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

SBIR 第一阶段：三维画板：课堂几何可视化软件

• 批准号: 9660861
• 负责人: Nicholas Jackiw
• 金额: $ 7.49万
• 依托单位: Key Curriculum Press
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-01-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9660861&HistoricalAwards=false
• 关键词: SBIR; Phase; Three; Dimensional; Sketchpad

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.

这个小企业创新研究第一阶段的项目建立在几何学家的Sketchpad的成功基础上，这是一个对中学数学教学产生重要影响的教育软件。该研究将为下一代软件3d Sketchpad制作原型，这是一个用于创建、分析和研究三维和高维数学的集成探索环境。Geometer的Sketchpad允许用户使用标准的二维工具和转换（欧几里得的指南针和直线工具，通过反射，旋转和膨胀增强）进行几何构造。用户可以随时用计算机鼠标拖动草图中的一个或多个对象，其他所有对象都将动态调整其位置和大小，以保持所构建的关系。这个简单的想法对数学的教与学有着深远的影响。将其推广到三维空间，Sketchpad带来的几何教育革命有机会拓宽几何课程，并将其与数学和科学的其他领域相关联。这个第一阶段研究项目的目标是设计和制作3D Sketchpad的关键元素，并描述和制作支持材料的原型，以便将其引入课堂。几何学家的Sketchpad在商业上取得了巨大的成功。如果提出的研究达到了它的目标，那么产生的软件和支持材料将在初中、中学和大学中有更大的应用。