Looking Into Mathematics: A Visual Invitation to Mathematical Thinking

探究数学：数学思维的视觉邀请

• 批准号: 9653029
• 负责人: Wallace Feurzeig
• 金额: $ 20.43万
• 依托单位: BBN Systems & Technologies Corporation
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-03-15 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9653029&HistoricalAwards=false
• 关键词: Looking; Into; Mathematics; Visual; Invitation

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.

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，在不知所措和不屑一顾之间摇摆不定。因此，他们不仅在私人生活中失去了一些东西：作为公民，他们更不具备评估人类与物质和社会世界不断变化的关系中许多重大发展的能力。我们的目标是通过真正让学生参与数学思维来吸引和保持他们对数学的兴趣。如果有些人在数学或科学方面继续前进，那就更好了。然而，与其说我们在招募数学家，不如说我们在结交数学的朋友。 我们将开发教学材料，活动和软件工具，在一个互动的，可视化的，以实验为导向的课程，传达现代数学的精神和风味，强调各种关键和中心的观点（如本地/全球，内在/外在，动态/静态，离散/连续，代数/几何）。我们将实现半严格的交互式实验-手动和虚拟-与丰富多样的复杂，有趣的数学对象，如曲线，曲面，连杆，结和辫子。学生将使用新的视觉工具探索这些领域，这些工具既强大又强大。 该项目的目标受众特别包括不打算主修数学或科学的大学一年级学生和未来的数学教师。试点部分将在布兰迪斯大学、哈佛大学、克拉克大学和波士顿的马萨诸塞州大学授课。我们将开发材料，以便在各种学院和大学中使用，无论是在数学入门课程中还是在加强现有课程中。将免费提供文本和软件供采用和传播。