Intelligent Microworlds for Scaffolding Number Concept Development

这个研发项目使用智能微世界向中小学生传授数字和运算的基本概念。这项工作将考察将计算机融入以概念为导向的数学教学的创新方法。将讨论以下问题：(A)计算机如何支持而不是取代人与人的互动；(B)数学概念的讨论如何加强概念学习；(C)图形和符号表示如何为讨论奠定基础；(D)智能微世界如何通过提供可数学化情景的可视表示并将其与抽象联系起来，促进问题解决和数学理解。将开发一个完整的计算机微世界系统。这些微观世界将以直接可操作的图形形式表示抽象的数学概念，允许展示和探索小学和中学教授的一系列基本数字概念。该系统将包括算术运算符不同意义的不同表示法，以及将这些特定意义的表示法链接到更抽象的公式的图形和符号表示法的设施。该系统将被用来支撑教师主导的数学概念讨论，以及儿童独立的数学作业。

This program of research and development uses intelligent microworlds to teach fundamental concepts of number and operation to elementary and middle school children. The work will examine innovative ways of incorporating computers into conceptully oriented mathematics instruction. The following questions will be addressed: (a) how computers can support human interaction instead of replacing it; (b) how discussion of mathematical ideas ay enhance conceptual lerning; (c) how graphical and symbolic representations scaffold discussion; and (d) how intelligent miroworlds facilitate problem solving and mathematics understanding by providing visible representations of mathematizable situations and connecting them to abstractions. An integrated system of computer microworlds will be developed. These microworlds will represent abstract mathematical concepts in a directly manipulable graphical form, permitting display and exploration of a range of basic number concepts taught in elementary and middle schools. The system will include distinct representations for the different senses of arithmetic operators, along with facilities for linking these sense-specific representations to more abstract graphic and symbolic representations of equations. The system will be used to scaffold both teacher-led discussion of mathematics concepts, and independent mathematics work by children.