Enhancing and Assessing Spatial Cognition through Computational Craftwork

当专业数学家和科学家讨论他们自己创造力的本质和起源时，他们经常提到视觉和空间思维所起的中心作用。但是，尽管视觉/空间认知在数学和科学教育中显然很重要，但针对数学和科学专业学生的空间推理的理解、提高和评估的研究仍然相对较少。更重要的是，很少有人试图将新颖的计算媒体与空间和数学上丰富的动手制作活动结合起来，这些活动影响并激励了前几代科学家。我们相信，通过努力整合，可以在这两个方面--基础认知研究和教育学发展--上取得进展。也就是说：通过设计有趣的、创造性的和技术复杂的教材来练习和增强空间认知，我们可以利用这些教材作为探索和理解空间认知基本问题的手段。在这个项目的过程中，我们计划：*在理解三维形式方面表征空间专业知识的性质，同时创建灵活的评估技术来确保这种专业知识的发展；*设计一个实用的空间课程教材，旨在增强和练习空间认知。这门课程将基于实践工作和创造性的计算论文制作活动的结合。*扩展我们现有的软件研究环境(HyperGami和Java Gami)，加入在线空间顾问，帮助学生思考、理解、玩耍和解释三维多面体形式；以及*创建新的软件，探索传统和新的数学论文制作领域，如弹出窗口、弯曲图形、变形艺术和表面模型。在探索这些领域时，我们寻求通过开发计算媒体的创新潜力来扩大传统数学纸制品的景观。

When professional mathematicians and scientists discuss the nature andorigins of their own creativity, they often mention the central roleplayed by visual and spatial thinking. But despite the apparent importanceof visual/spatial cognition in mathematics and science education, there isstill relatively little research aimed at understanding, enhancing, andassessing spatial reasoning in math and science students. Even more, thereare few efforts that seek to blend novel computational media with thesorts of spatially and mathematically rich hands-on crafting activitiesthat influenced and motivated earlier generations of scientists. Webelieve that progress can be made on both these fronts--on both basiccognitive research and pedagogical development--by an effort atintegration. That is: by designing playful, creative, and technologicallysophisticated educational materials for exercising and enhancing spatialcognition, we can use those materials as the means to explore andunderstand fundamental issues in spatial cognition as well.In the course of this project, then, we plan to:* Characterize the nature of spatial expertise in the understanding ofthree-dimensional forms, while creating flexible assessment techniques tomeasure development of that expertise;* Devise a practical spatial curriculum of materials designed to enhanceand exercise spatial cognition. This curriculum will be based on acombination of both hands-on work and creative computational papercraftingactivities.* Extend our current software research environments (HyperGami andJavaGami) to incorporate online spatial advisors that assist students inreflecting upon, understanding, playing with, and interpretingthree-dimensional polyhedral forms; and* Create new software to explore both traditional and novel realms ofmathematical papercrafting, such as pop-ups, flexagons, anamorphic art,and surface models. In exploring these areas, we seek to expand thelandscape of traditional mathematical papercrafts by exploiting thecreative potential of computational media.