The Mathematician's Sketchpad

这个小企业创新研究第一阶段项目建立在Geeter‘s Sketchpad(几何画板)的成功基础上，这是极少数对中学数学教学产生实际影响的教育软件之一。这项拟议的研究将设计和制作这种软件的下一代原型--数学家的画板--一个利用陈述性约束作为新的数学建模工具的代数和几何的集成探索环境。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，这些工具增加了反射、旋转和膨胀。用户可以随时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其位置和大小，以保持构建的关系。这个简单的想法有着深远的影响。数学家的画板将结合这些工具和方法，并超越它们，允许用户在对象构造后声明约束，并允许对约束进行代数规范。几何画板给几何教学带来的革命，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其他部分的机会。这一第一阶段研究项目的目标是设计和制作数学家画板的关键元素，并描述和制作辅助材料，以便于将其引入课堂。

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.