Enhancing and Assessing Spatial Cognition through Computational Craftwork

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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.