Interactive Internet-Based Teaching of Multivariable Calculus and Geometry

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Mathematical Sciences (21)The objective of this project is to develop two internet-based courses at the university, and to interest faculty at institutions in the Atlanta area in using these methods in their courses. The primary problems being addressed are the implementation of internet based teaching methods, and the use of computers to further the teaching of visualization in mathematics. Because the methods can be easily transferred to many settings without specialized software and hardware, internet-based methods provide an opportunity for innovation in teaching. The power of visualization provided by computers has become central in scientific research, and such tools should become an important part of undergraduate education. Intellectual Merit. This project is disseminating the internet-based teaching methods developed by Professor Thomas F. Banchoff for which he has received the NSF Director's Award for Distinguished Teaching Scholars. His innovations provide a setting in which students develop software for college courses central to the curricula of mathematics, science, and engineering majors. With Dr. Banchoff as a consultant, this project is developing further his interactive design of a multivariable calculus course, and extending his methods to the teaching of geometry for prospective secondary mathematics teachers. This course has grown out of a modern synthesis of computer visualization and research in geometry.An important feature of this project is the adaptation of interactive internet-based tools to the instruction of a new population of students - prospective secondary school teachers. Faculty members are team-teaching an experimental course for Mathematics Education majors, and the work is being integrated with that department's NSF funded Center for Proficiency in Teaching Mathematics.Broader Impact. These activities are impacting the teaching of calculus, geometry, and other central mathematics courses at a wide range of colleges and universities in the Atlanta area. In addition to the large state universities (University of Georgia, Georgia Institute of Technology, and Georgia State University), a number of highly regarded smaller colleges in the Atlanta area (including Spelman College, Morehouse College, Emory University, and Agnes Scott College) are involved. Faculty from these institutions are attending seminars and workshops. The project is also coordinating with the Mathematical Association of America to disseminate the results via workshops.