Symmetry Across the Curriculum: Symbolic and Visual Learning In the Arts, Mathematics, and Basic Science

该项目的长期目标是提出发展多学科课程的战略，这些课程经过精简，以传达包括数学分析和建模在内的几门学科的累积影响，以处理和解决社会广泛关注的科学或环境问题。该项目这一阶段的目标是提出一种开发这种新材料的方法，利用一个特殊的感知吸引力和人类亲和力的统一概念，即对称性。为了促进该项目的广泛影响，重要的是同时解决更新现有课程的相关问题，从而逐步将它们转变为具有当代意义的这种多学科专题。为了实现上述目标，将开发一系列课程单元，以涵盖各种主题，其中对称、几何变换和几何结构在跨学科背景下发挥关键作用。这些模块在内容和格式上将足够灵活，它们的跨学科性质有助于形成与其他模块的接口和联系，这一因素将被证明是易于组装和多种模块组合的关键。讲师从艺术、生物、化学、数学、物理和心理学中挑选一些模块，以形成一个连贯的多学科通用本科课程，并考虑到他们的目标受众。通过设计，这些课程强调对称性和几何结构作为统一的潜在主题，因此包含大量的分析和视觉内容。这些单元有两个组成部分：(A)文本和其他形式的多媒体材料，传达与手头主题有关的信息；(B)鼓励学生通过简化的数值和符号计算以及可视化来实践该主题的实际计算方面的软件。软件组件的目的是通过教师指导的计算机实验室会议来加强课程的讲授，让学生参与发现过程并积极参与探索量化方面的问题。讲课应该是说明性的，一般听众都能听懂，如果可能的话，留出深入的探索，作为应该在实验部分处理的项目的一部分。这些模块不需要超过标准的高中水平的数学和科学，因此旨在主要吸引那些没有主修数学和物理科学的学生。将特别强调吸引未来的科学和数学教师，并鼓励他们尝试类似的课程开发想法，建议修改软件和教材，以适应他们计划教授的K-12受众。评估计划包括在威斯康星大学(麦迪逊)、蒙大拿州立大学(Bozeman)和罗格斯大学(New Ark)教授试点课程。在试点课程的过程中，除了征求学生、教师和评审员的标准评估答复外，还将研究对学生学习和态度改善的评估、实验项目中的创造力以及计算机辅助定量问题的使用(如果适用，将在下一年进行跟踪并与标准课程进行比较。)此外，一些模块将被纳入参与机构的现有课程：克莱姆森大学、威斯康星大学麦迪逊分校、加州大学伯克利分校、蒙大拿州立大学和伊利诺伊理工学院。传播计划包括通过主要商业公司出版文本和附带的多媒体软件，通过示范和培训课程积极招募未来的用户，这些课程将与国家和区域专业会议一起组织，特别是在蒙大拿州和中西部。这些材料将在WWW上提供，许多软件将使用Java等与RM无关的平台语言来开发，以鼓励更广泛的公开和采用。预计这一项目产生的课程将吸引文科、人文科学和软科学的广泛受众，作为定量推理标准本科生要求的替代方案，并吸引他们发展更强大的科学和数学背景。在这个等式的另一端，这些模块展示了艺术和人文是如何丰富硬科学教学的。此外，有些课程模块适用于替代教育方案，例如使用远程学习或在延伸和非正式教育的背景下。

The long-term goal of this project is to propose strategies for development of multi-disciplinary courses that are streamlined to convey the cumulative impact of several subjects, including mathematical analysis and modeling, to address and solve a scientific or environmental problem of broad societal interest. The objective of this phase of the project is to propose a method for development of such new materials by taking advantage of a unifying concept of exceptional perceptual appeal and human affinity, namely symmetry. To facilitate widespread impact of the project, it is important to address at the same time the related problem of updating the existing courses thus, gradually transforming them into such multi-disciplinary topics of contemporary relevance. To accomplish the above-mentioned objectives, a sequence of course-modules will be developed to cover a variety of topics in which symmetry, geometric transformations and geometric structures play a key role in an interdisciplinary context. The modules will be sufficiently flexible in content and format, and their interdisciplinary nature serves to fashion interfaces and links to other modules, a factor that will prove essential for ease of assembly and multitude of modular combinations. The instructors select a number of modules from the Arts, Biology, Chemistry, Mathematics, Physics and Psychology to form a coherent multi-disciplinary general undergraduate course with their targeted audience in mind. By design, such courses emphasize symmetry and geometric structures as a unifying underlying theme, thus containing substantial analytic and visual content. The modules have two components: (a) text and other forms of multi-media materials that convey information regarding the topic at hand ; (b) software pieces that encourage the students to experiments hands-on computational aspects of the topic, through simplified numerical and symbolic computations, and visualization. The purpose of the software components is to enhance the lectures in t he course by instructor-supervised computer lab sessions that engage the students in the process of discovery and active participation to explore the quantitative aspects. The lectures are intended to be expository and accessible to a general audience, and when possible, leaving in depth exploration as part of projects that should be dealt with in the lab component. The modules do not require mathematics and science beyond standard high school level, thus aiming to attract primarily the students who have not majored in mathematics and the physical sciences. Special emphais will be placed to attract future teachers of science and mathematics, and to encourage them to experiment with similar course-development ideas, proposing modifications of the software and the text to suite K-12 audience that they will plan to teach. The evaluation plan includes teaching pilot courses at University of Wisconsin (Madison) and Montana State University (Bozeman), and Rutgers University (New Ark). In the course of pilot courses, besides soliciting standard evaluation responses from the students, instructors, and reviewers, assessment of student learning and attitude improvement, creativity in lab projects, and facility with computer-assisted quantitative problems will be studied (and where applicable, it will be followed up in the subsequent year and compared to standard courses.) Further, a number of modules will be incorporated in existing courses at the participating institutions: Clemson University, UW Madison, UC Berkeley, Montana State University, and Illinois Institute of Technology. The dissemination plans include publication of a text and accompanying multi-media software through major commercial companies, active recruiting of future users through demonstration and training sessions that will be organized in conjunction with national and regional professional meetings, in particular in Montana and Midwest. The materials will be available on the WWW, and much of the software will be developed using platfo rm-independent languages such as Java, to encourage wider exposure and adoption. It is expected that the courses resulting from this project would be attractve to a wide audience from the arts, humanities and soft sciences as alternatives to standard undergraduate requirements for quantitative reasoning, and to attract them to develop a stronger background in science and mathematics. On the other end of this equation, the modules illustrate how art and humanities enrich teaching of hard sciences. In addition, some of the course-modules are suitable for adapotion in alternative educational programs, e.g. using distance learning or in the context of extended and informal education.