The Mathematician's Sketchpad

数学家的画板

• 批准号: 9460644
• 负责人: William Finzer
• 金额: $ 7.4万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-01-01 至 1996-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9460644&HistoricalAwards=false
• 关键词: Mathematician; Sketchpad

This Small Business Innovation Research Phase I project builds on the success of The Geometer's Sketchpad(, one of very few pieces of educational software to have a real effect on the teaching of mathematics in secondary schools. The proposed research will design and prototype a next generation of this software --The Mathematician's Sketchpad --an integrated exploratory environment for algebra and geometry utilizing declarative constraints as a new mathematical modeling tool. The Geometer's Sketchpad allows users to carry out geometric constructions using Euclid's compass and straightedge tools augmented by reflection, rotation, and dilation. At any time, users may drag 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. The Mathematician's Sketchpad will incorporate these tools and methods and go beyond them by allowing users to declare constraints on objects after they have been constructed, and by allowing algebraic specification of constraints. The revolution in the teaching of geometry being brought about by The Geometer's Sketchpad, reveals the opportunity to spread its fundamental ideas of constraint-based modeling and dynamic dragging to the rest of the secondary mathematics curriculum. The objectives of this Phase I research project are to design and prototype the critical elements of The Mathematician's Sketchpad and describe and prototype the support materials that will ease its introduction into classrooms.

这个小企业创新研究第一阶段项目建立在几何画板（，对中学数学教学有真实的影响的为数不多的教育软件之一）的成功基础上。拟议中的研究将设计和原型的下一代软件-数学家的画板-一个集成的探索环境，代数和几何利用声明性约束作为一种新的数学建模工具。几何画板允许用户使用欧几里得的指南针和直尺工具进行几何构造，并通过反射、旋转和膨胀进行增强。在任何时候，用户都可以使用计算机鼠标拖动草图中的对象，所有其他对象将动态调整它们的位置和大小，以保持构建的关系。这个简单的想法有着深刻的含义。数学家的画板将结合这些工具和方法，并通过允许用户在对象构建后声明对象上的约束以及允许约束的代数规范来超越它们。几何画板带来的几何教学革命，揭示了将其基于约束的建模和动态拖动的基本思想传播到中学数学课程的机会。这个第一阶段的研究项目的目标是设计和原型的数学家的画板的关键要素，并描述和原型的支持材料，这将有助于将其引入课堂。