Using Computers to Expand Reform Beyond Calculus

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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.