Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by making the essential relationships and patterns more accessible to learners. Based on our research with pre-service elementary school teachers, we show how both the visual representations embedded in the microworld, and the possibilities afforded for experimentation affect learners' understanding and appreciation of basic concepts in elementary number theory. We also discuss the aesthetic and affective dimensions of the research participants' engagement with the learning environment.