Looking Into Mathematics: A Visual Invitation to Mathematical Thinking

许多大学生对数学不感兴趣。他们对数学的感觉在消极和敌对之间摇摆，在不知所措和不屑一顾之间摇摆。因此，他们不仅在私人生活中缺少了一些东西：作为公民，他们没有足够的能力来评估人类与物质世界和社会世界不断变化的关系中的许多重大发展。我们的目标是通过真正地让学生参与数学思维来吸引和维持他们对数学的兴趣。如果有些人继续从事数学或科学研究，那就更好了。然而，我们的目的与其说是招募数学家，不如说是与数学交朋友。我们将开发教学材料、活动和软件工具，以互动、可视化、实验为导向的课程，传达现代数学的精神和风格，强调各种关键和中心观点（如局部/全局、内在/外在、动态/静态、离散/连续、代数/几何）。我们将使半严格的互动实验-手动和虚拟-与丰富多样的复杂，有趣的数学对象，如曲线，表面，连杆，结和辫子。学生将使用新的可视化工具探索这些领域，这些工具既强大又授权。该项目的目标受众包括，特别是不打算主修数学或科学的大一学生，以及未来的数学教师。试点部分将在布兰代斯大学、哈佛大学、克拉克大学和马萨诸塞大学波士顿分校教授。我们将开发材料，以便在各种学院和大学中广泛使用，无论是在入门数学课程中还是在现有课程中进行改进。文本和软件都将免费提供，供采用和传播。

Many undergraduates are turned off by mathematics. Their feelings about mathematics veer between negative and hostile, between overwhelmed and dismissive. As a consequence, they are not only missing something in their private lives: as citizens, they are less equipped to evaluate many significant developments in humanity's changing relationship to the physical and social world. Our objective is to engage and sustain students' interest in mathematics by genuinely involving them in mathematical thinking. If some go on in mathematics or science, so much the better. We do not, however, seek so much to recruit mathematicians as to make friends of mathematics. We will develop instructional materials, activities, and software tools in an interactive, visual, experimentally-oriented curriculum that conveys the spirit and flavor of modern mathematics emphasizing a variety of key and central perspectives (such as local/global, intrinsic/extrinsic, dynamic/static, discrete/continuous, and algebraic/geometric). We will enable semi-rigorous interactive experimentation--both manual and virtual--with a rich variety of complex, interesting mathematical objects like curves, surfaces, linkages, knots, and braids. Students will explore these areas using new visual tools that are both powerful and empowering. The audiences targeted by the project include, especially, first-year college students who do not intend to major in mathematics or science, and future mathematics teachers. Pilot sections will be taught at Brandeis Universitiy, Harvard University, Clark University, and the University of Massachusetts, Boston. We will develop materials with a view to their use in a wide variety of colleges and universities, either in introductory mathematics courses or for enhancement of existing courses. Both text and software will be made freely available for adoption and dissemination.