Abrahamson, D. (2006). Bottom-up stats: Toward an agent-based “unified” probability and statistics.

Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.


Computational environments can do more than display old ideas in a new medium. Building on Wilensky and Papert (Wilensky, 2006; Wilensky & Papert, 2006), I examine multi-agent modeling-and-simulation technology that both restructures old ideas in probability and statistics and illuminates connections between these domains of practice. I first present two computer-based activities, one in probability and one in statistics (ProbLab, Abrahamson & Wilensky, 2002), and then compare between them in terms of perceptual, procedural, and conceptual dimensions. I demonstrate how ‘student-with-computer’ overlapping experiences in the probability and the statistics simulations—in terms of obtaining samples, in terms of the temporal dimension of these acts, and in terms of visual metaphors apt for thinking about either activity—suggest a restructuring of probability-and-statistics practices as nuanced epistemological variants governed by the parameter ‘experimentation vs. exploration.’ I implement this restructuration (Wilensky & Papert, 2006) as a proposed design object—the Platonic combinatorial space, a “population” from which random compound-event outcomes are “drawn” in probability experiments. Finally, I present a “bottom-up statistics” explorative conceptual model that builds a Law-of-Large-Numbers explanation for the Central Limit Theorem.