Overview of Object-Oriented Microworlds for Learning Mathematics Through Inquiry

by David J. McArthur, Matthew W. Lewis

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This Note discusses computer microworlds that have been designed to support the learning of specific mathematical skills involved in discovering, confirming, explaining, and communicating patterns of relationships among variables in mathematical objects. It discusses the software tools themselves and how they promote learning through guided inquiry. The microworlds software is built on a kernel, including an object-oriented language for representing mathematical objects, a constraint mechanism for propagating information about values of properties of mathematical objects, and tools for multiple representations of patterns of relationships among mathematical properties. The authors report the results of fielding their first microworld — Polygons — with high school students. They discuss some of the problems or barriers to learning through discovery that they noticed, describe how software is designed to overcome some of these barriers, and outline ways they propose to extend the microworlds to provide improved learning support.

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