SBIR Phase I: Three-Dimensional Sketchpad: Geometry Visualization Software for the Classroom

9660861 Jackiw这个小企业创新研究第一阶段项目建立在几何画板的成功基础上，这是一款对中学数学教与学产生了重要影响的教育软件。这项研究将制作这种软件的下一代原型--3D SketchPad--一个用于创建、分析和研究三维和更高维数学的集成探索环境。几何仪的画板允许用户使用标准的二维工具和变换(欧几里得的指南针和直尺工具，通过反射、旋转和膨胀来增强)来进行几何构造。在任何时候，用户都可以使用计算机鼠标拖动草图中的一个或多个对象，所有其他对象将动态调整其位置和大小，以保持构建的关系。这一简单的思想对数学的教与学有着深远的影响。概括到三个维度，SketchPad带来的几何教育革命有机会拓宽几何课程，并将其扩展到数学和科学的其他领域。这一第一阶段研究项目的目标是设计和制作3D画板的关键元素，并描述和制作支持材料，以便于将其引入课堂。《几何画板》在商业上取得了巨大成功。如果拟议的研究达到其目标，由此产生的软件和支持材料将在中学、中学和大学得到更大的应用。

9660861 Jackiw This Small Business Innovation Research Phase I project builds on the success of The Geometer's Sketchpad, a piece of educational software that has had an important impact on the teaching and learning of mathematics in secondary schools. The research will prototype a next generation of this software--3-D Sketchpad--an integrated exploratory environment for creating, analyzing, and investigating three- and higher-dimensional mathematics. The Geometer's Sketchpad allows users to carry out geometric constructions using standard 2-D tools and transformations (Euclid's compass and straightedge tools augmented by reflection, rotation, and dilation). At any time, users may drag one or more objects in the sketch using the computer's mouse, and all of the other objects will dynamically adjust their position and size to maintain the constructed relationships. This simple idea has profound implications in the teaching and learning of mathematics. Generalized to three dimensions, the revolution in geometry education brought about by Sketchpad has the opportunity to broaden the geometry curriculum and to extend its relevance to other areas in mathematics and science. The objectives of this Phase I research project are to design and prototype critical elements of 3D Sketchpad and to describe and prototype the support materials that will ease its introduction into classrooms. The Geometer's Sketchpad has enjoyed substantial commercial success. If the proposed research meets its goals, the resulting software and support materials will have even greater application in middle schools, secondary schools, and colleges.