One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning process of children who interacted with a computer microworld that incorporated the central objectives and relations of transformational geometry. The qualitative model in this research focused on discerning changes in students' content knowledge, changes in their strategies for using the microworld environment, and changes in their goal behavior. Included in the report are the theoretical framework, methods of data collection, preliminary results, and examples of microworld activities. Even though the small sample size of this case study (n=12) prevented tests for statistical significance, specific results included an increase of 9 percent on the most difficult transformation task (identifying rotations) to an increase of 25 percent on the easiest task (executing reflections). Further, the results yield support for previous conclusions that students require meaningful problem-solving activities to facilitate the construction of new knowledge. (11 references) (JJK)