensive software packages like GAP and Maple, which are designed for professional use but can be adapted for use by students who are still learning the mathematical concepts they involve. Some existing linear algebra materials known as ATLAST are being adapted to Maple. The project is also developing materials for teaching informal geometry to future elementary and middle school teachers. These materials use existing software packages to develop preservice teachers' understanding of the abstract concepts underlying the concrete activities that their students will be performing in precollege classrooms. The computer science course addressed by the project primarily serves students majoring in the sciences, engineering, and education. New pedagogical strategies are being incorporated, and new materials are giving students experience with large programming projects related to their major discipline.