Reasoning about Probabilistic Phenomena: Lessons Learned and Applied in Software Design

In this paper we provide a glimpse of the iterations of design, research and theorizing of a probability simulation tool, Probability Explorer, that have occurred over the past decade. We provide a brief description of the key features of the technology designed to allow young students opportunities to explore probabilistic situations. This is followed by details about several research observations made in multiple investigations of student explorations with this probability micro-world software package. We then explicate how research results suggest that a focus on a bidirectional interplay between theoretical distribution and empirical data can promote reasoning about probabilistic phenomena, and offer implications for instruction. The paper concludes with a discussion of a next generation innovation in the software for representing a theoretical distribution that we believe may promote better students reasoning about the bidirectional connection between theoretical distributions and empirical data