Using Computers to Expand Reform Beyond Calculus

该项目正在将微积分“改革”的教学方法变化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。主要的重点是在入门线性代数、抽象代数和高级线性代数中以证明为导向的课程，这些课程的目标是利用技术来培养学生的直觉和概念理解，同时支持而不是取代对主题的公理处理。这样的处理对所有数学专业的学生都很重要，包括未来的中学教师，他们对认证的要求包括熟悉抽象代数和公理系统。教学材料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，这些软件包是为专业用途而设计的，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，正在被改编为Maple。该项目还为未来的中小学教师开发非正式几何教学材料。这些材料使用现有的软件包来培养职前教师对抽象概念的理解，这些抽象概念隐藏在学生将在大学前课堂上进行的具体活动中。本计画所涉及的计算机科学课程，主要服务于理工科和教育学专业的学生。新的教学策略正在被纳入，新的材料正在给学生提供与他们的专业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.