Intelligent Microworlds for Scaffolding Number Concept Development

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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.