Intelligent Microworlds for Scaffolding Number Concept Development

这个研究和开发项目利用智能微世界向中小学生教授数字和运算的基本概念。这项工作将研究将计算机纳入以概念为导向的数学教学的创新方法。本研究将探讨以下问题：(a)电脑如何支援而非取代人类互动；(b)讨论数学概念如何促进概念学习；(c)图形和符号表示如何支撑讨论；(d)智能微世界如何通过提供可数学情境的可见表示并将其与抽象联系起来来促进问题解决和数学理解。将开发一个计算机微世界的综合系统。这些微世界将以可直接操作的图形形式表示抽象的数学概念，允许展示和探索中小学教授的一系列基本数字概念。该系统将包括不同意义的算术运算符的不同表示，以及将这些特定意义的表示与更抽象的图形和方程的符号表示联系起来的设施。该系统将用于支持教师主导的数学概念讨论，以及儿童独立的数学工作。

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.