The Odds of Understanding the Law of Large Numbers: a Design for Grounding Intuitive Probability in Combinatorial Analysis

Twenty-eight Grade 4 – 6 students participated in 1 hr. clinical interviews in a design-based study that investigated: (a) probability-related intuitions; (b) the affordances of a set of innovative mixed-media learning tools for articulating these intuitions; and (c) the utility of the learning-axes-and-bridging-tools framework supporting diagnosis, design, and data-analysis. Students intuited qualitative predictions of mean and variance, yet only through grounding computer-based simulations of probability experiments in discrete–scalar, non-uniform, multiplicative transformations on a special combinatorial space, the combinations tower, could students articulate their intuitions. We focus on a key learning axis, students’ confusing likelihoods of unique events with those of classes of events.