Interactive Internet-Based Teaching of Multivariable Calculus and Geometry

数学科学（21）这个项目的目标是在大学开发两个基于互联网的课程，并在亚特兰大地区的机构在他们的课程中使用这些方法的兴趣教师。主要解决的问题是基于网络的教学方法的实施，并利用计算机来进一步在数学可视化教学。由于这些方法可以很容易地转移到许多设置没有专门的软件和硬件，基于互联网的方法提供了一个机会，创新的教学。计算机提供的可视化功能已经成为科学研究的核心，这些工具应该成为本科教育的重要组成部分。 智力优势。这个项目是传播托马斯F教授开发的基于互联网的教学方法。班乔夫，他已收到美国国家科学基金会主任奖的杰出教学学者。他的创新提供了一个环境，学生开发软件的大学课程的核心数学，科学和工程专业的课程。Banchoff博士作为顾问，该项目正在进一步发展他的多变量微积分课程的互动设计，并将他的方法扩展到未来的中学数学教师的几何教学。本课程是计算机可视化和几何研究的现代综合体。本项目的一个重要特点是采用基于互联网的交互式工具来指导新的学生群体-未来的中学教师。教师们正在为数学教育专业的学生进行一门实验课程的团队教学，这项工作正在与该部门的NSF资助的数学教学能力中心相结合。这些活动正在影响亚特兰大地区广泛的学院和大学的微积分，几何和其他中央数学课程的教学。除了大型州立大学（格鲁吉亚大学、格鲁吉亚理工学院和格鲁吉亚州立大学）外，亚特兰大地区一些备受推崇的小型学院（包括斯佩尔曼学院、莫尔豪斯学院、埃默里大学和艾格尼丝·斯科特学院）也参与其中。这些机构的教员正在参加研讨会和讲习班。该项目还与美国数学协会协调，通过讲习班传播成果。

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.