Educational computing has much to offer mathematics education, particularly when software is designed which provides students with the opportunity to go beyond practicing basic skills and solving routine problems, and instead supports mathematical discovery and exploration. Although drill and practice is still the category of software employed most frequently by mathematics and science teachers who use computers [1], software which functions as a cognitive tool for exploration and sense-making is becoming more evident in both classroom and research environments [2, 3]. The purpose of this article is to report on the results of a research study involving an exploratory learning environment, or mathematical microworld, for transformation geometry. The goal is to outline the principles underlying the design of the environment as well as to present an analysis of the learning of a group of middle school students who interacted with the microworld over a period of several weeks.
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