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多学科课程的开发策略，这些课程经过简化，可以传达包括数学分析和建模在内的多个学科的累积影响，以解决具有广泛社会利益的科学或环境问题。该项目此阶段的目标是提出一种开发此类新材料的方法，利用特殊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，从而逐渐将其转变为具有当代意义的多学科主题。为了实现上述目标，将开发一系列课程模块，以涵盖对称、几何变换和几何结构在跨学科背景下发挥关键作用的各种主题。这些模块在内容和格式上将足够灵活，其跨学科性质有助于塑造与其他模块的接口和链接，这一因素对于易于组装和多种模块化组合至关重要。教师从艺术、生物、化学、数学、物理和心理学中选择多个模块，根据目标受众形成连贯的多学科普通本科课程。通过设计，此类课程强调对称性和几何结构作为统一的基本主题，因此包含大量的分析和视觉内容。这些模块有两个组成部分：(a) 文本和其他形式的多媒体材料，传达有关当前主题的信息； (b) 鼓励学生通过简化的数值和符号计算以及可视化来实验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监督的计算机实验室课程来增强课程中的讲座，让学生参与发现和积极参与探索定量方面的过程。这些讲座旨在向普通观众提供说明性的内容，并在可能的情况下，将深入的探索作为应在实验室部分处理的项目的一部分。这些模块不需要超出标准高中水平的数学和科学，因此旨在主要吸引没有主修数学和物理科学的学生。我们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理念，提出对软件和文本的修改建议，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（博兹曼）和罗格斯大学（新方舟）教授试点课程。在试点课程过程中，除了征求学生、教师和审稿人的标准评估反馈外，还将研究对学生学习和态度改善、实验室项目创造力以及计算机辅助定量问题设施的评估（如果适用，将在随后的一年进行跟进，并与标准课程进行比较）。此外，一些模块将纳入参与机构的现有课程中：克莱姆森大学、威斯康辛大学麦迪逊分校、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随附的多媒体软件，通过演示和培训课程积极招募未来用户，这些课程将与国家和地区专业会议（特别是在蒙大拿州和中西部）一起组织。这些材料将在 WWW 上提供，并且大部分软件将使用独立于平台的语言（例如 Java）开发，以鼓励更广泛的接触和采用。 预计该项目产生的课程将吸引艺术、人文和软科学领域的广泛受众，作为定量推理标准本科要求的替代方案，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，这些模块说明了艺术和人文学科如何丰富硬科学的教学。此外，一些课程模块适合适应替代教育计划，例如使用远程学习或在扩展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.