Seeing Beauty in Mathematics: Using Fractal Geometry to Build a Spirit of Mathematical Inquiry

将设计和使用先进的工具和适当的活动来进行数学视觉和实验思维，并将用来展示这样的环境如何1)极大地改变学生摆出、探索和解决问题的方式，2)使学生能够处理比学生在传统的课堂数学符号世界中处理的更复杂和更多样的问题。这个项目将：o在传统和当代数学中选择适合于可视化方法的主题(包括但不限于主题自然产生于对分形学的研究)，以及适当的相关科学内容；O调查基于视觉的问题提出、推理(“视觉校样”)选项，在选定的领域进行数学研究可以从根本上改变学生对数学的积极参与和积极认知；O使用交互式计算机图形工具和辅助教材确定学习环境的组成部分和特点；这将最好地支持和加强学生对选定数学领域的调查；O当7到12年级的学生利用强大的交互式图形工具进行实验时，深入了解他们的数学能力，对数学对象和过程进行具体的探索和修补，并进行直观的推理；和o表明，视觉/实验的数学方法足够好地概括了各种领域，形成了现实的未来课程发展的基础。

Advanced tools and appropriate activities for thinking visually and experimentally in mathematics will be designed and will be used to demonstrate how such an environment can 1) dramatically change how students pose, explore, and solve problems, and 2) make accessible more complex and varied problems than students can handle in the traditional symbolic world of classroom mathematics. This project will: o select topics in traditional and contemporary mathematics that lend themselves to visual approaches (including but not restricted to topics arising naturally from the study of fractal forms), and appropriately related science content; o investigate how visually-based options for problem-posing, reasoning ("visual proofs"), and mathematical research in selected domains can result in fundamental changes in students' active engagement in and positive perception of mathematics; o identify the components and features of a learning environment using interactive computer graphics tools and supporting teaching materials, that will best support and enhance students' investigations of the selected mathematical domains; o give insight into the mathematical capabilities of 7th through 12th graders when they are availed of powerful, interactive graphics tools with which to experiment, explore, and tinker with mathematical objects and processes concretely and to reason visually; and o show that visual/experimental approaches to mathematics generalize well enough over a variety of domains to form the basis for realistic future curriculum development.