The Mathematician's Sketchpad

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，这是为数不多的对中学数学教学有真正影响的教育软件之一。提出的研究将设计和原型该软件的下一代-数学家的Sketchpad -一个集成的探索环境代数和几何利用声明性约束作为一个新的数学建模工具。几何学家的素描板允许用户使用欧几里得的指南针和通过反射、旋转和膨胀增强的直线工具进行几何构造。在任何时候，用户都可以使用计算机的鼠标在草图中拖动对象，所有其他对象将动态调整其位置和大小，以保持所构建的关系。这个简单的想法有着深刻的含义。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之后声明约束，并允许对约束进行代数规范。几何画板带来的几何教学革命，揭示了将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。这个第一阶段研究项目的目标是设计和制作《数学家画板》的关键元素的原型，并描述和制作支持材料的原型，以便将其引入课堂。

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.